Comparison of Risk asjusted Returns
To be able to compare returns on your portfolio with a benchmark
index, you need to equalize the differences in risk and return. For
example, a 5 percent return on a portfolio of Treasury securities is
not the same as a 5 percent return on a portfolio of smallcap
growth stocks because of the greater risk in the latter portfolio.
Investors would prefer the 5 percent return from the lowrisk
Treasury security portfolio.
Three different measures adjust returns for the risk associated
with a portfolio:
* Sharpe index
* Treynor index
* Jensen index
These measures allow you to compare different returns on a riskadjusted
basis.
The Sharpe Index
The Sharpe index is a riskadjusted measure of performance that
standardizes the risk premium of a portfolio using the standard
deviation of the portfolio return.
Sharpe index = (portfolio return  riskfree rate)/
standard deviation of portfolio returns
The riskadjusted return of a portfolio is the risk premium for
a portfolio (portfolio return  riskfree return) divided by the standard
deviation of the portfolio’s returns. For example, suppose that
a portfolio has an annual return of 7 percent and an annual standard
deviation of 20 percent. The average Treasury bill rate during the
year was 3.5 percent. What is the Sharpe index?
Sharpe index = (rp  rf )/σp
= (0.07  0.035)/0.2 = 0.175
The result is put in perspective when it is compared with
another portfolio or the market. Assume that during the same year
the market return is 6 percent, with a standard deviation of 18 percent
and a riskfree rate of 3.5 percent. The Sharpe index for the
market is 0.1389:
Sharpe index = (0.06  0.035)/ 0.18 = 0.1389
The performance of the portfolio is superior to the return of the
market because of the higher result (0.175 compared with 0.1389).
The higher return of the portfolio more than balances the higher
standard deviation or risk (20 percent for the portfolio versus 18
percent for the market).


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