NISM Series X-A Chapter 15: Portfolio Construction Process Practice Questions

Question 1

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

Accepted Answer

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

Question 2

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?

Accepted Answer

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.'

Question 3

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

Accepted Answer

Over longer holding periods, unless 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.'

Question 4

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

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

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.'

Question 7

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?

Accepted Answer

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

Question 8

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

Accepted Answer

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.. 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.'

Question 9

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

Accepted Answer

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.'

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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.. 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)

Question 12

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?

Accepted Answer

Geometric Mean Return (GMR). 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

Question 13

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

Accepted Answer

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

Question 14

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?

Accepted Answer

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. If we wish to estimate the expected return over a multiyear horizon conditioned on past experience, we may use the arithmetic average."

Question 15

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?

Accepted Answer

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.. 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

Question 16

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?

Accepted Answer

Discretionary portfolio managers. 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.'

Question 17

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?

Accepted Answer

Rs. 1,17,75,000. 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

Question 18

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?

Accepted Answer

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.'

Question 19

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

Accepted Answer

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

Question 20

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?

Accepted Answer

13.88%. 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

Question 21

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

Accepted Answer

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

Question 22

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

Accepted Answer

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

Question 23

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?

Accepted Answer

Geometric Mean Return (GMR). 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

Question 24

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?

Accepted Answer

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

Question 25

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

Accepted Answer

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

Question 26

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?

Accepted Answer

13.88%. 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%

Question 27

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

Accepted Answer

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

Question 28

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

Accepted Answer

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

Question 29

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

Accepted Answer

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

Question 30

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

Accepted Answer

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

Question 31

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

Accepted Answer

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

Question 32

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

Accepted Answer

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

Question 33

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?

Accepted Answer

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

Question 34

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)?

Accepted Answer

24%. 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%

Question 35

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?

Accepted Answer

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

Question 36

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

Accepted Answer

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.'

Question 37

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?

Accepted Answer

GMR is always less than or equal to AMR.. 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.' This implies GMR ≤ AMR

Question 38

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

Accepted Answer

Money Weighted Rate of Return (MWRR). 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'

Question 39

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

Accepted Answer

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

Question 40

What does 'Gross Return' on an investment represent?

Accepted Answer

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

Question 41

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?

Accepted Answer

20.00%. 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

Ch.15: Portfolio Construction Process

What You Will Learn in This Chapter

Multiple Choice Questions (108)

Case-Based Questions (5 sets)

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