C17 - Investment Performance Measurement (25-30 Qs C15-C17) BC Flashcards by Nina Blackie

An investor can choose between the following 4 diversified portfolios.
If the risk free return is 4%, which portfolio should the investor choose?
A) Expected return = 12% beta = 1.2
B) Expected return = 11% beta = 0.9
C) Expected return = 10% beta = 1.3
D) Expected return = 12% beta = 0.9

D - Expected return = 12% beta = 0.9

We can use the highest Treynor ratio to access the best return for the risk taken

Exam tip: Must be the option 1 or 4 (highest return at 12%), then pick the lowest risk (beta at 0.9)

A risk-free rate of return is the theoretical interest rate an investor would earn on an investment that has zero risk. It’s a starting point for many valuation models and is used to calculate the cost of equity and cost of debt.

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Assuming risk free assets yield 4%, which of the following portfolios give the greatest excess return measured on a total risk basis?
A) Return 5%, standard deviation 1.0, beta 0.4
B) Return 7.5%, standard deviation 3.0, beta 0.5
C) Return 10%, standard deviation 3.5, beta 1.2
D) Return 12%, standard deviation 6.0, beta 2.0

C - Return 10%, standard deviation 3.5, beta 1.2

As previous - must be C has the second highest highest return, out of the two highest returns it has the lower risk (beta) and the lower stanard deviation - with Sharpe ratios: (Rp-Rf)/Standard Deviation

Sharpe Ratio= (Rp-Rf)/σp where:
Rp=return of portfolio
Rf =risk-free rate
σp=standard deviation of the portfolio’s excess return

The Sharpe ratio compares the return of an investment with its risk. It’s a mathematical expression of the insight that excess returns over a period of time may signify more volatility and risk, rather than investing skill. The Sharpe ratio’s numerator is the difference over time between realized, or expected, returns and a benchmark such as the risk-free rate of return or the performance of a particular investment category. Its denominator is the standard deviation of returns over the same period of time, a measure of volatility and risk.

Key Takeaways
* The Sharpe ratio divides a portfolio’s excess returns by a measure of its volatility to assess risk-adjusted performance.
* Excess returns are those above an industry benchmark or the risk-free rate of return.
* The calculation may be based on historical returns or forecasts.
* A higher Sharpe ratio is better when comparing similar portfolios.
* The Sharpe ratio has inherent weaknesses and may be overstated for some investment strategies.

Standard deviation is derived from the variability of returns for a series of time intervals adding up to the total performance sample under consideration.

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The time weighted annual rate of return to a fund is 15%

The return to the market over the same period is 14%, assuming risk exposure is the same, this implies:
A) The fund has been well managed
B) The fund has been poorly managed
C) It is impossible to guage the fund’s performance without more information
D) The fund must have a beta of less than 1

A - The fund has been well managed

It is tracking above (performing better than) the market

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A fund has TWRR of 20%. The value at the end of year 2 is £140.00. £20 invested at the end of year 1 resulted in the fund’s value being £127.00

What was the start value of the fund?
A) £89.29
B) £98.29
C) £120.10
D) £130.10

TWRR - time weighted rate of return

B - £98.29

(140/127)x(107/start) = 1.2
Rearrange and solve to give start = 0.9829

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What measure is most suitable where funds have withdrawals and deposits throughout the period of assessment?
A) Time weighted rate of return
B) Money weighted rate of return
C) Holding period return
D) Jensen Measure

B - Money weighted rate of return

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Total return less the risk-free for a fund equals:
A) Return due to a client’s risk PLUS return due to market timing and security selection
B) Return due to client’s risk PLUS return due to market timing
C) Return due to client’s risk PLUS return due to security selection
D) None of the above

A - Return due to a client’s risk PLUS return due to market timing and security selection

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What is the return due to clients risk preferences if the risk-free return is 3%, return due to market timing (asset allocation) is 5%, return due to security selection is 10% and the total return is 30%

