Treynor measures are quite similar in these respects; they, however, differ in their
definition of risk.
Treynor defines risk as being the unsystematic risk or beta. His measure of performance
is the risk premium per unit of systematic risk (beta). To compute this measure, we must
first estimate the beta of the portfolio. This is done in exactly the same way as for
individual securities as described earlier in this book. Then we divide the risk premium
by the beta to get the Treynor measure.
Example .2
Mr. P has been managing the portfolio of a large mutual fund for the last two years. He
found that his portfolio had earned a return of 70.60% and had a beta of 1.121. During
the same period, the return on the market as a whole was 41.40%. Assuming that the
risk-free rate was 12%, compute the Treynor measure for the portfolio and comment on
P’s performance according to this measure. Show the result graphically.
Solution
The risk premium for P’s portfolio is 70.60 – 12.00 = 58.60. The Treynor measure is
therefore 58.60/1.121 = 52.3%.
To comment on how well P has done, we compare this value of 52.3% with the Treynor
measure for the market. Since the market, by definition, has a beta of 1.0, its Treynor
measure is (41.40 – 12.00)/1.0 = 29.4%. This means that P has earned 52.3% per unit of
risk borne while the market as a whole earned only 29.4% per unit of risk borne. This
makes it clear that P has significantly outperformed the market.