This abstraction is the notion of an "index model," specifying the process by which security returns are generated. Our discussion of the index model also introduces the concept of multifactor models of security returns, a concept at the heart of contemporary investment theory and its applications.

III. Equilibrium In Capital Markets

10. Single−Index and Multifactor Models The McGraw−Hill

Companies, 2001

CHAPTER 10 Single-Index and Multifactor Models 293

10.1 A SINGLE-INDEX SECURITY MARKET

Systematic Risk versus Firm-Specific Risk

The success of a portfolio selection rule depends on the quality of the input list, that is, the estimates of expected security returns and the covariance matrix. In the long run, efficient portfolios will beat portfolios with less reliable input lists and consequently inferior re- ward-to-risk trade-offs.

Suppose your security analysts can thoroughly analyze 50 stocks. This means that your input list will include the following:

n 50 estimates of expected returns

n 50 estimates of variances

(n2 n)/2 1,225 estimates of covariances

1,325 estimates

This is a formidable task, particularly in light of the fact that a 50-security portfolio

is relatively small. Doubling n to 100 will nearly quadruple the number of estimates to

5,150. If n 3,000, roughly the number of NYSE stocks, we need more than 4.5 million