A) 22%
B) 17%
C) 15%
D) 12%

D - 12%

30 - (3 + 5 + 10) = 12%

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Given the following information on a fund’s performance. Total return is 25%, Risk-free is 8%, Return due to the client’s risk is 10.6% and return due to market timing is 12%

We can say that the fund manager is:
A) Good at stock selection
B) Bad at market timing
C) Good at market timing and bad at stock selection
D) Good at both market timing and stock selection

C - Good at market timing and bad at stock selection

Total return = risk-free rate + return due to client’s risk + return due to security selection + return due to market timing

25% = 8% + 10.6% + return due to security selection + 12%

Return of security selection isn’t given SO:
Rearrange: return due to security selection: -5.6%

Therefore, the fund manager has been good at market timing but bad at stock selection

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What is the variance of a fund whose Sharpe performance measure is 2, actual return is 20%, if the risk-free return is 6%?
A) 7
B) 10
C) 49
D) 100

C - 49

Rearranging Sharpe we get = (20-6)/2 = 7 = Standard Deviation
Therefore standard deviation = 7^2 = 49

Sharpe Ratio= (Rp-Rf)/σp where:
* Rp=return of portfolio
* Rf =risk-free rate
* σp=standard deviation of the portfolio’s excess return

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If the risk-free rate is 7.5%, the market risk premium is 8%, the actual return on a portfolio is 20% and its beta is 0.7, what is its Jensen measure of portfolio performance?
A) 4.55%
B) 6.9%
C) 19.7%
D) 20.0%

B - 6.9%

Jensen = Rp - CAPM
CAPM = 7.5% + (0.7 x 8) = 13.1%
Therefore, 20% - 13.1% = 6.9%

Jensen’s alpha is a measure used in finance to evaluate the performance of an investment portfolio relative to a benchmark index. It calculates the excess return generated by the portfolio over the expected return, which is predicted by the capital asset pricing model (CAPM). It takes into account the beta and the average market return of the portfolio or the investment.

Assuming the CAPM is correct, Jensen’s measure is calculated using the following four variables:
*Alpha = R(i) - (R(f) + B x (R(m) - R(f)))
Where:
* R(i) = the realized return of the portfolio or investment
* R(m) = the realized return of the appropriate market index
* R(f) = the risk-free rate of return for the time
* B = the beta of the investment portfolio related to the chosen market index

Calculating this metric using the formula above can result in one of three possible outcomes:
* Positive: If the alpha is positive, it means that the asset outperforms the market or benchmark.
* Negative: A negative alpha means that the security is underperforming the market or benchmark.
* Zero: This happens when the alpha is neutral. As such, it performs consistently with or tracks the market or benchmark.

The capital asset pricing model, or CAPM, is a financial model that calculates the expected rate of return for an asset or investment.

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If the DIJA rises from 10,500 to 10,700 at the same time as the exchange rate moves from $1.50 per £1 to $1.40 per £1, what is the holding period in sterling?
A) 1.35%
B) 13.27%
C) -1.33%
D) 9.18%

D - 9.18%

($10,700/$1.40)/(10,500/$1.50) - 1 = 0.0918 i.e. 9.18%

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The Jensen measure is most suitable for:
A) A diversified portfolio
B) An undiversified portfolio
C) A portfolio with a beta greater than 1
D) A portfolio with a beta less than 1

A - A diversified portfolio

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The time weighted return:
A) Will equal the money weighted return when there are only INFLOWS to the market
B) Gives equal weighting to the return each period
C) Will equal the money weighted return when there are only OUTFLOWS from the fund
D) Gives the total rate of return when there are only INFLOWS to the fund

B - Gives equal weighting to the return each period

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If you are given Rp and Rf and want to calculate the Sharpe measure - what do you require?
A) Standard Deviation of the portfolio
B) Return of the benchmark
C) Beta of the portfolio
D) Standard deviation of the market

A - Standard Deviation of the portfolio

Sharpe Ratio= (Rp-Rf)/σp where:
Rp=return of portfolio
Rf =risk-free rate
σp=standard deviation of the portfolio’s excess return

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The value of a fund at the end of year 1 is £55m, and at the end of year 2 is £50m (before cash inflow). If cash inflow at the end of year 2 is £4m and the time weighted return over the two year period to the end of year 3 is 1.01.

