NISM Series X-A Ch.16: Portfolio Performance Measurement and Evaluation — 175 Practice Questions

Q: A fund has a portfolio return of 15.00%, a risk-free rate of 5.00%, and a portfolio beta of 1.25. Calculate the Treynor Ratio for this fund.

0.08. As per section 16.4.2, the Treynor Ratio formula is: Treynor Ratio (T) = (Rp – Rf) / Bp Where: Rp = Portfolio return = 15.00% = 0.15 Rf = Risk-free return = 5.00% = 0.05 Bp = Portfolio beta = 1.25 T = (0.15 - 0.05) / 1.25 T = 0.10 / 1.25 T = 0.08

Q: A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate is 5%. Calculate the Sharpe Ratio for this portfolio.

0.875. As per section 16.4.1, the Sharpe Ratio formula is: Sharpe Ratio = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12% (0.12) Rf = Risk-free return = 5% (0.05) Sigma p = Standard deviation of return on the portfolio = 8% (0.08) Sharpe Ratio = (0.12 - 0.05) / 0.08 Sharpe Ratio = 0.07 / 0.08 Sharpe Ratio = 0.875

Q: Using the same portfolio data as in the Sharpe Ratio example (annualized return = 10.50%, risk-free rate = 5.50%), if the beta of the fund is 1, what is its Treynor Ratio?

0.05. As per section 16.4.2, the Treynor Ratio formula is T = (Rp - Rf) / Beta_p. Rp = 10.50% Rf = 5.50% Beta_p = 1 Treynor Ratio = (10.50% - 5.50%) / 1 = 5.00% / 1 = 0.05

Q: A portfolio consists of three stocks: Stock X with a Beta of 1.3 and a weight of 30%, Stock Y with a Beta of 0.9 and a weight of 50%, and Stock Z with a Beta of 1.1 and a weight of 20%. What is the Beta of this portfolio?

1.06. The Beta of the portfolio is calculated as the weighted average of the individual securities' Betas. Portfolio Beta = (Weight of X * Beta of X) + (Weight of Y * Beta of Y) + (Weight of Z * Beta of Z) Portfolio Beta = (0.30 * 1.3) + (0.50 * 0.9) + (0.20 * 1.1) Portfolio Beta = 0.39 + 0.45 + 0.22 Portfolio Beta = 1.06

Q: Tracking error is always calculated against which type of index?

Total Returns Index. As per the text, 'Tracking Error is always calculated against the Total Returns Index which shows the returns on the Index portfolio, inclusive of dividend.'

Q: Which of the following is NOT listed as a criterion for a good benchmark in the provided text?

The benchmark is composed of at least 50 constituents.. The text lists criteria for a good benchmark: 'The identity of constituents and their weights in the benchmark are clearly defined.', 'The benchmark is investable...', 'The benchmark is consistent with the portfolio’s investment approach.', 'The benchmark is having the same risk-return profile as the portfolio', 'The performance of the benchmark is measurable.' The number of constituents is not mentioned as a criterion

Q: According to the text, which type of risk can be diversified away?

Unsystematic risk, linked to sector-specific factors.. Section 16.3.6 states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk cannot be diversified away

Multiple Choice Questions (150)

Q1 MCQ · 1 mark MediumTreynor Ratio

A fund has a portfolio return of 15.00%, a risk-free rate of 5.00%, and a portfolio beta of 1.25. Calculate the Treynor Ratio for this fund.

A0.12

✓0.08

C0.10

D0.05

💡 As per section 16.4.2, the Treynor Ratio formula is: Treynor Ratio (T) = (Rp – Rf) / Bp Where: Rp = Portfolio return = 15.00% = 0.15 Rf = Risk-free return = 5.00% = 0.05 Bp = Portfolio beta = 1.25 T = (0.15 - 0.05) / 1.25 T = 0.10 / 1.25 T = 0.08

Q2 MCQ · 1 mark HardCharacteristics of Benchmarks

All of the following are stated characteristics of a good benchmark EXCEPT:

AIts identity of constituents and their weights are clearly defined.

BIt is investable, allowing for passive exposure.

✓It must consist of a fixed set of components that never change to ensure consistency.

DIts performance is measurable.

💡 Section 16.5.1 lists several characteristics of a good benchmark, including clearly defined constituents/weights, investability, consistency with investment approach, same risk-return profile, and measurable performance. The text does not state that a benchmark must consist of a fixed set of components that never change; in fact, section 16.5.3 implies that changes in components can occur and need to be reviewed ('The benchmark should not be witnessing huge changes in its components otherwise this would need to be reviewed for its effectiveness.').

Q3 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio (IR = (Rp – Rb)/Stdev (p-b)), what does the denominator, Stdev (p-b), represent?

AThe portfolio manager’s ability to generate active return.

BThe total risk of the portfolio.

CThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is also referred to as tracking error.

💡 The text states: 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. ... It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q4 MCQ · 1 mark MediumSharpe Ratio

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate is 5%. Calculate the Sharpe Ratio for this portfolio.

A0.625

✓0.875

C1.50

D2.40

💡 As per section 16.4.1, the Sharpe Ratio formula is: Sharpe Ratio = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12% (0.12) Rf = Risk-free return = 5% (0.05) Sigma p = Standard deviation of return on the portfolio = 8% (0.08) Sharpe Ratio = (0.12 - 0.05) / 0.08 Sharpe Ratio = 0.07 / 0.08 Sharpe Ratio = 0.875

Q5 MCQ · 1 mark MediumTreynor Ratio Calculation

Using the same portfolio data as in the Sharpe Ratio example (annualized return = 10.50%, risk-free rate = 5.50%), if the beta of the fund is 1, what is its Treynor Ratio?

A0.7692

✓0.05

C1.05

D0.50

💡 As per section 16.4.2, the Treynor Ratio formula is T = (Rp - Rf) / Beta_p. Rp = 10.50% Rf = 5.50% Beta_p = 1 Treynor Ratio = (10.50% - 5.50%) / 1 = 5.00% / 1 = 0.05.

Q6 MCQ · 1 mark MediumPortfolio Beta Calculation

A portfolio consists of three stocks: Stock X with a Beta of 1.3 and a weight of 30%, Stock Y with a Beta of 0.9 and a weight of 50%, and Stock Z with a Beta of 1.1 and a weight of 20%. What is the Beta of this portfolio?

A1.05

✓1.06

C1.10

D1.15

💡 The Beta of the portfolio is calculated as the weighted average of the individual securities' Betas. Portfolio Beta = (Weight of X * Beta of X) + (Weight of Y * Beta of Y) + (Weight of Z * Beta of Z) Portfolio Beta = (0.30 * 1.3) + (0.50 * 0.9) + (0.20 * 1.1) Portfolio Beta = 0.39 + 0.45 + 0.22 Portfolio Beta = 1.06

Q7 MCQ · 1 mark EasyTracking Error

Tracking error is always calculated against which type of index?

APrice Index

BMarket Capitalization Index

✓Total Returns Index

DSectoral Index

💡 As per the text, 'Tracking Error is always calculated against the Total Returns Index which shows the returns on the Index portfolio, inclusive of dividend.'

Q8 MCQ · 1 mark MediumBenchmarking Characteristics

Which of the following is NOT listed as a criterion for a good benchmark in the provided text?

AThe benchmark is investable.

BThe benchmark is consistent with the portfolio’s investment approach.

✓The benchmark is composed of at least 50 constituents.

DThe performance of the benchmark is measurable.

💡 The text lists criteria for a good benchmark: 'The identity of constituents and their weights in the benchmark are clearly defined.', 'The benchmark is investable...', 'The benchmark is consistent with the portfolio’s investment approach.', 'The benchmark is having the same risk-return profile as the portfolio', 'The performance of the benchmark is measurable.' The number of constituents is not mentioned as a criterion.

Q9 MCQ · 1 mark HardSharpe vs. Treynor Measure

An investor holds a poorly diversified portfolio. Which risk-adjusted return measure would be more appropriate for evaluating its performance, and why?

ATreynor Ratio, because it considers only systematic risk, which is the most relevant for poorly diversified portfolios.

✓Sharpe Ratio, because it adjusts return for total portfolio risk, which includes both systematic and unsystematic risk relevant for poorly diversified portfolios.

CInformation Ratio, because it measures the manager's ability to generate active returns, irrespective of diversification.

DModigliani and Modigliani Ratio (M2), because it adjusts the portfolio's risk to match the market portfolio, making it suitable for any diversification level.

💡 According to section 16.4.3, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios.' This is because Sharpe Ratio uses total risk (standard deviation), which captures both systematic and unsystematic risk, both of which are significant in a poorly diversified portfolio.

Q10 MCQ · 1 mark EasySystematic and Unsystematic Risk

According to the text, which type of risk can be diversified away?

ASystematic risk, measured by Beta.

BSystematic risk, linked to common risk factors.

✓Unsystematic risk, linked to sector-specific factors.

DUnsystematic risk, measured by Alpha return.

💡 Section 16.3.6 states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk cannot be diversified away.

Q11 MCQ · 1 mark EasyTracking Error

What is the primary cause of tracking errors between a portfolio and its target benchmark?

✓Mismatches between the portfolio's risk profile and the benchmark's risk profile.

BDifferences in the liquidity of assets held in the portfolio compared to the benchmark.

CFluctuations in systematic risk factors like interest rates and exchange rates.

DThe inability to accurately measure the total returns of the benchmark index.

💡 According to the text, 'Tracking errors primarily arises due to mismatches between portfolio’s risk profile and the benchmark’s risk profile.'

Q12 MCQ · 1 mark MediumRisk-Adjusted Return Measures

An investor holds a poorly diversified portfolio and wishes to evaluate its performance. Which risk-adjusted return measure would be most suitable for this investor?

ATreynor Ratio

BInformation Ratio

✓Sharpe Ratio

DModigliani and Modigliani Ratio (M2)

💡 The text states, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. Therefore, Sharpe Ratio is suitable for a poorly diversified portfolio.

Q13 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For an investor whose wealth is not adequately diversified, which risk-adjusted return measure is generally more suitable for evaluating portfolio performance?

ATreynor Ratio, because it considers only systematic risk.

✓Sharpe Ratio, because it adjusts return to the total portfolio risk.

CInformation Ratio, as it measures active return against active risk.

DSortino Ratio, as it focuses on downside risk.

Q14 MCQ · 1 mark EasyTracking Error

What is tracking error in the context of portfolio performance measurement?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund's return to fluctuations in the market index.

DThe risk that the borrower is not able to repay amounts on time to the lender.

💡 As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes tracking difference, C describes Beta, and D describes Credit risk.

Q15 MCQ · 1 mark EasyTracking Error

What is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return?

ATracking difference

BSystematic risk

✓Tracking error

DUnsystematic risk

💡 Tracking error is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return. Tracking difference is a simpler point-to-point difference, while systematic and unsystematic risks are different categories of risk.

Q16 MCQ · 1 mark MediumTracking Error vs. Tracking Difference

What is the key distinction between Tracking Error and Tracking Difference?

ATracking Error is a simple point-to-point difference, while Tracking Difference is the standard deviation of return differences.

BTracking Error measures deviations from the market return, while Tracking Difference measures deviations from the risk-free rate.

✓Tracking Error is the standard deviation of return differences between a portfolio and its benchmark, while Tracking Difference is the simple point-to-point difference between index return and fund return.

DTracking Error arises from systematic risk, while Tracking Difference arises from unsystematic risk.

💡 Section 16.3.5 states: 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' It also states: 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q17 MCQ · 1 mark HardTreynor Ratio Calculation

A fund has a portfolio return (Rp) of 12.00%, a risk-free rate (Rf) of 4.00%, and a portfolio Beta (Bp) of 1.5. Calculate the Treynor Ratio for this fund.

A0.08

✓0.053

C0.06

D0.12

💡 As per section 16.4.2, the Treynor Ratio formula is T = (Rp - Rf) / Bp. Given: Rp = 12.00% = 0.12 Rf = 4.00% = 0.04 Bp = 1.5 Treynor Ratio = (0.12 - 0.04) / 1.5 Treynor Ratio = 0.08 / 1.5 Treynor Ratio ≈ 0.0533

Q18 MCQ · 1 mark HardInformation Ratio

In the Information Ratio formula, IR = (Rp – Rb) / Stdev (p-b), what does the denominator 'Stdev (p-b)' primarily represent?

AThe total risk of the portfolio.

BThe systematic risk of the portfolio (Beta).

✓The active risk or tracking error of the portfolio.

DThe semi-standard deviation of the portfolio's negative returns.

💡 The text states: 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. The numerator is often referred to as the active return on the portfolio whereas denominator is referred to as the active risk. It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q19 MCQ · 1 mark HardSharpe Ratio Calculation

A portfolio has an annualized return of 12.0% and an annualized standard deviation of 8.0%. If the risk-free rate of return is 4.0%, what is the Sharpe ratio for this portfolio?

A0.50

✓1.00

C1.50

D2.00

💡 The Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12.0% Rf = Risk-free return = 4.0% Sigma p = Standard deviation of return on the portfolio = 8.0% S = (12.0% - 4.0%) / 8.0% S = 8.0% / 8.0% S = 1.00

Q20 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

A portfolio has generated a return of 30% with a standard deviation of 35%. The market portfolio has generated a return of 20% with a standard deviation of 25%. The treasury bill rate is 5%. Using the M2 measure, what is the risk-adjusted return of the portfolio (rp*)?

