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180 Part Two RiskNotice that as N increases, the portfolio variance steadily approaches the average covari-
ance. If the average covariance were zero, it would be possible to eliminate all risk by holding
a sufficient number of securities. Unfortunately common stocks move together, not indepen-
dently. Thus most of the stocks that the investor can actually buy are tied together in a web of
positive covariances that set the limit to the benefits of diversification. Now we can under-
stand the precise meaning of the market risk portrayed in Figure 7.11. It is the average cova-
riance that constitutes the bedrock of risk remaining after diversification has done its work.Do I Really Have to Add up 25 Million Boxes?
“Adding up the boxes” in Figure 7.13 sounds simple enough, until you remember that there
are nearly 5,000 companies listed on the New York and NASDAQ stock exchanges. A portfo-
lio manager who tried to include every one of those companies’ stocks would have to fill up
about 5,000 × 5,000 = 25,000,000 boxes! Of course the boxes above the diagonal line of red
boxes in Figure 7.13 match the boxes below. Nevertheless getting accurate estimates of about
12,500,000 covariances is just impossible. Getting unbiased forecasts of rates of return for
about 5,000 stocks is likewise impossible.
Smart investors don’t try. They don’t try to forecast portfolio risk or return by “adding up
the boxes” for thousands of stocks. But they do understand how portfolio risk is determined
by the covariances across securities. (See the nearby example.) They appreciate the power of
diversification, and they want more of it. They want a well-diversified portfolio. Often they
end up holding the entire stock market, as represented by a market index.
You can “buy the market” by purchasing shares in an index fund: a mutual fund or exchange
traded fund (ETF) that invests in the market index that you want to track. Well-run index
funds track the market almost exactly and charge very low management fees, often less than
0.1% per year. The most widely used U.S. index is the Standard & Poor’s Composite, which
includes 500 of the largest stocks. Index funds that “track the S&P” have attracted about $2
trillion from investors.
If you have no special information about any of the stocks in the index, it makes sense to
be an indexer, that is, to buy the market as a passive rather than active investor. In that case,
there is only one box to add up. Just think of the market portfolio as occupying the top-left
box in Figure 7.13.
If you want to try out as an active investor, you are well-advised to (1) start with a widely
diversified portfolio, for example a market index fund, and then (2) concentrate on a few
stocks as possible additions. You may decide to trade off some investment in the stocks that
you are especially fond of against the resulting loss of diversification. In this case, the market
index fund occupies the top-left box, and the possible additions occupy a few adjacent boxes.
But our main takeaway so far is this: Smart and serious investors hold widely diversified
portfolios; their starting portfolio is often the market itself. How then should such investors
assess the risk of individual stocks? Clearly they have to ask how much risk each stock con-
tributes to the risk of a diversified portfolio.● ● ● ● ●7-4 How Individual Securities Affect Portfolio RiskThis brings us to our next major takeaway: The risk of a well-diversified portfolio depends
on the market risk of the securities included in the portfolio. Tattoo that statement on your
forehead if you can’t remember it any other way. It is one of the most important ideas in
this book.BEYOND THE PAGEmhhe.com/brealey12eCorrelations
between markets