NISM Series X-A Ch.15: Portfolio Construction Process — 175 Practice Questions

Q: Which type of average return is considered the best estimate of a future year's return based on a random distribution of prior years' returns?

Arithmetic Mean Return (AMR). The text states: 'The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average.'

Q: According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which performance measure are discretionary portfolio managers prescribed to disclose for the immediately preceding three years?

Time Weighted Rate of Return (TWRR). The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ‘Time Weighted Rate of Return’ for the immediately preceding three years.'

Q: An individual achieves a 5% pre-tax rate of return for stock XYZ and is subject to a capital gains tax of 15%. What is the post-tax rate of return, according to the example provided?

4.25%. The text provides the calculation: 'Post-tax return = Pre-tax return x (1-tax rate) = 5% x (1-15%) = 4.25%'

Q: Under what specific condition will the Geometric Mean Return (GMR) be equal to the Arithmetic Mean Return (AMR) over a longer holding period?

When all individual yearly returns are exactly the same.. The text states: 'But over longer holding periods the geometric average return is always less than the arithmetic return except when all the individual yearly returns are exactly the same, in which case the geometric return equals the arithmetic return.'

Multiple Choice Questions (150)

Q1 MCQ · 1 mark MediumTime Weighted Rate of Return

Which of the following sequences correctly outlines the general steps for calculating Time Weighted Rate of Return (TWRR) over multiple sub-periods?

ACalculate wealth relatives, then sub-period returns, then chain link them.

BCalculate sub-period returns, then link them, then calculate wealth relatives.

✓Calculate sub-period returns, then convert to wealth relatives, then chain link them.

DCalculate the terminal value, then discount cash flows, then apply the IRR formula.

💡 The text describes TWRR calculation steps as: 'First step towards calculating the TWRR is to calculate each period return...' followed by 'The next step is to link these five sub period return together. For chain linking these sub period return, we have to calculate wealth relatives. Wealth relative is ending value of one unit of money. Hence what needs to be done to create wealth relative is to add one to each period return...' and then 'create a cumulative wealth relative for the entire evaluation period by multiplying each period wealth relative'.

Q2 MCQ · 1 mark EasyArithmetic Mean Return (AMR)

Which type of average return is considered the best estimate of a future year's return based on a random distribution of prior years' returns?

AGeometric Mean Return (GMR)

BTime Weighted Rate of Return (TWRR)

✓Arithmetic Mean Return (AMR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: 'The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average.'

Q3 MCQ · 1 mark HardGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

When is the geometric average return always less than the arithmetic return?

AOnly when individual yearly returns are consistently positive.

BOnly when individual yearly returns are consistently negative.

✓Over longer holding periods, unless all individual yearly returns are exactly the same.

DOnly for a one-year holding period.

💡 The text states, 'But over longer holding periods the geometric average return is always less than the arithmetic return except when all the individual yearly returns are exactly the same, in which case the geometric return equals the arithmetic return.'

Q4 MCQ · 1 mark HardGross vs. Net Return

Based on the provided example for Net Return calculation, how is the Fixed Management Fee of 1.50% determined?

A1.50% of the Capital Contribution made at the beginning of the investment period.

B1.50% of the Gross Value of the Portfolio at the end of the investment period.

C1.50% of the Assets Under Management (AUM) at the beginning of the period.

✓1.50% on the average value of the initial capital contribution and the gross value of the portfolio.

💡 The text explicitly states for Fixed Management fee: 'charged on average of capital contribution and gross value of portfolio (e.g. 1.5%)'. The calculation in the table confirms this: '[1.5% on average value of initial and terminal value]'. The initial capital contribution is Rs. 1,00,00,000 and the gross value of the portfolio at the end is Rs. 1,20,00,000. The average is (1,00,00,000 + 1,20,00,000) / 2 = Rs. 1,10,00,000. The fee is 1.5% of 1,10,00,000 = Rs. 1,65,000.

Q5 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

An investor is evaluating two portfolio choices over a multi-year horizon. Portfolio X had annual returns of -50% and +100%, while Portfolio Y had annual returns of +10% and +10%. Based on the provided text, which of the following statements is TRUE?

✓Portfolio X has a higher average arithmetic return, but Portfolio Y results in a higher terminal value.

BThe geometric mean return for Portfolio X is 25%.

CThe arithmetic mean return is always less than the geometric mean return over longer holding periods.

DTo estimate the expected return over a multiyear horizon, the geometric average should be used.

💡 For Portfolio X: AMR = (-50% + 100%) / 2 = 25%. GMR = (((1 - 0.50) * (1 + 1.00))^(1/2)) - 1 = ((0.5 * 2)^(1/2)) - 1 = (1^(1/2)) - 1 = 0%. If initial investment is Rs. 100,000, terminal value for X is Rs. 100,000 * (1 - 0.50) * (1 + 1.00) = Rs. 100,000. For Portfolio Y: AMR = (10% + 10%) / 2 = 10%. GMR = (((1 + 0.10) * (1 + 0.10))^(1/2)) - 1 = ((1.1 * 1.1)^(1/2)) - 1 = (1.21^(1/2)) - 1 = 1.1 - 1 = 10%. If initial investment is Rs. 100,000, terminal value for Y is Rs. 100,000 * (1 + 0.10) * (1 + 0.10) = Rs. 121,000. Statement A is true because Portfolio X's AMR (25%) is higher than Portfolio Y's AMR (10%), but Portfolio Y's terminal value (Rs. 121,000) is higher than Portfolio X's (Rs. 100,000). The text explicitly states that 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' Statement B is false, GMR for Portfolio X is 0%. Statement C is false, the text states 'the geometric average return is always less than the arithmetic return except when all the individual yearly returns are exactly the same'. Statement D is false, the text states 'If we wish to estimate the expected return over a multiyear horizon conditioned on past experience, we may use the arithmetic average'.

Q6 MCQ · 1 mark MediumSEBI Regulations

According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which performance measure are discretionary portfolio managers prescribed to disclose for the immediately preceding three years?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

CMoney Weighted Rate of Return (MWRR)

✓Time Weighted Rate of Return (TWRR)

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ‘Time Weighted Rate of Return’ for the immediately preceding three years.'

Q7 MCQ · 1 mark MediumPost-Tax Return

An individual achieves a 5% pre-tax rate of return for stock XYZ and is subject to a capital gains tax of 15%. What is the post-tax rate of return, according to the example provided?

A5.88%

✓4.25%

C3.50%

D6.00%

💡 The text provides the calculation: 'Post-tax return = Pre-tax return x (1-tax rate) = 5% x (1-15%) = 4.25%'.

Q8 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR), Geometric Mean Return (GMR), and Compounded Annual Growth Rate (CAGR)

Which of the following statements accurately describes the relationship between Time Weighted Rate of Return (TWRR), Geometric Mean Return (GMR), and Compounded Annual Growth Rate (CAGR) as per the provided text?

ATWRR is always greater than GMR, but less than CAGR.

BTWRR is distinct from GMR and CAGR, though all are measures of return.

✓TWRR, GMR, and CAGR are essentially the same calculation representing the compound annual return.

DGMR is used for short-term periods, while TWRR and CAGR are for long-term periods.

💡 The text explicitly states: 'The TWRR is the same as geometric return.' and 'The calculation is same as the calculation of CAGR or geometric mean return.' It also defines TWRR as 'the compound rate of growth over the stated period' and CAGR as 'a measure of an investment’s annual growth rate over time, with compounding.' Therefore, these three measures represent the same concept of compound annual return.

Q9 MCQ · 1 mark MediumClient vs Fund Manager

According to the text, what is the primary reason a client is typically concerned with MWRR, while TWRR is mandated for fund managers?

AMWRR provides a standardized comparison across different fund managers, while TWRR reflects personal cash flows.

BTWRR accounts for the investor's individual contributions and withdrawals, whereas MWRR measures the fund manager's skill.

✓Clients are bothered about the actual amount they are taking home (influenced by their cash flows), while TWRR provides a uniform measure for fund manager performance comparison.

DMWRR is easier to calculate for clients, and TWRR is used for complex regulatory reporting.

💡 The text explicitly states, 'At the end of the day the client is bothered about how much s/he is taking home; TWRR is for the fund manager for uniformity in reporting and comparing.'

Q10 MCQ · 1 mark MediumGeometric Mean Return vs. Arithmetic Mean Return

Under what specific condition will the Geometric Mean Return (GMR) be equal to the Arithmetic Mean Return (AMR) over a longer holding period?

✓When all individual yearly returns are exactly the same.

BWhen the portfolio value at the end of the period is the same as the beginning.

CWhen there are no external cash flows during the period.

DWhen the investment period is exactly one year.

Q11 MCQ · 1 mark EasyPerformance Reporting Mandates

As per the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, how are discretionary portfolio managers required to disclose performance?

AUsing Money Weighted Rate of Return (MWRR) for the immediately preceding three years.

BUsing Holding Period Return (HPR) for the entire investment period.

✓Using Time Weighted Rate of Return (TWRR) for the immediately preceding three years.

DUsing Compounded Annual Growth Rate (CAGR) for the last five years.

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q12 MCQ · 1 mark EasyHolding Period Return

What is a key assumption made by the Holding Period Return (HPR) measure regarding income distributions?

AAll income distributions are reinvested immediately.

BIncome distributions are made at the beginning of the period.

✓All income distributions are made at the end of the year.

DIncome distributions are tax-exempt.

💡 The text states that HPR "assumes that all income distributions are made at the end of the year."

Q13 MCQ · 1 mark MediumMWRR Definition

Which of the following best describes the Money Weighted Rate of Return (MWRR)?

AIt is the compound rate of growth over a stated period, valued every time there is an external cash flow.

BIt is an indicator of performance that assumes all income distributions are made at the end of the year.

✓It is the annual rate of return at which cumulative contributions grow over the measurement period, and it depends on the timing of cash flows.

DIt is the simple average of individual total yearly returns, best for estimating a future year's return.

💡 MWRR (Money Weighted Rate of Return) is the annual rate of return at which the cumulative contributions grow over the measurement period, and it depends on the timing of the cash flow. It is also referred to as Internal Rate of Return (IRR).

Q14 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

According to SEBI (Portfolio Managers) Regulation, 2020, which rate of return are discretionary portfolio managers prescribed to disclose for performance for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BHolding Period Return (HPR)

CArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR)

💡 The text explicitly states: "Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ‘Time Weighted Rate of Return’ for the immediately preceding three years."

Q15 MCQ · 1 mark HardGeometric Mean Return vs Arithmetic Mean Return

An investor's portfolio started with Rs. 100,000. In the first year, it experienced a -50% return, dropping to Rs. 50,000. In the second year, it gained 100%, returning to Rs. 100,000. Which return measure, as described in the text, would accurately reflect that the investor's initial capital remained unchanged over the two years?

AArithmetic Mean Return (AMR)

✓Geometric Mean Return (GMR)

CHolding Period Return (HPR)

DMoney Weighted Rate of Return (MWRR)

💡 The text provides this exact example, stating: 'In case of the first scheme at the end of the second year the investor will end up with Rs. 100,000... For the first choice GMR = (((1+-50%)*(1+100%))^(1/2)) -1 = 0'. It also emphasizes that 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' The AMR for this scenario would be 25%, which is misleading.

Q16 MCQ · 1 mark EasyArithmetic Mean Return (AMR)

How is the arithmetic mean return (AMR) calculated, according to the provided text?

ABy multiplying individual yearly returns.

✓By summing all of the returns in the series and dividing by the number of values.

CBy calculating wealth relatives and compounding them.

DBy discounting terminal value and cash flow contributions.

💡 The text defines AMR as 'the “simple average” of a series of returns, calculated by summing all of the returns in the series and dividing by the number of values.'

Q17 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

An investor is trying to estimate the expected return over a multiyear horizon conditioned on past experience. Which method of calculating returns is suggested as the best estimate for this purpose?

AGeometric Mean Return (GMR)

✓Arithmetic Mean Return (AMR)

CHolding Period Return (HPR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: "The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average. If we wish to estimate the expected return over a multiyear horizon conditioned on past experience, we may use the arithmetic average."

Q18 MCQ · 1 mark HardAMR vs GMR Interpretation

An investor invests Rs. 100,000 in a portfolio that produces a holding-period return of -50% in the first year and 100% in the second year. What is the Arithmetic Mean Return (AMR) for this two-year period, and what does the text indicate about its usefulness in this scenario?

AAMR is 25%; it is the best estimate of the multiyear expected return.

BAMR is 0%; it accurately reflects the long-term accumulation.

✓AMR is 25%; it can be misleading as the portfolio value returned to its initial level, making GMR a better measure for long-term accumulation.

DAMR is 0%; it is useful for comparing short-term performance.

💡 As per the text, AMR = (-50% + 100%) / 2 = 25%. The portfolio value at the end of year 2 would be Rs. 100,000 * (1 - 0.50) * (1 + 1.00) = Rs. 50,000 * 2 = Rs. 100,000. The text uses this exact example to show that 'the value of the portfolio is the same, as it was two years ago, though the average annual return on the portfolio is 25 percent,' and concludes that Geometric Mean Return (GMR) is better for comparing long-term accumulations because it explains what has really happened.

Q19 MCQ · 1 mark EasySEBI Regulations

According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which type of portfolio managers are prescribed to disclose performance using 'Time Weighted Rate of Return' for the immediately preceding three years?

AAll registered Mutual Funds

✓Discretionary portfolio managers

CNon-discretionary portfolio managers only

DInvestment Advisers

💡 The text explicitly states that 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q20 MCQ · 1 mark HardGross vs. Net Return

An investment adviser manages a portfolio with a Capital Contribution of Rs. 1,00,00,000. Over a year, the portfolio makes a 20% profit on the capital contribution. Other Expenses are 0.50% of the Gross Value of the Portfolio at the end of the investment period. Fixed Management Fees are 1.5% charged on the average of the capital contribution and the gross value of the portfolio. What is the portfolio value AFTER deducting Other Expenses and Fixed Management Fees?

ARs. 1,19,40,000

✓Rs. 1,17,75,000

CRs. 1,16,20,000

DRs. 1,13,87,600

💡 1. Capital Contribution (Beginning Value): Rs. 1,00,00,000 2. Profit made: 20% of Rs. 1,00,00,000 = Rs. 20,00,000 3. Gross Value of the Portfolio at the end of the investment period: Rs. 1,00,00,000 + Rs. 20,00,000 = Rs. 1,20,00,000 4. Other Expenses: 0.50% of Gross Value = 0.50% of Rs. 1,20,00,000 = Rs. 60,000 5. Portfolio Value after Other Expenses: Rs. 1,20,00,000 - Rs. 60,000 = Rs. 1,19,40,000 6. Average value for Fixed Management Fees: (Capital Contribution + Gross Value of Portfolio) / 2 = (Rs. 1,00,00,000 + Rs. 1,20,00,000) / 2 = Rs. 1,10,00,000 7. Fixed Management Fees: 1.5% of Average Value = 1.5% of Rs. 1,10,00,000 = Rs. 1,65,000 8. Portfolio Value after charging Fixed Management Fees: Rs. 1,19,40,000 - Rs. 1,65,000 = Rs. 1,17,75,000

Q21 MCQ · 1 mark EasyPre-tax vs Post-tax Return

An individual achieves a 5% pre-tax rate of return for an investment and is subject to a capital gains tax of 15%. What is the post-tax rate of return?