What is the value of the fund at the end of year 3?
A) £60.0m
B) £49.6m
C) £51.1m
D) £51.0m

A - £60m

(50/55) x (? x 54) = 1.01
? = (1.01/(50/55)) x 54 = 59.99m

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Rank the following funds according to the Jensen measure of portfolio performance, lowest first.
Actual Return % / Beta
1. 15 / 1.8
2. 35 / 0.4
3. 10 / 1.3

The risk free return is 6% and the market risk premium is 8%
A) 3, 1 and then 2
B) 2, 1 and then 3
C) 1, 2 and then 3
D) 3, 2 and then 1

A - 3, 1 and then 2

Jensens alpha = actual return - expected return per CAPM (Capital Asset Pricing Model).
1. 15% - (6% + 1.8x8%) = -5.4%
2. 35% - (6% + 0.4x8%) = +25%
3. 10% - (6% + 1.3x8%) = -6.4%

Therefore, ranking is 3 (-6.4%), 1 (-5.4%) and then 2 (+25%).

Exam tip: Fund 2 must be the highest performing as it has the highest return at 35% and the lowest risk (with beta at 0.4) so must be an answer with Fund 2 ranks last (in this case there is only one, but where there are more - the above anlysis will then help you rank the other two

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Which of the following funds has the lowest Sharpe measure of portfolio performance?
Actual Return % / Beta / Variance
1. +20 / 1.6 / 4
2. 7 / 0.2 / 1
3. +15 / -0.8 / 36
4. +30 / 1 / 9

The risk free return is 6%
A) Fund 1
B) Fund 2
C) Fund 3
D) Fund 4

B - Fund 2 (7 / 0.2 / 1)

Sharpe = (portfolio return - risk free rate)/standard deviation
1. (20-6) / 2 = 7
2. (7-6) / 1 = 1
3. (15-6) / 6 = 1.5
4. (30-6) / 3 = 8

Therefore 2 have the lowest Sharpe ratio

BOOK HAS NOT EXPLAINED HOW TO GET THE NUMBERS IN BOLD SO NEED TO LOOK INTO THIS FURTHER AND EXPLAIN

Given the following informatio aboout a fund:
* Value at the beginning of the year: £3m
* Value at the end of the year: £3.3m
* Benchmarkn portfolio equals 60% equities and 40% gilts
* The Fund manager is assessed against the following indicies:
Index / First Half Year rise / Second Half Year Rise
Equity Index / 10% / -2%
Gilt index / 3% / 4%

At the beginning of the year the fund has the same asset mix and proportions as the benchmarks. Halfway through the year the proportions are rearranged to give 80% equities and 20% gilts.

Which of the following is TRUE of the fund manager:
1. Outperformed the benchmark
2. Underperformed the benchmark
3. Poor at market timing
4. Good at market timing

A) 2 and 3
B) 2 and 4
C) 1 and 3
D) 1 and 4

C - 1 (Outperformed) and 3 (Poor at Market Timing)

Benchmark Value = (£3m x 0.6 (60% allocation) x 1.1 (10%) x 0.98 (-2%)) + (£3m x 0.4 x 1.03 x 1.04) = £3.2258. Therefore the fund manager outperformed the benchmark by £3.3m - £3.2258m = +£0.0742m

Recalculating the benchmark with reallocation:
* First 6 months: (£3m x 0.6 x 1.1) + (£3m x 0.4 x 1.03) = £3.216m
* Second 6 months: (£3.216m x 0.8 x 0.98) + (£3.216 x 0.2 x 1.04) = £3.1903m

Therfore the fund manager was poor at market timing £3.1903m - £3.2258m = -£0.0355m asset

A fund manager selecting undervalued bonds will select bonds with a:
A) Negative alpha
B) Positive alpha
C) Negative beta
D) Positive beta

B - A positive Alpha

Potential for Higher Returns: Positive Alpha signifies outperformance relative to a benchmark, suggesting that the investment can potentially yield higher returns. For investors seeking to maximize their wealth, targeting positive Alpha can be an attractive objective.

