Why do the Sharpe and Treynor measure give opposite results in the case of Mr. P? The
reason is that P’s portfolio has a disproportionate amount of unsystematic risk; it looks
like a poorly diversified portfolio. Hence a measure which uses total risk gives a result
very different from one which uses only systematic risk. What do we do in a situation
like this? Does it mean that one of the measures is wrong? The answer is that both
measures are right, but they are relevant in different contexts. In our situation where the
portfolio is a mutual fund, the appropriate measure to use depends on the type of investor.
For those investors who use P’s mutual fund as the principal vehicle for investment in
equity, there is no scope for diversifying away the large unsystematic risk. The relevant
measure is the Sharpe measure which indicates that P has not done as well a s the market.
On the other hand, consider an investor who holds a large portfolio of shares and is
considering adding some units of P’s fund to it just as if it were another security. For this
investor, the large unsystematic risk of the fund does not matter. It will be diversified
away when it is included in the investor’s total portfolio. For such an investor, what is
relevant is the systematic risk which cannot be diversified. The Treynor measure is
appropriate for this investor and this measure indicate that the mutual fund is very
attractive having significantly outperformed the market.
In general, we can say that to measure the performance of the total portfolio of an
investor, the Sharpe measure is always the right one. To measure the performance of a
sub-portfolio, the Treynor measure is correct provide the investor has taken reasonable
care to ensure that his total portfolio is well diversified.
In practice, however, in a large number of cases, the Sharpe and Treynor measure of
performance produce very similar rankings of portfolios; typically, therefore, they agree
on whether a particular portfolio has done better than the market or not. The situation of
disagreement which we found for P’s portfolio is the exception rather than the rule.
Excess Returns
The Sharpe and Treynor measures of performance are both ratios. This means that
though they can be used to rank portfolios, they are not readily interpretable in monetary
terms or in terms of percentage returns. Often, we would like to measure a portfolio’s
superior performance in terms of the extra return that it has earned beyond what was
mandated by its level of risk. If we know the size of the portfolio, we can then convert
this into a rupee amount as saying that the portfolio manager’s efforts were worth so
much of money in extra return earned.
This kind of performance measurement is also possible using the SML and CML
diagrams that we have shown in Examples 2 and 3 what we are now looking at is the
vertical distance of the portfolio from the SML and from the CML.
If we take beta or systematic risk as the appropriate measure of risk, then the SML
indicates the return that a portfolio should earn for any given level of risk. The difference
between that and the actual return is a measure of the excess return that has been earned
over and above what is mandated for its level of systematic risk. This performance
measure is known as Jensen’s measure after its originator.