A5.15%

✓4.25%

C3.50%

D5.00%

💡 The formula for post-tax return is Pre-Tax Return x (1 - tax rate). Post-tax return = 5% x (1 - 15%) = 0.05 x (1 - 0.15) = 0.05 x 0.85 = 0.0425 or 4.25%.

Q22 MCQ · 1 mark MediumAMR vs GMR

For analyzing the long-run return on assets, which average return measure is considered far more important and explains what has really happened to the investments?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

CMoney Weighted Rate of Return (MWRR)

✓Geometric Mean Return (GMR)

💡 The text emphasizes, 'The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets.' It also states, 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.'

Q23 MCQ · 1 mark MediumPre-tax vs Post-tax Return

An investment achieves a 7.5% pre-tax rate of return. If the investor is subject to a capital gains tax rate of 20%, what would be the post-tax rate of return?

A7.5%

✓6.0%

C5.5%

D9.375%

💡 Using the formula provided: Post-tax return = Pre-Tax Return x (1 - tax rate). Post-tax return = 7.5% x (1 - 0.20) = 7.5% x 0.80 = 6.0%.

Q24 MCQ · 1 mark EasyMoney Weighted Rate of Return (MWRR)

What is another term used interchangeably with Money Weighted Rate of Return (MWRR) in the provided text?

AHolding Period Return (HPR)

BTime Weighted Rate of Return (TWRR)

✓Internal Rate of Return (IRR)

DCompounded Annual Growth Rate (CAGR)

💡 The text explicitly states: 'IRR is also referred as MWRR (Money Weighted rate of return).'

Q25 MCQ · 1 mark MediumNet Return Calculation

Based on the example provided in the text for Gross versus Net return, if the Capital Contribution at the beginning of the investment period was Rs. 1,00,00,000 and the Net Value of the Portfolio after all charges was Rs. 1,13,87,600, what was the Net Return?

A20.00%

B10.00%

✓13.88%

D1.39%

💡 The text provides the formula and calculation: Net Return = (Net value of the portfolio – Capital Contribution)/Capital Contribution. Using the given values: Net Return = (Rs. 1,13,87,600 – Rs. 1,00,00,000) / Rs. 1,00,00,000 = Rs. 13,87,600 / Rs. 1,00,00,000 = 0.13876, which is 13.88% when rounded to two decimal places.

Q26 MCQ · 1 mark EasyGross vs Net Return

Why is focusing on net return more important for an investor than gross return?

AGross return is difficult to calculate.

✓Net return is the actual return the investor makes after all deductions.

CGross return does not account for market fluctuations.

DNet return is typically higher than gross return.

💡 The text states: "Net return is the return investor actually makes, hence focusing on gross return can be misleading."

Q27 MCQ · 1 mark MediumAnnualizing Return

What is the primary purpose of reporting the rate of return on an annualized basis, as stated in the text?

ATo reduce the impact of cash flow timing.

BTo simplify the calculation of wealth relatives.

✓To facilitate comparison of investments.

DTo ensure that all income distributions are made at the end of the year.

💡 The text states: 'For facilitating comparison, rate of return is reported on annualized basis.'

Q28 MCQ · 1 mark HardGross vs. Net Return

Based on the provided example for calculating Gross and Net Return, if the Capital Contribution made at the beginning of the investment period was Rs. 1,00,00,000 and the Portfolio Value after charging Exit Load was Rs. 1,13,87,600, what is the Net Return?

A20.00%

✓13.88%

C10.00%

D15.15%

💡 The text provides the formula and calculation: Net Return = (Net value of the portfolio – Capital Contribution) / Capital Contribution. Using the given values: Net Return = (Rs. 1,13,87,600 – Rs. 1,00,00,000) / Rs. 1,00,00,000 = Rs. 13,87,600 / Rs. 1,00,00,000 = 0.13876 or 13.88%.

Q29 MCQ · 1 mark MediumCAGR and GMR

The text states that the process of calculating the Compounded Annual Growth Rate (CAGR) is the same as the calculation of which other return measure?

AHolding Period Return (HPR)

BMoney Weighted Rate of Return (MWRR)

✓Geometric Mean Return (GMR)

DArithmetic Mean Return (AMR)

💡 The text explicitly states, 'The TWRR is the same as geometric return.' and later under Annualizing return, 'The calculation is same as the calculation of CAGR or geometric mean return.' This implies CAGR is synonymous with GMR and TWRR.

Q30 MCQ · 1 mark HardGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

An investor is comparing two portfolio choices over a two-year period. Portfolio X returned -50% in year 1 and 100% in year 2. Portfolio Y returned 10% in year 1 and 10% in year 2. According to the text, which statement accurately reflects the utility of Geometric Mean Return (GMR) in this scenario?

AGMR is less important for long-run asset analysis compared to AMR.

BGMR for Portfolio X is 25%, indicating it performed better than Portfolio Y with 10% GMR.

✓GMR explains what has *really* happened to the investments and for Portfolio X it is 0%, while for Portfolio Y it is 10%.

DGMR is the best estimate for a future year's return based on a random distribution of prior years' returns.

💡 The text states: "The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets... Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments." It also provides the specific calculations: "For the first choice GMR = (((1+-50%)*(1+100%))^(1/2)) -1 = 0" and "For the first choice GMR = (((1+10%)*(1+10%))^(1/2)) -1 = 10%". Option D describes AMR.

Q31 MCQ · 1 mark MediumHolding Period Return

An investment has a Beginning Value (B) of Rs. 100,000, an Ending Value (E) of Rs. 120,000, and generated Income (I) of Rs. 5,000 during the period. What is the Holding Period Return (HPR)?

A15%

B20%

✓25%

D30%

💡 Using the formula HPR = (I + (E - B)) / B: HPR = (5000 + (120000 - 100000)) / 100000 HPR = (5000 + 20000) / 100000 HPR = 25000 / 100000 = 0.25 or 25%.

Q32 MCQ · 1 mark EasyHolding Period Return

Based on Equation 2 for Holding Period Return (HPR), which of the following components is NOT directly part of the numerator?

AIncome (I)

BEnding Value (E)

CBeginning Value (B)

✓Time period (t)

💡 The HPR formula given is (I + (E - B)) / B. Income (I), Ending Value (E), and Beginning Value (B) are all components of the numerator (I + (E - B)) or denominator (B). Time period (t) is not explicitly represented as a direct variable in this specific formula, although the return is for a defined holding period.

Q33 MCQ · 1 mark HardGross vs. Net Return

An investor made a capital contribution of Rs. 1,00,00,000. The portfolio generated a profit of 20% on the capital contribution. Other expenses were 0.50% of the gross value of the portfolio. Fixed Management Fees were 1.5% on the average of capital contribution and gross value of portfolio. A hurdle rate of 10% was applied, with performance fees of 20% of profits over the hurdle rate. An exit load of 2% was also charged. What is the Net Return for the investor?

A20.00%

B16.20%

✓13.88%

D11.25%

💡 1. Capital Contribution: Rs. 1,00,00,000 2. Profit made during the year: 20% of Rs. 1,00,00,000 = Rs. 20,00,000 3. Gross Value of the Portfolio at the end: Rs. 1,00,00,000 + Rs. 20,00,000 = Rs. 1,20,00,000 4. Less: Other Expenses (0.50% of Gross Value): 0.005 * Rs. 1,20,00,000 = Rs. 60,000 5. Average Value for Fixed Management Fees: (Rs. 1,00,00,000 + Rs. 1,20,00,000) / 2 = Rs. 1,10,00,000 6. Less: Fixed Management Fees (1.50% of Average Value): 0.015 * Rs. 1,10,00,000 = Rs. 1,65,000 7. Portfolio Value after Other Expenses & Fixed Management Fees: Rs. 1,20,00,000 - Rs. 60,000 - Rs. 1,65,000 = Rs. 1,17,75,000 8. Required Portfolio Value @ Hurdle Rate (10% of Capital Contribution): Rs. 1,00,00,000 * 1.10 = Rs. 1,10,00,000 9. Profit over Hurdle Level: Rs. 1,17,75,000 - Rs. 1,10,00,000 = Rs. 7,75,000 10. Less: Performance Fee (20% of Profits over Hurdle Level): 0.20 * Rs. 7,75,000 = Rs. 1,55,000 11. Portfolio Value after charging Performance Fees: Rs. 1,17,75,000 - Rs. 1,55,000 = Rs. 1,16,20,000 12. Less: Exit Load (2% of Portfolio Value after Performance Fees): 0.02 * Rs. 1,16,20,000 = Rs. 2,32,400 13. Net Value of the Portfolio: Rs. 1,16,20,000 - Rs. 2,32,400 = Rs. 1,13,87,600 14. Net Return = (Net Value of the Portfolio - Capital Contribution) / Capital Contribution Net Return = (Rs. 1,13,87,600 - Rs. 1,00,00,000) / Rs. 1,00,00,000 = Rs. 13,87,600 / Rs. 1,00,00,000 = 0.13876 or 13.88%.

Q34 MCQ · 1 mark MediumGeometric Mean Return (GMR) and TWRR

Which statement accurately describes the relationship between Time Weighted Rate of Return (TWRR) and Geometric Mean Return (GMR)?

ATWRR is always greater than GMR.

BTWRR is always less than GMR.

✓TWRR is the same as geometric return.

DTWRR is the arithmetic average of GMRs.

💡 The text clearly states, 'The TWRR is the same as geometric return.'

Q35 MCQ · 1 mark MediumPre-tax vs. Post-tax Return

According to the text, why do investors make investment decisions primarily on the basis of post-tax performance?

APre-tax returns are too complex to calculate.

✓Post-tax return is what really matters to the investor.

CPre-tax returns enable comparisons across different investments.

DTax rates are uniform for all investors, simplifying post-tax calculations.

💡 The text states: 'However, what really matters to the investor is post-tax return. Hence they make investment decision on the basis of post-tax performance.'

Q36 MCQ · 1 mark MediumCompounded Annual Growth Rate (CAGR)

What is a fundamental assumption when calculating Compounded Annual Growth Rate (CAGR)?

AThat the investment period must be exactly one year.

✓That any dividend, income, or rent declared by the investment is reinvested.

CThat the market experiences consistent growth throughout the period.

DThat there are no additional capital contributions or withdrawals.

💡 The text explicitly states: 'It assumes that any dividend/income/rent declared by the investment is re-invested in the same investment on that day’s market price.'

Q37 MCQ · 1 mark MediumArithmetic Mean Return (AMR) vs. Geometric Mean Return (GMR)

When analyzing the long-run return on assets, which method of calculating returns is considered far more important, and why, according to the text?

AArithmetic Mean Return (AMR), because it is the simple average of individual yearly returns.

✓Geometric Mean Return (GMR), because it explains what has really happened to the investments and depends only on initial and final values.

CArithmetic Mean Return (AMR), because it is the best estimate of a future year's return based on a random distribution.

DGeometric Mean Return (GMR), because it is always greater than the arithmetic return over longer holding periods.

💡 The text states: 'The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets... It depends only on the initial and final values of the portfolio, not on the path by which that value was realized... Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' Option D is incorrect as GMR is always less than AMR unless returns are identical.

Q38 MCQ · 1 mark HardTWRR vs MWRR Application

According to the text, which statement is TRUE regarding the use of MWRR and TWRR in different contexts?

ATWRR is preferred for wealth manager software systems reporting client returns over long holding periods.

BMWRR is mandated by SEBI for discretionary portfolio managers to disclose performance.

CThe client is generally bothered about how much s/he is taking home, which aligns with TWRR.

✓In PMS, since portfolios are customized and there is no NAV, SEBI has mandated TWRR for fund managers.

💡 The text states: "In PMS, since portfolios are customized and there is no NAV, SEBI has mandated TWRR for fund managers." Option A is incorrect because wealth manager systems use MWRR. Option B is incorrect because SEBI mandated TWRR. Option C is incorrect because the client's take-home aligns with MWRR, while TWRR is for fund managers for uniformity.

Q39 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

According to the text, for what primary reason does SEBI mandate the use of Time Weighted Rate of Return (TWRR) for discretionary portfolio managers?

ATo reflect the actual amount an investor takes home.

BTo account for the precise timing of individual investor cash flows.

✓To provide uniformity in reporting and comparing fund manager performance.

DTo simplify the calculation of returns for customized portfolios with multiple cash flows.

💡 The text states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ‘Time Weighted Rate of Return’ for the immediately preceding three years.' It further clarifies: 'TWRR is for the fund manager for uniformity in reporting and comparing.'

Q40 MCQ · 1 mark HardMWRR vs TWRR Interpretation

Based on the provided example, an investor's portfolio over five years had an MWRR of 15.15% and a TWRR of 6.021%. The MWRR is significantly higher than the TWRR. What is the most appropriate conclusion for the investor based on the text?

AThe fund manager's skill is best reflected by the 15.15% return.

BThe investor's actual wealth accumulation is best described by the 6.021% return.

✓The investor's timing of contributions positively impacted their personal return.

DThe TWRR being lower than MWRR implies the investor would have been better off investing a lump sum.

💡 The text states that 'MWRR depends on the timing of the cash flow' and 'At the end of the day the client is bothered about how much s/he is taking home; TWRR is for the fund manager for uniformity in reporting and comparing.' If MWRR (15.15%) is higher than TWRR (6.021%), it indicates that the investor's specific cash flow timing (contributions at the beginning of each year in this example) was beneficial, leading to a higher personal return than the underlying investment performance (TWRR) alone. Therefore, the timing of contributions positively impacted their personal return. Option A is incorrect as TWRR reflects fund manager's skill. Option B is incorrect as MWRR reflects the investor's actual wealth accumulation based on their cash flows. Option D is an inference not directly supported by the text.

Q41 MCQ · 1 mark EasyHolding Period Return (HPR)

An investment has a Beginning Value (B) of Rs. 50,000, generates Income (I) of Rs. 2,000, and has an Ending Value (E) of Rs. 60,000. Assuming all income distributions are made at the end of the year, what is the Holding Period Return (HPR)?

A20%

✓24%

C28%

D30%

💡 The formula for Holding Period Return (HPR) is: HPR = (I + (E - B)) / B. Given: I = Rs. 2,000, E = Rs. 60,000, B = Rs. 50,000. HPR = (2,000 + (60,000 - 50,000)) / 50,000 HPR = (2,000 + 10,000) / 50,000 HPR = 12,000 / 50,000 HPR = 0.24 or 24%

Q42 MCQ · 1 mark MediumTWRR vs MWRR

Which of the following statements accurately describes the fundamental difference between Money Weighted Rate of Return (MWRR) and Time Weighted Rate of Return (TWRR) as per the text?

✓MWRR is influenced by the timing of cash flows, while TWRR aims to calculate performance without this influence.

BTWRR is used for short-term investments, whereas MWRR is preferred for long-term investments.

CMWRR requires calculating wealth relatives, while TWRR uses a simple average of annual returns.

DTWRR is mandated by SEBI for mutual funds, while MWRR is used for portfolio managers.

💡 The text states: 'MWRR depends on the timing of the cash flow.' and 'Alternatively, in order to calculate the underlying investment performance without being influenced by the timing of cash flow, TWRR can be calculated.'

Q43 MCQ · 1 mark HardReturn Measure Equivalence

Which of the following statements about different return measures is TRUE, according to the text?

