Question

You are given the following information for two funds A and B, relating to the ir performance over the last five years. Cumulative Total Covariance of Return Standard deviation Return over 5 Years of Return with Market A 76.20% 0.22 0.044 101.10% 0.32 0.075 Market 92.50% 0.25 Risk-free Investment 40.30% Calculate the Treyno r, Sharpe and Jensen performance measures for Funds A and B. What do they tell you about the performance of the funds? WRA:

Answer 1

a). Beta(i) = Cov{r(i) * r(m)} / Variance(m)

Beta(A) = 0.044 / (0.25)² = 0.044 / 0.0625 = 0.704

Beta(B) = 0.075 / (0.25)² = 0.075 / 0.0625 = 1.200

Treynor Measure(i) = [r(i) - rF] / Beta(i)

Treynor Measure(A) = [76.20% - 40.30%] / 0.704 = 35.90% / 0.704 = 50.99%

Treynor Measure(B) = [101.10% - 40.30%] / 1.200 = 60.8% / 1.200 = 50.67%

Higher Treynor ratio suggest the better performance of the fund. So investor are advised to pick the investment with treynor ratio.

So, Sharpe Ratio tells us that A is better.

b). Sharpe Ratio(i) = [r(i) - rF] / std. dev.(i)

Sharpe Ratio(A) = [76.20% - 40.30%] / 22% = 35.90% / 22% = 1.63

Sharpe Ratio(B) = [101.10% - 40.30%] / 32% = 60.8% / 32% = 1.90

Greater the Sharpe ratio of the fund represents the higher risk adjusted performance. So the investors are advised to pick the investment with higher Sharpe ratio.

So, Sharpe Ratio tells us that B is better.

c). Jensen's Alpha(i) = r(i) - [rf + {Beta * (E(rm) - rf)}]

Jensen's Alpha(A) = 76.20% - [40.30% + {0.704 * (92.50% - 40.30%)}]

= 76.20% - [40.30% + {0.704 * 52.20%}]

= 76.20% - [40.30% + 36.75%]

= 76.20% - 77.05% = -0.85%

Jensen's Alpha(B) = 101.10% - [40.30% + {1.200 * (92.50% - 40.30%)}]

= 101.10% - [40.30% + {1.200 * 52.20%}]

= 101.10% - [40.30% + 62.64%]

= 101.10% - 102.94% = -1.84%

Jensen's Alpha of both is negative represents the under-performance of the fund.