Two fixed income portfolios have received returns of 8% (Fund X) and 10% (Fund Y) over the previous 12 months. Fund X’s duration was 9 years and Fund Y’s duration was 13 years. The risk free return and duration of the market portfolio were 4% and 7 years.

What can we say about the performance of the two funds?
A) Their risk adjusted performance was equal
B) Fund X’s risk-adjusted performance exceeded that of Fund Y’s
C) Fund Y’s risk-adjusted performance exceeded that of Fund X’s
D) None of the above

C - Fund Y’s risk-adjusted performance exceeded that of Fund X’s

Using Treynor = (portfolio return - risk-free rate)/beta
Treynor for X = (8% - 4%) / (9/7) = 3.11
Treynor for Y = (10% - 4%) / (13/7) = 3.23

Therefore Fund Y exceeded Fund X

Return due to marking timing plus return due to security selection for a fund equals:
A) Total return LESS the risk-free return PLUS the return due to client’s risk
B) Total return PLUS the risk-free return LESS the return due to client’s risk
C) Risk-free return PLUS return due to client’s risk
D) Total return LESS the risk-free return LESS the return due to client’s risk

D - Total return LESS the risk-free return LESS the return due to client’s risk

Total return less the risk-free return for a fund equals:
A) Return due to client’s risk PLUS return sue to market timing AND security selection
B) Return due to client’s risk PLUS return due to market timing
C) Return due to client’s risk PLUS return due to security selection
D) None of the above

A - Return due to client’s risk PLUS return sue to market timing AND security selection

You add all the risks together to get the total return.

Rank the following funds using the Treynor measure of the portfolio portfmance - highest first.
Actual return % / Beta / Standard Deviation
1. 10 / 0.4 / 4
2. 20 / 0.6 / 8
3. 30 / 1.2 / 12

The risk free rate equals 4%
A) 3, 2 and then 1
B) 1, 2 and then 3
C) They are equal in rank
D) 2, 3 and then 1

D - 2, 3 and then 1

Treynor = (Actual return - riskfree rate) / beta
1. (10% - 4%) / 0.4 = 15
2. (20% - 4%) / 0.6 = 26.67
3. (30% - 4%) / 1.2 = 21.67

Therefore ranked highest to lowest is is 2 (26.67), 3 (21.67) and then 1 (15)

Given the following information about a fund:
Value at the beginning of the year: £50m
Value at the end of the year: £45m
Benchmark portfolo equals 20% equities and 80% gilts
Benchmark returns:
Equities: minus 20%
Gilts: Plus 2%

By how much has the fund manager out (+) or under (-) performed the benchmark?
A) 7.6%
B) -7.6%
C) 5.6%
D) -5.6%

B: -7.6% (UNDER-PERFORMED)

(£50m x 0.2 x 0.8) + (£50m x 0.8 x 1.02) = £48.8m Benchmark value
£45m - £48.8 = -£3.8m
-£3.8m /£50m = -0.076 so -7.6%

Given the following information, by how much has the fund manager outperformed the index? Value of the fund at the beginning of the year: £150m Value of the fund at the end of the year: £175m Benchmark portfolio = 55% gilts and 45% equities The manager is assessed against the following indicies (1st half year rise/2nd half year rise): * Gilt index: 5% / 6% * Equity Index: 8% / 7% At the beginning of the year, the fund manager has the same asset mix and proportions as the benchmark and halfway through the year the proportions are rearranged to give 50% gilts and 50% equities. A) -2.61% B) 2.61% C) -3.45% D) 3.45%

**D - 3.45%** (150m x 0.55 x 1.05 x 1.06) + (150m x 0.45 x 1.08 x 1.07) = £169.8255m Benchmark value Therefore outperformance = £175m - £169.8255m = +£5.1745m As a percentage of the starting value: £5.1745m / £150m = 0.0345 so +3.45%