AThe TWRR is always greater than the MWRR.

BThe process of calculating GMR is different from TWRR.

CCAGR is calculated using a formula distinct from TWRR and geometric mean return.

✓The TWRR is the same as geometric return, and CAGR calculation is the same as TWRR or geometric mean return.

💡 The text states: 'The TWRR is the same as geometric return.' And under the CAGR section, it mentions: 'The calculation is same as the calculation of CAGR or geometric mean return.'

Q44 MCQ · 1 mark MediumGeometric vs. Arithmetic Mean Return

Which of the following statements is true regarding the relationship between Geometric Mean Return (GMR) and Arithmetic Mean Return (AMR) over holding periods longer than one year?

AGMR is always greater than AMR.

BAMR is always less than GMR.

✓GMR is always less than or equal to AMR.

DGMR and AMR are always identical.

Q45 MCQ · 1 mark EasyTime Weighted Rate of Return vs. Money Weighted Rate of Return

Which rate of return measure explicitly depends on the timing of cash flows?

AHolding Period Return (HPR)

BTime Weighted Rate of Return (TWRR)

✓Money Weighted Rate of Return (MWRR)

DCompounded Annual Growth Rate (CAGR)

💡 The text states: 'MWRR depends on the timing of the cash flow.' In contrast, TWRR calculates underlying investment performance 'without being influenced by the timing of cash flow'.

Q46 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

What does MWRR (Money Weighted Rate of Return) represent?

AThe average daily return of a portfolio over a measurement period.

✓The annual rate of return at which cumulative contributions grow over the measurement period.

CThe rate of return that eliminates the impact of cash flows.

DThe simple average of annual holding period returns.

💡 The text defines MWRR as 'the annual rate of return at which the cumulative contributions grow over the measurement period.'

Q47 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Under what specific condition will the Geometric Mean Return (GMR) equal the Arithmetic Mean Return (AMR) over a holding period longer than one year?

✓When all individual yearly returns are exactly the same.

BWhen the portfolio experiences no losses during the period.

CWhen the initial and final values of the portfolio are identical.

DNever; GMR is always less than AMR for periods longer than one year.

Q48 MCQ · 1 mark HardCompounded Annual Growth Rate (CAGR)

An investor invested Rs. 100,000. After five years, the investment grew to Rs. 1,33,960. Using the Compound Annual Growth Rate (CAGR) formula, what is the CAGR for this investment?

A5.00%

✓6.02%

C7.50%

D8.10%

💡 CAGR = (Closing Wealth / Opening Wealth)^(1 / Time Period) - 1 CAGR = (1,33,960 / 1,00,000)^(1/5) - 1 CAGR = (1.3396)^(0.2) - 1 CAGR = 1.06021 - 1 = 0.06021 or 6.02% (rounded)

Q49 MCQ · 1 mark EasyGross Return

What does 'Gross Return' on an investment represent?

AThe return earned after deducting all fees, expenses, and commissions.

✓The total return generated on investment before the deduction of any fees, expenses or commissions.

CThe return adjusted for the investor's specific tax bracket.

DThe average annual return calculated using the geometric mean method.

💡 The text defines: 'The gross return is the total return generated on investment before the deduction of any fees, expenses or commissions.'

Q50 MCQ · 1 mark MediumGross Return

A portfolio starts with a Capital Contribution of Rs. 1,00,00,000 and makes a Profit of 20% during the year. What is the Gross Return on this investment?

A19.40%

✓20.00%

C13.88%

D17.75%

💡 As per the text, Gross Return is calculated as: (Gross value of the portfolio – Capital Contribution) / Capital Contribution. Capital Contribution = Rs. 1,00,00,000 Profit made during the year = 20% of Rs. 1,00,00,000 = Rs. 20,00,000 Gross Value of the Portfolio at the end of the investment period = Rs. 1,00,00,000 + Rs. 20,00,000 = Rs. 1,20,00,000 Gross Return = (Rs. 1,20,00,000 - Rs. 1,00,00,000) / Rs. 1,00,00,000 = Rs. 20,00,000 / Rs. 1,00,00,000 = 0.20 or 20%. Other expenses are deducted for Net Return, not Gross Return.

Q51 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR) vs. Money Weighted Rate of Return (MWRR)

As per SEBI (Portfolio Managers) Regulation, 2020, which method is prescribed for discretionary portfolio managers to disclose performance for the immediately preceding three years?

AHolding Period Return (HPR)

BMoney Weighted Rate of Return (MWRR)

✓Time Weighted Rate of Return (TWRR)

DArithmetic Mean Return (AMR)

💡 The text explicitly states: "Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years."

Q52 MCQ · 1 mark EasyTime Weighted Rate of Return (TWRR)

As per the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which type of entity is prescribed to disclose performance using 'Time Weighted Rate of Return' for the immediately preceding three years?

AMutual Funds

✓Discretionary portfolio managers

CWealth manager software systems

DIndividual investors

💡 The text states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q53 MCQ · 1 mark EasyGross Return

What does 'Gross return' represent as per the provided text?

AThe return earned after all fees and expenses.

✓The total return generated on investment before the deduction of any fees, expenses or commissions.

CThe return adjusted for taxes.

DThe return influenced by the timing of cash flows.

💡 The text defines: 'The gross return is the total return generated on investment before the deduction of any fees, expenses or commissions.'

Q54 MCQ · 1 mark EasyPre-tax vs. Post-tax Return

What is the primary reason mentioned in the text for communicating the performance of investments as pre-tax rate of return?

ATo simplify the calculation for financial advisors.

✓To allow investors to compare different investments and strategies, as they belong to different tax brackets.

CBecause post-tax returns are too complex to calculate for individual investors.

DTo ensure uniformity in reporting across all investment products.

💡 The text states: 'Investors belong to different tax brackets. Hence the performance of the investments is communicated as pre-tax rate of return. Pre-Tax return enables comparisons across different investments and strategies, since different investors may be subject to different levels of taxation.'

Q55 MCQ · 1 mark MediumNet Return

Based on the example provided in the text for Gross versus Net return, what was the calculated Net Return for the sample portfolio?

A20%

B10%

✓13.88%

D15.15%

💡 The text explicitly calculates: 'Net Return = (Rs. 1,13,87,600 – Rs. 1,00,00,000) / Rs.1,00,00,000 = 13.88%'.

Q56 MCQ · 1 mark EasyGross vs Net Return

A portfolio has a Capital Contribution made at the beginning of the investment period of Rs. 1,00,00,000. At the end of the investment period, the Gross Value of the Portfolio is Rs. 1,20,00,000. What is the Gross Return for this portfolio?

A13.88%

✓20%

C10%

D15.15%

💡 As per the text, Gross Return = (Gross value of the portfolio – Capital Contribution) / Capital Contribution. Gross Return = (Rs. 1,20,00,000 – Rs. 1,00,00,000) / Rs. 1,00,00,000 Gross Return = Rs. 20,00,000 / Rs. 1,00,00,000 = 0.20 or 20%.

Q57 MCQ · 1 mark EasyTime Weighted Rate of Return

According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which specific performance measure is prescribed for discretionary portfolio managers to disclose?

AMoney Weighted Rate of Return (MWRR)

BArithmetic Mean Return (AMR)

CCompounded Annual Growth Rate (CAGR)

✓Time Weighted Rate of Return (TWRR)

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q58 MCQ · 1 mark EasyHolding Period Return (HPR)

Which of the following is an assumption made when calculating Holding Period Return (HPR)?

AAll income distributions are reinvested immediately.

✓All income distributions are made at the end of the year.

CThe portfolio value remains constant throughout the holding period.

DThe investment period must be exactly one year.

💡 The text states, 'This measure assumes that all income distributions are made at the end of the year.'

Q59 MCQ · 1 mark MediumCompounded Annual Growth Rate

When considering an initial and final wealth value over a period, assuming no intermediate cash flows, the Compounded Annual Growth Rate (CAGR) calculation is described as being the same as which other return measure?

AHolding Period Return (HPR)

BMoney Weighted Rate of Return (MWRR)

CArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR) / Geometric Mean Return (GMR)

💡 The text states: 'The TWRR is the same as geometric return.' and 'The process of calculating the GMR is the same as TWRR.' It also notes that 'The calculation is same as the calculation of CAGR or geometric mean return.'

Q60 MCQ · 1 mark EasyMWRR vs TWRR

Which of the following rate of return measures depends on the timing of external cash flows?

AHolding Period Return

BTime Weighted Rate of Return

✓Money Weighted Rate of Return

DGeometric Mean Return

💡 Money Weighted Rate of Return (MWRR) depends on the timing of the cash flow, as it is essentially the Internal Rate of Return (IRR) which discounts cash flows.

Q61 MCQ · 1 mark HardGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Consider two portfolio choices. Portfolio 1 produces returns of -50% in year 1 and 100% in year 2. Portfolio 2 produces 10% in year 1 and 10% in year 2. Both start with Rs. 100,000. Which of the following statements is TRUE regarding these portfolios based on the text?

APortfolio 1 has a higher Geometric Mean Return (GMR) than Portfolio 2.

BPortfolio 2 has a higher Arithmetic Mean Return (AMR) than Portfolio 1.

✓The investor is better off with Portfolio 2, despite Portfolio 1 having a higher AMR.

DThe Geometric Mean Return is identical to the Arithmetic Mean Return for Portfolio 1.

💡 For Portfolio 1: AMR = (-50% + 100%)/2 = 25%; GMR = (((1-0.50)*(1+1.00))^(1/2)) - 1 = 0%. For Portfolio 2: AMR = (10% + 10%)/2 = 10%; GMR = (((1+0.10)*(1+0.10))^(1/2)) - 1 = 10%. The text states: "Clearly, investor is better off with the second scheme, although it produces average annual return lower than the first scheme."

Q62 MCQ · 1 mark MediumGross vs Net Return

An investment portfolio had a Capital Contribution of Rs. 1,00,00,000. After accounting for all fees and expenses, the Net Value of the Portfolio was Rs. 1,13,87,600. What is the Net Return on this investment?

A20.00%

✓13.88%

C15.15%

D6.02%

💡 Net Return is calculated as (Net value of the portfolio – Capital Contribution) / Capital Contribution. Net Return = (Rs. 1,13,87,600 – Rs. 1,00,00,000) / Rs. 1,00,00,000 Net Return = Rs. 13,87,600 / Rs. 1,00,00,000 = 0.13876 or 13.88%.

Q63 MCQ · 1 mark HardNet Return Calculation Components

Based on the example provided in the text for a sample portfolio, what was the calculated Performance Fee, given a Hurdle Rate of 10% and a performance fee of 20% of profits over the hurdle rate?

ARs. 1,65,000

BRs. 60,000

✓Rs. 1,55,000

DRs. 2,32,400

💡 1. Capital Contribution (i) = Rs. 1,00,00,000 2. Profit made during the year = 20% of Capital Contribution = 0.20 * 1,00,00,000 = Rs. 20,00,000 3. Gross Value of the Portfolio at the end = 1,00,00,000 + 20,00,000 = Rs. 1,20,00,000 4. Less: Other Expenses (0.50% of Gross Value) = 0.0050 * 1,20,00,000 = Rs. 60,000 5. Value after Other Expenses = 1,20,00,000 - 60,000 = Rs. 1,19,40,000 6. Average value for Fixed Management Fees = (Initial Capital + Gross End Value) / 2 = (1,00,00,000 + 1,20,00,000) / 2 = Rs. 1,10,00,000 7. Less: Fixed Management Fees (1.50% of Average Value) = 0.0150 * 1,10,00,000 = Rs. 1,65,000 8. Portfolio Value after Fixed Management Fees = 1,19,40,000 - 1,65,000 = Rs. 1,17,75,000 9. Required Portfolio Value @ Hurdle Rate (10%) = Initial Capital * (1 + Hurdle Rate) = 1,00,00,000 * 1.10 = Rs. 1,10,00,000 10. Profit over Hurdle Level = (Portfolio Value after Fixed Management Fees) - (Required Portfolio Value @ Hurdle Rate) = 1,17,75,000 - 1,10,00,000 = Rs. 7,75,000 11. Performance Fee (20% of Profit over Hurdle Level) = 0.20 * 7,75,000 = Rs. 1,55,000

Q64 MCQ · 1 mark EasyHolding Period Return

In the Holding Period Return (HPR) formula, HPR = (I + (E -B)) / B, what does the variable 'I' represent?

AInitial Investment

✓Income generated during the period

CInterest rate

DInflation rate

💡 According to the text, 'I' stands for Income in the Holding Period Return formula.

Q65 MCQ · 1 mark HardGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

When analyzing the long-run return on assets and comparing long-term accumulations, which return measure is considered 'far more important' and the 'only way to compare long-term accumulations' according to the text?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

CMoney Weighted Rate of Return (MWRR)

✓Geometric Mean Return (GMR)

💡 The text emphasizes the importance of GMR for long-term analysis: 'The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets.' It further states: 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.'

Q66 MCQ · 1 mark MediumTWRR vs MWRR Use Cases

For what primary reason do fund managers, particularly in PMS, use Time Weighted Rate of Return (TWRR) for performance disclosure, as per the text?

ABecause it best reflects what the client is taking home.

BTo reflect the impact of the timing of client contributions and withdrawals.

✓For uniformity in reporting and comparing performance.

DSince PMS portfolios are not customized and have a daily NAV.

💡 The text explains: 'In PMS, since portfolios are customized and there is no NAV, SEBI has mandated TWRR for fund managers;...TWRR is for the fund manager for uniformity in reporting and comparing.'

Q67 MCQ · 1 mark MediumPre-tax vs. Post-tax Return

Why is the performance of investments typically communicated as pre-tax rate of return, according to the text?

APre-tax return is easier to calculate than post-tax return.

✓Investors belong to different tax brackets, making pre-tax return suitable for comparison across different investments and strategies.

CPost-tax return is less relevant for investment decision-making.

DPre-tax return always yields a higher numerical value, which is preferred for reporting.

💡 The text states: 'Investors belong to different tax brackets. Hence the performance of the investments is communicated as pre-tax rate of return.' It further adds: 'Pre-Tax return enables comparisons across different investments and strategies, since different investors may be subject to different levels of taxation.'

Q68 MCQ · 1 mark EasyGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Which type of return is considered the best estimate of a future year's return based on a random distribution of prior years' returns?

AGeometric Mean Return (GMR)

✓Arithmetic Mean Return (AMR)

CHolding Period Return (HPR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: 'The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average.'

Q69 MCQ · 1 mark EasyTWRR Application

As per SEBI (Portfolio Managers) Regulation, 2020, which rate of return measure is prescribed for discretionary portfolio managers to disclose performance?

AMoney Weighted Rate of Return

BHolding Period Return

✓Time Weighted Rate of Return

DArithmetic Mean Return

💡 The Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.

Q70 MCQ · 1 mark EasyHolding Period Return

What specific assumption does the Holding Period Return (HPR) measure make regarding income distributions?

AAll income distributions are made at the beginning of the year.

✓All income distributions are made at the end of the year.

CIncome distributions are reinvested immediately upon receipt.

DIncome distributions are ignored in the calculation.

💡 The text explicitly states, 'This measure assumes that all income distributions are made at the end of the year.'

