Question

In: Finance

You are evaluating the performance of two portfolio managers, and you have gathered annual return data...

You are evaluating the performance of two portfolio managers, and you have gathered annual return data for the past decade:

Year Manager X Return (%) Manager Y Return (%)
1 -1.0 -5.0
2 -1.0 -4.0
3 -1.0 -3.5
4 -0.5 1.5
5 0.0 3.0
6 2.5 3.5
7 3.5 7.5
8 9.0 8.5
9 11.0 10.5
10 15.0 15.5
  1. For each manager, calculate (1) the average annual return, (2) the standard deviation of returns, and (3) the semi-deviation of returns. Do not round intermediate calculations. Round your answers to two decimal places.
    Average annual return Standard deviation of returns Semi-deviation of returns
    Manager X % % %
    Manager Y % % %
  2. Assuming that the average annual risk-free rate during the 10-year sample period was 3.0%, calculate the Sharpe ratio for each portfolio. Based on these computations, which manager appears to have performed the best? Do not round intermediate calculations. Round your answers to three decimal places.

    Sharpe ratio (Manager X):

    Sharpe ratio (Manager Y):

    Based on Sharpe ratio -Select-Manager XManager Y has performed the best.

  3. Calculate the Sortino ratio for each portfolio, using the average risk-free rate as the minimum acceptable return threshold. Based on these computations, which manager appears to have performed the best? Do not round intermediate calculations. Round your answers to three decimal places.

    Sortino ratio (Manager X):

    Sortino ratio (Manager Y):

    Based on Sortino ratio -Select-Manager XManager Y has performed the best.

  4. When would you expect the Sharpe and Sortino measures to provide (1) the same performance ranking, or (2) different performance rankings?

    The Sharpe and Sortino measures should provide the same performance ranking when the return distributions are -Select-symmetricalasymmetric for the funds or managers under consideration. The performance rankings should differ when the return distributions are -Select-symmetricalasymmetric .

Solutions

Expert Solution

1. The following table calculates the average, Standard deviation and Semi deviation

Mean for X = 3.75%, SD for X = 5.85% (Sample deviation) , Semi Deviation = 1.53%

Mean for Y = 3.75%, SD for Y = 6.75% (Sample deviation) , Semi Deviation = 2.88%

Mean = Sum of All values / Total Values

Sample Variance = Sum of All Square deviation / (N-1)

Sample SD = Sample Variance ^ 0.5Semideviation = SD of all values less than the mean

Year Manager X Return (%) Xi Manager Y Return (%) Yi Deviation from Mean for X
(Xi - Xm)
Deviation from Mean for Y
(Yi - Ym)
(Xi - Xm)^2 (Yi - Ym)^2 Values for Semi deviation Xi Values for Semi deviation Yi
1 -1.00% -5.00% -4.75% -8.75% 0.0023 0.0077 -1.00% -5.00%
2 -1.00% -4.00% -4.75% -7.75% 0.0023 0.0060 -1.00% -4.00%
3 -1.00% -3.50% -4.75% -7.25% 0.0023 0.0053 -1.00% -3.50%
4 -0.50% 1.50% -4.25% -2.25% 0.0018 0.0005 -0.50% 1.50%
5 0.00% 3.00% -3.75% -0.75% 0.0014 0.0001 0.00% 3.00%
6 2.50% 3.50% -1.25% -0.25% 0.0002 0.0000 2.50% 3.50%
7 3.50% 7.50% -0.25% 3.75% 0.0000 0.0014 3.50% 0.00%
8 9.00% 8.50% 5.25% 4.75% 0.0028 0.0023 0.00% 0.00%
9 11.00% 10.50% 7.25% 6.75% 0.0053 0.0046 0.00% 0.00%
10 15.00% 15.50% 11.25% 11.75% 0.0127 0.0138 0.00% 0.00%
TOTAL 37.50% 37.50% 0.00% 0.00%      0.0308         0.0415
Mean 3.75% 3.75%
Variance      0.0034         0.0046
SD 5.85% 6.79% 1.53% 2.88%

Sharpe Ratio = (Average Return of X - Risk Free Rate)/ SD of X

Risk free rate = 3%

Sharpe Ratio for X = (3.75% - 3.0%)/ 5.85% = 0.128

Sharpe Ratio for Y = (3.75% - 3.0%)/ 6.79% = 0.110

Higher the Sharpe Ratio the better. Thus Manager X has performed better than Manager Y

3. Sortino Ratio = (Average Return of X - Risk free rate) / Semi Deviation

Sortino Ratio for X = (3.75% - 3.0%)/ 1.53% = 0.49

Sortino Ratio for Y = (3.75% - 3.0%)/ 2.88% = 0.34

Higher the Sortino Ratio the better. Thus Manager of X has performed better than Manager of Y