Assuming a risk free rate of 4% which of the following portfolios gives the greatest excess return measured on total risk basis? A) Beta 0.8 / Standard deviation 2.0 / return 5% B) Beta 1.0 / Standard deviation 4.0 / return 7% C) Beta 1.9 / Standard deviation 6.0 / return 14% D) Beta 1.7 / Standard deviation 8.0 / return 15%

**C - Beta 1.9 / Standard deviation 6.0 / return 14%** As we are lookin at total risk, we should use the Sharpe ratio = (portfolio return - risk free rate)/standard deviation. SO: A) (5%-4%)/2 = 0.5 B) (7%-4%)/4 = 0.75 C) (14%-4%)/6 = 1.67 D) (15%-4%)/8 = 1.38 The highest Sharpe ratio is C *Exam tip: as you are looking for the greatest excess start and workdown - will likely only need to do 3 equations*

*A share analyst thinks that a company's dividends will grow at 5% from now on. The current share price is £2.00 and year end price is expected to be £2.10. The Dividend that was just paid was 8p* What is the expected holding period return? A) 4.00% B) 8.00% C) 5.00% D) 9.20%

**D - 9.20%** HRP = (Expected end value + expected dividend - Starting share price) / Starting share price SO HRP = (£2.10 + (0.08 x 1.05) - £2.00)/£2.00 = 0.092 i.e. 9.2%

An active fund manager, when deciding which bonds to invest in, will select bonds with a: A) Negative Alpha B) Negative Covariance C) Positive Alpha D) Positive Covariance

**C - Positive Alpha** *Potential for Higher Returns: Positive Alpha signifies outperformance relative to a benchmark, suggesting that the investment can potentially yield higher returns. For investors seeking to maximize their wealth, targeting positive Alpha can be an attractive objective.* *Covariance is a statistical measurement that shows how the returns of two assets move in relation to each other. It's used in investment management to help investors understand how assets perform together and how to diversify their portfolios. A positive covariance means asset prices are moving in the same general direction. A negative covariance means asset prices are moving in opposite directions.*

If you are given return on a portfolio and the risk free return, and you wish to calculate the Sharpe measure of portoflio management, what other information do you require? A) Standard Deviation of the benchmarch B) Standard Deviation of the covariance of the benchmark C) Stanard Deviation of the beta of the portfolio D) Standard Deviation of the portfolio

**D - Standard Deviation of the portfolio** Sharpe Ratio= (Rp-Rf)/σp *where:* * Rp=return of portfolio * Rf =risk-free rate * σp=standard deviation of the portfolio’s excess return

*A fund starts the year with a value of £100m, grows by 10% over the year and at the end of the year receives a further investment of £15m. At the end of the next year, the fund is worth £145m* What is the time weighted return over the period? A) 26.1% B) 27.6% C) 31.8% D) 20.8%

**B - 27.6%** TWRR = (1.10 x (145/125)) -1 = 0.276 i.e. 27.6% 125 is from (£100m x 10%) + £15m

In a Jensen measure of performance, the benchmark is chosen to be: A) A passively managed portfolio with the same covariance as the actual fund B) A passively managed portfolio with a higher beta than the actual fund C) A passively managed portfolio with the same beta as the actual fund D) A passively managed portfolio with a lower beta than the actual fund

**C - A passively managed portfolio with the same beta as the actual fund** *Beta is a statistical measurement that shows how volatile a security's price is compared to the overall stock market. It's a risk-reward measurement that helps investors understand how sensitive their portfolios are to market changes. What does beta mean?* * Beta of 1: The security's price moves in line with the market * Beta greater than 1: The security's price is more volatile than the market * Beta less than 1: The security's price is less volatile than the market * Negative beta: The security's price moves in the opposite direction of the market

Holding period returns are calculated as: A) Change in market price DIVIDED by change in income received B) Change in market price PLUS income received and reinvested C) Change in market price PLUS income received and reinvested DIVIDED by market price at the START of the period D) Change in market price PLUS income received and reinvested DIVIDED by market price at the MID-POINT of the period