Q71 MCQ · 1 mark HardReturn Measures Comparison

Which of the following statements about return measures are correct according to the provided text? I. Money Weighted Rate of Return (MWRR) is influenced by the timing of cash flows. II. Time Weighted Rate of Return (TWRR) is fundamentally the same as geometric return. III. The process for calculating Geometric Mean Return (GMR) involves the same steps as TWRR, including calculating wealth relatives and chain linking. IV. The calculation method for Compounded Annual Growth Rate (CAGR) is identical to that of the geometric mean return.

AI and II only

BI, II, and III only

✓I, II, III, and IV

DII and IV only

💡 I. The text states: 'MWRR depends on the timing of the cash flow.' (Correct) II. The text states: 'The TWRR is the same as geometric return.' (Correct) III. The text states: 'The process of calculating the GMR is the same as TWRR. We are required to calculate wealth relatives for each HPR. Then we have to link these sub period returns.' (Correct) IV. The text states under 'Annualizing return': 'The calculation is same as the calculation of CAGR or geometric mean return.' (Correct) Therefore, all four statements are correct.

Q72 MCQ · 1 mark EasyPost-tax Return

An investment yields a 5% pre-tax rate of return, and the investor is subject to a capital gains tax of 15%. What is the post-tax rate of return for this investment?

A5.88%

✓4.25%

C4.75%

D3.50%

💡 Post-tax return = Pre-tax return x (1 - tax rate) Post-tax return = 5% x (1 - 0.15) Post-tax return = 5% x 0.85 = 4.25%

Q73 MCQ · 1 mark MediumGeometric Mean Return vs Arithmetic Mean Return

An investor is evaluating two portfolio choices over a two-year period. Portfolio X had annual returns of -50% and 100%, while Portfolio Y had annual returns of 10% and 10%. According to the text, which return measure should be used to understand what has 'really happened' to the investments and to compare long-term accumulations?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

✓Geometric Mean Return (GMR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' It also uses the example of -50% and 100% returns to illustrate how AMR can be misleading for long-term accumulation.

Q74 MCQ · 1 mark MediumCAGR

Which key assumption is made when calculating the Compounded Annual Growth Rate (CAGR)?

AAll income distributions are made at the end of the year.

BThe investment value is adjusted for external cash flows.

✓Any income/dividend is re-invested in the same investment.

DThe return is independent of the timing of cash flows.

💡 CAGR assumes that any dividend/income/rent declared by the investment is re-invested in the same investment on that day’s market price.

Q75 MCQ · 1 mark MediumGeometric Mean Return (GMR)

If an investor wishes to analyze the long-run return on assets, which average return measure is considered 'far more important' according to the text?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

✓Geometric Mean Return (GMR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: 'The average geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets.'

Q76 MCQ · 1 mark EasyHolding Period Return (HPR)

What is the primary limitation of the Holding Period Return (HPR) measure as stated in the text?

✓It assumes all income distributions are made at the end of the year.

BIt does not account for capital gains.

CIt cannot be used for periods longer than one year.

DIt is not a generally accepted indicator of performance.

💡 The text explicitly states: 'This measure assumes that all income distributions are made at the end of the year.' It also clarifies that 'in spite of this limitation, Holding Period Return measure is widely used and generally accepted indicator of performance,' making option D incorrect.

Q77 MCQ · 1 mark HardMoney Weighted Rate of Return

The Money Weighted Rate of Return (MWRR) is essentially the Internal Rate of Return (IRR). In the context of the provided example for MWRR calculation, what does the calculated IRR of 15.15% represent?

AThe constant annual growth rate if no further investments were made after the initial contribution.

✓The annual rate of return at which the cumulative contributions grow over the measurement period, considering the timing of those contributions.

CThe average of the annual holding period returns, uninfluenced by the cash flow timing.

DThe rate at which the portfolio's ending value would have been achieved if all income distributions were made at the end of the final year.

💡 The text states: 'MWRR is the annual rate of return at which the cumulative contributions grow over the measurement period. MWRR depends on the timing of the cash flow.' Option B directly matches this definition.

Q78 MCQ · 1 mark MediumGeometric Mean Return vs Arithmetic Mean Return

Under what specific condition will the Geometric Mean Return (GMR) be equal to the Arithmetic Mean Return (AMR) over a holding period longer than one year?

AWhen the portfolio's value experiences significant fluctuations.

✓When all individual yearly returns are exactly the same.

CWhen the market is in a bear phase.

DWhen the investment period is exactly two years.

Q79 MCQ · 1 mark HardGross vs Net Return

Why does the text emphasize that focusing on Net Return is more crucial for an investor, even though Gross Return can be used to evaluate performance at a broader level?

ANet Return is easier to calculate and compare across different investment products.

BGross Return includes all income distributions, which can inflate perceived performance.

✓Net Return is the actual return an investor makes after all fees, expenses, and commissions, directly reflecting the take-home profit.

DGross Return is only applicable for short-term investments, while Net Return is for long-term.

💡 The text states, 'Net return is calculated after adjusting gross return for fees, expenses or commissions. Net return is the return investor actually makes, hence focusing on gross return can be misleading though it can be used to evaluate the performance of investments at a broader level.' This highlights that Net Return represents the real profit the investor takes home, making it more crucial from their perspective.

Q80 MCQ · 1 mark EasyHolding Period Return (HPR)

An investment had a Beginning Value (B) of Rs. 100,000, an Ending Value (E) of Rs. 120,000, and generated Income (I) of Rs. 5,000. Calculate the Holding Period Return (HPR) using the formula provided in the text.

A20%

✓25%

C15%

D30%

💡 The formula is HPR = (I + (E - B)) / B. * HPR = (5000 + (120000 - 100000)) / 100000 * HPR = (5000 + 20000) / 100000 * HPR = 25000 / 100000 * HPR = 0.25 = 25%

Q81 MCQ · 1 mark HardTime Weighted Rate of Return (TWRR)

An investment adviser is evaluating the performance of a discretionary portfolio manager for the immediately preceding three years as per SEBI regulations. Which rate of return measure is mandated for this disclosure?

AMoney Weighted Rate of Return (MWRR)

BArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR)

DHolding Period Return (HPR)

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q82 MCQ · 1 mark MediumHolding Period Return

An investment begins with a value of Rs. 50,000, generates an income of Rs. 2,000, and has an ending value of Rs. 60,000. What is the Holding Period Return (HPR)?

A20%

B22%

✓24%

D25%

💡 The Holding Period Return (HPR) is calculated using the formula: HPR = (Income + (Ending Value - Beginning Value)) / Beginning Value. HPR = (2,000 + (60,000 - 50,000)) / 50,000 HPR = (2,000 + 10,000) / 50,000 HPR = 12,000 / 50,000 = 0.24 or 24%.

Q83 MCQ · 1 mark MediumMoney Weighted Rate of Return

Which of the following is a defining characteristic of the Money Weighted Rate of Return (MWRR) as described in the text?

AIt is calculated without being influenced by the timing of cash flows.

BIt is identical to the Time Weighted Rate of Return (TWRR).

✓It depends on the timing of the cash flow.

DIt is primarily used by fund managers for uniformity in reporting.

💡 The text states, 'MWRR depends on the timing of the cash flow.' It also contrasts this with TWRR, which is calculated 'without being influenced by the timing of cash flow'.

Q84 MCQ · 1 mark EasyGross vs. Net Return

Based on the example provided for Gross and Net Return, if the Capital Contribution was Rs. 1,00,00,000 and the Gross Value of the Portfolio at the end of the investment period was Rs. 1,20,00,000, what was the Gross Return?

A13.88%

✓20%

C10%

D25%

💡 The text provides the calculation: "Gross Return = (Gross value of the portfolio – Capital Contribution)/Capital Contribution. Gross Return = (Rs. 1,20,00,000 Lacs. - Rs. 1,00,00,000 Lacs.) / Rs. 1,00,00,000 Lacs. Gross Return = 20 %".

Q85 MCQ · 1 mark MediumPre-tax vs. Post-tax Return

An individual achieves a 5% pre-tax rate of return for an investment and is subject to a capital gains tax of 15%. What is the post-tax rate of return?

✓4.25%

B4.50%

C5.75%

D5.00%

💡 Using the formula: Post-tax return = Pre-Tax Return x (1-tax rate) Post-tax return = 5% x (1 - 15%) Post-tax return = 0.05 x (1 - 0.15) Post-tax return = 0.05 x 0.85 = 0.0425 or 4.25%.

Q86 MCQ · 1 mark HardGeometric Mean Return (GMR)

A key characteristic of the compound (geometric) return mentioned in the text is that it depends solely on which of the following?

AThe path by which the portfolio value was realized.

BThe number of external cash flows during the period.

✓The initial and final values of the portfolio.

DThe average annual volatility of returns.

💡 The text states: 'A characteristic of the compound return is that it depends only on the initial and final values of the portfolio, not on the path by which that value was realized.'

Q87 MCQ · 1 mark HardTime Weighted Rate of Return (TWRR) Regulation

As per the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 mentioned in the text, which performance measure are discretionary portfolio managers prescribed to disclose for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BHolding Period Return (HPR)

CCompounded Annual Growth Rate (CAGR)

✓Time Weighted Rate of Return (TWRR)

Q88 MCQ · 1 mark EasyTWRR Usage and Regulation

According to SEBI regulations mentioned in the text, which entity is prescribed to disclose performance using 'Time Weighted Rate of Return' for the immediately preceding three years?

AMutual Funds

BWealth managers for client reporting

✓Discretionary portfolio managers

DIndividual investors calculating post-tax returns

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q89 MCQ · 1 mark EasyRegulatory Disclosure for Portfolio Managers

Which specific return measure is mandated by the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, for discretionary portfolio managers to disclose their performance for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BHolding Period Return (HPR)

✓Time Weighted Rate of Return (TWRR)

DArithmetic Mean Return (AMR)

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q90 MCQ · 1 mark HardGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

An investor has two portfolio choices. Scheme 1 yields -50% in year 1 and 100% in year 2. Scheme 2 yields 10% in year 1 and 10% in year 2. Both start with Rs. 100,000. Why is Scheme 2 preferred, despite Scheme 1 having a higher Arithmetic Mean Return (AMR)?

AScheme 1 involves higher transaction costs not accounted for in AMR.

✓Scheme 2 provides a higher terminal wealth, accurately reflected by its Geometric Mean Return (GMR).

CScheme 1's returns are not representative of future performance.

DScheme 2 has a lower standard deviation of returns.

💡 The text explains: 'In case of the first scheme at the end of the second year the investor will end up with Rs. 100,000... With the second choice the value of the portfolio at the end of the second year is Rs.121,000... Clearly, investor is better off with the second scheme, although it produces average annual return lower than the first scheme.' It further states, 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' Scheme 1's GMR is 0%, while Scheme 2's GMR is 10%.

Q91 MCQ · 1 mark EasyHolding Period Return

What is the primary limitation of the Holding Period Return (HPR) measure as stated in the provided text?

AIt fails to account for any income distributions made during the holding period.

✓It assumes that all income distributions are made at the end of the year.

CIt is not a widely accepted or generally used indicator of performance.

DIt cannot be used as a starting point for performance measurement exercises.

💡 The text states: 'This measure assumes that all income distributions are made at the end of the year. In spite of this limitation, Holding Period Return measure is widely used and generally accepted indicator of performance.'

Q92 MCQ · 1 mark HardNet Return Calculation

A portfolio has an initial capital contribution of Rs. 1,00,00,000. It generates a profit of 20% during the year. Other expenses are 0.50% charged on the gross value of the portfolio at the end of the period. What would be the 'Gross Value of the Portfolio less Other Expenses'?

ARs. 1,20,00,000

✓Rs. 1,19,40,000

CRs. 1,17,75,000

DRs. 1,00,00,000

💡 1. Capital Contribution = Rs. 1,00,00,000 2. Profit made during the year = 20% of Rs. 1,00,00,000 = Rs. 20,00,000 3. Gross Value of the Portfolio at the end = Capital Contribution + Profit = Rs. 1,00,00,000 + Rs. 20,00,000 = Rs. 1,20,00,000 4. Other Expenses = 0.50% of Gross Value = 0.50% of Rs. 1,20,00,000 = Rs. 60,000 5. Gross Value of the Portfolio less Other Expenses = Rs. 1,20,00,000 - Rs. 60,000 = Rs. 1,19,40,000. This follows the steps illustrated in the 'Gross versus net return' example.

Q93 MCQ · 1 mark EasyTime Weighted Rate of Return (TWRR) vs. Money Weighted Rate of Return (MWRR)

According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which rate of return must discretionary portfolio managers disclose for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR)

DHolding Period Return (HPR)

Q94 MCQ · 1 mark EasyHolding Period Return (HPR)

According to the provided text, what is a key assumption made when calculating the Holding Period Return (HPR)?

AAll income distributions are reinvested immediately.

BAll income distributions are made at the beginning of the year.

✓All income distributions are made at the end of the year.

DIncome distributions are irrelevant for HPR calculation.

💡 The text states: "This measure assumes that all income distributions are made at the end of the year."

Q95 MCQ · 1 mark HardTWRR Calculation

A portfolio generated the following annual wealth relatives over a five-year period: 0.95, 0.848, 1.081, 1.3075, and 1.1765. What is the Time Weighted Rate of Return (TWRR) for this period?

A5.75%

✓6.021%

C6.50%

D7.15%

💡 To calculate TWRR, first, multiply the wealth relatives to get the cumulative wealth relative: Cumulative wealth relative = 0.95 × 0.848 × 1.081 × 1.3075 × 1.1765 = 1.3396. Then, calculate the TWRR using the formula: TWRR = (Cumulative wealth relative ^ (1/Number of years)) - 1. TWRR = (1.3396 ^ (1/5)) - 1 = 1.06021 - 1 = 0.06021 or 6.021%.

Q96 MCQ · 1 mark EasyMWRR vs. TWRR

Which of the following statements accurately describes a key difference between Money Weighted Rate of Return (MWRR) and Time Weighted Rate of Return (TWRR)?

AMWRR is unaffected by the timing of cash flows, while TWRR is.

BTWRR is also referred to as Internal Rate of Return (IRR), while MWRR is not.

✓MWRR depends on the timing of cash flows, while TWRR aims to calculate performance without being influenced by it.

DTWRR is primarily used by wealth managers for client reporting, while MWRR is mandated by SEBI for portfolio managers.

Q97 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

Which measure of return is primarily used by fund managers for uniformity in reporting and comparing performance, especially when portfolios are customized and there is no daily NAV?

AMoney Weighted Rate of Return (MWRR)

BHolding Period Return (HPR)

✓Time Weighted Rate of Return (TWRR)

DArithmetic Mean Return (AMR)

💡 The text states: 'In PMS, since portfolios are customized and there is no NAV, SEBI has mandated TWRR for fund managers; TWRR is for the fund manager for uniformity in reporting and comparing.'

Q98 MCQ · 1 mark MediumCAGR and Other Returns

The calculation for Compounded Annual Growth Rate (CAGR) is explicitly stated to be the same as which other return calculation method(s) discussed in the text?

AHolding Period Return (HPR)

BArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR) and Geometric Mean Return (GMR)

DMoney Weighted Rate of Return (MWRR)

💡 The text states: 'The TWRR is the same as geometric return.' and 'The process of calculating the GMR is the same as TWRR.' Furthermore, for CAGR, it explicitly says: 'The calculation is same as the calculation of CAGR or geometric mean return.' Therefore, CAGR, TWRR, and GMR share the same underlying calculation methodology.

