"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

Risk-Adjusted Performance 301
Nonetheless, we checked our results using geometric returns, and for the selection
of funds analyzed, the results are very similar. Given the industry standard
for geometric returns, we plan to devote further study to this issue.
Recombining Portfolios for Superior Performance—Protection
Against “Idiosyncratic” Risk
While RAP unambiguously identifies the “best” single portfolio for any set of
portfolios with the same benchmark, it does not consider new combinations of
those portfolios that could be optimal. It is conceivable that an even better portfolio
could be constructed by combining the set of existing portfolios.
For instance, in theory, a new portfolio could be created consisting of the combination
of the second- and third-ranked portfolios to produce a superior riskadjusted
return and ranking above the number one-ranked portfolio. The lower
the correlation between any two portfolios, the more likely it is that combining
them would produce a superior risk-adjusted return.
One special case of this condition is the market benchmark combined with any
other portfolio. For the selection of funds we analyze in table 12.1, we looked at
whether any portfolio could be recombined in any proportion with the S&P 500
to produce a higher risk-adjusted return than the number one-ranked portfolio.
We found that the funds tend to be highly correlated with the market, and therefore
recombining them with the S&P 500 does not produce superior performance.
Nonetheless, as with any other portfolio selection method, portfolio optimization
techniques should be employed to evaluate the recombination of assets for
superior performance. (Note that performance should always be measured on a
risk-adjusted basis as with RAP.)
Similarly, when selecting a fund that is to be combined with other investments
in a portfolio, investors should consider the correlation between asset returns.
Given the composition of an investor’s total portfolio of wealth (including, for
instance, earning capacity or real estate) and the resulting exposure to specific
idiosyncratic risk, an investor may wish to consider diversifying into specialized
funds (such as an energy portfolio). A fund that is best by the RAP criterion is
not necessarily the optimal addition to an existing portfolio. Portfolio optimization
techniques should also be employed to help identify the best addition to an
existing portfolio as the addition that leads to the best risk-adjusted performance
(RAP) for the portfolio as a whole.
Tracking Error and the Information Ratio
One performance measure that has been gaining in popularity is the so-called
information ratio, defined as the portfolio’s average excess return above the