**C - Change in market price PLUS income received and reinvested DIVIDED by market price at the START of the period** HRP = (Expected end value + expected dividend - Starting share price) / Starting share price

If the Jensen measure on a share is -10%, the stick has returned 1%, the risk-free rate is 2% and the market risk premium is 6%, what is the stock's beta? A) 1.5 B) 2.0 C) 1.0 D) 0.5

**A - 1.5** Jensen's Alpha = Actual return - required return per CAPM (capital asset pricing model) SO: -10% = 1% - [2% + (beta6%)] Rearranged: -10% - 1% + 2% = beta6% Beta = -9/-6 = 1.5

A portfolio achieves the following quarterly returns: 3%, 5%, 6%, -8%. If the value of the fund at the start was £10,000,000. What was the value at the end of the year? A) £10,349,376 B) £10,546,788 C) £10,600,000 D) £10,983,736

**B - £10,546,788** Simply compound each quarter return: £10m x 1.03 x 1.05 x 1.06 x 0.92 = £10,546,788

Which term correctly describes the difference in returns of a tracker fund and that of the index of which the tracker fund is mimicking? A) Base Risk B) Tracking error C) Sovereign risk D) Standard deviation

**B - Tracking Erorr** The answer is tracking error, since the tracker fund is set up to mimic the return of an index e.g. FTSE 100. Any difference will be classified as tracking error, probably to differing portfolio contents to that of the index

If the risk-free rate is 7.5%, the market risk premium is 8%, the actual return on the portfolio is 20% and its beta is 0.7, what is the Jensen measure of the portfolio? A) 4.5% B) 6.9% C) 19.7% D) 20.0%

**B - 6.9%** Using CAPM (Capital Asset Pricing Model): Expected Return = 7.5 + 0.7(8) = 13.1%. Therefore the Jensen measure (abnormal return or 'alpha') = 20% - 13.1% = 6.9%

*An investor buys 300 shares for 320p. Just after receiving a dividend of 6p, the shares are sold for 326p.* What is the holding period of return? A) 1.88% B) 3.75% C) 7.50% D) 10.00%

**B - 3.75%** HRP = ( [ (MVend - MVstart) + Income] / MVstart ) x 100 SO ( [ (326p - 320p) + 6p] / 320p ) x 100 = 0.0375 x 100 = 3.75%

*A pension fund has a value of £80m at the beginning of the year. By the end of the year the fund has grown to £91m. In the middle of the year, the trustees paid £7m into the fund. At the time of this payment, the fund was worth £82m.* What is the time-weighted rate of return (TWRR) on this fund over the year? A) 13.75% B) 8.75% C) 4.80% D) 6.70%

**C - 4.80** **T0** = £80m. **T½** = £82m then £89m after £7m pay. **T1** = £91m SO: [ (82/80) x (91/89) ] - 1 = 0.048 SO 4.8% ## Footnote *Another way of calculating this calculating the Holding Period return for each half year looking at the values and ignore income and then times these HRPs together SO* *HPR1 = ( [ (82 - 80) + 0 for income] / 80) x 100 = 2.5%* *HPR2 = ( [ (91 - 89) + 0 for income] / 89) x 100 = 2.25%* *1.025 x 1.0225 - 1 = 0.048 so 4.8%*

*A fund manager manages a portfolio of equities with an initial value of £300m. The index benchmark set for the manager over the forthcoming year is combination of the FTSE 100 and S&P 500. The manager is expected to achieve a return at least as good as allocating 75% of the portfolio to the FTSE 100 and the remainder of the portfolio to the S&P 500. At the end of the year, the portfolio is worth £325m, and over the same period the FTSE 100 and S&P 500 have risen by 4% and 8% respectively* Has the fund manager managed to outperform the benchmark index? A) He has outperformed by £10m B) He has outperformed by £5m C) He has underperformed by £10m D) He has underperformed by £5m

