Question

1. A mutual fund house has four portfolio managers. Their performance statistics are given as below: ManagerAverage monthly return Standard Beta (compounded to annual basis) deviation 8% 1.2 2.2 0.6 1.6 1.0 10 7 3 4 SP500 The T-bill rate is 5% a What is the Treynor's performance measure for Manager B? (5 pts b) What is the Sharpe's performance measure for Manager C? (5 pts) c) What is the M2 performance measure for Manager D? (5 pts) d) For Manager A, the Jensen's performance measure regression equation is as follows: Excess return from A =-0.004 + 0.6 * excess return from SP500 (0.14) (0.03) The p-values are in parentheses. What is the Jensen's performance measure for Manager A? Does the manager statistically significant outperform the market? (5 pts)

Answer 1

a) The treynor's ratio here is computed as:

= (Average portfolio return - Risk free rate of return ) / Beta

= (5 - 5) / 2.2

= 0

Therefore 0 is the required value here

b) The Sharpe ratio here is computed as:

= (Average portfolio return - Risk free rate of return ) / Standard Deviation

= (10 - 5)/3

= (5/3)

Therefore (5/3) is the required ratio here.

c) The M² measure is computed here as:

$= \frac{R_p - R_f}{\sigma_p}\sigma_{bench} +R_f$

$= \frac{7-5}{4}*8 +5 = 9$

Therefore 9 is the required value here.

d) The jensen's performance measure is computed as the coefficient of the excess return which is given as 0.6

Therefore 0.6 is the Jensen's performance measure here. It is statistically significant as we can see the p-value here is given as 0.03 < 0.05 which is generally taken as the level of significance.