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Risk-Adjusted Performance 299
On the other hand, funds with average total return below the market may have
significantly higher risk-adjusted returns, causing them to outperform the market.
The Income Fund of America, for instance, has a total return of only 11.3 percent
for the ten years ending in mid-1996 compared with a much higher average return
of 14.1 percent for the S&P 500 over the same time period. On a risk-adjusted
basis, however, the Income Fund of America returned 15.9 percent, significantly
more than the S&P 500.
In fact, of the seven funds listed in table 12.1, the Income Fund of America has
the lowest total return but the highest risk-adjusted return, illustrating the importance
of adjusting for risk. It is the “best” fund in table 12.1, in that, levered to
any desired level, it would have produced the highest return for any level of risk.
Qualifications to the RAP Approach
While we believe that RAP is a broadly applicable and practical measure of riskadjusted
performance, we recognize that there are legitimate qualifications to our
approach. We have found five worth considering, and outline them below. (A
more thorough treatment will have to wait for a companion article.)
Historical versus Future Performance
Our approach measures historical performance, which, as any investment
prospectus will tell you, is not necessarily indicative of future performance. A
number of studies have attempted to evaluate the predictive value of historical
performance, with mixed results.
We conclude that while historical results may not be a perfect indicator of
future performance, they remain useful and interesting information. Before deciding
how to invest going forward, investors are likely to want to know how various
fund managers performed in the past, and whether they were adequately compensated
for the risks to which they were exposed.
Alternative Measures of Risk
In keeping with modern portfolio theory, we have chosen standard deviation as
our measure of risk, and return as our measure of reward, deriving our equations
accordingly. A result of this choice is that RAP ranks portfolios the same way the
Sharpe ratio does (probably the current most popular measure of risk-adjusted
return). It may well be that investors feel more comfortable with other measures
of risk such as “downside risk,” however.
We therefore note that the RAP equation is a valid measure of risk-adjusted
performance that will identify the “best” portfolio for any measure of risk such