Example 3
Mr. P of Example 2 finds that the standard deviation of returns on his portfolio is 41.3%
while that of the market as a whole is 19.44%. Compute the Sharpe measure for P’s
portfolio and comment on his performance according to this measure. Portray the result
graphically.
Solution
As in example 2, the risk premium earned by Mr. P is 58.60%. The Sharpe measure of
his portfolio is 58.60/41.31 = 1.418.
For the market, the Sharpe measure is 41.40 – 12.00)/19.44 = 1.512. The Sharpe measure
thus indicates that P has not done as well as the market.
We portray the situation graphically, plotting return on the vertical axis and total risk on
the horizontal axis. The line joining the risk-free rate to the market (M) is the Capital
Market Line discussed earlier in the book. It indicates the relationship between return
and total risk for all well-diversified portfolios. It can be seen that P’s portfolio lies
below the CML indicating that it has earned less than what is required for its level of total
risk.
Fig. 2 Capital Market Line.