68 Corporate Finance
diversification diminish beyond a certain limit. Most textbooks conclude that 10–12 stocks are adequate to
reap the benefits of diversification. The marginal costs (like transaction and information costs) offset the
gains from diversification thereafter. More recently, Statman (1987)^2 proves that for a borrowing investor at
least 30 stocks are required and for a lending investor at least 40 stocks are required. When one plots the
distribution of historical returns of a diversified portfolio (of, say, 100 stocks) and compares it with the
distribution of returns of a single security, one finds that the standard deviation of returns of a single stock
is much more than that of the portfolio; yet the average return of the stock is lower than that of the portfolio.
What does this imply? Does the market not reward the higher riskiness of a stock with higher returns?
The answer lies in the benefits of diversification.
Standard deviation Portfolio return
HLL Colgate (percent) (percent)
100 percent 0 percent 4.012 0.974
90 10 3.848 0.884
80 20 3.728 0.794
70 30 3.654 0.704
60 40 3.63 0.614
50 50 3.657 0.524
40 60 3.734 0.433
30 70 3.857 0.343
20 80 4.023 0.253
10 90 4.227 0.163
0 100 4.463 0.073
Realized returns will be more in line with systematic risk rather than total risk. Wagner and Lau (1971)
divided 200 New York Stock Exchange (NYSE) stocks into six subgroups based on Standard & Poor stock
quality rating (from highest to lowest); randomly selected portfolios from each of the subgroups containing
from 1–20 stocks. Exhibit 3.9 presents the average monthly returns and standard deviation for the first sub-
group. It can be seen that although average return is unrelated to the number of stocks in the portfolio, the
standard deviation declines as the number of stocks increases. Almost 40 percent of risk can be eliminated
by holding 20 stocks.Exhibit 3.9 Effect of diversification on risk
No. of stocks Avg. monthly return S.D. per month (percent)
1 0.88 7.0
2 0.69 5.0
3 0.74 4.8
4 0.65 4.6
5 0.71 4.6
10 0.68 4.2
15 0.69 4.0
20 0.67 3.9(^2) Statman, Meir (1987). ‘How Many Stocks Make a Diversified Portfolio?’, Journal of Financial and Quantitative Analysis,
Vol. 22, No. 3.