A21.43%

✓22.86%

C20.00%

D25.00%

💡 To calculate the M2 risk-adjusted return (rp*), we first need to adjust the portfolio's risk to match the market's risk. 1. Calculate the proportion of the portfolio (P) to hold to match the market's standard deviation: Proportion in P = (Market's Standard Deviation) / (Portfolio's Standard Deviation) Proportion in P = 25% / 35% = 5/7 ≈ 0.714286 2. Calculate the proportion to hold in the risk-free asset (T-bills): Proportion in T-bills = 1 - Proportion in P = 1 - (5/7) = 2/7 ≈ 0.285714 3. Calculate the risk-adjusted return (rp*): rp* = (Proportion in P * Return on Portfolio) + (Proportion in T-bills * Risk-free rate) rp* = (5/7 * 0.30) + (2/7 * 0.05) rp* = (1.50/7) + (0.10/7) rp* = 1.60/7 ≈ 0.22857 rp* ≈ 22.86%

Q21 MCQ · 1 mark EasyTracking Error

What is the primary difference between 'tracking error' and 'tracking difference' as described in the text?

ATracking error measures market return deviations, while tracking difference measures portfolio risk profile mismatches.

✓Tracking error is the standard deviation of the difference between portfolio and benchmark total return, while tracking difference is the simple point-to-point difference between index and fund return.

CTracking error considers only unsystematic risk, while tracking difference considers systematic risk.

DTracking error is calculated against a price index, while tracking difference is calculated against a total return index.

💡 As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' and 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q22 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

A portfolio has generated a return of 30% with a standard deviation of 40%. The market portfolio returned 20% with a standard deviation of 25%. The treasury bill rate is 5%. Using the Modigliani and Modigliani (M2) Measure, if the portfolio's risk is adjusted to match the market's standard deviation, what is the adjusted return of the portfolio (rp*)?

A18.75%

✓20.63%

C19.38%

D21.25%

💡 As per section 16.4.6, the M2 measure adjusts the risk of the portfolio to match the market portfolio's standard deviation by levering or de-levering. 1. Determine the proportion of the portfolio (P) and T-bills (Rf) to match market volatility: Market's standard deviation = 25% Portfolio's standard deviation = 40% Proportion in Portfolio (P) = Market's std dev / Portfolio's std dev = 25% / 40% = 0.625 Proportion in T-bills = 1 - Proportion in Portfolio = 1 - 0.625 = 0.375 2. Calculate the adjusted portfolio return (rp*): rp* = (Proportion in P * Return of Portfolio) + (Proportion in T-bills * Risk-free rate) rp* = (0.625 * 0.30) + (0.375 * 0.05) rp* = 0.1875 + 0.01875 rp* = 0.20625 = 20.625% Rounding to two decimal places, this is 20.63%.

Q23 MCQ · 1 mark EasyTracking Error

According to the text, what primarily causes tracking errors?

AFluctuations in the risk-free rate.

✓Mismatches between the portfolio’s risk profile and the benchmark’s risk profile.

CChanges in the market's overall volatility.

DThe simple point-to-point difference between index return and fund return.

💡 The text states: 'Tracking errors primarily arises due to mismatches between portfolio’s risk profile and the benchmark’s risk profile.'

Q24 MCQ · 1 mark MediumPortfolio Beta Calculation

A portfolio consists of Stock X with a beta of 1.3 and Stock Y with a beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the beta of the portfolio?

✓1.18

B1.25

C1.05

D1.10

💡 The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9) Portfolio Beta = 0.91 + 0.27 Portfolio Beta = 1.18

Q25 MCQ · 1 mark HardSharpe Ratio Calculation

A portfolio has an annualized return of 15.00% and an annualized standard deviation of 10.00%. If the risk-free rate of return is 6.00%, what is the Sharpe Ratio for this portfolio?

✓0.90

B1.50

C0.60

D0.75

💡 As per section 16.4.1, the Sharpe Ratio formula is S = (Rp - Rf) / Sigma_p. Given: Rp = 15.00% = 0.15 Rf = 6.00% = 0.06 Sigma_p = 10.00% = 0.10 Sharpe Ratio = (0.15 - 0.06) / 0.10 Sharpe Ratio = 0.09 / 0.10 Sharpe Ratio = 0.90

Q26 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which type of risk, as described in the text, can be diversified away?

ASystematic risk

BInterest rate risk

✓Unsystematic risk

DExchange rate risk

💡 The text states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk, interest rate risk, and exchange rate risk are all forms of systematic risk which cannot be diversified away.

Q27 MCQ · 1 mark EasyLiquidity Risk

Which type of risk is defined as the uncertainty introduced by the secondary market of an investment, relating to the ease of converting an asset into cash at close to its economic worth?

ACredit risk

BSystematic risk

✓Liquidity risk

DTracking error

💡 Section 16.3.8 states, 'Liquidity risk is the uncertainty introduced by the secondary market of an investment.' and 'Liquidity is defined as ease of converting an asset into cash at close to its economic worth.'

Q28 MCQ · 1 mark HardSharpe vs. Treynor Measure

For which type of investor is the Treynor Ratio generally a more appropriate measure of performance compared to the Sharpe Ratio?

AAn investor who has not achieved adequate diversification on their wealth as a whole.

✓An investor whose wealth is already well diversified, with minimal unsystematic risk.

CAn investor primarily concerned with downside risk.

DAn investor evaluating mutually exclusive portfolios.

💡 Section 16.4.3 states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. This is because the Treynor Ratio focuses on systematic risk, which is the only risk that matters for well-diversified investors.

Q29 MCQ · 1 mark HardPortfolio Beta Calculation

A portfolio consists of Stock X with a Beta of 1.3 and Stock Y with a Beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the Beta of the portfolio?

✓1.18

B1.02

C1.22

D0.98

💡 As per section 16.3.7, the Beta of the portfolio is the weighted average beta of the individual securities. Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q30 MCQ · 1 mark EasyTracking Error

Which of the following best defines Tracking Error?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe uncertainty introduced by the secondary market of an investment.

DThe risk that the borrower is not able to repay amounts on time to the lender.

Q31 MCQ · 1 mark MediumTreynor Ratio Calculation

A fund has an annualized return of 13.00% and a beta of 1.2. If the risk-free rate of return is 5.00%, what is the Treynor ratio for this fund?

✓0.0667

B0.08

C0.015

D0.1083

💡 The Treynor Ratio is calculated as: Treynor Ratio = (Rp - Rf) / Bp Where: Rp = Portfolio return = 13.00% Rf = Risk-free return = 5.00% Bp = Portfolio beta = 1.2 Treynor Ratio = (13.00% - 5.00%) / 1.2 = 8.00% / 1.2 = 0.06666... Rounded to 0.0667

Q32 MCQ · 1 mark MediumGood Benchmark Characteristics

Which of the following is NOT listed as a criterion for a good benchmark?

AThe benchmark is investable.

BThe benchmark's constituents and their weights are clearly defined.

✓The benchmark is actively managed to outperform the portfolio.

DThe benchmark has the same risk-return profile as the portfolio.

💡 The text lists the criteria for a good benchmark: 'The identity of constituents and their weights in the benchmark are clearly defined.', 'The benchmark is investable...', 'The benchmark is consistent with the portfolio’s investment approach.', 'The benchmark is having the same risk-return profile as the portfolio', and 'The performance of the benchmark is measurable.' An actively managed benchmark designed to outperform the portfolio is not mentioned as a criterion.

Q33 MCQ · 1 mark EasyTracking Error

According to the text, what is tracking error?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund’s return to fluctuations in the market index.

DThe variability of negative returns in an investment.

💡 Tracking error is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return. Option A describes tracking difference, not tracking error.

Q34 MCQ · 1 mark EasyPortfolio Beta

A portfolio consists of two stocks: Stock X with a beta of 1.3 and Stock Y with a beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the Beta of the portfolio?

A1.02

✓1.18

C1.24

D1.08

💡 The Beta of a portfolio is the weighted average beta of the individual securities. Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9) Portfolio Beta = 0.91 + 0.27 Portfolio Beta = 1.18

Q35 MCQ · 1 mark EasyBenchmark Characteristics

Which of the following is NOT a characteristic of a good benchmark for portfolio performance evaluation?

AThe benchmark is investable, allowing for passive exposure.

BThe identity of constituents and their weights are clearly defined.

✓The benchmark has a significantly different risk-return profile than the portfolio to highlight manager skill.

DThe benchmark is consistent with the portfolio’s investment approach.

💡 A good benchmark should have 'the same risk-return profile as the portfolio', as stated in the text. A significantly different risk-return profile would make it an unsuitable comparison for evaluating performance.

Q36 MCQ · 1 mark HardBenchmarking

Which of the following is NOT a characteristic of a good benchmark as per the provided text?

AThe benchmark is consistent with the portfolio’s investment approach.

BThe benchmark is easily investable, allowing for passive exposure.

CThe benchmark's constituents and their weights are clearly defined.

✓The benchmark exclusively consists of market-based indices to avoid customization costs.

💡 Section 16.5.1 and 16.5.2 list characteristics of good benchmarks and discuss customized benchmarks. Options A, B, and C are explicitly mentioned as criteria for a good benchmark. Option D is incorrect because the text acknowledges that 'market-based indices may not meet the above criteria' and 'Such situation demands for appropriate customized benchmark', indicating that good benchmarks are not exclusively market-based indices.

Q37 MCQ · 1 mark EasyTracking Error

What is the primary distinction between 'tracking error' and 'tracking difference'?

ATracking error is a point-to-point measure, while tracking difference is a standard deviation measure.

BTracking error measures deviations from the market return, while tracking difference measures deviations from the risk-free rate.

✓Tracking error is the standard deviation of the difference between portfolio and benchmark returns, while tracking difference is the simple point-to-point difference.

DTracking error is calculated using the Total Returns Index, while tracking difference uses only price returns.

💡 The text states, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return,' and 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q38 MCQ · 1 mark MediumPortfolio Beta Calculation

Stock P has a beta of 1.3 and Stock Q has a beta of 0.9. If a portfolio is constructed with 70% invested in Stock P and 30% in Stock Q, what is the Beta of the portfolio?

A1.20

✓1.18

C1.15

D1.05

💡 As per section 16.3.7, 'Beta of the portfolio can also be calculated by taking the weighted average beta of the individual securities/investments in the portfolio.' Portfolio Beta = (Weight of Stock P * Beta of Stock P) + (Weight of Stock Q * Beta of Stock Q) Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9) Portfolio Beta = 0.91 + 0.27 Portfolio Beta = 1.18

Q39 MCQ · 1 mark MediumCredit Risk

Credit risk primarily arises in the case of which type of financial instruments?

AEquity instruments

✓Debt instruments

CCommodity futures

DReal estate investments

💡 Section 16.3.9 states, 'Credit risk arises in case of debt instruments.'

Q40 MCQ · 1 mark MediumBeta Calculation

An investment portfolio consists of two stocks, Stock X and Stock Y. Stock X has a beta of 1.3 and makes up 70% of the portfolio. Stock Y has a beta of 0.9 and makes up 30% of the portfolio. What is the Beta of this portfolio?

A1.05

✓1.18

C1.25

D1.00

💡 The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. Portfolio Beta (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q41 MCQ · 1 mark HardTreynor Ratio & Interpretation

A fund has an annualized return of 15%, a risk-free rate of 5%, and a portfolio beta of 1.25. Calculate the Treynor Ratio and interpret its meaning.

A8.0; The fund generated 8.0 percentage points of excess return for each percentage point of standard deviation.

✓0.08; The fund generated 0.08 percentage points of excess return for every unit of systematic risk.

C12.5; The fund generated 12.5 percentage points of excess return for every unit of total risk.

D0.125; The fund generated 0.125 percentage points of excess return for every unit of systematic risk.

💡 The Treynor Ratio (T) is calculated as (Rp - Rf) / Bp. Rp = 15% = 0.15 Rf = 5% = 0.05 Bp = 1.25 T = (0.15 - 0.05) / 1.25 = 0.10 / 1.25 = 0.08 Interpretation: The text states, 'This indicates that the fund has generated 0.05-percentage point excess returns for every unit of systematic risk.' Applying this logic, 0.08 means the fund generated 0.08 percentage points of excess return for every unit of systematic risk.

Q42 MCQ · 1 mark EasyBenchmarking Characteristics

According to the text, which of the following is NOT a characteristic of a good benchmark?

AThe benchmark is investable.

BThe benchmark is consistent with the portfolio’s investment approach.

✓The benchmark's performance data is not always required to be measurable.

DThe identity of constituents and their weights in the benchmark are clearly defined.

💡 As per section 16.5.1, one of the criteria for a good benchmark is: 'The performance of the benchmark is measurable.' Therefore, option C, which states the opposite, is NOT a characteristic of a good benchmark.

Q43 MCQ · 1 mark MediumGood Benchmark Characteristics

Which of the following is NOT listed as a criterion for a good benchmark?

AThe benchmark is investable.

BThe benchmark is consistent with the portfolio’s investment approach.

CThe benchmark's constituents and their weights are clearly defined.

✓The benchmark is comprised solely of market-based indices.

💡 Section 16.5.1 lists the characteristics of a good benchmark, which include options A, B, and C. The text also discusses customized benchmarks (16.5.2) when market-based indices are not suitable, indicating that benchmarks are not solely market-based.

Q44 MCQ · 1 mark MediumTreynor Ratio Calculation

A portfolio has an annualized return of 15.00%, and the risk-free rate is 5.00%. If the portfolio's Beta is 1.2, what is its Treynor Ratio?

✓0.0833

B0.1200

C0.1000

D0.0917

💡 Treynor Ratio = (Rp - Rf) / Bp Given: Rp = 15.00% (0.15) Rf = 5.00% (0.05) Bp = 1.2 Treynor Ratio = (0.15 - 0.05) / 1.2 Treynor Ratio = 0.10 / 1.2 Treynor Ratio = 0.0833 (approximately)

Q45 MCQ · 1 mark MediumBenchmarking Characteristics

Which of the following is NOT listed as a criterion for a good benchmark?

AThe benchmark is investable, allowing for passive exposure.

BThe identity of constituents and their weights in the benchmark are clearly defined.

✓The benchmark is designed to maximize returns regardless of risk.

DThe benchmark is consistent with the portfolio's investment approach.