4. The Sharpe and Sortino measures should provide the same performance ranking when the return distributions are Symmetrical for the funds or managers under consideration. The performance rankings should differ when the return distributions are Asymmetric


Related Solutions

You are evaluating two investment alternatives. One is a passive market portfolio with an expected return...
You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 8% and a standard deviation of 12%. The other is a fund that is actively managed by your broker. This fund has an expected return of 11% and a standard deviation of 14%. The risk-free rate is currently 4%. Answer the questions below based on this information. a. What is the slope of the Capital Market Line? b. What is the slope of...
You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z)
You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z). You consider the following historical average return, standard deviation, and CAPM beta estimates for these two managers over the past five years:PortfolioActual Avg. ReturnStandard DeviationBetaManager Y11.30%13.20%1.20Manager Z8.00%7.80%0.90Additionally, your estimate for the risk premium for the market portfolio is 4.00 percent and the risk-free rate is currently 5.00 percent.For both Manager Y and Manager...
2. You have formed a portfolio of two securities. The portfolio weights, expected return, standard deviation...
2. You have formed a portfolio of two securities. The portfolio weights, expected return, standard deviation (SD) of the individual securities and the correlation between security 1 and 2 are as follows: Security 1: weight = 1.4 , expected return = 15% , standard deviation = 25%, Security 2: weight = -0.4, expected return = 5% , standard deviation = 5% Correlation (1,2) = 0.85 Also, there is a market portfolio and the market portfolio's expected return is E(R)=10% and...
You are attempting to predict the return on Dog Heavy Equipment. You have gathered the following...
You are attempting to predict the return on Dog Heavy Equipment. You have gathered the following data on the firm’s returns, relevant Treasury rates (for a risk-free rate), and the S&P 1500 (which you plan to use as a market portfolio): Year Dog Treasury S & P 500 1 12% 2% 14% 2 7% 2% 8% 3 14% 1% 9% 4 8% 1% 12% 5 4% 1% 7% 6 12% 0% 9% 7 9% 0% 10% 8 1% 1% 12%...
A portfolio of $ 100,000 is composed of two assets: A stock whose expected annual return...
A portfolio of $ 100,000 is composed of two assets: A stock whose expected annual return is 10% with an annual standard deviation of 20%; A bond whose expected annual return is 5% with an annual standard deviation of 12%. The coefficient of correlation between their returns is 0.3. An investor puts 60% in the stock and 40% in bonds. What is the expected annual return, standard deviation of the portfolio What is the 1-year 95% VaR? Explain in non-technical...
Suppose you observe the investment performance of 500 portfolio managers for ten years and rank them...
Suppose you observe the investment performance of 500 portfolio managers for ten years and rank them by investment returns during each year. After ten years, you find that 10 of the funds have investment returns that place the fund in the top half of the sample in each and every year of your sample. Such consistency of performance indicates to you that these must be the funds whose managers are in fact, skilled, and you invest your money in these...
Portfolio analysis You have been given the return data shown in the first table on three...
Portfolio analysis You have been given the return data shown in the first table on three assets—F, G, and H—over the period 2010–2013. Expected return Year Asset F Asset G Asset H 2010 16% 17% 14% 2011 17% 16% 15% 2012 18% 15% 16% 2013 19% 14% 17% Using these assets, you have isolated the three investment alternatives shown in the following table: Alternative Investment 1 100% of asset F 2 50% of asset F and 50% of asset G...
Portfolio Analysis. You have been given the expected return data shown in the first table on...
Portfolio Analysis. You have been given the expected return data shown in the first table on three assets-F,G and H- over the period 2016-2019. Expected return Year          Asset F               Asset G             Asset H 2016         16%                    17%                    14% 2017          17                       16                       15 2018          18                        15                       16 2019           19                       14                       17 Using these assets, you have isolated the three investment alternatives shown in the following table: Alternative              Investment 1                            100% of asset F 2                            50% of asset F and 50% of asset G...
The expected annual return on the market portfolio is 7.54%. The mean annual return on T-bills...
The expected annual return on the market portfolio is 7.54%. The mean annual return on T-bills if 2.79%. Beta for The Boeing Company is 1.14. Based on the CAPM, what is the expected annual rate of return for Boeing? Do not round at intermediate steps in your calculation. Express your answer in percent. Round to two decimal places.
1. An investor is evaluating a two-asset portfolio of the following securities: Stock Expected Return Expected...
1. An investor is evaluating a two-asset portfolio of the following securities: Stock Expected Return Expected Risk (?) Correlation (?) Google (U.S.) 18.60% 22.80% .60 Vodafone (U.K.) 16.00% 24.00% a. If the two securities have a correlation of .60 what is the expected risk and return for a portfolio that is equally weighted? b. If the two securities have a correlation of .60 what is the expected risk and return for a portfolio that is 70% Google and 30% Vodafone?...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT