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Risk-Adjusted Performance 297
relation to the market return r M . RAP is found by moving along the portfolio’s
leverage opportunity line, l i , until reaching the perpendicular line through s M , and
then reading the corresponding return on the return-axis. At that point, the difference
between RAP(i) and r M represents the over- or underperformance of portfolio
P i in basis points.
From figure 12.1 we see that while portfolio 1, represented by point P 1 , has a
higher total return, r 1 , than the market, r M , its risk-adjusted performance, RAP(1),
is lower than that of the market. This indicates the relative to the market benchmark,
portfolio 1 does not achieve a return sufficiently above the market to compensate
investors for its extra risk. Similarly, while portfolio 2, represented by
point P 2 , has a lower total return, r 2 , than the market, r M , its risk-adjusted performance,
RAP(2), is higher than that of the market. This indicates that investors
are more than adequately compensated for the risk that they take with portfolio
2 compared with the market benchmark.
Also, portfolio 2, with the highest RAP, achieves the highest level of return at
not only the market level of risk, s M , but also at every level of risk. An investor
levering or unlevering portfolio 2 would move along its leverage line, l 2 , thereby
achieving the highest return for any given level of sigma corresponding to a
desired level of risk.
Application of the RAP Measure
In table 12.1 we have applied RAP to a selection of portfolios to illustrate the
difference between total and risk-adjusted return and to demonstrate the usefulness
of the RAP measure. The exhibit shows that some of the most glamorous
funds turn out to be far less attractive on a risk-adjusted basis.
Consider, for example, the T. Rowe Price New Horizon fund. Over the last ten
years, the New Horizon fund produced an average annual return of 16 percent,
significantly outperforming the 14.1 percent return of the S&P 500. It was substantially
more volatile than the market, however.
An evaluation of risk-adjusted performance requires that portfolios be measured
on a risk-equivalent basis. In order to “dampen” the New Horizon fund’s
volatility to match it to that of that of the S&P 500, it would have been necessary
to liquidate 36 percent of the fund and invest the proceeds in risk-free assets
(see last column of table 12.1). The yield of this restructured portfolio is precisely
RAP and, as reported in column (5), is but 12.2 percent, well below the market’s
14.1 percent. By the same token, investors who preferred the greater level of
volatility associated with the New Horizon fund could have made higher returns
by levering the S&P 500 (22 percent versus 16 percent).