💡 Section 16.5.1 lists characteristics of good benchmarks. Options A, B, and D are all listed. Option C, 'The benchmark is designed to maximize returns regardless of risk,' is not a criterion; instead, a good benchmark should have 'the same risk-return profile as the portfolio.'

Q46 MCQ · 1 mark HardBeta Calculation

Stock P has a beta of 1.3 and Stock Q has a beta of 0.9. If a portfolio is constructed with 70% in Stock P and 30% in Stock Q, what is the Beta of the portfolio?

A1.25

✓1.18

C1.20

D1.15

💡 As per section 16.3.7, 'Beta of the portfolio can also be calculated by taking the weighted average beta of the individual securities/investments in the portfolio.' Portfolio Beta = (Weight of Stock P * Beta of Stock P) + (Weight of Stock Q * Beta of Stock Q) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q47 MCQ · 1 mark EasyTracking Error

What is tracking error primarily defined as?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund’s return to fluctuations in the market index.

DThe risk that the borrower is not able to repay amounts on time.

💡 As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.'

Q48 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate of return is 4%. Calculate the Sharpe Ratio for this portfolio.

A1.50

✓1.00

C0.75

D2.00

💡 The Sharpe Ratio is calculated as (Return of the portfolio - Risk-free return) / Standard deviation of return on the portfolio. Sharpe Ratio = (Rp - Rf) / Sigma p Sharpe Ratio = (12% - 4%) / 8% Sharpe Ratio = 8% / 8% Sharpe Ratio = 1.00

Q49 MCQ · 1 mark EasySortino Ratio

The Sortino Ratio adjusts a portfolio's excess return to which specific type of risk?

ASystematic risk

BTotal portfolio risk

✓Downside risk

DCredit risk

💡 The text explicitly states, 'Sortino Ratio adjusts portfolio’s excess return to the downside risk.'

Q50 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

What is the primary adjustment made to a portfolio when calculating the Modigliani and Modigliani Ratio (M2) measure?

AThe portfolio's unsystematic risk is eliminated.

BThe portfolio's return is adjusted to match the risk-free rate.

✓The portfolio's risk is adjusted to match the risk of the market portfolio.

DThe portfolio's beta is set to 1.

💡 The text states: 'They have adjusted the risk of the portfolio to match the risk of the market portfolio.' and 'To adjust the risk of the portfolio, they resorted to levering or de-levering.'

Q51 MCQ · 1 mark HardSharpe vs. Treynor Measure

An investor is evaluating two portfolios, Fund X and Fund Y. Fund X is a poorly diversified portfolio, while Fund Y is a completely well-diversified portfolio. Based on the provided text, which statement regarding their ranking by Sharpe and Treynor Ratios is most accurate?

ABoth Sharpe and Treynor ratios will give identical rankings for both funds because they both measure risk-adjusted return.

✓For Fund Y (well-diversified), Sharpe and Treynor ratios will give identical rankings, but for Fund X (poorly diversified), the Treynor ratio ranking might be higher than the Sharpe ratio ranking.

CFor Fund X (poorly diversified), Sharpe and Treynor ratios will give identical rankings, but for Fund Y (well-diversified), the Sharpe ratio ranking might be higher.

DSharpe ratio is more suitable for Fund Y, and Treynor ratio is more suitable for Fund X.

💡 Section 16.4.3 states: 'For a completely well-diversified portfolio, the two measures give identical ranking, because total risk and systematic risk would be the same. However, for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio as Treynor ratio, ignores unsystematic risk. Thus any difference in rankings based on Sharpe Ratio and Treynor ratio is due difference in portfolio diversification levels.'

Q52 MCQ · 1 mark HardSharpe vs. Treynor Measure

An investor is evaluating two actively managed portfolios, Portfolio A and Portfolio B. Portfolio A is poorly diversified, while Portfolio B is very well-diversified. Which of the following statements is most accurate regarding the use of Sharpe Ratio and Treynor Ratio for these portfolios?

AThe Sharpe Ratio would be more suitable for Portfolio B, and the Treynor Ratio for Portfolio A.

BBoth Sharpe Ratio and Treynor Ratio would give identical rankings for Portfolio A due to its poor diversification.

✓The Sharpe Ratio is more suitable for Portfolio A, while the Treynor Ratio is more appropriate for Portfolio B.

DThe Treynor Ratio would likely give a lower ranking for Portfolio A compared to its Sharpe Ratio ranking.

💡 The text states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios.' Therefore, for the poorly diversified Portfolio A, Sharpe Ratio is more suitable. For the very well-diversified Portfolio B, Treynor Ratio is more appropriate. Option B is incorrect because for a poorly diversified portfolio, the rankings would differ as Treynor ignores unsystematic risk. Option D is incorrect; for a poorly diversified portfolio, the Treynor Ratio ranking could be higher than the Sharpe Ratio ranking because Treynor ignores unsystematic risk.

Q53 MCQ · 1 mark MediumBeta Interpretation

A portfolio has a Beta of 0.8. What does this indicate about the portfolio's volatility relative to the benchmark index?

AThe portfolio is more volatile than the benchmark index.

✓The portfolio is less volatile than the benchmark index.

CThe portfolio has the same volatility as the benchmark index.

DThe portfolio's volatility cannot be compared to the benchmark index using Beta alone.

💡 As per section 16.3.7, 'A beta that is greater than one means that the portfolio or stock is more volatile than the benchmark index, while a beta of less than one means that the security is less volatile than the index.'

Q54 MCQ · 1 mark EasyTracking Error

Which of the following best defines tracking error?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund’s return to fluctuations in the market index.

DThe risk that the borrower is not able to repay amounts on time to the lender.

💡 As per section 16.3.5, tracking error is defined as 'the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes tracking difference, not tracking error.

Q55 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what does the denominator, Stdev (p-b), represent?

AThe total portfolio risk.

BThe systematic risk of the portfolio.

✓The active risk, which is also referred to as the tracking error of the portfolio.

DThe downside risk of the portfolio.

💡 Section 16.4.5 states, 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. ... It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q56 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which of the following statements is true regarding unsystematic risk?

AIt is measured by Beta.

BIt is linked to supply and demand in various marketplaces.

✓It can be diversified away.

DIt affects all investments directly or indirectly.

💡 As per section 16.3.6, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Options A, B, and D describe characteristics of systematic risk.

Q57 MCQ · 1 mark EasyBenchmarking Criteria

Which of the following is NOT listed as a criterion for a good benchmark?

AThe benchmark is investable.

BThe benchmark is consistent with the portfolio’s investment approach.

✓The benchmark's performance is always higher than the portfolio being evaluated.

DThe identity of constituents and their weights in the benchmark are clearly defined.

💡 Section 16.5.1 lists criteria for a good benchmark. Having performance always higher is not a criterion; the purpose of a benchmark is objective evaluation, not guaranteed outperformance. Options A, B, and D are all listed criteria.

Q58 MCQ · 1 mark MediumSortino Ratio

Which characteristic makes the Sortino Ratio particularly appealing to certain investors?

AIt adjusts excess return for systematic risk, ignoring unsystematic risk.

BIt focuses on total portfolio risk, making it suitable for undiversified investors.

✓It adjusts portfolio's excess return to the downside risk, appealing to investors who view risk as chances of losing money.

DIt compares the portfolio's risk-adjusted return to the market portfolio's risk-adjusted return.

💡 The text states: 'Sortino Ratio adjusts portfolio’s excess return to the downside risk. This ratio may be very appealing to some investors who view risk as chances of losing money, rather the uncertainty around expected return.'

Q59 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

✓1.00

B1.50

C0.50

D0.75

💡 The Sharpe Ratio is calculated as: Sharpe Ratio = (Rp - Rf) / Sigma_p Where: Rp = Return of the portfolio = 12.00% (or 0.12) Rf = Risk-free return = 4.00% (or 0.04) Sigma_p = Standard deviation of return on the portfolio = 8.00% (or 0.08) Sharpe Ratio = (0.12 - 0.04) / 0.08 Sharpe Ratio = 0.08 / 0.08 Sharpe Ratio = 1.00

Q60 MCQ · 1 mark MediumPortfolio Beta Calculation

An investment portfolio consists of two stocks, Stock X and Stock Y. Stock X has a Beta of 1.3 and makes up 70% of the portfolio, while Stock Y has a Beta of 0.9 and makes up 30% of the portfolio. What is the Beta of this portfolio?

✓1.18

B1.25

C1.10

D1.08

💡 The Beta of a portfolio is calculated as the weighted average beta of the individual securities in the portfolio. Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9) Portfolio Beta = 0.91 + 0.27 Portfolio Beta = 1.18

Q61 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For an investor who has not achieved adequate diversification on their wealth as a whole, which risk-adjusted return measure is more suitable to evaluate portfolio performance?

ATreynor Ratio

✓Sharpe Ratio

CSortino Ratio

DInformation Ratio

💡 As per section 16.4.3, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole...'

Q62 MCQ · 1 mark MediumCharacteristics of Benchmarks

All of the following are criteria for a good benchmark, EXCEPT:

AThe benchmark's constituents and their weights are clearly defined.

✓The benchmark is always a market-based index to ensure objectivity.

CThe benchmark is investable, allowing for passive exposure.

DThe benchmark has the same risk-return profile as the portfolio.

💡 The text lists characteristics of a good benchmark, including clearly defined constituents, investability, consistency with portfolio's investment approach, and similar risk-return profile. However, it also mentions customized benchmarks when market-based indices are not suitable, implying that a benchmark is not *always* a market-based index.

Q63 MCQ · 1 mark MediumPortfolio Beta

If Stock X has a beta of 1.3 and Stock Y has a beta of 0.9, and a portfolio consists of 70% in Stock X and 30% in Stock Y, what is the Beta of the portfolio?

A1.20

✓1.18

C1.15

D1.25

💡 The Beta of the portfolio is calculated as the weighted average beta of the individual securities. Portfolio Beta (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q64 MCQ · 1 mark HardSharpe vs. Treynor Measure

The text states that for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio. What is the reason provided for this potential difference in ranking?

ATreynor Ratio considers only downside risk, while Sharpe Ratio considers total variability.

BSharpe Ratio adjusts for systematic risk, while Treynor Ratio adjusts for total risk.

✓Treynor Ratio ignores unsystematic risk, which is significant in a poorly diversified portfolio.

DSharpe Ratio is suitable for well-diversified portfolios, whereas Treynor Ratio is not.

💡 The text explicitly states: 'However, for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio as Treynor ratio, ignores unsystematic risk.'

Q65 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2) Measure

A managed portfolio has generated a return of 30% with a standard deviation of 40%. The market portfolio generated a return of 25% with a standard deviation of 20%. The Treasury bill rate is 5%. Based on the Modigliani and Modigliani (M2) Measure, how did the managed portfolio perform relative to the market?

AIt outperformed the market by 7.5%.

✓It underperformed the market by 7.5%.

CIt outperformed the market by 2.5%.

DIt underperformed the market by 2.5%.

💡 To apply the M2 measure, we adjust the portfolio's risk to match the market's risk. 1. Calculate the proportion of the portfolio needed to match the market's standard deviation: Proportion in Portfolio (P) = Market's Std Dev / Portfolio's Std Dev = 20% / 40% = 0.5 2. Calculate the proportion in T-bills (risk-free asset): Proportion in T-bills (Rf) = 1 - Proportion in P = 1 - 0.5 = 0.5 3. Calculate the adjusted portfolio return (rp*): rp* = (Proportion in P * Portfolio Return) + (Proportion in T-bills * T-bill Rate) rp* = (0.5 * 0.30) + (0.5 * 0.05) = 0.15 + 0.025 = 0.175 or 17.5% 4. Compare rp* with the market return: Market Return = 25% Performance difference = rp* - Market Return = 17.5% - 25% = -7.5% The managed portfolio underperformed the market by 7.5%.

Q66 MCQ · 1 mark MediumBeta Calculation

A portfolio consists of Stock X with a beta of 1.3 and Stock Y with a beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the Beta of the portfolio?

✓1.18

B1.25

C1.06

D1.20

💡 The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities/investments in the portfolio. Bp = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q67 MCQ · 1 mark EasyLiquidity Risk

Which of the following best describes liquidity risk according to the text?

AThe risk that the borrower is unable to repay amounts on time.

✓The uncertainty introduced by the secondary market of an investment regarding its conversion to cash.

CRisk due to common risk factors like interest rates and exchange rates.

DThe standard deviation of the difference between portfolio and benchmark total return.

💡 The text defines liquidity risk as 'the uncertainty introduced by the secondary market of an investment' regarding the ease of converting an asset into cash at close to its economic worth. Option A describes credit risk, Option C describes systematic risk, and Option D describes tracking error.

Q68 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which of the following statements about systematic risk is correct?

AIt can be completely diversified away by investing in a variety of assets.

BIt is measured by Alpha and represents reward for bearing unsystematic risk.

CIt arises due to company-specific factors and can be hedged but not diversified.

✓It is linked to common risk factors like interest rates and exchange rates and cannot be diversified away.

💡 The text defines systematic risk as 'risk due to common risk factors, like interest rates, exchange rates, commodities prices.' It also states that 'Systematic risks cannot be diversified away, though it can be hedged.'

Q69 MCQ · 1 mark MediumTreynor Ratio Calculation

A portfolio generated an annualized return of 15.00%. The risk-free rate is 5.00%, and the portfolio's beta is 1.25. Calculate the Treynor Ratio for this portfolio.

✓0.08

B0.12

C0.10

D0.06

💡 According to section 16.4.2, the Treynor Ratio formula is: T = (Rp - Rf) / Bp Where: Rp = Portfolio return = 15.00% (0.15) Rf = Riskless return = 5.00% (0.05) Bp = Portfolio beta = 1.25 Treynor Ratio = (0.15 - 0.05) / 1.25 Treynor Ratio = 0.10 / 1.25 Treynor Ratio = 0.08

Q70 MCQ · 1 mark MediumBeta Calculation

Stock A has a beta of 1.2 and Stock B has a beta of 1.1. If a portfolio is constructed with Stock A and Stock B in the ratio of 60:40 respectively, what is the Beta of the portfolio?