Q99 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

According to the text, which characteristic is true for the Money Weighted Rate of Return (MWRR)?

AIt is calculated to assess investment performance without the influence of cash flow timing.

BIt represents the compound rate of growth over a specified period, similar to a geometric return.

✓It is the annual rate of return at which cumulative contributions grow, and it depends on the timing of cash flow.

DIt requires the portfolio to be re-valued every time an external cash flow occurs.

💡 The text defines MWRR as: 'MWRR is the annual rate of return at which the cumulative contributions grow over the measurement period. MWRR depends on the timing of the cash flow.' Options A, B, and D describe aspects of Time Weighted Rate of Return (TWRR).

Q100 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

Which rate of return measure, according to the text, is primarily influenced by the timing of cash flows?

ATime Weighted Rate of Return (TWRR)

BHolding Period Return (HPR)

✓Money Weighted Rate of Return (MWRR)

DCompounded Annual Growth Rate (CAGR)

💡 The text explicitly states: 'MWRR depends on the timing of the cash flow.' It further clarifies that TWRR is calculated 'without being influenced by the timing of cash flow.'

Q101 MCQ · 1 mark MediumTime Weighted Rate of Return

According to SEBI (Portfolio Managers) Regulation, 2020, which performance measure are discretionary portfolio managers prescribed to disclose for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BHolding Period Return (HPR)

✓Time Weighted Rate of Return (TWRR)

DArithmetic Mean Return (AMR)

💡 The text explicitly states: 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q102 MCQ · 1 mark EasyPre-tax vs Post-tax Return

An investor achieves a 7% pre-tax rate of return on an investment and is subject to a capital gains tax of 10%. What is the post-tax rate of return?

A7.70%

✓6.30%

C7.00%

D6.00%

💡 The post-tax return is calculated using the formula: Post-tax return = Pre-Tax Return × (1 - tax rate). Post-tax return = 7% × (1 - 0.10) Post-tax return = 7% × 0.90 = 6.30%.

Q103 MCQ · 1 mark EasyTime Weighted Rate of Return (TWRR)

According to the text, which regulatory body prescribes discretionary portfolio managers to disclose performance using Time Weighted Rate of Return (TWRR) for the immediately preceding three years?

AReserve Bank of India (RBI)

BInsurance Regulatory and Development Authority of India (IRDAI)

✓Securities Exchange Board of India (SEBI)

DPension Fund Regulatory and Development Authority (PFRDA)

💡 The text explicitly mentions, 'Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years.'

Q104 MCQ · 1 mark EasyPre-tax vs. Post-tax Return

Why is the performance of investments often communicated as a pre-tax rate of return?

AIt is easier to calculate pre-tax returns.

BPre-tax returns are always higher, making investments look more attractive.

✓Investors belong to different tax brackets, making pre-tax return suitable for comparison.

DTax rates frequently change, making post-tax return calculations unreliable.

💡 The text states, 'Investors belong to different tax brackets. Hence the performance of the investments is communicated as pre-tax rate of return. Pre-Tax return enables comparisons across different investments and strategies, since different investors may be subject to different levels of taxation.'

Q105 MCQ · 1 mark EasyHolding Period Return (HPR)

What is a key assumption made when calculating the Holding Period Return (HPR) as described in the text?

AAll income distributions are re-invested immediately.

BThe investment period must be exactly one year.

✓All income distributions are made at the end of the year.

DTaxes are deducted before calculating the return.

💡 The text states that the Holding Period Return (HPR) measure "assumes that all income distributions are made at the end of the year."

Q106 MCQ · 1 mark EasyHolding Period Return

What does the variable 'I' represent in the Holding Period Return (HPR) formula: HPR = (I + (E - B)) / B?

AInitial Investment

✓Income

CInterest Rate

DInflation

💡 As per the text, HPR = holding-period return; I = Income; E = Ending Value; B = Beginning Value.

Q107 MCQ · 1 mark EasyHolding Period Return

According to the provided text, which components are used to calculate the Holding Period Return (HPR)?

✓Income, Ending Value, Beginning Value

BIncome, Initial Investment, Final Portfolio Value

CDividends, Capital Gains, Expense Ratio

DCash Flow, Market Value, Hurdle Rate

💡 Equation 2 in the text states: HPR = (I + (E -B)) / B, where HPR = holding-period return; I = Income; E = Ending Value; B = Beginning Value. Thus, Income, Ending Value, and Beginning Value are the components used.

Q108 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Under what specific condition will the geometric average return be equal to the arithmetic average return over longer holding periods?

✓When all individual yearly returns are exactly the same.

BWhen the portfolio value returns to its initial value.

CWhen only capital gains are considered, with no dividends.

DWhen the investment period is exactly one year.

Q109 MCQ · 1 mark EasyMWRR vs TWRR

Which rate of return measure depends on the timing of cash flows, such as contributions and withdrawals?

AHolding Period Return (HPR)

BTime Weighted Rate of Return (TWRR)

✓Money Weighted Rate of Return (MWRR)

DGeometric Mean Return (GMR)

💡 The text states, 'MWRR depends on the timing of the cash flow,' in contrast to TWRR which aims to calculate performance 'without being influenced by the timing of cash flow.'

Q110 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

What is the first step towards calculating the Time Weighted Rate of Return (TWRR) after identifying sub-periods?

ACalculate wealth relatives for each period.

BDiscount terminal value and cash flow contributions.

✓Calculate each period return using equation 1 i.e. (E-B)/B.

DDetermine the cumulative wealth relative.

💡 The text states: 'First step towards calculating the TWRR is to calculate each period return as shown below using equation 1 i.e. (E-B)/B.'

Q111 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Under what specific condition will the Geometric Mean Return (GMR) be equal to the Arithmetic Mean Return (AMR) for a multi-year holding period?

AWhen the portfolio value remains constant over the period.

✓When all individual yearly returns are exactly the same.

CWhen the number of years in the holding period is exactly one.

DWhen there are no external cash flows during the period.

Q112 MCQ · 1 mark MediumCompounded Annual Growth Rate (CAGR)

The Compounded Annual Growth Rate (CAGR) calculation assumes which of the following regarding income generated by an investment?

AIncome is distributed to the investor at the end of each year.

BIncome is re-invested in a different asset class.

✓Any dividend/income/rent declared is re-invested in the same investment.

DIncome is not considered in the growth rate calculation.

💡 The text states: 'It assumes that any dividend/income/rent declared by the investment is re-invested in the same investment on that day’s market price.'

Q113 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR) vs. Money Weighted Rate of Return (MWRR)

What is the primary factor that influences Money Weighted Rate of Return (MWRR) but not Time Weighted Rate of Return (TWRR)?

AThe overall market conditions during the investment period.

✓The timing of external cash flows (contributions or withdrawals).

CThe volatility of the portfolio's underlying assets.

DThe total duration of the investment period.

💡 The text states, 'MWRR depends on the timing of the cash flow. Alternatively, in order to calculate the underlying investment performance without being influenced by the timing of cash flow, TWRR can be calculated.'

Q114 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

In the calculation of Time Weighted Rate of Return (TWRR), after calculating each sub-period return, what is the next step to chain link these returns?

ADiscounting the terminal value and cash flow contributions.

✓Calculating wealth relatives by adding one to each period return.

CFinding the simple average of all sub-period returns.

DMultiplying the initial investment by each sub-period return.

💡 The text states: "The next step is to link these five sub period return together. For chain linking these sub period return, we have to calculate wealth relatives. Wealth relative is ending value of one unit of money. Hence what needs to be done to create wealth relative is to add one to each period return..."

Q115 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR) vs. Money Weighted Rate of Return (MWRR)

Which statement accurately describes the Money Weighted Rate of Return (MWRR) as per the provided text?

AMWRR is the compound rate of growth over the stated period, uninfluenced by cash flow timing.

✓MWRR is also referred to as the Internal Rate of Return (IRR) and depends on the timing of cash flows.

CMWRR is used by discretionary portfolio managers for disclosing performance for the immediately preceding three years.

DMWRR is the same as the geometric return.

💡 The text states: 'IRR is also referred as MWRR (Money Weighted rate of return). Financial calculators and spreadsheet have inbuilt function for solving the IRR. MWRR is the annual rate of return at which the cumulative contributions grow over the measurement period. MWRR depends on the timing of the cash flow.' Options A and D describe TWRR, and C describes the mandate for TWRR.

Q116 MCQ · 1 mark MediumCompounded Annual Growth Rate (CAGR)

What assumption does the Compounded Annual Growth Rate (CAGR) make regarding any dividend, income, or rent declared by an investment?

AIt is distributed to the investor immediately.

BIt is ignored in the calculation.

✓It is reinvested in the same investment on that day’s market price.

DIt is used to offset management fees.

💡 The text states: 'It assumes that any dividend/income/rent declared by the investment is re-invested in the same investment on that day’s market price.'

Q117 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

Which statement accurately describes the primary use of Money Weighted Rate of Return (MWRR) in practice?

AIt is used by fund managers for standardized performance comparison across different portfolios.

BIt measures the underlying investment performance without being influenced by the timing of cash flows.

✓It is typically used in wealth manager software systems and client reporting as it reflects what the client actually takes home.

DIt is mandated by SEBI for discretionary portfolio managers for reporting purposes.

💡 The text states: 'Wealth manager software systems / adviser excel reporting’s on client returns are on MWRR basis as money flows multiple times over a long holding period; At the end of the day the client is bothered about how much s/he is taking home;'.

Q118 MCQ · 1 mark HardGMR vs AMR

Which of the following statements is true regarding Geometric Mean Return (GMR) and Arithmetic Mean Return (AMR) over longer holding periods?

AGMR is always greater than AMR.

BGMR is always equal to AMR.

✓GMR is always less than AMR, unless all yearly returns are exactly the same.

DGMR can be greater than AMR only if there are negative returns.

💡 Over longer holding periods, the geometric average return is always less than the arithmetic return, except when all the individual yearly returns are exactly the same, in which case the geometric return equals the arithmetic return.

Q119 MCQ · 1 mark EasyHolding Period Return

Based on Equation 2 provided in the text, if Income (I) is Rs. 5,000, Ending Value (E) is Rs. 120,000, and Beginning Value (B) is Rs. 100,000, what is the Holding Period Return (HPR)?

A20%

✓25%

C15%

D30%

💡 The formula for HPR is (I + (E - B)) / B. Substituting the given values: HPR = (5000 + (120000 - 100000)) / 100000 HPR = (5000 + 20000) / 100000 HPR = 25000 / 100000 HPR = 0.25 or 25%.

Q120 MCQ · 1 mark MediumGross vs. Net Return

What is the key difference between gross return and net return?

AGross return includes only capital appreciation, while net return includes income distributions.

✓Gross return is calculated before deduction of fees, expenses, or commissions, while net return is calculated after.

CGross return is always higher than net return.

DGross return is for long-term investments, while net return is for short-term.

💡 The text defines: 'The gross return is the total return generated on investment before the deduction of any fees, expenses or commissions. ... Net return is calculated after adjusting gross return for fees, expenses or commissions.'

Q121 MCQ · 1 mark HardTime Weighted Rate of Return

Which of the following statements is TRUE regarding the calculation and nature of Time Weighted Rate of Return (TWRR) as described in the text?

ATWRR requires subtracting one from each period's return to calculate wealth relatives.

BTWRR is always expressed as an annual rate, irrespective of the sub-period duration.

✓The final step in calculating TWRR involves raising the cumulative wealth relative to the power of the reciprocal of the number of years in the evaluation period, then subtracting one.

DTWRR is primarily influenced by the timing of cash flows, making it suitable for client reporting.

💡 Option A is false; the text states 'what needs to be done to create wealth relative is to add one to each period return'. Option B is false; the text notes 'unless the sub periods constitute exactly one year, time-weighted rate of return will not be expressed as an annual rate'. Option D is false; MWRR is influenced by timing, and TWRR is for fund managers for uniformity, not primarily for client reporting on money flows. Option C is true, as the formula shown is 'TWRR = (Cumulative wealth relative ^ (1/n)) - 1'.

Q122 MCQ · 1 mark HardTime Weighted Rate of Return (TWRR) Calculation Process

Which of the following describes the correct sequence of steps to calculate the Time Weighted Rate of Return (TWRR) over multiple periods?

ACalculate cumulative wealth relative, then calculate sub-period returns, then link sub-period returns.

BCalculate sub-period returns, then link them to create wealth relatives, then calculate cumulative wealth relative.

✓Calculate sub-period returns, then create wealth relatives by adding one to each return, then multiply wealth relatives to get cumulative wealth relative, then apply (cumulative wealth relative^(1/n)) - 1.

DCalculate Money Weighted Rate of Return (MWRR), then convert it to TWRR by removing cash flow influences.

💡 The text outlines the process: 'First step towards calculating the TWRR is to calculate each period return... The next step is to link these five sub period return together. For chain linking these sub period return, we have to calculate wealth relatives. Wealth relative is ending value of one unit of money. Hence what needs to be done to create wealth relative is to add one to each period return... The next step is to create a cumulative wealth relative for the entire evaluation period by multiplying each period wealth relative... TWRR = (1.3396 ^ (1/5)) - 1'.

Q123 MCQ · 1 mark EasyGross vs. Net Return

What does 'Net Return' primarily represent for an investor?

AThe total return generated on investment before the deduction of any fees, expenses, or commissions.

✓The return earned after adjusting the gross return for all applicable fees, expenses, or commissions.

CThe return used for evaluating performance at a broader market level.

DThe theoretical maximum return achievable without any market fluctuations.

💡 The text defines Net Return as: 'Net return is calculated after adjusting gross return for fees, expenses or commissions. Net return is the return investor actually makes...'

Q124 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR) Calculation Process

According to the text, what is the *first step* towards calculating the Time Weighted Rate of Return (TWRR) when there are multiple sub-periods?

ACalculate the cumulative wealth relative for the entire evaluation period.

BCalculate wealth relatives by adding one to each period return.

✓Calculate each period return using the formula (E-B)/B.

DAnnualize the return by raising the cumulative wealth relative to the power of (1/n).

💡 The text states: 'In this example, there are five sub periods. First step towards calculating the TWRR is to calculate each period return as shown below using equation 1 i.e. (E-B)/B.'

Q125 MCQ · 1 mark EasyGross vs Net Return

According to the text, why can focusing solely on gross return be misleading for an investor?

ABecause gross return does not consider the initial capital contribution.

BBecause gross return is the return generated after all fees and expenses.

✓Because net return is the return the investor actually makes after adjusting for fees, expenses, or commissions.

DBecause gross return is only applicable to short-term investments.

💡 The text explains: 'Net return is the return investor actually makes, hence focusing on gross return can be misleading though it can be used to evaluate the performance of investments at a broader level.' Gross return is defined as 'before the deduction of any fees, expenses or commissions.'

Q126 MCQ · 1 mark EasyHolding Period Return

What is a key limitation of the Holding Period Return (HPR) measure as stated in the text?

AIt does not account for capital gains.

✓It assumes all income distributions are made at the end of the year.

CIt cannot be used for periods longer than one year.

DIt requires complex financial calculators for its computation.

💡 The text explicitly states regarding HPR: 'This measure assumes that all income distributions are made at the end of the year.'

