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

290 Miscellanea
gaining exposure to a higher level of risk. In other words, we want to know
whether a fund produces a return over and above the return that could have been
achieved simply by exploiting the opportunity that the market offers any
investor—to obtain higher expected returns in exchange for greater uncertainty.
The answer to the question of how to evaluate performance requires an
approach that takes risk differentials into account. In March 1995, the Securities
and Exchange Commission (SEC) solicited comment on how to improve mutual
fund risk disclosure. It received an overwhelming 3,700 comments and letters in
response. While there was general agreement that more information on risk is
desirable, there was little consensus on a suitable quantitative measure of either
risk or risk-adjusted performance.
Currently, the most common measure of risk-adjusted return is the “Sharpe
ratio,” which converts total returns to excess returns by subtracting the risk-free
rate, and then divides that result by a common measure of dispersion, the standard
deviation or sigma, to get a measure of “reward per unit of risk” (see Sharpe
[1966]). Other methods devised by Jensen [1968] (Jensen’s alpha) and Treynor
[1966] (the Treynor ratio) adjust excess returns for the capital asset pricing
model’s beta.
While experts may find these measures helpful in comparing funds, the resulting
figures are difficult to interpret, at least for the average investor not intimately
familiar with regression analysis and the modern theory of finance. This inaccessibility
at least partially explains the investment community’s lack of consensus
as to an appropriate measure of risk and the SEC’s decision not to adopt a
quantitative measure of risk or risk-adjusted performance, at least for the time
being.
An Alternative Measure of Risk-Adjusted Performance (RAP)
We propose an alternative measure of risk-adjusted performance (RAP) that is
grounded in modern finance theory and yet easy for the average investor to understand.
Following conventional methods, we propose measuring the performance
of any managed portfolio against that of a relevant unmanaged “market” portfolio.
Unlike prevailing methods, however, RAP makes the comparison in performance
only after properly adjusting the portfolio return for risk.
The basic idea underlying RAP is to use the market opportunity cost of risk,
or trade-off between risk and return, to adjust all portfolios to the level of risk in
the unmanaged market benchmark (e.g., the S&P 500), thereby matching a portfolio’s
risk to that of the market, and then measuring the returns of this riskmatched
portfolio. 1 Like the original return, the risk-adjusted performance of any