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Problem 18-05

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		-2.5		-6.5
2		-2.5		-5.5
3		-2.5		-2.0
4		-2.0		4.0
5		0.0		5.5
6		5.5		6.5
7		7.5		7.5
8		9.5		8.5
9		13.5		12.5
10		18.5		14.5

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 1.5%, 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 YItem 9 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 YItem 12 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-symmetricalasymmetricItem 13 for the funds or managers under consideration. The performance rankings should differ when the return distributions are -Select-symmetricalasymmetricItem 14 .