Sector diversification and second order risk

It is generally accepted that the average standard deviation (first order risk) of a randomly selected portfolio of ten shares is reduced very little by adding more shares. Davidson and Meyer show that the variability of the standard deviation (second order risk) of portfolios of ten shares is large. Investors need to increase the number of shares substantially to reduce second order risk. This paper evaluates sector diversification (selecting shares randomly from different sectors) as a potentially inexpensive method of reducing second order risk. We find that sector diversification reduces second order risk, but not sufficiently to eliminate the need for investors to hold portfolios with many shares. Our results lend support to those of Davidson and Meyer, who argue that second order risk explains the rise of large institutional investors, since individuals use large institutions as investment vehicles to reduce second order risk.