Q127 MCQ · 1 mark HardTime Weighted Rate of Return

In the process of calculating Time Weighted Rate of Return (TWRR), what is the primary purpose of calculating 'wealth relatives'?

ATo determine the average annual return for each sub-period.

BTo account for the impact of external cash flows on the portfolio value.

✓To express the ending value of one unit of money for each period, which are then linked together.

DTo convert the sub-period returns into an annual rate.

💡 The text explains: 'Wealth relative is ending value of one unit of money. Hence what needs to be done to create wealth relative is to add one to each period return...' and 'The next step is to create a cumulative wealth relative for the entire evaluation period by multiplying each period wealth relative'.

Q128 MCQ · 1 mark MediumTime Weighted Rate of Return (TWRR)

In the calculation of Time Weighted Rate of Return (TWRR), what is the purpose of calculating "wealth relatives" for each sub-period return?

ATo determine the impact of external cash flows on the portfolio.

BTo annualize the return for periods shorter than one year.

✓To represent the ending value of one unit of money for each period, enabling chain linking of returns.

DTo adjust the returns for any fees or expenses incurred during the period.

Q129 MCQ · 1 mark MediumGeometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Which statement accurately describes a characteristic of the Geometric Mean Return (GMR) compared to the Arithmetic Mean Return (AMR)?

AAMR is generally more important for analyzing long-run returns on assets.

BGMR depends on the path by which the portfolio value was realized.

✓GMR is always less than the AMR, except when all individual yearly returns are exactly the same.

DAMR is the only way to compare long-term accumulations.

💡 The text states: 'But over longer holding periods the geometric average return is always less than the arithmetic return except when all the individual yearly returns are exactly the same, in which case the geometric return equals the arithmetic return.' Option A is incorrect because the text says GMR is 'far more important' for long-run returns. Option B is incorrect because GMR 'depends only on the initial and final values of the portfolio, not on the path'. Option D is incorrect because 'Geometric return is the only way to compare long-term accumulations'.

Q130 MCQ · 1 mark EasyHolding Period Return

What is a stated limitation of the Holding Period Return (HPR) measure, as mentioned in the provided text?

AIt does not account for capital gains or losses.

✓It assumes all income distributions are made at the end of the year.

CIt is not a widely accepted indicator of performance.

DIt cannot be used for periods longer than one year.

Q131 MCQ · 1 mark EasyTime Weighted Rate of Return (TWRR) vs. Money Weighted Rate of Return (MWRR)

According to the Securities Exchange Board of India (Portfolio Managers) Regulation, 2020, which method is prescribed for discretionary portfolio managers to disclose performance for the immediately preceding three years?

AMoney Weighted Rate of Return (MWRR)

BArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR)

DCompounded Annual Growth Rate (CAGR)

Q132 MCQ · 1 mark EasyHolding Period Return (HPR)

What is a stated limitation of the Holding Period Return (HPR) measure as described in the text?

AIt does not account for capital appreciation.

✓It assumes all income distributions are made at the end of the year.

CIt cannot be used as a starting point for performance measurement.

DIt is not a widely accepted indicator of performance.

💡 The text explicitly states: 'This measure assumes that all income distributions are made at the end of the year. In spite of this limitation, Holding Period Return measure is widely used and generally accepted indicator of performance. This is considered as the starting point of performance measurement exercise.'

Q133 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

Which of the following statements accurately describes the Money Weighted Rate of Return (MWRR)?

AIt is primarily used by fund managers for uniformity in reporting.

BIt is also referred to as the Geometric Mean Return.

✓It depends on the timing of the cash flow.

DIt is calculated by linking sub-period returns using wealth relatives.

💡 The text states: "MWRR depends on the timing of the cash flow." Options A and D describe TWRR. Option B is incorrect as TWRR is the same as geometric return.

Q134 MCQ · 1 mark MediumNet Return Calculation

An investor made a capital contribution of Rs. 1,00,00,000. After one year, the gross value of the portfolio grew to Rs. 1,20,00,000. The total charges (fees and expenses) amounted to Rs. 6,12,400. What is the Net Return for the investor?

A20.00%

✓13.88%

C15.00%

D17.50%

💡 Net Value of the Portfolio = Gross Value of the Portfolio - Total Charges Net Value of the Portfolio = Rs. 1,20,00,000 - Rs. 6,12,400 = Rs. 1,13,87,600 Net Return = (Net Value of the Portfolio - Capital Contribution) / Capital Contribution Net Return = (Rs. 1,13,87,600 - Rs. 1,00,00,000) / Rs. 1,00,00,000 Net Return = Rs. 13,87,600 / Rs. 1,00,00,000 = 0.13876 or 13.88% (rounded)

Q135 MCQ · 1 mark EasyHolding Period Return

A portfolio had a beginning value of Rs. 100,000, an ending value of Rs. 120,000, and generated an income of Rs. 5,000 during the period. What is the Holding Period Return (HPR)?

A20%

✓25%

C30%

D15%

💡 HPR = (Income + (Ending Value - Beginning Value)) / Beginning Value HPR = (5000 + (120000 - 100000)) / 100000 HPR = (5000 + 20000) / 100000 HPR = 25000 / 100000 = 0.25 or 25%

Q136 MCQ · 1 mark MediumCompounded Annual Growth Rate (CAGR)

An investor invested Rs. 100,000, and it grew to Rs. 133,960 in five years. What is the Compounded Annual Growth Rate (CAGR) for this investment?

A5.00%

✓6.02%

C8.10%

D17.65%

💡 The formula for CAGR is (A / P)^(1 / t) – 1. * A = Closing wealth = Rs. 1,33,960 * P = Opening wealth = Rs. 1,00,000 * t = Time period in years = 5 * CAGR = (1,33,960 / 1,00,000)^(1/5) - 1 * CAGR = (1.3396)^(0.2) - 1 * CAGR = 1.0602 - 1 = 0.0602 = 6.02%

Q137 MCQ · 1 mark EasyPost-tax Return

An investor achieves a 5% pre-tax rate of return for an investment and is subject to a capital gains tax of 15%. What is the post-tax rate of return?

A5.88%

B5.00%

✓4.25%

D0.75%

💡 As per the text, Post-tax return = Pre-Tax Return x (1-tax rate). Post-tax return = 5% x (1 - 0.15) Post-tax return = 5% x 0.85 Post-tax return = 4.25%

Q138 MCQ · 1 mark MediumAMR vs GMR

For analyzing the long-run return on assets and comparing long-term accumulations, which of the following return measures is considered more appropriate?

AArithmetic Mean Return

BHolding Period Return

CMoney Weighted Rate of Return

✓Geometric Mean Return

💡 The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets. Geometric return is the only way to compare long-term accumulations.

Q139 MCQ · 1 mark EasyHolding Period Return

According to the provided text, what assumption is made regarding income distributions when calculating the Holding Period Return (HPR)?

AAll income distributions are made at the beginning of the year.

✓All income distributions are made at the end of the year.

CIncome distributions are reinvested immediately.

DIncome distributions are ignored in the calculation.

💡 The text states: 'This measure assumes that all income distributions are made at the end of the year.'

Q140 MCQ · 1 mark EasyHolding Period Return (HPR)

According to the provided text, what does 'B' represent in the Holding Period Return (HPR) formula?

AIncome

BEnding Value

✓Beginning Value

DHolding-period return

💡 The text states the HPR formula components as: 'HPR = holding-period return; I = Income; E = Ending Value; B = Beginning Value.' Therefore, B represents the Beginning Value.

Q141 MCQ · 1 mark MediumPre-tax versus Post-tax Return

An individual achieves a 7.5% pre-tax rate of return for an investment. If they are subject to a capital gains tax of 20%, what is their post-tax rate of return?

✓6.00%

B7.50%

C9.38%

D5.50%

💡 The formula for post-tax return is: Post-tax return = Pre-Tax Return x (1 - tax rate). Given: Pre-tax return = 7.5% (0.075) and tax rate = 20% (0.20). Post-tax return = 0.075 x (1 - 0.20) Post-tax return = 0.075 x 0.80 Post-tax return = 0.06 or 6.00%.

Q142 MCQ · 1 mark MediumGross vs. Net Return

Why is focusing on net return more relevant for an investor compared to gross return, as per the text?

✓Gross return can be misleading as it does not account for the actual fees and expenses incurred.

BNet return is primarily used for evaluating the performance of investments at a broader level.

CGross return is the return the investor actually makes after all deductions.

DNet return is always higher than gross return due to tax benefits.

💡 The text states: 'Net return is the return investor actually makes, hence focusing on gross return can be misleading though it can be used to evaluate the performance of investments at a broader level.'

Q143 MCQ · 1 mark MediumPre-tax vs. Post-tax Return

An individual achieves a 7% pre-tax rate of return for an investment and is subject to a capital gains tax of 20%. What is the post-tax rate of return?

✓5.6%

B1.4%

C7.0%

D8.4%

💡 Post-tax return = Pre-Tax Return x (1 - tax rate). In this case, Post-tax return = 7% x (1 - 20%) = 0.07 x (1 - 0.20) = 0.07 x 0.80 = 0.056 or 5.6%.

Q144 MCQ · 1 mark MediumMoney Weighted Rate of Return (MWRR)

Which statement accurately describes the Money Weighted Rate of Return (MWRR) as per the provided text?

✓MWRR depends on the timing of the cash flow.

BMWRR is the compound rate of growth over a stated period, independent of cash flows.

CMWRR is primarily used by fund managers for uniform reporting and comparison.

DMWRR requires valuing the portfolio every time there is an external cash flow.

💡 The text states: 'MWRR depends on the timing of the cash flow.' Options B, C, and D describe characteristics or uses of the Time Weighted Rate of Return (TWRR).

Q145 MCQ · 1 mark EasyTWRR Calculation

In the calculation of Time Weighted Rate of Return (TWRR), what is the purpose of calculating a 'wealth relative' for each sub-period return?

ATo adjust the return for inflation.

BTo annualize the sub-period return directly.

✓To represent the ending value of one unit of money.

DTo determine the average daily return.

💡 The text explains, 'Wealth relative is ending value of one unit of money. Hence what needs to be done to create wealth relative is to add one to each period return.'

Q146 MCQ · 1 mark EasyGross vs. Net Return

Which type of return represents the actual return an investor makes after all fees, expenses, or commissions have been deducted?

AGross Return

BPre-tax Return

✓Net Return

DHolding Period Return

💡 The text states: 'Net return is calculated after adjusting gross return for fees, expenses or commissions. Net return is the return investor actually makes'.

Q147 MCQ · 1 mark EasyArithmetic Mean Return (AMR)

According to the text, for what purpose is the Arithmetic Mean Return (AMR) considered the best estimate?

AAnalyzing the long-run return on assets.

BComparing long-term accumulations.

✓Estimating the holding-period return in a given future year.

DCalculating the rate at which an investment accumulates over multiple years.

💡 The text states: 'The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average. Statistically, it is our best guess for the holding-period return in a given year.' Options A, B, and D are more aligned with the Geometric Mean Return (GMR).

Q148 MCQ · 1 mark MediumPre-tax vs Post-tax Return

An individual achieves a 5% pre-tax rate of return for stock XYZ and is subject to a capital gains tax of 15%. What is the post-tax rate of return for this investment?

A5.88%

✓4.25%

C3.50%

D5.15%

💡 The formula for post-tax return is: Post-tax return = Pre-Tax Return x (1-tax rate). Given: Pre-tax return = 5% = 0.05, Tax rate = 15% = 0.15. Post-tax return = 0.05 x (1 - 0.15) = 0.05 x 0.85 = 0.0425 or 4.25%.

Q149 MCQ · 1 mark HardTWRR vs MWRR Purpose

The text explains that 'At the end of the day the client is bothered about how much s/he is taking home'. Which rate of return is generally reported by wealth manager software systems and adviser excel reporting to reflect this client concern, and why?

ATWRR, because it focuses on underlying investment performance without cash flow influence.

✓MWRR, because it depends on the timing of cash flow and reflects the actual growth of cumulative contributions.

CHPR, as it is a widely accepted indicator of performance.

DAMR, as it is the best estimate for future returns.

Q150 MCQ · 1 mark MediumGMR vs AMR

According to the text, for which purpose is the Arithmetic Mean Return (AMR) considered the best estimate?

AAnalyzing the long-run return on assets.

✓Estimating the expected return over a multiyear horizon conditioned on past experience.

CComparing long-term accumulations.

DEstimating the probability distribution of terminal wealth.

💡 The text states: 'The best estimate of a future year's return based on a random distribution of the prior years' returns is the arithmetic average. Statistically, it is our best guess for the holding-period return in a given year. If we wish to estimate the expected return over a multiyear horizon conditioned on past experience, we may use the arithmetic average.'

Case-Based Questions (5 sets)

Case 1 Case-Based · 2 marks each Portfolio Performance Measurement

Mr. Rajesh Sharma, aged 45, is evaluating the performance of his investment portfolio for the year 2022. He started the year 2022 with a portfolio value of Rs. 8,00,000. During the year, he received an income distribution of Rs. 10,000 from the portfolio, which was immediately reinvested. By the end of 2022, the portfolio's value had grown to Rs. 9,00,000. His investment adviser charges the following fees and expenses annually: 1. Other expenses (brokerages, DP charges): 0.50% of the gross value of the portfolio at the end of the year. 2. Fixed Management fee: 1.00% charged on the average of the beginning and end-of-year portfolio value. 3. Performance fee: 15% of profits over a hurdle rate of 10% (without catch-up). Mr. Sharma is in the 15% tax bracket for capital gains.

Easy Sub-question 1

What was the Holding Period Return (HPR) for Mr. Rajesh Sharma's portfolio for the year 2022, before any fees or taxes?

A12.50%

✓13.75%

C1.25%

D10.00%

💡 Holding Period Return (HPR) is calculated as: HPR = (Income + (Ending Value - Beginning Value)) / Beginning Value Beginning Value (B) = Rs. 8,00,000 Ending Value (E) = Rs. 9,00,000 Income (I) = Rs. 10,000 HPR = (10,000 + (9,00,000 - 8,00,000)) / 8,00,000 HPR = (10,000 + 1,00,000) / 8,00,000 HPR = 1,10,000 / 8,00,000 HPR = 0.1375 or 13.75%

Medium Sub-question 2

Calculate the portfolio value after deducting 'Other Expenses' for Mr. Sharma's portfolio for the year 2022.

ARs. 8,95,000

✓Rs. 8,95,500

CRs. 8,99,500

DRs. 8,91,000

💡 Gross Value of the Portfolio at the end of the investment period = Rs. 9,00,000 Other Expenses = 0.50% of Gross Value Other Expenses = 0.0050 * 9,00,000 = Rs. 4,500 Portfolio Value after Other Expenses = 9,00,000 - 4,500 = Rs. 8,95,500

Hard Sub-question 3

What is the Net Return for Mr. Rajesh Sharma's portfolio for the year 2022, after all specified fees and expenses, but before considering Mr. Sharma's personal tax implications?