**A - He has outperformed by £10m** According to the benchmark the portfolio would have: 75% (£225m) x 1.04 = £234m 25% (£75m) x 1.08 = £81m Total = £315m so incease £15m The portfolio has actually increased by £25m, so £10m more than the benchmark ## Footnote *Another way of calculating would be:* *75% x 4% + 25% x 8% = 5%* *£300m x 5% = £15m BM increase*

*A trustee is comparing two funds: Fund A has returned 10%, while fund B has returned 12% over the same period. The trustee calculates that the standard deviation on these funds over this period has been 12% for funds A and B, respectively. They also calculate the betas of funds A and B to have been 1.40 and 1.00, respectively. Assume a risk-free rate of interest of 4%* If the trustees was to use both the Sharpe and Treynor measures of performance, what might they conclude from the relative performances of the two funds? A) Fund A appears to have performed better than fund B according to the Treynor measure, but the revese is true for the Sharpe measure. B) Fund A appears to have performed better than fund B according to the Sharpe measure, but the revese is true for the Treynor measure. C) Both funds have performed equally well D) Fund A has outperformed fund B according to both meaures

**B - Fund A appears to have performed better than fund B according to the Sharpe measure, but the revese is true for the Treynor measure.** First layout the facts: Fund / Rp / σ / β A / 10% / 12% / 1.40 B / 12% / 18% / 1.0 **Sharpe = (Rp - Rf) / σ** SO: Fund A = (10 - 4) / 12 = 0.5%...higher figure wins! Fund B = (12 - 4) / 18 = 0.44% **Treynor = (Rp - Rf) / β** SO: Fund A = (10 - 4) / 1.40 = 4.29 Fund B = (12 - 4) / 1.0 = 8.00...higher figure wins! ## Footnote Rp = Return on the portfolio/fund σ = standard deviation β = beta Rf = Risk-free rate

*The trustee of a large UK equity pension fund set their fund manager the benchmark objective of outperforming the return on the UK equity portfolio with a capital asset pricing model (CAPM) beta coefficient of 1.50 over the previous year. During this period, the risk-free rate was 5% and the return on the market portfolio was 12%.The fund manager achieved a return of 14% over the year* How did the manager measure up against the benchmark? A) The fund manager has overperformed their benchmark by 1.5% B) The fund manager has outperformed their benchmark by 3% C) The fund manager has underperformed their benchmark by 1.5% D) The fund manager has underperformed their benchmark by 3%

**C - The fund manager has underperformed their benchmark by 1.5%** Using Jensen's Alpha calculation: **Jensen Alpha = Rp - Rb** **Rb = Rf + β x (Rm - Rf) ** SO: 5 + 1.5 x (12 - 5%) = 15.5% Therefore Jensen's Alpha = 14 - 15.5 = -1.5 So the manager has underperformed by 1.5% ## Footnote Rf - Risk free rate β - beta Rm - return on the market Rb = expected benchmark return

*Two fixed income portfolios, fund A and fund B, have achieved returns of 7% and 6% respectively over the past year. Over this period, fund A had an average duration of 15 years and fund B had an average duration of 10 years. The risk-free rate and duration on the market portfolio were 3% and 12 years respectively.* Using the risk-adjusted performance measure what can we say about the performance of the two funds? A) Their risk-adjusted performance are equal B) Fund B has achieved a better risk-adjusted performance than fund A C) Fund A has achieved a better risk-adjusted performance than fund B D) None of the above

**B - Fund A has achieved a better risk-adjusted performance than fund B** For bond portflio, a relative measure of performance is the Duration-Adjusted excess return measure being: **P = (Rp - Rf) / (Dp / Dm)** So: Fund A = (7 - 3) / (15 / 12) = 3.2...lower number wins! Fund B = (6 - 3) / (10 / 12) = 3.6 Portfolio B has duration-adjusted return which is higher than portfolio A, so Fund A will make its money back quicker. ## Footnote Rp = return on portfolio Rf = risk free rate Dp = Duration of the portfolio Dm = Duration of the market overall