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

304 Miscellanea
Finally, one may wish to consider a variant of (12.A-2) that measures the difference
between risk-adjusted return and the return on the market as a percent of
the market return:
RARP = 100( e() i e M -1)
(12.A-3)
Notes
1. An alternative to the S&P 500 could be any unmanaged market portfolio (e.g., a global index fund)
that represents the universe of investments relevant to the portfolio manager (or a close
approximation).
2. The variance of r i , V(r i ), is not necessarily the same as the variance of e i , V(e i ) = V(r i - r f ) = V(r i )
+ V(r f ) - 2Cov(r i , r f ) unless r f is treated as a constant, making V(e i ) = V(r i ). We have found V(e i ) to
be very close to V(r i ) and have treated r f as constant throughout this article. Note that one way to
make r f constant is to set it equal to the rate (yield) on an n-year fixed-income security at the beginning
of the n years being evaluated (this is the expectation of the short-term rates for the future n
years).
3. Note that here we have assumed that the borrowing and lending rates are the same. Given that
investors can borrow against the equity portion of their portfolio, we do not expect the difference in
borrowing and lending rates to be great. Nonetheless, changing this assumption is a relatively minor
adjustment, which involves using the appropriate rate based on whether d i is positive or negative.
References
Jensen, Michael C. “The Performance of Mutual Funds in the Period 1945–1964.” Journal of Finance,
May 1968.
Sharpe, William F. “Mutual Fund Performance.” Journal of Business, Supplement on Security Prices,
39 (January 1966).
Treynor, Jack L. “How to Rate Management Investment Funds.” Harvard Business Review, 43
(January–February 1966).