A10.00%

✓10.74%

C11.25%

D9.50%

💡 1. Capital Contribution (Beginning Value) = Rs. 8,00,000 2. Gross Value of the Portfolio at the end of the investment period = Rs. 9,00,000 3. Profit made during the year = Ending Value - Beginning Value = 9,00,000 - 8,00,000 = Rs. 1,00,000 **Calculation of Net Value:** Gross Value of Portfolio at end = Rs. 9,00,000 Less: Other Expenses (0.50% of Gross Value) = 0.0050 * 9,00,000 = Rs. 4,500 Portfolio Value after Other Expenses = 9,00,000 - 4,500 = Rs. 8,95,500 Average Portfolio Value for Fixed Management Fee = (Beginning Value + Ending Value) / 2 = (8,00,000 + 9,00,000) / 2 = Rs. 8,50,000 Less: Fixed Management Fees (1.00% of Average Value) = 0.0100 * 8,50,000 = Rs. 8,500 Portfolio Value after Fixed Management Fees = 8,95,500 - 8,500 = Rs. 8,87,000 Required Portfolio Value at Hurdle Rate = Capital Contribution * (1 + Hurdle Rate) = 8,00,000 * (1 + 0.10) = Rs. 8,80,000 Profit over Hurdle Level = Portfolio Value after Fixed Management Fees - Required Portfolio Value at Hurdle Rate = 8,87,000 - 8,80,000 = Rs. 7,000 Less: Performance Fee (15% of Profit over Hurdle) = 0.15 * 7,000 = Rs. 1,050 Net Value of the Portfolio (after all fees) = 8,87,000 - 1,050 = Rs. 8,85,950 **Calculation of Net Return:** Net Return = (Net Value of the Portfolio - Capital Contribution) / Capital Contribution Net Return = (8,85,950 - 8,00,000) / 8,00,000 Net Return = 85,950 / 8,00,000 = 0.1074375 or 10.74% (rounded to two decimal places)

Easy Sub-question 4

If Mr. Sharma's portfolio was managed by a discretionary portfolio manager, which return measure would SEBI mandate for disclosing performance?

AMoney Weighted Rate of Return (MWRR)

BArithmetic Mean Return (AMR)

✓Time Weighted Rate of Return (TWRR)

DCompounded Annual Growth Rate (CAGR)

💡 As per the chapter text, "Securities Exchange Board of India (Portfolio Managers) Regulation, 2020 prescribes discretionary portfolio managers to disclose performance using ’Time Weighted Rate of Return’ for the immediately preceding three years."

Medium Sub-question 5

Based on the calculated Net Return (before tax) from the previous question, what is Mr. Sharma's Post-tax Return for the year 2022?

✓9.13%

B10.74%

C12.64%

D8.59%

💡 Pre-tax return (Net Return) = 10.74375% (from previous calculation) Tax rate = 15% Post-tax return = Pre-Tax Return x (1 - tax rate) Post-tax return = 0.1074375 * (1 - 0.15) Post-tax return = 0.1074375 * 0.85 Post-tax return = 0.091321875 or 9.13% (rounded to two decimal places)

Case 2 Case-Based · 2 marks each Portfolio Performance Measurement

Mr. Anil Sharma, a 45-year-old software engineer, approached an investment adviser to manage his portfolio. He made an initial investment of Rs. 2,00,000 at the beginning of 2018. At the end of 2018, his portfolio's capital value stood at Rs. 2,30,000, and he received dividends of Rs. 5,000. In early 2019, he added another Rs. 50,000 to his portfolio. The annual holding period returns (HPRs) for his portfolio over the past three years were: * 2018: 17.50% * 2019: -10.00% * 2020: 25.00% At the end of 2020, the portfolio's gross value (before any fees for 2020) was Rs. 3,15,000. The investment adviser charges the following fees annually: * Other Expenses (brokerage, DP charges): 0.75% of the gross value of the portfolio at year-end. * Fixed Management Fee: 1.00% of the average of the total capital contributed by the investor (initial + additions) and the gross portfolio value at year-end. * Performance Fee: 15% of profits over a hurdle rate of 8% per annum on the initial capital contribution (Rs. 2,00,000), without a catch-up clause. * Exit Load: 1% on the portfolio value after all other fees, if redeemed. Mr. Sharma falls into the 20% tax bracket for capital gains and investment income.

Medium Sub-question 1

Mr. Sharma's initial investment was Rs. 2,00,000 at the start of 2018, an additional Rs. 50,000 at the start of 2019, and the portfolio value at the end of 2020 was Rs. 3,15,000. Considering these cash flows, which of the following statements about the Money Weighted Rate of Return (MWRR) for his portfolio over the entire period (2018-2020) is correct?

✓MWRR is equivalent to the Internal Rate of Return (IRR) and accurately reflects the investor's actual return considering the timing and size of his cash flows.

BMWRR would likely be higher than the Compounded Annual Growth Rate (CAGR) for this period because a large additional investment was made just before a year with a significant negative return.

CMWRR is the preferred performance measure for discretionary portfolio managers as mandated by SEBI for uniform reporting.

DMWRR does not consider the actual amounts invested by the investor, only the percentage returns generated by the fund manager.

💡 Option A is correct. The chapter text explicitly states that Internal Rate of Return (IRR) is also referred to as Money Weighted Rate of Return (MWRR). It further clarifies that MWRR depends on the timing and magnitude of cash flows, thereby reflecting the investor's actual return. Option B is incorrect. MWRR would likely be *lower* than the CAGR (Time Weighted Rate of Return) in this scenario because Mr. Sharma made a significant additional investment (Rs. 50,000) at the beginning of 2019, which was followed by a negative HPR of -10.00% for that year. Exposing a larger sum to a negative return tends to reduce the MWRR relative to the TWRR/CAGR. Option C is incorrect. SEBI (Portfolio Managers) Regulation, 2020, prescribes discretionary portfolio managers to disclose performance using 'Time Weighted Rate of Return' (TWRR), not MWRR, for uniformity in reporting. Option D is incorrect. MWRR directly incorporates the timing and size of all cash flows (investments and withdrawals), making it highly sensitive to the amounts invested by the investor.

Hard Sub-question 2

If Mr. Sharma decides to redeem his entire portfolio at the end of 2020, and assuming the entire profit (Gross Value at end of 2020 minus total capital contributed) is subject to a 20% capital gains tax. What would be his approximate post-tax return on his *total capital contributed* (Rs. 2,50,000) over the entire investment period (2018-2020)?

✓13.69%

B15.25%

C17.11%

D20.00%

💡 To calculate the post-tax return, we first determine the pre-tax return for the entire period based on the net value after all fees, then apply the tax rate. **Step 1: Determine Total Capital Contributed and Net Value.** * Total Capital Contributed = Rs. 2,00,000 (2018) + Rs. 50,000 (2019) = Rs. 2,50,000 * Net Value of the Portfolio at End of 2020 (after all fees, including exit load, from Q4 calculation) = Rs. 2,92,783.21 **Step 2: Calculate Pre-Tax Return for the entire period.** Pre-Tax Return = (Net Value of Portfolio - Total Capital Contributed) / Total Capital Contributed Pre-Tax Return = (2,92,783.21 - 2,50,000) / 2,50,000 Pre-Tax Return = 42,783.21 / 2,50,000 Pre-Tax Return = 0.17113284 or 17.11% **Step 3: Calculate Post-Tax Return.** Post-Tax Return = Pre-Tax Return x (1 - Tax Rate) Tax Rate = 20% (0.20) Post-Tax Return = 0.17113284 x (1 - 0.20) Post-Tax Return = 0.17113284 x 0.80 Post-Tax Return = 0.136906272 or 13.69% (rounded to two decimal places)

Easy Sub-question 3

Calculate the Holding Period Return (HPR) for Mr. Sharma's portfolio for the year 2018.

A15.00%

✓17.50%

C20.00%

D22.50%

💡 The Holding Period Return (HPR) is calculated using the formula: HPR = (Income + (Ending Value - Beginning Value)) / Beginning Value. For 2018: Beginning Value (B) = Rs. 2,00,000 Ending Value (E) = Rs. 2,30,000 Income (I) = Rs. 5,000 (dividends) HPR = (5,000 + (2,30,000 - 2,00,000)) / 2,00,000 HPR = (5,000 + 30,000) / 2,00,000 HPR = 35,000 / 2,00,000 HPR = 0.175 or 17.50%

Hard Sub-question 4

Assuming Mr. Sharma's portfolio value at the end of 2020 was Rs. 3,15,000 (gross value before any fees for 2020), calculate the Net Return for his portfolio for the year 2020, considering all applicable fees for that year.

✓16.18%

B17.50%

C18.25%

D20.00%

💡 To calculate the Net Return for 2020, we first need to determine the portfolio's value at the beginning of 2020 and then deduct all applicable fees from the gross ending value. **Step 1: Calculate Portfolio Value at the beginning of 2020.** * Initial Investment (Start 2018): Rs. 2,00,000 * Value End 2018 (after 17.50% HPR): 2,00,000 * (1 + 0.175) = Rs. 2,35,000. (Note: The HPR calculation in Q1 shows ending capital value of 2,30,000 + 5,000 income, so the capital value at end of 2018 is Rs. 2,30,000) * Value Start 2019 (after Rs. 50,000 addition): 2,30,000 + 50,000 = Rs. 2,80,000 * Value End 2019 (after -10.00% HPR): 2,80,000 * (1 - 0.10) = Rs. 2,52,000 * **Beginning Value for 2020 = Rs. 2,52,000** * **Gross Value at End of 2020 (before 2020 fees) = Rs. 3,15,000** **Step 2: Calculate Fees for 2020.** 1. **Other Expenses:** 0.75% of Gross Value at end of 2020 = 0.0075 * 3,15,000 = Rs. 2,362.50 *Portfolio Value after Other Expenses = 3,15,000 - 2,362.50 = Rs. 3,12,637.50* 2. **Fixed Management Fee:** 1.00% of the average of total capital contributed and gross portfolio value at year-end. * Total Capital Contributed = 2,00,000 (initial) + 50,000 (addition) = Rs. 2,50,000 * Average Value = (2,50,000 + 3,15,000) / 2 = Rs. 2,82,500 * Fixed Management Fee = 0.01 * 2,82,500 = Rs. 2,825.00 *Portfolio Value after Fixed Management Fees = 3,12,637.50 - 2,825.00 = Rs. 3,09,812.50* 3. **Performance Fee:** 15% of profits over hurdle rate. * Hurdle Rate: 8% per annum on the initial capital contribution (Rs. 2,00,000). *Required Portfolio Value @ Hurdle Rate = 2,00,000 * (1 + 0.08) = Rs. 2,16,000* * Profit over Hurdle = Portfolio Value after Fixed Management Fees - Required Portfolio Value @ Hurdle Rate = 3,09,812.50 - 2,16,000 = Rs. 93,812.50 * Performance Fee = 0.15 * 93,812.50 = Rs. 14,071.88 *Portfolio Value after Performance Management Fees = 3,09,812.50 - 14,071.88 = Rs. 2,95,740.62* 4. **Exit Load:** 1% on the portfolio value after all other fees. * Exit Load = 0.01 * 2,95,740.62 = Rs. 2,957.41 *Net Value of the Portfolio at End of 2020 = 2,95,740.62 - 2,957.41 = Rs. 2,92,783.21* **Step 3: Calculate Net Return for 2020.** Net Return = (Net Value of Portfolio at End of 2020 - Beginning Value for 2020) / Beginning Value for 2020 Net Return = (2,92,783.21 - 2,52,000) / 2,52,000 Net Return = 40,783.21 / 2,52,000 Net Return = 0.16183 or 16.18% (rounded to two decimal places)

Medium Sub-question 5

What is the Compounded Annual Growth Rate (CAGR) of Mr. Sharma's portfolio based on the annual HPRs from 2018 to 2020, assuming no intermediate cash flows within these years?

A8.33%

B9.17%

✓9.76%

D10.83%

💡 The Compounded Annual Growth Rate (CAGR) is equivalent to the Geometric Mean Return (GMR) of the annual holding period returns (HPRs) when there are no intermediate cash flows within the sub-periods. Annual HPRs: 2018: 17.50% (0.175) 2019: -10.00% (-0.10) 2020: 25.00% (0.25) Step 1: Calculate wealth relatives (1 + HPR) for each year. Wealth Relative 2018 = 1 + 0.175 = 1.175 Wealth Relative 2019 = 1 - 0.10 = 0.900 Wealth Relative 2020 = 1 + 0.25 = 1.250 Step 2: Calculate the cumulative wealth relative by multiplying the individual wealth relatives. Cumulative Wealth Relative = 1.175 * 0.900 * 1.250 = 1.321875 Step 3: Calculate CAGR using the formula: CAGR = (Cumulative Wealth Relative ^ (1/Number of Years)) - 1 Number of Years = 3 CAGR = (1.321875 ^ (1/3)) - 1 CAGR = 1.0975608 - 1 CAGR = 0.0975608 or 9.76% (rounded to two decimal places)

Case 3 Case-Based · 2 marks each Portfolio Performance Measurement

Mr. and Mrs. Sharma, a couple aged 45 and 42, established an investment portfolio with an initial capital of Rs. 1,00,000 at the beginning of 2020. At the end of 2020, the portfolio's value stood at Rs. 1,10,000, and they received a dividend income of Rs. 2,000. At the beginning of 2021, they made an additional contribution of Rs. 20,000. For the year 2021, the portfolio generated a return of 15%. At the beginning of 2022, they added another Rs. 30,000 to their portfolio. By the end of 2022, the portfolio's value reached Rs. 1,85,000. They are now evaluating a new Portfolio Management Service (PMS) for a fresh investment of Rs. 1,50,000 for one year. The PMS has provided the following fee structure: * Expected Profit on initial capital: 22% * Other Expenses (e.g., brokerage, DP charges): 0.80% of the gross value of the portfolio at year-end. * Fixed Management Fee: 1.00% of the average of initial capital contribution and gross value of the portfolio at year-end. * Hurdle Rate: 10% of the initial capital contribution. * Performance Fee: 18% of profits over the hurdle rate (without catch-up). * Exit Load: 1.5% on the portfolio value after all other charges. Mr. Sharma is in the 20% tax bracket for capital gains and investment income.

Easy Sub-question 1

For Mr. and Mrs. Sharma's historical portfolio, which measure of return is most appropriate for analyzing the long-run accumulation of their wealth over the multiple years (2020-2022)?

AArithmetic Mean Return (AMR)

BHolding Period Return (HPR)

✓Geometric Mean Return (GMR)

DMoney Weighted Rate of Return (MWRR)

💡 The chapter text states, 'The average annual geometric return is far more important than the average arithmetic return if one is analyzing the long-run return on assets.' It also mentions, 'Geometric return is the only way to compare long-term accumulations. It explains what has really happened to the investments.' Therefore, GMR is most appropriate for analyzing long-run wealth accumulation.

Easy Sub-question 2

Based on their initial investment in 2020, what was the Holding Period Return (HPR) for Mr. and Mrs. Sharma's portfolio for the year 2020?

A10%

✓12%

C11%

D12.5%

💡 HPR = (Income + (Ending Value - Beginning Value)) / Beginning Value. For 2020: Beginning Value (B) = Rs. 1,00,000 Ending Value (E) = Rs. 1,10,000 Income (I) = Rs. 2,000 HPR = (Rs. 2,000 + (Rs. 1,10,000 - Rs. 1,00,000)) / Rs. 1,00,000 HPR = (Rs. 2,000 + Rs. 10,000) / Rs. 1,00,000 HPR = Rs. 12,000 / Rs. 1,00,000 = 0.12 or 12%.

Hard Sub-question 3

Calculate the Net Return for Mr. and Mrs. Sharma's new PMS investment, assuming the expected profit is realized.