A1.10

B1.14

✓1.16

D1.20

💡 The Beta of a portfolio is calculated by taking the weighted average beta of the individual securities/investments in the portfolio. Beta of portfolio = (Weight of Stock A * Beta of Stock A) + (Weight of Stock B * Beta of Stock B) Beta of portfolio = (0.60 * 1.2) + (0.40 * 1.1) Beta of portfolio = 0.72 + 0.44 Beta of portfolio = 1.16

Q71 MCQ · 1 mark MediumBeta Calculation

A portfolio consists of two stocks, Stock X and Stock Y, in the ratio of 70:30. If Stock X has a Beta of 1.3 and Stock Y has a Beta of 0.9, what is the Beta of the portfolio?

✓1.18

B1.20

C1.22

D1.16

Q72 MCQ · 1 mark MediumTreynor Ratio

A portfolio has a return of 15.00%, a beta of 1.2, and the riskless return is 5.00%. Calculate the Treynor Ratio for this portfolio.

✓0.0833

B0.125

C0.10

D0.15

💡 As per section 16.4.2, the Treynor Ratio formula is: T = (Rp - Rf) / Bp Where: Rp = portfolio return = 15.00% Rf = riskless return = 5.00% Bp = portfolio beta = 1.2 Treynor Ratio = (15.00% - 5.00%) / 1.2 Treynor Ratio = 10.00% / 1.2 Treynor Ratio = 0.10 / 1.2 = 0.0833 (approximately)

Q73 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

A0.50

✓1.00

C1.50

D2.00

💡 The Sharpe Ratio is calculated as (Rp - Rf) / Sigma p, where Rp is the return of the portfolio, Rf is the risk-free return, and Sigma p is the standard deviation of the portfolio. Sharpe Ratio = (12.00% - 4.00%) / 8.00% Sharpe Ratio = 8.00% / 8.00% Sharpe Ratio = 1.00

Q74 MCQ · 1 mark EasyInformation Ratio

What does the denominator of the Information Ratio (Stdev (p-b)) represent?

AThe total portfolio risk

BThe systematic risk of the portfolio

✓The active risk, which is also tracking error

DThe downside risk of the portfolio

💡 Section 16.4.5 states, 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns... It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q75 MCQ · 1 mark HardSharpe vs. Treynor Measure

An investor is evaluating two actively managed portfolios, Portfolio X and Portfolio Y, using both the Sharpe Ratio and the Treynor Ratio. Portfolio X is poorly diversified, while Portfolio Y is well-diversified. Which of the following statements is most accurate regarding the comparison of these two ratios for the given portfolios?

AFor Portfolio X, the Treynor Ratio will likely provide a higher ranking than the Sharpe Ratio because it considers unsystematic risk.

✓For Portfolio Y, the Sharpe Ratio and Treynor Ratio will likely give identical rankings because total risk and systematic risk are similar.

CThe Sharpe Ratio is more suitable for evaluating Portfolio Y, while the Treynor Ratio is better for Portfolio X.

DAny difference in rankings between the Sharpe Ratio and Treynor Ratio indicates an error in calculation, as they should always align.

💡 The text states: 'For a completely well-diversified portfolio, the two measures give identical ranking, because total risk and systematic risk would be the same.' Portfolio Y is well-diversified, so this statement applies. Option A is incorrect because the Treynor ratio *ignores* unsystematic risk. Option C is incorrect because Sharpe is suitable for poorly diversified portfolios (like X) and Treynor for well-diversified portfolios (like Y). Option D is incorrect as differences in rankings are due to diversification levels, not calculation errors.

Q76 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which type of risk, as described in the text, can be diversified away and is associated with Alpha return?

ASystematic risk

BLiquidity risk

✓Unsystematic risk

DCredit risk

💡 The text states: 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away. Alpha return is a reward for bearing unsystematic risk.'

Q77 MCQ · 1 mark EasyCredit Risk

According to the text, when does credit risk primarily arise?

AWhen an asset is difficult to convert into cash at close to its economic worth.

BIn situations involving common risk factors like interest rates and exchange rates.

✓In the case of debt instruments where the borrower may not repay amounts on time.

DWhen a portfolio's returns deviate significantly from its target benchmark.

💡 Section 16.3.9 defines credit risk as 'the risk that the borrower is not able to repay the amounts on time to the lender. ... Credit risk arises in case of debt instruments.'

Q78 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which statement accurately describes systematic and unsystematic risks?

ASystematic risks can be diversified away, while unsystematic risks cannot.

BSystematic risks are measured by Alpha, and unsystematic risks are measured by Beta.

✓Systematic risks are due to common risk factors and cannot be diversified away, whereas unsystematic risks are sector/company specific and can be diversified away.

DBoth systematic and unsystematic risks can be entirely hedged and diversified away.

💡 The text states: 'Systematic risk is defined as risk due to common risk factors... Systematic risks cannot be diversified away, though it can be hedged.' It also states: 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Beta measures systematic risk, and Alpha return is a reward for bearing unsystematic risk.

Q79 MCQ · 1 mark MediumSharpe Ratio

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate of return is 4%. Calculate the Sharpe Ratio for this portfolio.

✓1.00

B1.50

C0.67

D2.00

💡 The Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12% (0.12) Rf = Risk-free return = 4% (0.04) Sigma p = Standard deviation of return on the portfolio = 8% (0.08) Sharpe Ratio = (0.12 - 0.04) / 0.08 Sharpe Ratio = 0.08 / 0.08 Sharpe Ratio = 1.00

Q80 MCQ · 1 mark MediumTreynor Ratio

A fund has a portfolio return of 15%, a risk-free rate of 5%, and a portfolio beta of 1.25. Calculate the Treynor Ratio for this fund.

A0.12

✓0.08

C0.10

D0.06

💡 The Treynor Ratio formula is: T = (Rp - Rf) / Bp Where: Rp = Portfolio return = 15% (0.15) Rf = Risk-free return = 5% (0.05) Bp = Portfolio beta = 1.25 Treynor Ratio = (0.15 - 0.05) / 1.25 Treynor Ratio = 0.10 / 1.25 Treynor Ratio = 0.08

Q81 MCQ · 1 mark EasyTracking Error

According to the text, what does tracking error primarily measure?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund’s return to fluctuations in the market index.

DThe uncertainty introduced by the secondary market of an investment.

💡 The text states: 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes tracking difference.

Q82 MCQ · 1 mark EasyCredit Risk

In the context of debt instruments, what does credit risk primarily refer to?

AThe uncertainty introduced by the secondary market of an investment.

✓The risk that the borrower is not able to repay the amounts on time to the lender.

CThe sensitivity of the fund’s return to fluctuations in the market index.

DThe standard deviation of the difference between the portfolio and its target benchmark.

💡 Section 16.3.9 defines credit risk as 'the risk that the borrower is not able to repay the amounts on time to the lender.' Option A describes liquidity risk, C describes Beta, and D describes tracking error.

Q83 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what does the denominator, 'Stdev (p-b)', represent?

AThe total risk of the portfolio.

BThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is also known as tracking error.

DThe downside risk of the portfolio.

💡 Section 16.4.5 explains that 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns.' It further clarifies, 'It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q84 MCQ · 1 mark MediumSystematic and Unsystematic Risk

Which of the following statements about systematic risk is TRUE?

AIt is linked to company-specific factors and can be diversified away.

BIt is measured by Alpha and represents the reward for bearing unsystematic risk.

✓It is due to common risk factors like interest rates and exchange rates, and cannot be diversified away.

DIt is also known as liquidity risk and is the uncertainty introduced by the secondary market.

💡 Section 16.3.6 states that 'Systematic risk is defined as risk due to common risk factors, like interest rates, exchange rates, commodities prices.' and 'Systematic risks cannot be diversified away, though it can be hedged.' Options A and B describe unsystematic risk and Alpha, respectively. Option D describes liquidity risk.

Q85 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For an investor whose wealth is not adequately diversified, which risk-adjusted return measure is generally more suitable for evaluating portfolio performance?

ATreynor Ratio, because it considers systematic risk.

✓Sharpe Ratio, because it adjusts return to the total portfolio risk.

CInformation Ratio, as it measures the fund manager's skill.

DModigliani and Modigliani Ratio (M2), as it adjusts the portfolio risk to match the market.

💡 The text states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole' because 'Sharpe ratio adjusts return to the total portfolio risk.' Treynor Ratio is more appropriate for investors with well-diversified portfolios, as it focuses on systematic risk.

Q86 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what does the denominator, Stdev (p-b), primarily represent?

AThe total risk of the portfolio.

BThe systematic risk of the benchmark.

✓The residual (unsystematic) risk or active risk (tracking error) of the portfolio.

DThe risk-free rate of return.

💡 The text states, 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q87 MCQ · 1 mark MediumSortino Ratio

The Sortino Ratio adjusts a portfolio's excess return to which specific type of risk?

ASystematic risk

BTotal portfolio risk

✓Downside risk

DLiquidity risk

💡 As per section 16.4.4, 'Thus, Sortino Ratio adjusts portfolio’s excess return to the downside risk.'

Q88 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

What is the primary objective of the Modigliani and Modigliani (M2) Ratio in performance measurement?

ATo measure the portfolio's return in excess of the risk-free rate per unit of total risk.

✓To evaluate portfolio performance by adjusting its risk to match the market portfolio's risk, then comparing their returns.

CTo assess the fund manager's skill in generating active returns against the active risk taken.

DTo calculate the portfolio's return per unit of systematic risk.

💡 The text states: 'They have adjusted the risk of the portfolio to match the risk of the market portfolio. For such a risk adjusted portfolio, they calculated the return, and compared it with the market return to determine portfolio’s over or underperformance.' Option A describes the Sharpe Ratio, Option C describes the Information Ratio, and Option D describes the Treynor Ratio.

Q89 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which of the following statements accurately describes unsystematic risk according to the provided text?

AIt is measured by Beta and cannot be diversified away.

BIt is linked to supply and demand in various marketplaces and affects all investments.

✓It arises due to sector-specific/company-specific factors and can be diversified away.

DAlpha return is a reward for bearing systematic risk.

💡 Section 16.3.6 states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away. Alpha return is a reward for bearing unsystematic risk.' Options A and B describe systematic risk, and option D incorrectly links Alpha to systematic risk.

Q90 MCQ · 1 mark EasySystematic Risk

Which of the following statements accurately describes systematic risk?

AIt is risk due to company-specific factors and can be diversified away.

BIt is measured by Alpha and represents reward for bearing unsystematic risk.

✓It is risk due to common risk factors like interest rates, affects all investments, and cannot be diversified away.

DIt is the uncertainty introduced by the secondary market of an investment.

💡 The text states that 'Systematic risk is defined as risk due to common risk factors, like interest rates, exchange rates, commodities prices... All investments get affected by these common risk factors directly or indirectly. Systematic risks cannot be diversified away, though it can be hedged.' Option A describes unsystematic risk, Option B incorrectly links Alpha and unsystematic risk to systematic risk, and Option D describes liquidity risk.

Q91 MCQ · 1 mark MediumSharpe vs. Treynor Suitability

For an investor whose wealth as a whole has not achieved adequate diversification, which risk-adjusted performance measure is more suitable for evaluating a portfolio's performance?

ATreynor Ratio

BInformation Ratio

✓Sharpe Ratio

DSortino Ratio

Q92 MCQ · 1 mark MediumSharpe Ratio

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate is 4%. Calculate the Sharpe Ratio for this portfolio.

✓1.00

B0.50

C1.50

D0.75

💡 The Sharpe Ratio (S) is calculated as (Rp - Rf) / Sigma p. Rp = 12% = 0.12 Rf = 4% = 0.04 Sigma p = 8% = 0.08 Sharpe Ratio = (0.12 - 0.04) / 0.08 = 0.08 / 0.08 = 1.00

Q93 MCQ · 1 mark HardSharpe vs. Treynor Measure

What is the primary reason for any difference in rankings between portfolios when using the Sharpe Ratio versus the Treynor Ratio?

AThe Sharpe Ratio considers downside risk, while the Treynor Ratio considers total risk.

✓The Treynor Ratio ignores unsystematic risk, while the Sharpe Ratio accounts for total portfolio risk.

CThe Sharpe Ratio is used for actively managed portfolios, while the Treynor Ratio is for passive indices.

DThe Treynor Ratio uses the risk-free rate, while the Sharpe Ratio uses the benchmark return.

💡 Section 16.4.3 explains, 'The Sharpe ratio uses standard deviation of return as the measure of risk, whereas Treynor performance measure uses Beta (systematic risk). For a completely well-diversified portfolio, the two measures give identical ranking, because total risk and systematic risk would be the same. However, for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio as Treynor ratio, ignores unsystematic risk. Thus any difference in rankings based on Sharpe Ratio and Treynor ratio is due difference in portfolio diversification levels.'

Q94 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which type of risk, as described in the text, can be diversified away?

ASystematic risk

BMarket risk

✓Unsystematic risk

DInterest rate risk

💡 The text states: 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk (and its examples like market risk and interest rate risk) cannot be diversified away.

Q95 MCQ · 1 mark EasyBeta Calculation

Stock X has a beta of 1.3 and Stock Y has a beta of 0.9. If a portfolio is constructed with 70% in Stock X and 30% in Stock Y, what is the Beta of the portfolio?

✓1.18

B1.25

C1.14

D1.08

Q96 MCQ · 1 mark MediumInformation Ratio Components

In the Information Ratio formula, what does the denominator, Stdev (p-b), represent?

AThe total portfolio risk.

BThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is also its tracking error.

DThe downside risk of the portfolio.

