Page 211 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes This is all profound and important stuff. And, unfortunately, highly misleading. To be blunt, if
you think that you can do an adequate job of minimizing portfolio risk with 15 or 30 stocks, then
you are imperiling your financial future and the future of those who depend on you. The reason
is simple: There are critically important dimensions of portfolio risk beyond standard deviation.
The most important is so-called Terminal Wealth Dispersion (TWD). In other words, it is quite
possible (in fact, as we shall soon see, quite easy) to put together a 15-stock or 30-stock portfolio
with a very low SD, but whose lousy returns will put you in the poorhouse.
This issue has not been much investigated or discussed. One of the pioneers in this area is
Edward O’Neal of Auburn, who in a piece in Financial Analysts Journal a few years back
looked at TWD as a function of the number of mutual funds. His data show that the risk of TWD
falls off as 1/sqrt(n); in other words, a portfolio of four mutual funds is half as risky as one.
However, I’m not aware of any definitive studies of TWD as a function of the number of stocks.
In order to investigate this problem, I looked at the stocks constituting the S&P 500 as of 11/30/
99, and formed 98 random equally-weighted 15-stock portfolios for the 12/89-11/99 10-year
holding period. Below is a histogram of the annualized portfolio returns:

The “market return” (all 500 stocks held in equal proportion) was 24.15%. This is considerably
higher than the 18.94% return of the actual S&P for two reasons: First, the S&P is a cap-weighted,
not an equal-weighted, portfolio. Second, and much more important, many of the stocks in the
S&P on 11/30/99 were not in the index at the beginning of the period. The recently-added stocks
obviously had much higher returns than the companies they replaced, upwardly biasing the
entire series of returns. Nonetheless, these flaws in the methodology do not change the basic
conclusion; the TWD of these 15-stock portfolios is staggering—three-quarters of them failed to
beat “the market.” (Had the study been done with the S&P stocks extant on 12/1/99, it seems
certain that the positive kurtoskewness of the present sample would have been replaced with a
significant negative kurtoskewness—a much more important descriptor of risk. If anybody
wants to give me a survivorship-bias-free S&P database for the past 10 years, my modem and
mailbox are in fine working order.) Even so, the scatter of returns was quite high, with more
than a few portfolios underperforming “the market” by 5%-10% per annum.

The reason is simple: a grossly disproportionate fraction of the total return came from a very
few “superstocks” like Dell Computer, which increased in value over 550 times. If you didn’t
have one of the half-dozen or so of these in your portfolio, then you badly lagged the market.

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