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

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 % % %
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.
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.
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 .

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

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