💡 The text states: 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns... It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q97 MCQ · 1 mark MediumSharpe Ratio

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

✓1.00

B0.75

C1.50

D2.00

💡 As per section 16.4.1, the Sharpe Ratio formula is: Sharpe Ratio (S) = (Rp – Rf) / Sigma p Where: Rp = Return of the portfolio = 12.00% = 0.12 Rf = Risk-free return = 4.00% = 0.04 Sigma p = Standard deviation of return on the portfolio = 8.00% = 0.08 S = (0.12 - 0.04) / 0.08 S = 0.08 / 0.08 S = 1.00

Q98 MCQ · 1 mark MediumCredit Risk

In which type of financial instruments does credit risk primarily arise?

AEquity shares

✓Debt instruments

CReal estate

DCommodities

💡 As per section 16.3.9, 'Credit risk arises in case of debt instruments.'

Q99 MCQ · 1 mark MediumSharpe vs. Treynor Measure

According to the text, for which type of portfolio would the ranking based on the Treynor Ratio likely be higher than that on the Sharpe Ratio?

AA completely well-diversified portfolio.

✓A poorly diversified portfolio.

CA portfolio with zero systematic risk.

DA portfolio with a beta of exactly one.

💡 The text states, 'However, for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio as Treynor ratio, ignores unsystematic risk.' For a completely well-diversified portfolio, the two measures give identical rankings.

Q100 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

✓1.00

B1.25

C0.50

D0.75

💡 According to section 16.4.1, the Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12.00% (0.12) Rf = Risk-free return = 4.00% (0.04) Sigma p = Standard deviation of return on the portfolio = 8.00% (0.08) Sharpe Ratio = (0.12 - 0.04) / 0.08 Sharpe Ratio = 0.08 / 0.08 Sharpe Ratio = 1.00

Q101 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 10.50% and an annualized standard deviation of 6.50%. If the risk-free rate of return is 5.50%, what is the Sharpe ratio for this portfolio?

A0.05

✓0.7692

C1.6154

D1.9091

💡 The Sharpe Ratio formula is: (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 10.50% Rf = Risk-free return = 5.50% Sigma p = Standard deviation of return on the portfolio = 6.50% Sharpe Ratio = (10.50% - 5.50%) / 6.50% Sharpe Ratio = 5.00% / 6.50% Sharpe Ratio = 0.7692

Q102 MCQ · 1 mark EasyTracking Error

Which of the following best defines 'tracking error' in the context of portfolio performance measurement?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of the fund's return to fluctuations in the market index.

DThe risk that the borrower is not able to repay amounts on time to the lender.

💡 According to the text, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes 'tracking difference', Option C describes Beta, and Option D describes Credit risk.

Q103 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For which type of investor is the Treynor Ratio considered a more appropriate measure for evaluating portfolio performance?

AAn investor who has not achieved adequate diversification on their wealth as a whole.

BAn investor who views risk primarily as the chance of losing money (downside risk).

✓An investor whose wealth is already well diversified, with minimal unsystematic risk.

DAn investor solely interested in the total portfolio risk.

Q104 MCQ · 1 mark HardM2 Measure

A portfolio generated a return of 35% with a standard deviation of 42%. The market portfolio generated a return of 28% with a standard deviation of 30%. The Treasury bill rate is 6%. According to the M2 measure calculation provided, what is the adjusted return (rp*) of the hypothetical portfolio, and how did it perform relative to the market?

✓rp* = 26.7%, underperformed the market by 1.3%.

Brp* = 26.7%, outperformed the market by 1.3%.

Crp* = 35%, outperformed the market by 7%.

Drp* = 28%, performed identically to the market.

💡 As per section 16.4.6, the M2 measure adjusts the portfolio's risk to match the market's risk. 1. Calculate the scaling factor for the portfolio's volatility to match the market's: Market's vol / Portfolio's vol = 30% / 42% = 0.714 2. This means 0.714 of the hypothetical portfolio is invested in the original portfolio, and (1 - 0.714) = 0.286 is invested in T-bills to adjust risk. 3. Calculate the adjusted return (rp*): rp* = (Weight in Portfolio * Portfolio Return) + (Weight in T-bills * T-bill Rate) rp* = (0.714 * 0.35) + (0.286 * 0.06) rp* = 0.2499 + 0.01716 rp* = 0.26706 or 26.7% (approximately) 4. Compare rp* with market return: rp* (26.7%) is less than market return (28%). Difference = 28% - 26.7% = 1.3%. Therefore, the managed portfolio underperformed the market by 1.3%.

Q105 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

A1.50

✓1.00

C0.75

D2.00

💡 Sharpe Ratio = (Rp - Rf) / Sigma_p Given: Rp = 12.00% (0.12) Rf = 4.00% (0.04) Sigma_p = 8.00% (0.08) Sharpe Ratio = (0.12 - 0.04) / 0.08 Sharpe Ratio = 0.08 / 0.08 Sharpe Ratio = 1.00

Q106 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which of the following statements accurately describes systematic risk?

AIt is measured by Alpha and can be diversified away.

BIt is linked to company-specific factors and can be hedged but not diversified.

✓It is due to common risk factors like interest rates and cannot be diversified away, but can be hedged.

DIt represents the uncertainty introduced by the secondary market of an investment.

💡 Section 16.3.6 states, 'Systematic risk is defined as risk due to common risk factors, like interest rates, exchange rates, commodities prices.' and 'Systematic risks cannot be diversified away, though it can be hedged. Systematic risk is measured by Beta.'

Q107 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what do the numerator (Rp – Rb) and the denominator (Stdev (p-b)) primarily represent, respectively?

ASystematic risk and unsystematic risk.

✓Active return and active risk.

CTotal return and total risk.

DRisk-free return and market volatility.

💡 Section 16.4.5 states, 'The numerator is often referred to as the active return on the portfolio whereas denominator is referred to as the active risk.' It also clarifies that 'active risk is nothing but tracking error of the portfolio.'

Q108 MCQ · 1 mark HardSharpe Ratio Calculation

A portfolio has an annualized return (Rp) of 12.00% and an annualized standard deviation (Sigma p) of 8.00%. The risk-free rate of return (Rf) is 4.00%. Calculate the Sharpe Ratio for this portfolio.

A0.50

✓1.00

C1.50

D2.00

💡 The Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p Given: Rp = 12.00% = 0.12 Rf = 4.00% = 0.04 Sigma p = 8.00% = 0.08 Sharpe Ratio = (0.12 - 0.04) / 0.08 Sharpe Ratio = 0.08 / 0.08 Sharpe Ratio = 1.00

Q109 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what does the denominator 'Stdev (p-b)' represent?

AThe total risk of the portfolio.

BThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is also known as tracking error.

DThe downside risk of the portfolio.

💡 Section 16.4.5 states, 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q110 MCQ · 1 mark MediumBeta Calculation

If Stock X has a beta of 1.3 and Stock Y has a beta of 0.9, and a portfolio is constructed with 70% in Stock X and 30% in Stock Y, what is the Beta of the portfolio?

A1.25

✓1.18

C1.05

D1.20

💡 The Beta of the portfolio is calculated as the weighted average beta of the individual securities: Bp = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q111 MCQ · 1 mark EasyM2 Measure

What is the core concept behind the Modigliani and Modigliani Ratio (M2) Measure for performance evaluation?

✓To compare portfolio return to the market return after adjusting the portfolio's risk to match the market's risk.

BTo measure the portfolio's excess return per unit of total risk.

CTo assess the portfolio's return per unit of systematic risk.

DTo identify the downside risk of the portfolio using semi-standard deviation.

💡 Section 16.4.6 states, 'They have adjusted the risk of the portfolio to match the risk of the market portfolio. For such a risk adjusted portfolio, they calculated the return, and compared it with the market return to determine portfolio’s over or underperformance.'

Q112 MCQ · 1 mark EasyTracking Error

What does tracking error primarily measure?

AThe simple point-to-point difference between index return and fund return.

✓The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.

CThe sensitivity of a fund's return to fluctuations in the market index.

DThe risk that a borrower is not able to repay amounts on time to the lender.

💡 As per section 16.3.5, tracking error is defined as 'the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.'

Q113 MCQ · 1 mark EasyTracking Error

What is the primary difference between 'tracking error' and 'tracking difference' as defined in the text?

ATracking error measures deviations from the market return, while tracking difference measures deviations from the risk-free rate.

CTracking error is calculated using the market portfolio, while tracking difference is calculated against any target benchmark.

DTracking error accounts for dividends, while tracking difference does not.

💡 As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return...' and 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q114 MCQ · 1 mark MediumBenchmarking Characteristics

Which of the following is NOT a characteristic of a good benchmark for performance evaluation?

AThe benchmark is investable, allowing for passive exposure.

BThe identity of constituents and their weights in the benchmark are clearly defined.

✓The benchmark's performance data is easily accessible and always reflects only price returns.

DThe benchmark is consistent with the portfolio’s investment approach and has the same risk-return profile.

💡 A good benchmark should have measurable performance and available data. However, the text explicitly mentions, 'Increasingly the Total Return Index is a measure that is being used and if this kind of data is not available for the benchmark then it might not be able to give the correct picture.' This implies that a good benchmark should ideally reflect total returns (inclusive of dividends), not 'only price returns'. Options A, B, and D are all listed as characteristics of a good benchmark.

Q115 MCQ · 1 mark MediumPortfolio Beta Calculation

An investment portfolio consists of three stocks: Stock X, Stock Y, and Stock Z. Stock X has a beta of 1.2 and makes up 50% of the portfolio. Stock Y has a beta of 0.9 and makes up 30% of the portfolio. Stock Z has a beta of 1.1 and makes up 20% of the portfolio. What is the Beta of this portfolio?

✓1.09

B1.12

C1.15

D1.06

💡 The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities in the portfolio. Portfolio Beta (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) + (Weight of Stock Z * Beta of Stock Z) Bp = (0.50 * 1.2) + (0.30 * 0.9) + (0.20 * 1.1) Bp = 0.60 + 0.27 + 0.22 Bp = 1.09

Q116 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe Ratio for this portfolio?

✓1.0000

B0.6667

C1.5000

D2.0000

💡 The Sharpe Ratio is calculated as (Rp - Rf) / Sigma p. Rp = 12.00% Rf = 4.00% Sigma p = 8.00% Sharpe Ratio = (12.00% - 4.00%) / 8.00% = 8.00% / 8.00% = 1.0000

Q117 MCQ · 1 mark MediumTreynor Ratio Calculation

A fund has a portfolio return of 15.00%, a risk-free rate of 5.00%, and a portfolio Beta of 1.25. What is the Treynor Ratio for this fund?

A0.12

✓0.08

C0.06

D0.10

💡 The Treynor Ratio is calculated as (Rp - Rf) / Bp. Rp = 15.00% Rf = 5.00% Bp = 1.25 Treynor Ratio = (15.00% - 5.00%) / 1.25 = 10.00% / 1.25 = 0.08

Q118 MCQ · 1 mark EasySystematic Risk

How is systematic risk typically measured according to the provided text?

ABy Alpha return

BBy Standard deviation

✓By Beta

DBy Tracking error

💡 The text explicitly states, 'Systematic risk is measured by Beta.'

Q119 MCQ · 1 mark MediumTreynor Ratio

A fund generated an annualized return of 15% with a Beta of 1.2. If the risk-free rate is 6%, what is the Treynor Ratio for this fund?

✓0.075

B0.125

C0.09

D0.18

💡 As per section 16.4.2, the Treynor Ratio formula is: Treynor Ratio = (Rp - Rf) / Bp Where: Rp = Portfolio return = 15% (0.15) Rf = Risk-free return = 6% (0.06) Bp = Portfolio beta = 1.2 Treynor Ratio = (0.15 - 0.06) / 1.2 Treynor Ratio = 0.09 / 1.2 Treynor Ratio = 0.075

Q120 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which type of risk can be diversified away by combining various assets in a portfolio?

ASystematic risk

BMarket risk

✓Unsystematic risk

DInterest rate risk

💡 According to section 16.3.6, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk, market risk, and interest rate risk are all forms of systematic risk and cannot be diversified away.

Q121 MCQ · 1 mark MediumLiquidity Risk

Which of the following assets, as per the text, would typically have almost no liquidity risk?

AA rare piece of art.

BA corporate bond.

✓A Treasury bill.

DAn illiquid real estate property.

💡 Section 16.3.8 states, 'Treasury bills have almost no liquidity risk. They can be sold in a fraction of minute at a price worth their economic value.' A piece of art is given as an example of an asset with higher liquidity risk.

Q122 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

A portfolio manager uses the Modigliani and Modigliani (M2) Ratio. After adjusting the portfolio's risk to match the market, the calculated return (rp*) is 25%. If the market (benchmark) portfolio generated a return of 28%, what does this indicate about the managed portfolio's performance?

AThe managed portfolio outperformed the market by 3%.

✓The managed portfolio underperformed the market by 3%.

CThe managed portfolio performed equally to the market.

DThe M2 ratio cannot be interpreted without the risk-free rate.

💡 The M2 measure adjusts the risk of the portfolio to match the market portfolio and then compares its return (rp*) directly with the market return. Since the adjusted portfolio return (rp* = 25%) is less than the market return (28%), the managed portfolio underperformed the market by 3% (28% - 25%).

Q123 MCQ · 1 mark HardTreynor Ratio Calculation

A portfolio has an annualized return of 15%, a Beta of 1.2, and the risk-free rate is 5%. Calculate the Treynor Ratio for this portfolio.

✓0.0833

B0.10

C0.125

D0.09

💡 Treynor Ratio (T) = (Portfolio Return (Rp) - Risk-free Rate (Rf)) / Portfolio Beta (Bp) Rp = 15% = 0.15 Rf = 5% = 0.05 Bp = 1.2 T = (0.15 - 0.05) / 1.2 T = 0.10 / 1.2 T = 0.08333...

Q124 MCQ · 1 mark MediumSharpe vs. Treynor Measure

An investor whose wealth is already well diversified and primarily concerned with return per unit of systematic risk would find which performance measure most appropriate?

ASharpe Ratio

BSortino Ratio

CInformation Ratio

✓Treynor Ratio

💡 Section 16.4.3 states, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. Section 16.4.2 further clarifies that Treynor ratio is appropriate for investors 'whose wealth is already well diversified, wherein the unsystematic risk is very minimal, and hence the only risk that matters for such investors is excess return over and above the systematic risk.'

Q125 MCQ · 1 mark EasyTracking Error

What is the primary difference between 'tracking error' and 'tracking difference' as defined in portfolio performance measurement?

ATracking error is the simple point-to-point difference, while tracking difference is the standard deviation of the difference.

✓Tracking error is the standard deviation of the difference between portfolio and benchmark total return, while tracking difference is the simple point-to-point difference.

CTracking error measures systematic risk, while tracking difference measures unsystematic risk.

DTracking error is calculated using the market portfolio, while tracking difference uses any target index.

💡 As per the text, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Conversely, 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q126 MCQ · 1 mark EasyTracking Error

What is the primary difference between 'tracking error' and 'tracking difference' as defined in the context of portfolio performance?

ATracking error measures deviations from market return, while tracking difference measures deviations from risk-free return.

✓Tracking error is the standard deviation of the difference between portfolio and benchmark returns, while tracking difference is the simple point-to-point difference.

CTracking error is calculated inclusive of dividends, while tracking difference excludes dividends.

DTracking error applies to actively managed funds, while tracking difference applies to passively managed funds.

Q127 MCQ · 1 mark EasySharpe vs. Treynor Ratio

For an investor who has not achieved adequate diversification on their wealth as a whole, which risk-adjusted return measure is most suitable?

ATreynor Ratio

BSortino Ratio

✓Sharpe Ratio

DInformation Ratio

Q128 MCQ · 1 mark EasyBeta Calculation

Stock A has a beta of 1.2 and Stock B has a beta of 1.1. If a portfolio is constructed with Stock A and Stock B in the ratio of 60:40 respectively, what is the Beta of the portfolio?

A1.10

B1.14

✓1.16

D1.20

💡 As per section 16.3.7, the Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. Bp = (Weight of Stock A * Beta of Stock A) + (Weight of Stock B * Beta of Stock B) Bp = (0.60 * 1.2) + (0.40 * 1.1) Bp = 0.72 + 0.44 Bp = 1.16

Q129 MCQ · 1 mark MediumSharpe vs Treynor Measure

For which type of investor is the Sharpe Ratio more suitable for evaluating portfolio performance, as per the text?

AAn investor whose wealth is already well diversified.

BAn investor who wishes to evaluate a portfolio in combination with other actively managed portfolios.

✓An investor who has not achieved adequate diversification on his wealth as a whole.

DAn investor for whom only systematic risk matters due to minimal unsystematic risk.

Q130 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For an investor whose wealth is not adequately diversified, which risk-adjusted return measure is more suitable for evaluating portfolio performance according to the text?

ATreynor Ratio

BSortino Ratio

✓Sharpe Ratio

DInformation Ratio

💡 The text states, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole.'

Q131 MCQ · 1 mark MediumBenchmarking

Which of the following is NOT listed as a characteristic of a good benchmark in the provided text?

AThe benchmark is investable.

BThe benchmark's constituents and their weights are clearly defined.

✓The benchmark is always a market-based index.

DThe benchmark is consistent with the portfolio’s investment approach.

💡 The text lists characteristics such as investability, clearly defined constituents, consistency with investment approach, same risk-return profile, and measurable performance. It does not state that a good benchmark is *always* a market-based index; in fact, the text discusses customized benchmarks when market-based indices may not be suitable.

Q132 MCQ · 1 mark EasyLiquidity Risk

Which risk is defined as the ease of converting an asset into cash at close to its economic worth?

ACredit risk

BSystematic risk

✓Liquidity risk

DUnsystematic risk

💡 Section 16.3.8 defines liquidity as 'ease of converting an asset into cash at close to its economic worth.' Therefore, liquidity risk is the uncertainty associated with this conversion.

Q133 MCQ · 1 mark MediumBenchmark Characteristics

All of the following are stated characteristics of a good benchmark, according to the text, EXCEPT:

AThe benchmark is investable.

BThe benchmark is consistent with the portfolio’s investment approach.

✓The benchmark is composed solely of liquid assets.

DThe performance of the benchmark is measurable.

💡 The text lists several criteria for a good benchmark, including being investable, consistent with the portfolio's investment approach, and having measurable performance. While investability implies a degree of liquidity, the text does not state that a good benchmark must be *solely* composed of liquid assets.

Q134 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 10.50% and an annualized standard deviation of 6.50%. If the risk-free rate of return is 5.50%, what is the Sharpe Ratio for this portfolio?

✓0.7692

B0.05

C0.714

D1.615

💡 As per section 16.4.1, the Sharpe Ratio formula is S = (Rp - Rf) / Sigma_p. Rp = 10.50% Rf = 5.50% Sigma_p = 6.50% Sharpe Ratio = (10.50% - 5.50%) / 6.50% = 5.00% / 6.50% = 0.7692.

Q135 MCQ · 1 mark HardSharpe Ratio Calculation

A portfolio has an annualized return of 18%, a standard deviation of 12%, and the risk-free rate is 6%. Calculate the Sharpe Ratio for this portfolio.

A1.50

✓1.00

C1.25

D0.75

💡 Sharpe Ratio (S) = (Portfolio Return (Rp) - Risk-free Rate (Rf)) / Portfolio Standard Deviation (Sigma p) Rp = 18% = 0.18 Rf = 6% = 0.06 Sigma p = 12% = 0.12 S = (0.18 - 0.06) / 0.12 S = 0.12 / 0.12 S = 1.00

Q136 MCQ · 1 mark EasyLiquidity Risk

According to the text, which of the following assets has almost no liquidity risk?

AA piece of art

BDebt instruments

✓Treasury bills

DBlue-chip stocks

💡 The text states: 'Treasury bills have almost no liquidity risk. They can be sold in a fraction of minute at a price worth their economic value.'

Q137 MCQ · 1 mark EasyTracking Error vs. Tracking Difference

What is the fundamental distinction between 'tracking error' and 'tracking difference' as defined in portfolio performance measurement?

ATracking error is a simple point-to-point difference, while tracking difference is the standard deviation of the difference.

BTracking error measures deviations from the market return, whereas tracking difference measures deviations from the risk-free rate.

✓Tracking error is the standard deviation of the difference between portfolio and benchmark total return, while tracking difference is the simple point-to-point difference.

DTracking error arises due to mismatches in risk profiles, while tracking difference arises from market volatility.

💡 The text defines 'tracking error' as 'the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' It defines 'tracking difference' as 'layman’s approach - just the simple point-to-point difference between index return and fund return.'

Q138 MCQ · 1 mark MediumSystematic and Unsystematic Risk

Which of the following statements about systematic and unsystematic risk is INCORRECT?

✓Systematic risk can be diversified away.

BUnsystematic risks are due to sector-specific or company-specific factors.

CSystematic risk is measured by Beta.

DAlpha return is a reward for bearing unsystematic risk.

💡 Section 16.3.6 states, 'Systematic risks cannot be diversified away, though it can be hedged.' Options B, C, and D are all correct statements from the text.

Q139 MCQ · 1 mark HardSharpe Ratio

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 4.00%, what is the Sharpe ratio for this portfolio?

A1.50

✓1.00

C0.50

D0.75

💡 As per section 16.4.1, the Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p Where: Rp = Return of the portfolio = 12.00% Rf = Risk-free return = 4.00% Sigma p = Standard deviation of return on the portfolio = 8.00% Sharpe Ratio = (12.00% - 4.00%) / 8.00% Sharpe Ratio = 8.00% / 8.00% Sharpe Ratio = 1.00

Q140 MCQ · 1 mark MediumBeta Calculation

A portfolio consists of two stocks: Stock X with a beta of 1.3, making up 70% of the portfolio, and Stock Y with a beta of 0.9, making up 30% of the portfolio. What is the Beta of this portfolio?

✓1.18

B1.10

C1.25

D1.00

💡 As per section 16.3.7, the Beta of a portfolio is calculated by taking the weighted average beta of the individual securities. Beta of Portfolio (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q141 MCQ · 1 mark HardInformation Ratio

In the Information Ratio formula, IR = (Rp – Rb) / Stdev (p-b), what does the denominator, Stdev (p-b), represent?

AThe total risk of the portfolio.

BThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is also tracking error.

DThe downside risk of the portfolio.

Q142 MCQ · 1 mark MediumInformation Ratio

In the Information Ratio formula, what does the denominator, Stdev (p-b), primarily represent?

AThe total risk of the portfolio.

BThe systematic risk of the portfolio.

✓The active risk of the portfolio, which is tracking error.

DThe downside risk of the portfolio.

💡 Section 16.4.5 states, 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. It has to be noted that active risk is nothing but tracking error of the portfolio.'

Q143 MCQ · 1 mark MediumLiquidity Risk

Which of the following assets is explicitly stated in the text as having almost no liquidity risk?

AA piece of art

BCorporate bonds

CEquity shares

✓Treasury bills

💡 The text states, 'Treasury bills have almost no liquidity risk. They can be sold in a fraction of minute at a price worth their economic value.'

Q144 MCQ · 1 mark MediumBeta Calculation

Stock X has a beta of 1.3 and Stock Y has a beta of 0.9. If a portfolio is constructed with 70% in Stock X and 30% in Stock Y, what is the Beta of the portfolio?

A1.05

✓1.18

C1.14

D1.25

💡 As per section 16.3.7, Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. Portfolio Beta (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y) Bp = (0.70 * 1.3) + (0.30 * 0.9) Bp = 0.91 + 0.27 Bp = 1.18

Q145 MCQ · 1 mark MediumSharpe Ratio Calculation

A portfolio has an annualized return of 12.00% and an annualized standard deviation of 8.00%. If the risk-free rate of return is 5.00%, what is the Sharpe ratio for this portfolio?

✓0.875

B1.500

C0.625

D1.250

💡 The Sharpe Ratio is calculated as: Sharpe Ratio = (Rp - Rf) / Sigma_p Where: Rp = Return of the portfolio = 12.00% Rf = Risk-free return = 5.00% Sigma_p = Standard deviation of return on the portfolio = 8.00% Sharpe Ratio = (12.00% - 5.00%) / 8.00% = 7.00% / 8.00% = 0.875

Q146 MCQ · 1 mark MediumSharpe vs. Treynor Measure

For which type of investor is the Sharpe Ratio more suitable to evaluate portfolio performance, and why?

AAn investor with a well-diversified portfolio, because it focuses on systematic risk.

✓An investor who has not achieved adequate diversification, because it adjusts return to total portfolio risk.

CAn investor primarily concerned with downside risk, because it uses semi-standard deviation.

DAn investor whose wealth is already well diversified, because unsystematic risk is minimal.

💡 Section 16.4.3 states, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. The Sharpe ratio adjusts return to total portfolio risk (standard deviation), which is relevant for poorly diversified portfolios.

Q147 MCQ · 1 mark EasySystematic and Unsystematic Risk

Which type of risk is measured by Beta and cannot be diversified away, though it can be hedged?

ALiquidity risk

BUnsystematic risk

CCredit risk

✓Systematic risk

💡 Section 16.3.6 states, 'Systematic risks cannot be diversified away, though it can be hedged. Systematic risk is measured by Beta.'

Q148 MCQ · 1 mark HardSharpe vs. Treynor Comparison

For a poorly diversified portfolio, why might the ranking based on the Treynor Ratio be higher than that based on the Sharpe Ratio?

AThe Treynor Ratio uses the total risk (standard deviation) which is higher for poorly diversified portfolios.

BThe Sharpe Ratio ignores diversification potential, while the Treynor Ratio accounts for it by using beta.

✓The Treynor Ratio only considers systematic risk, ignoring the higher unsystematic risk present in a poorly diversified portfolio, thus potentially giving a more favorable (higher) ratio.

DThe Sharpe Ratio is more suitable for investors with well-diversified portfolios, making its ranking lower for poorly diversified ones.

💡 The text states: 'However, for a poorly diversified portfolio, the ranking based on Treynor Ratio could be higher than that on Sharpe ratio as Treynor ratio, ignores unsystematic risk. Thus any difference in rankings based on Sharpe Ratio and Treynor ratio is due difference in portfolio diversification levels.' The Sharpe ratio uses total risk (standard deviation), which includes both systematic and unsystematic risk, while Treynor uses only systematic risk (Beta). For a poorly diversified portfolio, unsystematic risk is significant, making its total risk higher. By ignoring this higher unsystematic risk, the Treynor ratio can appear more favorable.

Q149 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

A portfolio generated a return of 30% with a standard deviation of 40%. The market portfolio had a return of 20% and a standard deviation of 25%. The treasury bill rate is 5%. Using the Modigliani and Modigliani (M2) measure, how did the managed portfolio perform compared to the market?

✓Outperformed the market by 0.625%

BUnderperformed the market by 0.625%

COutperformed the market by 1.25%

DUnderperformed the market by 1.25%

💡 As per section 16.4.6, the M2 measure involves adjusting the portfolio's risk to match the market's risk and then comparing returns. 1. Calculate the proportion of the portfolio needed to match market volatility: Proportion in Portfolio (P) = Market Std Dev / Portfolio Std Dev = 25% / 40% = 0.625 or 5/8 2. Calculate the proportion to be invested in Treasury bills: Proportion in T-bills (Rf) = 1 - Proportion in P = 1 - 0.625 = 0.375 or 3/8 3. Calculate the adjusted portfolio return (rp*): rp* = (Proportion in P * Portfolio Return) + (Proportion in T-bills * Risk-free Rate) rp* = (0.625 * 0.30) + (0.375 * 0.05) rp* = 0.1875 + 0.01875 rp* = 0.20625 = 20.625% 4. Compare rp* with the Market Return: Market Return = 20% Difference = rp* - Market Return = 20.625% - 20% = 0.625% Since the adjusted portfolio return (20.625%) is higher than the market return (20%), the managed portfolio outperformed the market by 0.625%.

