In this section, we look at some issues surrounding the theory of portfolio selection and the practical implementation of the model.

Index Model’s Approximations to the Covariance Structure

The inputs to mean-variance analysis include expected returns, variance of returns, and either covariance or correlation of returns between each pair of securities. For example, an analysis that allows 200 securities as possible candidates for portfolio selection requires 200 expected returns, 200 variances of return, and 19,900 correlations or covariances. An investment team tracking 200 securities may reasonably be expected to summarize their analyses in terms of 200 means and variances; but it is clearly unreasonable for them to produce 19,900 carefully considered correlations or covariances.
EXHIBIT 3.12 The Effect of Restricting Short Selling: Constrained versus Unconstrained Efficient Frontiers Constructed from 18 Countries from the MSCI World Index
It was clear to Markowitz that some kind of model of covariance structure was needed for the practical application of normative analysis to large portfolios. One model he proposed to explain the correlation structure among security returns assumed that the return on the security depends on an “underlying factor, the general prosperity of the market as expressed by some index.” Mathematically, the relationship ...

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