Example 4
From fig 1 and the data in Example 2 compute the Jensen measure of P’s performance.
Solution
In Fig. 1 we see that portfolio P’s beta of 1.121 mandated a return of only 44.95% while
it actual return was 70.60%. P, therefore, lies above the SML, and the vertical distance
from the SML to P is 25.65% (i.e. 70.60 – 44.95). This is the excess return (Jensen
measure) that P has earned after adjusting for systematic risk.
We can compute the Jensen measure numerically without drawing a graph, as follows.
We multiply the beta of the portfolio by the risk premium of the market and add the result
to the risk-free rate to get the return mandated by the SML. For portfolio P this gives
12.00 +1.121 (41.40 – 12.00) = 44.95%. The Jensen measure is then found by
subtracting this return from the actual return on the portfolio: 70.60 – 44.95 = 25.65%.
The Jensen measure was based on systematic risk and therefore looked at the SML. If we
are interested in total risk we can look at the distance from the CML instead of from the
SML. The vertical distance from the portfolio to the CML is Fama’s measure of net
selectivity. It represents the excess return earned over and above the return required for
its level of total risk.
Example 5
From Fig 2 and the data in Example 3 compute the Fama measure of net selectivity for
P’s performance.
Solution
In Fig 2, we see that portfolio P’s total risk of 41.31% mandated a return of 74.47% while
its actual return was 70.60%. P, therefore, lies below the SML, and the vertical distance
from the SML to P is -3.87% (i.e. 70.60 – 74.47). This is the Fame measure of net
selectivity for P. Since it is negative, P has underperformed the market by 3.87%.
We can compute the Fama measure of net selectivity numerically without drawing a
graph as follows. We first compute the ratio of the standard deviation of the portfolio to
that of the market. For P’s portfolio this ratio is 41.31/19.44 = 2.125. We then multiply
this ratio by the risk premium of the market and add the result to the risk-free rate to get
the return mandated by the CML. This gives 12.00 + 2.125(41.40 – 12.00) = 74.47%.