Q150 MCQ · 1 mark HardModigliani and Modigliani Ratio (M2)

A portfolio generated a return of 35% with a standard deviation of 42%. The market portfolio had a return of 28% and a standard deviation of 30%. The treasury bill rate is 6%. Using the M2 measure, what is the conclusion about the managed portfolio's performance?

AThe portfolio outperformed the market by 1.3%.

✓The portfolio underperformed the market by 1.3%.

CThe portfolio performed exactly as the market, with no over or underperformance.

DThe portfolio outperformed the market by 7%.

💡 The M2 measure adjusts the risk of the portfolio to match the market portfolio and then compares returns. 1. Determine the proportion of the portfolio to hold to match market volatility: Proportion in portfolio (P) = Market's standard deviation / Portfolio's standard deviation = 30% / 42% = 0.714 2. The remaining proportion is invested in T-bills: (1 - 0.714) = 0.286 3. Calculate the risk-adjusted portfolio return (rp*): rp* = (Proportion in P * Return of P) + (Proportion in T-bills * T-bill rate) rp* = (0.714 * 0.35) + (0.286 * 0.06) rp* = 0.2499 + 0.01716 = 0.26706 or 26.71% 4. Compare rp* with the market return: Adjusted portfolio return (rp*) = 26.71% Market return = 28% Since 26.71% < 28%, the managed portfolio underperformed the market. The underperformance is 28% - 26.71% = 1.29%, approximately 1.3%.

Case-Based Questions (5 sets)

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

Mr. and Mrs. Sharma, aged 48 and 46 respectively, have been actively investing for the past five years. They recently decided to review the performance of their diversified portfolio, which is managed by 'WealthGrow Advisers'. Their portfolio, valued at ₹2.5 Crores, primarily consists of a mix of large-cap equity funds, mid-cap equity funds, and corporate bond funds. For the last financial year (FY23-24), their overall portfolio generated an annualized return (Rp) of 14.50%. The blended benchmark chosen by WealthGrow Advisers for their portfolio delivered an annualized return (Rb) of 13.00%. The annualized standard deviation of the Sharma's portfolio (Sigma p) was 18%, while the benchmark's standard deviation (Sigma b) was 15%. The prevailing risk-free rate (Rf), represented by 91-day T-Bills, was 6.00%. The overall portfolio's beta (Bp) against its blended benchmark was calculated to be 1.15. Mr. Sharma is particularly interested in understanding the risk-adjusted returns and how well the portfolio manager has managed systematic and unsystematic risks. Mrs. Sharma, on the other hand, is concerned about the consistency of returns compared to the benchmark and the potential for downside risk. They are also considering adding a new equity fund to their existing equity portfolio, which has a beta of 1.35 and would constitute 20% of the new combined equity portfolio. Their current equity portfolio (before this proposed addition) has a beta of 1.10.

Medium Sub-question 1

Calculate the Sharpe Ratio for Mr. and Mrs. Sharma's portfolio for the last financial year.

A0.7692

✓0.4722

C0.0739

D0.6500

💡 The Sharpe Ratio is calculated as (Rp - Rf) / Sigma p. Rp (Portfolio Return) = 14.50% = 0.145 Rf (Risk-free return) = 6.00% = 0.06 Sigma p (Portfolio Standard Deviation) = 18% = 0.18 Sharpe Ratio = (0.145 - 0.06) / 0.18 = 0.085 / 0.18 = 0.4722

Medium Sub-question 2

Calculate the Treynor Ratio for Mr. and Mrs. Sharma's portfolio for the last financial year.

A0.0500

B0.1261

✓0.0739

D0.0850

💡 The Treynor Ratio is calculated as (Rp - Rf) / Bp. Rp (Portfolio Return) = 14.50% = 0.145 Rf (Risk-free return) = 6.00% = 0.06 Bp (Portfolio Beta) = 1.15 Treynor Ratio = (0.145 - 0.06) / 1.15 = 0.085 / 1.15 = 0.0739

Easy Sub-question 3

Considering Mr. and Mrs. Sharma's 'diversified portfolio', which risk-adjusted performance measure, Sharpe Ratio or Treynor Ratio, would be more appropriate for evaluating their portfolio manager's performance, and why?

ASharpe Ratio, because it considers total risk, which is always relevant for any investor.

✓Treynor Ratio, because it focuses on systematic risk, assuming unsystematic risk is largely diversified away in a well-diversified portfolio.

CSharpe Ratio, because it is easier to calculate and more widely used.

DTreynor Ratio, because it ignores diversification potential, making it suitable for diversified portfolios.

💡 The chapter text states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios.' Since Mr. and Mrs. Sharma's portfolio is described as 'diversified', the Treynor Ratio is more appropriate as it measures return per unit of systematic risk, assuming unsystematic risk has been diversified away.

Hard Sub-question 4

If Mr. and Mrs. Sharma proceed with adding the new equity fund, which has a beta of 1.35 and will constitute 20% of their new combined equity portfolio, what would be the new beta of their equity portfolio? Their current equity portfolio (before this proposed addition) has a beta of 1.10.

✓1.15

B1.22

C1.10

D1.25

💡 The new beta of the equity portfolio will be a weighted average of the existing equity portfolio's beta and the new fund's beta. Weight of existing equity portfolio = 100% - 20% = 80% = 0.80 Weight of new fund = 20% = 0.20 Beta of existing equity portfolio = 1.10 Beta of new fund = 1.35 New Equity Portfolio Beta = (0.80 * 1.10) + (0.20 * 1.35) = 0.88 + 0.27 = 1.15

Easy Sub-question 5

What does the concept of 'tracking error' primarily measure in the context of Mr. and Mrs. Sharma's portfolio performance against its benchmark?

AThe simple point-to-point difference between the portfolio return and the benchmark return.

✓The standard deviation of the difference between the portfolio's total return and its target benchmark's total return.

CThe risk that the portfolio manager fails to generate positive alpha.

DThe sensitivity of the portfolio's return to fluctuations in the market index.

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

Mr. and Mrs. Sharma, aged 55 and 52 respectively, are reviewing their investment portfolio with their financial adviser. Their current portfolio, valued at ₹2.5 Crores, is primarily invested in a diversified equity fund managed by "Growth Maximizers" and some debt instruments. They are moderately aggressive investors with a long-term horizon, aiming for capital appreciation while managing risk effectively. Over the past year, their portfolio generated an annualized return (Rp) of 14.50%. The benchmark index (Nifty 50 Total Return Index) delivered an annualized return (Rb) of 12.00% during the same period. The prevailing risk-free rate (Rf), represented by government treasury bills, was 6.00% per annum. The "Growth Maximizers" fund has an annualized standard deviation (σp) of 18.00%, while the Nifty 50 TR Index has an annualized standard deviation (σb) of 15.00%. The portfolio's beta (βp) against the Nifty 50 TR Index is 1.25. The standard deviation of the difference between the portfolio and benchmark returns (tracking error) over the year was 3.00%. Mr. Sharma is keen to understand how their portfolio has performed on a risk-adjusted basis and whether their fund manager has added value compared to the benchmark. Mrs. Sharma is particularly concerned about downside risk and wants to ensure the portfolio is well-diversified, understanding how different risk measures reflect this.

Hard Sub-question 1

Calculate the Modigliani and Modigliani (M2) measure for the 'Growth Maximizers' fund and determine if it outperformed or underperformed the market.

✓M2 = 13.08%; The fund outperformed the market by 1.08%.

BM2 = 12.00%; The fund performed exactly as the market.

CM2 = 14.50%; The fund significantly outperformed the market by 2.50%.

DM2 = 11.50%; The fund underperformed the market by 0.50%.

💡 The M2 measure adjusts the portfolio's risk to match the market's risk (standard deviation) and then compares its return to the market return. 1. **Determine the weight (w) in the portfolio to match market risk:** To equalize the standard deviations, the proportion of the portfolio (P) to be combined with the risk-free asset (T-bills) is calculated as (Market Standard Deviation / Portfolio Standard Deviation). Weight in Portfolio (w) = σb / σp = 15.00% / 18.00% = 0.8333 2. **Determine the weight in T-bills:** Weight in T-bills (1 - w) = 1 - 0.8333 = 0.1667 3. **Calculate the adjusted portfolio return (rp*):** rp* = (w * Rp) + ((1 - w) * Rf) rp* = (0.8333 * 14.50%) + (0.1667 * 6.00%) rp* = (0.8333 * 0.145) + (0.1667 * 0.06) rp* = 0.1208285 + 0.010002 rp* = 0.1308305 ≈ 13.08% 4. **Compare rp* with the market return (Rb):** Adjusted Portfolio Return (rp*) = 13.08% Market Return (Rb) = 12.00% Since rp* (13.08%) is greater than Rb (12.00%), the managed portfolio outperformed the market by 13.08% - 12.00% = 1.08%.

Easy Sub-question 2

Calculate the Sharpe Ratio for Mr. and Mrs. Sharma's portfolio.

✓0.4722

B0.3889

C0.7692

D0.5833

💡 The Sharpe Ratio is calculated as (Return of the portfolio - Risk-free return) / Standard deviation of return on the portfolio. Given: Rp = 14.50% Rf = 6.00% σp = 18.00% Sharpe Ratio = (14.50% - 6.00%) / 18.00% = 8.50% / 18.00% = 0.4722

Easy Sub-question 3

Calculate the Treynor Ratio for Mr. and Mrs. Sharma's portfolio.

A0.050

✓0.068

C0.116

D0.085

💡 The Treynor Ratio is calculated as (Return of the portfolio - Risk-free return) / Portfolio Beta. Given: Rp = 14.50% Rf = 6.00% βp = 1.25 Treynor Ratio = (14.50% - 6.00%) / 1.25 = 8.50% / 1.25 = 0.068

Medium Sub-question 4

Based on the calculated Sharpe and Treynor Ratios, what can be inferred about the diversification level of Mr. and Mrs. Sharma's portfolio?

AThe portfolio is perfectly diversified, as both ratios use total risk.

BThe portfolio is poorly diversified because its beta is greater than 1.

✓The portfolio is not perfectly diversified, as unsystematic risk is still contributing to total risk, making the Sharpe Ratio more appropriate for them.

DThe portfolio is well-diversified, and the Treynor Ratio is the most suitable measure for its evaluation.

💡 The Sharpe Ratio uses total risk (standard deviation), while the Treynor Ratio uses only systematic risk (Beta). The chapter text states that for a completely well-diversified portfolio, total risk and systematic risk would be the same, and the two measures would give identical rankings. Any difference in rankings or the need to consider total risk over systematic risk indicates the presence of unsystematic risk. Since Mr. and Mrs. Sharma's portfolio has a standard deviation (18.00%) that includes both systematic and unsystematic components, and the Sharpe Ratio (which accounts for total risk) is being considered, it implies that the portfolio is not perfectly diversified and unsystematic risk is still a factor. The text also notes that the Sharpe Ratio is more suitable for investors who have not achieved adequate diversification.

Medium Sub-question 5

Calculate the Information Ratio for the 'Growth Maximizers' fund and explain what it signifies for Mr. and Mrs. Sharma.

✓0.8333; It measures the fund manager's ability to generate active return per unit of active risk.

B0.4167; It indicates the fund's excess return over the risk-free rate.

C1.0000; It shows the portfolio's total risk relative to the benchmark's total risk.

D0.6667; It represents the systematic risk contribution to the portfolio's return.

💡 The Information Ratio (IR) is calculated as (Return on the Portfolio - Return on the benchmark) / Standard deviation of the differences between the return of the portfolio and return of the benchmark (tracking error). Given: Rp = 14.50% Rb = 12.00% Stdev(p-b) (Tracking Error) = 3.00% IR = (14.50% - 12.00%) / 3.00% = 2.50% / 3.00% = 0.8333 The Information Ratio signifies the fund manager’s ability to use their skill and information to generate a portfolio return that differs from the benchmark (active return) per unit of active risk (tracking error). A higher Information Ratio indicates superior skill in generating excess returns relative to the benchmark.

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

Mr. Rajesh Sharma, a 45-year-old software engineer, has entrusted his investment adviser with managing his portfolio of ₹50 lakhs, aiming for long-term wealth creation. Over the past year, his portfolio generated an annualized return (Rp) of 15% with an annualized standard deviation (σp) of 18%. The portfolio's beta (βp), reflecting its sensitivity to market movements, was calculated to be 1.2. For performance evaluation, Mr. Sharma's adviser uses a broad market index as a benchmark (Rb). This benchmark delivered an annualized return of 12% with an annualized standard deviation (σb) of 15% over the same period. The prevailing risk-free rate (Rf), represented by Treasury bills, was 6% annually. The standard deviation of the difference between Mr. Sharma's portfolio returns and the benchmark returns (tracking error) was 4%. Mr. Sharma is keen to understand how his portfolio has performed on a risk-adjusted basis and whether his adviser is adding value. He is also concerned about the level of diversification of his overall wealth, as this managed portfolio represents a significant portion of his investments, and he holds limited other diversified assets.

Easy Sub-question 1

What is the Sharpe Ratio for Mr. Sharma's portfolio?

A0.75

✓0.50

C0.67

D0.83

💡 The Sharpe Ratio is calculated as (Portfolio Return - Risk-free Rate) / Portfolio Standard Deviation. Sharpe Ratio = (Rp - Rf) / σp Rp = 15% or 0.15 Rf = 6% or 0.06 σp = 18% or 0.18 Sharpe Ratio = (0.15 - 0.06) / 0.18 = 0.09 / 0.18 = 0.50

Medium Sub-question 2

What is the Information Ratio for Mr. Sharma's portfolio?

