In: Finance
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 |
Average annual return | Standard deviation of returns | Semi-deviation of returns | |
Manager X | % | % | % |
Manager Y | % | % | % |
Sharpe ratio (Manager X):
Sharpe ratio (Manager Y):
Based on Sharpe ratio -Select-Manager XManager Y has performed the best.
Sortino ratio (Manager X):
Sortino ratio (Manager Y):
Based on Sortino ratio -Select-Manager XManager Y has performed the best.
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 .
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