A22.00%

B18.55%

✓16.36%

D15.00%

💡 1. **Initial Capital (P):** Rs. 1,50,000 2. **Expected Profit:** 22% of Rs. 1,50,000 = Rs. 33,000 3. **Gross Value of Portfolio at year-end:** Rs. 1,50,000 + Rs. 33,000 = Rs. 1,83,000 **Fee Calculations:** * **Other Expenses:** 0.80% of Gross Value = 0.0080 * Rs. 1,83,000 = Rs. 1,464 * Portfolio Value after Other Expenses: Rs. 1,83,000 - Rs. 1,464 = Rs. 1,81,536 * **Fixed Management Fee:** 1.00% of (Average of Initial Capital and Gross Value at year-end) * Average Value = (Rs. 1,50,000 + Rs. 1,83,000) / 2 = Rs. 1,66,500 * Fixed Management Fee = 0.01 * Rs. 1,66,500 = Rs. 1,665 * Portfolio Value after Fixed Management Fee: Rs. 1,81,536 - Rs. 1,665 = Rs. 1,79,871 * **Hurdle Rate Value:** 10% of Initial Capital = 0.10 * Rs. 1,50,000 = Rs. 15,000 * Required Portfolio Value @ Hurdle Rate = Initial Capital + Hurdle Amount = Rs. 1,50,000 + Rs. 15,000 = Rs. 1,65,000 * **Performance Fee:** 18% of (Profits over Hurdle Level) * Profits over Hurdle Level = (Portfolio Value after Fixed Management Fee) - (Required Portfolio Value @ Hurdle Rate) = Rs. 1,79,871 - Rs. 1,65,000 = Rs. 14,871 * Performance Fee = 0.18 * Rs. 14,871 = Rs. 2,676.78 ≈ Rs. 2,677 * Portfolio Value after Performance Fee: Rs. 1,79,871 - Rs. 2,677 = Rs. 1,77,194 * **Exit Load:** 1.5% on Portfolio Value after all other charges * Exit Load = 0.015 * Rs. 1,77,194 = Rs. 2,657.91 ≈ Rs. 2,658 * Net Value of Portfolio: Rs. 1,77,194 - Rs. 2,658 = Rs. 1,74,536 **Net Return Calculation:** Net Return = (Net Value of Portfolio - Initial Capital) / Initial Capital Net Return = (Rs. 1,74,536 - Rs. 1,50,000) / Rs. 1,50,000 Net Return = Rs. 24,536 / Rs. 1,50,000 = 0.163573... ≈ 16.36%

Medium Sub-question 4

Considering Mr. and Mrs. Sharma's multiple contributions to their historical portfolio over the years (2020, 2021, 2022), which rate of return measure would best reflect the actual return an investor received, taking into account the timing and size of their cash flows?

ATime Weighted Rate of Return (TWRR)

BHolding Period Return (HPR)

✓Money Weighted Rate of Return (MWRR)

DArithmetic Mean Return (AMR)

💡 The Money Weighted Rate of Return (MWRR) is the annual rate of return at which the cumulative contributions grow over the measurement period. It depends on the timing and size of the cash flows, making it suitable for evaluating an investor's actual return when there are multiple contributions or withdrawals. TWRR, on the other hand, removes the impact of cash flows and is typically used by fund managers for performance comparison.

Medium Sub-question 5

If Mr. Sharma's new PMS investment generates a gross profit of 22% and he is in the 20% tax bracket for capital gains and investment income, what would be his post-tax return on this investment, assuming no other fees or charges for simplicity in this specific calculation?

A22.00%

B19.80%

✓17.60%

D16.50%

💡 Post-tax return = Pre-Tax Return x (1 - tax rate). Given: Pre-tax return = 22% Tax rate = 20% Post-tax return = 22% x (1 - 0.20) Post-tax return = 22% x 0.80 = 17.60%.

Case 4 Case-Based · 2 marks each Portfolio Performance Measurement

Mr. and Mrs. Sharma, aged 45 and 42 respectively, approached their investment adviser to review their portfolio's performance. They had invested Rs. 50,00,000 in a discretionary portfolio management service (PMS) exactly one year ago. The PMS firm informed them that the portfolio generated a 20% profit on their initial capital contribution during this year, before any fees or expenses. The PMS firm's fee structure is as follows: * Other Expenses (brokerage, DP charges): 0.50% of the gross value of the portfolio at the end of the year. * Fixed Management Fee: 1.50% annually, charged on the average of the initial capital contribution and the gross value of the portfolio at year-end. * Hurdle Rate: 10% of the amount invested. * Performance Fee: 20% of profits over the hurdle rate (without catch-up). * Exit Load: 2% on the portfolio value after all other fees (including performance fee) but before exit load. * The Sharmas are in the 20% tax bracket for investment income and capital gains. Separately, the Sharmas had made a lump-sum investment of Rs. 10,00,000 in a diversified equity mutual fund five years ago. The annual holding period returns for this mutual fund were: Year 1: -5.00%, Year 2: 10.00%, Year 3: 15.00%, Year 4: 20.00%, Year 5: 12.00%. At the end of the five-year period, the final value of their mutual fund investment was Rs. 15,50,000.

Medium Sub-question 1

Calculate the net return on Mr. and Mrs. Sharma's PMS portfolio for the year, after considering all fees.

A12.55%

✓13.88%

C15.00%

D16.20%

💡 1. Initial Capital Contribution: Rs. 50,00,000 2. Profit made: 20% of Rs. 50,00,000 = Rs. 10,00,000 3. Gross Value of Portfolio at end of year: Rs. 50,00,000 + Rs. 10,00,000 = Rs. 60,00,000 Fees Calculation: a) Other Expenses: 0.50% of Gross Value = 0.0050 * Rs. 60,00,000 = Rs. 30,000 Portfolio Value after Other Expenses = Rs. 60,00,000 - Rs. 30,000 = Rs. 59,70,000 b) Fixed Management Fee: 1.50% on average of initial and gross value Average Value = (Rs. 50,00,000 + Rs. 60,00,000) / 2 = Rs. 55,00,000 Fixed Management Fee = 0.0150 * Rs. 55,00,000 = Rs. 82,500 Portfolio Value after Fixed Management Fees = Rs. 59,70,000 - Rs. 82,500 = Rs. 58,87,500 c) Performance Fee: 20% of profits over hurdle rate Hurdle Rate: 10% of initial investment = 0.10 * Rs. 50,00,000 = Rs. 5,00,000 Required Portfolio Value at Hurdle Rate = Rs. 50,00,000 * (1 + 0.10) = Rs. 55,00,000 Profit over Hurdle Level = Portfolio Value after Fixed Management Fees - Required Portfolio Value at Hurdle Rate Profit over Hurdle Level = Rs. 58,87,500 - Rs. 55,00,000 = Rs. 3,87,500 Performance Fee = 0.20 * Rs. 3,87,500 = Rs. 77,500 Portfolio Value after Performance Fees = Rs. 58,87,500 - Rs. 77,500 = Rs. 58,10,000 d) Exit Load: 2% on portfolio value after all other fees Exit Load = 0.02 * Rs. 58,10,000 = Rs. 1,16,200 Portfolio Value after Exit Load = Rs. 58,10,000 - Rs. 1,16,200 = Rs. 56,93,800 Net Value of the Portfolio = Rs. 56,93,800 Net Return = (Net Value of the Portfolio - Capital Contribution) / Capital Contribution Net Return = (Rs. 56,93,800 - Rs. 50,00,000) / Rs. 50,00,000 Net Return = Rs. 6,93,800 / Rs. 50,00,000 = 0.13876 or 13.876% (approximately 13.88%)

Hard Sub-question 2

What is the Compounded Annual Growth Rate (CAGR) for Mr. and Mrs. Sharma's mutual fund investment over the five-year period?

✓9.15%

B10.40%

C11.25%

D12.00%

💡 Initial Investment (P) = Rs. 10,00,000 Final Value (A) = Rs. 15,50,000 Time Period (t) = 5 years CAGR = (A / P)^(1/t) - 1 CAGR = (15,50,000 / 10,00,000)^(1/5) - 1 CAGR = (1.55)^(0.2) - 1 CAGR = 1.091530 - 1 CAGR = 0.091530 or 9.15% (approximately)

Easy Sub-question 3

Based on the net return of their PMS portfolio, what is Mr. and Mrs. Sharma's post-tax return, given their tax bracket?

✓11.00%

B13.88%

C17.35%

D19.29%

💡 Net Return (Pre-tax) = 13.876% (from previous calculation) Tax Rate = 20% Post-tax return = Pre-Tax Return x (1 - tax rate) Post-tax return = 13.876% x (1 - 0.20) Post-tax return = 13.876% x 0.80 = 11.0008% (approximately 11.00%)

Medium Sub-question 4

Calculate the Arithmetic Mean Return (AMR) for Mr. and Mrs. Sharma's mutual fund investment over the five-year period.

A9.15%

✓10.40%

C12.00%

D15.00%

💡 The annual holding period returns are: -5.00%, 10.00%, 15.00%, 20.00%, 12.00%. Arithmetic Mean Return (AMR) = Sum of annual returns / Number of years AMR = (-5% + 10% + 15% + 20% + 12%) / 5 AMR = (52%) / 5 = 10.40%

Easy Sub-question 5

What is the gross return on Mr. and Mrs. Sharma's PMS portfolio for the year?

A10.00%

B15.00%

✓20.00%

D25.00%

💡 The case context states that the PMS firm generated a 20% profit on their initial capital contribution during this year, before any fees or expenses. This directly represents the gross return. Gross Return = (Gross value of the portfolio – Capital Contribution) / Capital Contribution Gross Return = 20%

Case 5 Case-Based · 2 marks each Portfolio Performance Measurement

Mr. Raj Sharma, a 45-year-old salaried professional, engaged an investment adviser to manage a portion of his savings. He made an initial investment of Rs. 5,00,000 at the beginning of 2021. The portfolio generated the following annual holding period returns (HPRs) over the next three years: * 2021: 10.00% * 2022: -5.00% * 2023: 20.00% At the beginning of 2022, Mr. Sharma made an additional contribution of Rs. 1,00,000. At the beginning of 2023, he made another contribution of Rs. 1,50,000. The investment adviser charges the following fees annually: * Fixed Management Fee: 1.5% on the average of capital contribution (at the beginning of the year) and gross value of the portfolio (before other expenses) at the end of the year. * Performance Fee: 15% of profits over a hurdle rate of 8% (without catch-up). * Other Expenses (brokerage, DP charges): 0.5% on the gross value of the portfolio at the end of the year. * Mr. Sharma falls under the 30% tax bracket for capital gains and investment income.

Medium Sub-question 1

Calculate the Arithmetic Mean Return (AMR) for Mr. Sharma's portfolio over the three-year period (2021-2023).

A7.82%

✓8.33%

C10.00%

D25.00%

💡 The Arithmetic Mean Return (AMR) is the simple average of the individual yearly returns. AMR = (HPR_2021 + HPR_2022 + HPR_2023) / Number of years AMR = (10.00% + (-5.00%) + 20.00%) / 3 AMR = (0.10 - 0.05 + 0.20) / 3 AMR = 0.25 / 3 AMR = 0.08333... or 8.33%

Medium Sub-question 2

What is the Time Weighted Rate of Return (TWRR) for Mr. Sharma's portfolio over the three-year period (2021-2023)?

✓7.82%

B8.33%

C6.02%

D12.54%

💡 1. Calculate wealth relatives for each period: Wealth Relative (2021) = 1 + HPR_2021 = 1 + 0.10 = 1.10 Wealth Relative (2022) = 1 + HPR_2022 = 1 + (-0.05) = 0.95 Wealth Relative (2023) = 1 + HPR_2023 = 1 + 0.20 = 1.20 2. Calculate the cumulative wealth relative: Cumulative Wealth Relative = 1.10 * 0.95 * 1.20 = 1.254 3. Calculate the TWRR (annualized): TWRR = (Cumulative Wealth Relative ^ (1 / Number of years)) - 1 TWRR = (1.254 ^ (1/3)) - 1 TWRR = 1.078207 - 1 TWRR = 0.078207 or 7.82% (rounded to two decimal places)

Easy Sub-question 3

What was the Holding Period Return (HPR) for Mr. Sharma's portfolio in the year 2022?

A10.00%

✓-5.00%

C20.00%

D5.00%

💡 The Holding Period Return (HPR) for the year 2022 is directly provided in the case context as -5.00%.

Hard Sub-question 4

Calculate the Net Return for Mr. Sharma's portfolio for the year 2021, considering all applicable fees (excluding exit load).

A10.00%

✓7.88%

C8.50%

D9.13%

💡 1. **Initial Investment (Beginning of 2021):** Rs. 5,00,000 2. **HPR for 2021:** 10.00% 3. **Profit made during 2021:** 5,00,000 * 0.10 = Rs. 50,000 4. **Gross Value of Portfolio at end of 2021 (before fees):** 5,00,000 + 50,000 = Rs. 5,50,000 **Fee Calculations:** * **a) Other Expenses:** 0.5% on Gross Value of Portfolio Other Expenses = 0.005 * 5,50,000 = Rs. 2,750 Value after Other Expenses = 5,50,000 - 2,750 = Rs. 5,47,250 * **b) Fixed Management Fee:** 1.5% on average of Capital Contribution (beginning) and Gross Value (end) Average Value = (5,00,000 + 5,50,000) / 2 = Rs. 5,25,000 Fixed Management Fee = 0.015 * 5,25,000 = Rs. 7,875 Value after Fixed Management Fee = 5,47,250 - 7,875 = Rs. 5,39,375 * **c) Performance Fee:** 15% of profits over hurdle rate of 8% Capital Contribution (beginning 2021) = Rs. 5,00,000 Required Portfolio Value @ Hurdle Rate = 5,00,000 * (1 + 0.08) = Rs. 5,40,000 Portfolio Value after Fixed Management Fee (for comparison) = Rs. 5,39,375 Since Rs. 5,39,375 is less than the Hurdle Rate value of Rs. 5,40,000, there is no profit over the hurdle. Performance Fee = Rs. 0 Value after Performance Fee = Rs. 5,39,375 5. **Net Value of the Portfolio at end of 2021 (after all fees):** Rs. 5,39,375 6. **Net Return for 2021:** Net Return = (Net Value of Portfolio - Capital Contribution) / Capital Contribution Net Return = (5,39,375 - 5,00,000) / 5,00,000 Net Return = 39,375 / 5,00,000 Net Return = 0.07875 or 7.875% Rounded to two decimal places: 7.88%

Easy Sub-question 5

If Mr. Sharma's portfolio generated a pre-tax return of 12% in a particular year, what would be his post-tax return considering his tax bracket?

A12.00%

✓8.40%

C3.60%

D7.00%

💡 Post-tax return = Pre-Tax Return x (1 - tax rate) Post-tax return = 12% x (1 - 30%) Post-tax return = 12% x 0.70 Post-tax return = 8.40%

About this content: These practice questions are based on the NISM-Series-X-A: Investment Adviser (Level 1) Certification Examination Workbook published by the National Institute of Securities Markets (NISM), Mumbai. NISM is a SEBI-established institution. Questions cover Portfolio Construction Process with verified answers and explanations. BullWiser is an independent exam preparation platform — not affiliated with NISM or SEBI. Last updated: July 08, 2026.

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