A0.60

✓0.75

C0.80

D0.50

💡 The Information Ratio (IR) is calculated as (Portfolio Return - Benchmark Return) / Tracking Error. IR = (Rp - Rb) / Stdev(p-b) Rp = 15% or 0.15 Rb = 12% or 0.12 Stdev(p-b) (tracking error) = 4% or 0.04 IR = (0.15 - 0.12) / 0.04 = 0.03 / 0.04 = 0.75

Hard Sub-question 3

Using the Modigliani and Modigliani (M2) Measure, what is the M2 adjusted return (rp*) for Mr. Sharma's portfolio, and how does it compare to the benchmark return?

Arp* = 13.50%; The portfolio underperformed the benchmark by 1.50%.

Brp* = 14.25%; The portfolio outperformed the benchmark by 2.25%.

✓rp* = 13.50%; The portfolio outperformed the benchmark by 1.50%.

Drp* = 12.00%; The portfolio matched the benchmark performance.

💡 The M2 Measure adjusts the portfolio's risk to match the market's standard deviation and then compares its return to the market. 1. Calculate the proportion to invest in the portfolio (P) to match market volatility: Proportion in P = σb / σp = 15% / 18% = 0.8333 2. Calculate the proportion to invest in the risk-free asset (T-bills): Proportion in T-bills = 1 - Proportion in P = 1 - 0.8333 = 0.1667 3. Calculate the M2 adjusted return (rp*): rp* = (Proportion in P * Rp) + (Proportion in T-bills * Rf) rp* = (0.8333 * 0.15) + (0.1667 * 0.06) rp* = 0.124995 + 0.010002 = 0.134997 ≈ 13.50% 4. Compare rp* with the benchmark return (Rb): rp* = 13.50% Rb = 12% Since 13.50% > 12%, the portfolio outperformed the benchmark by 1.50% (13.50% - 12%).

Easy Sub-question 4

Calculate the Treynor Ratio for Mr. Sharma's portfolio.

✓0.075

B0.125

C0.090

D0.150

💡 The Treynor Ratio is calculated as (Portfolio Return - Risk-free Rate) / Portfolio Beta. Treynor Ratio = (Rp - Rf) / βp Rp = 15% or 0.15 Rf = 6% or 0.06 βp = 1.2 Treynor Ratio = (0.15 - 0.06) / 1.2 = 0.09 / 1.2 = 0.075

Medium Sub-question 5

Considering Mr. Sharma's concern about his overall wealth not being fully diversified, which risk-adjusted performance measure would be more appropriate for evaluating his portfolio, and why?

ATreynor Ratio, because it focuses on systematic risk, which is the only relevant risk for active management.

✓Sharpe Ratio, because it considers total risk, which is important for a poorly diversified investor.

CInformation Ratio, as it measures the manager's ability to generate excess returns relative to the benchmark.

DModigliani and Modigliani (M2) Ratio, as it directly compares the portfolio's risk-adjusted return to the market.

💡 The chapter states that the Sharpe Ratio is more suitable for evaluating a portfolio's performance for an investor who has not achieved adequate diversification on their wealth as a whole. This is because the Sharpe Ratio adjusts return to total portfolio risk (both systematic and unsystematic risk), which is relevant when the investor's overall wealth is not well-diversified. The Treynor Ratio, on the other hand, is more appropriate for well-diversified investors as it only considers systematic risk.

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

Mr. Raj Sharma, aged 48, and his wife, Priya, aged 46, have been diligently saving for their retirement. They have two investment portfolios, "Growth Portfolio" (managed by Advisor G) and "Conservative Portfolio" (managed by Advisor C), each with an initial investment of ₹50 lakhs. They are evaluating the performance of these portfolios over the last year. For the past year (ending March 31, 2024), the following data is available: * **Growth Portfolio (GP):** * Annualized Return (Rp_GP): 18.0% * Annualized Standard Deviation (Sigma_GP): 16.0% * Beta (Bp_GP): 1.3 * **Conservative Portfolio (CP):** * Annualized Return (Rp_CP): 12.0% * Annualized Standard Deviation (Sigma_CP): 8.0% * Beta (Bp_CP): 0.7 * **Market Portfolio (M) / Benchmark Index:** * Annualized Return (Rm): 14.0% * Annualized Standard Deviation (Sigma_M): 12.0% * **Risk-Free Rate (Rf):** 6.0% Mr. Sharma is considering consolidating their investments into a single, well-diversified portfolio under one advisor, or maintaining separate portfolios based on performance evaluation.

Medium Sub-question 1

If Mr. Sharma's overall wealth is already well-diversified through other assets, which risk-adjusted measure would be more appropriate for evaluating the Conservative Portfolio, and why?

ASharpe Ratio, because it considers total risk which is relevant for well-diversified portfolios.

✓Treynor Ratio, because it focuses on systematic risk, which is the primary concern for well-diversified investors.

CSortino Ratio, because it only considers downside risk.

DInformation Ratio, because it measures active management skill.

💡 The chapter text states: "The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios." For a well-diversified investor, unsystematic risk is largely diversified away, making systematic risk (measured by Beta) the most relevant risk factor. Therefore, the Treynor Ratio, which adjusts for systematic risk, is more appropriate.

Easy Sub-question 2

Calculate the Sharpe Ratio for the Growth Portfolio.

✓0.75

B1.125

C1.33

D0.875

💡 Sharpe Ratio = (Rp - Rf) / Sigma p For Growth Portfolio: Rp_GP = 18.0% (0.18) Rf = 6.0% (0.06) Sigma_GP = 16.0% (0.16) Sharpe Ratio = (0.18 - 0.06) / 0.16 = 0.12 / 0.16 = 0.75 The Growth Portfolio generated 0.75 percentage points of return above the risk-free rate for each percentage point of total risk (standard deviation).

Medium Sub-question 3

Calculate the Treynor Ratio for the Conservative Portfolio.

A0.1714

✓0.0857

C0.12

D0.05

💡 Treynor Ratio = (Rp - Rf) / Bp For Conservative Portfolio: Rp_CP = 12.0% (0.12) Rf = 6.0% (0.06) Bp_CP = 0.7 Treynor Ratio = (0.12 - 0.06) / 0.7 = 0.06 / 0.7 ≈ 0.0857 The Conservative Portfolio generated 0.0857 percentage points of excess return for every unit of systematic risk.

Hard Sub-question 4

Using the Modigliani and Modigliani (M2) measure, evaluate the performance of the Growth Portfolio against the Market Portfolio. Did it outperform or underperform, and by how much?

✓Outperformed by 1.0%

BUnderperformed by 1.0%

COutperformed by 2.0%

DUnderperformed by 2.0%

💡 The M2 measure adjusts the portfolio's risk to match the market's risk and then compares the adjusted return with the market return. 1. **Equalize Standard Deviations:** We need to find the proportion of the Growth Portfolio (GP) to hold, and the rest in the risk-free asset, to match the market's standard deviation. Scale factor (w) = Sigma_M / Sigma_GP = 12.0% / 16.0% = 0.75 This means 75% of the adjusted portfolio is in GP, and (1 - 0.75) = 25% is in the risk-free asset (T-bills). 2. **Calculate Adjusted Portfolio Return (rp*):** rp* = (Weight in GP * Rp_GP) + (Weight in T-bills * Rf) rp* = (0.75 * 0.18) + (0.25 * 0.06) rp* = 0.135 + 0.015 = 0.15 = 15.0% 3. **Compare Adjusted Return with Market Return:** Adjusted Growth Portfolio Return (rp*) = 15.0% Market Portfolio Return (Rm) = 14.0% Since rp* (15.0%) > Rm (14.0%), the Growth Portfolio outperformed the market. Outperformance = rp* - Rm = 15.0% - 14.0% = 1.0%

Easy Sub-question 5

What does a Beta of 1.3 for the Growth Portfolio signify?

AThe Growth Portfolio is less volatile than the market index.

✓The Growth Portfolio is more volatile than the market index.

CThe Growth Portfolio's returns are exactly in line with the market index.

DThe Growth Portfolio has higher unsystematic risk.

💡 As per the chapter text, a beta greater than one means that the portfolio or stock is more volatile than the benchmark index. A Beta of 1.3 for the Growth Portfolio indicates that it is 30% more volatile than the market index.

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

Mr. Anand Sharma, a 45-year-old software engineer, has been investing diligently for the past 15 years. He currently holds a diversified equity-oriented portfolio managed by an investment adviser, with a total value of ₹2.5 Crores. For the last financial year, his portfolio generated an annualized return of 14.0%. He is keen to understand how his portfolio has performed, especially considering the associated risks, and wants to compare it against relevant benchmarks. During the same period, the broad market index, which serves as a common benchmark for equity portfolios, delivered an annualized return of 12.0%. The risk-free rate, typically represented by Treasury Bills, stood at 6.0% annually. Mr. Sharma's investment adviser provided him with further statistics: his portfolio's annualized standard deviation was 18.0%, and its beta was calculated to be 1.15. The market index's standard deviation was 15.0%. The standard deviation of the difference between his portfolio's return and the benchmark's return (tracking error) was 4.5%. Mr. Sharma considers his wealth adequately diversified through various asset classes beyond this equity portfolio. He wants to evaluate his portfolio manager's skill in generating returns adjusted for different types of risks and also understand how his portfolio compares to the market on a risk-adjusted basis.

Easy Sub-question 1

What is Mr. Sharma's portfolio's Sharpe Ratio for the last financial year?

✓0.444

B0.667

C0.778

D0.800

💡 The Sharpe Ratio is calculated as (Portfolio Return - Risk-free Rate) / Portfolio Standard Deviation. Given: Portfolio Return (Rp) = 14.0% = 0.14 Risk-free Rate (Rf) = 6.0% = 0.06 Portfolio Standard Deviation (Sigma_p) = 18.0% = 0.18 Sharpe Ratio = (0.14 - 0.06) / 0.18 Sharpe Ratio = 0.08 / 0.18 Sharpe Ratio = 0.4444 (approximately 0.444)

Medium Sub-question 2

Based on the provided Beta of Mr. Sharma's portfolio, how does its volatility compare to the market index?

AThe portfolio is less volatile than the market index.

BThe portfolio has the same volatility as the market index.

✓The portfolio is more volatile than the market index.

DBeta does not measure volatility, it measures unsystematic risk.

💡 Beta measures systematic risk and reflects the sensitivity of the fund’s return to fluctuations in the market index. A beta greater than one means that the portfolio or stock is more volatile than the benchmark index. Mr. Sharma's portfolio Beta is 1.15, which is greater than 1, indicating it is more volatile than the market index.

Easy Sub-question 3

Given that Mr. Sharma's wealth is adequately diversified, what is the most appropriate risk-adjusted performance measure to evaluate his portfolio, and what is its value?

ASharpe Ratio, 0.444

✓Treynor Ratio, 0.070

CInformation Ratio, 0.444

DM2 Measure, 0.67%

💡 For investors whose wealth is already well diversified, the Treynor Ratio is more appropriate as it considers only systematic risk (Beta), which is the relevant risk for a well-diversified portfolio. The Treynor Ratio is calculated as (Portfolio Return - Risk-free Rate) / Portfolio Beta. Given: Portfolio Return (Rp) = 14.0% = 0.14 Risk-free Rate (Rf) = 6.0% = 0.06 Portfolio Beta (Beta_p) = 1.15 Treynor Ratio = (0.14 - 0.06) / 1.15 Treynor Ratio = 0.08 / 1.15 Treynor Ratio = 0.06956 (approximately 0.070)

Hard Sub-question 4

To compare Mr. Sharma's portfolio performance directly against the market return after adjusting for risk, what would be the M2 (Modigliani and Modigliani) measure and its interpretation?

✓M2 = 0.67%; The portfolio outperformed the market by 0.67% after risk adjustment.

BM2 = -0.67%; The portfolio underperformed the market by 0.67% after risk adjustment.

CM2 = 1.33%; The portfolio outperformed the market by 1.33% after risk adjustment.

DM2 = -1.33%; The portfolio underperformed the market by 1.33% after risk adjustment.

💡 The M2 measure adjusts the portfolio's risk to match the market's risk and then compares the adjusted return with the market return. 1. **Calculate the weight for levering/de-levering:** Weight in portfolio (w) = Market Standard Deviation / Portfolio Standard Deviation w = Sigma_b / Sigma_p = 15.0% / 18.0% = 0.15 / 0.18 = 0.8333 2. **Calculate the return of the risk-adjusted portfolio (rp*):** The remaining portion (1-w) is assumed to be invested in the risk-free asset. rp* = (w * Portfolio Return) + ((1 - w) * Risk-free Rate) rp* = (0.8333 * 0.14) + ((1 - 0.8333) * 0.06) rp* = (0.8333 * 0.14) + (0.1667 * 0.06) rp* = 0.116662 + 0.010002 rp* = 0.126664 or 12.67% 3. **Calculate the M2 measure:** M2 = rp* - Market Return (Rb) M2 = 12.67% - 12.0% M2 = 0.67% Interpretation: Since M2 is positive (0.67%), the managed portfolio outperformed the market by 0.67% after its risk was adjusted to match that of the market portfolio.

Medium Sub-question 5

What is the Information Ratio for Mr. Sharma's portfolio, and what does it primarily measure?

A0.444; Reward per unit of total risk.

B0.070; Reward per unit of systematic risk.

✓0.444; Active return per unit of active risk (tracking error).

D0.67%; Performance relative to a risk-adjusted market portfolio.

💡 The Information Ratio (IR) is calculated as (Portfolio Return - Benchmark Return) / Standard deviation of (Portfolio Return - Benchmark Return). Given: Portfolio Return (Rp) = 14.0% = 0.14 Benchmark Return (Rb) = 12.0% = 0.12 Standard deviation of (p-b) (Tracking Error) = 4.5% = 0.045 Information Ratio = (0.14 - 0.12) / 0.045 Information Ratio = 0.02 / 0.045 Information Ratio = 0.4444 (approximately 0.444) The Information Ratio measures the fund manager’s ability to generate active return (return above the benchmark) per unit of active risk (tracking error).

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 Performance Measurement and Evaluation 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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