In Chapters 7 and 8 we examined several models that were developed to simplify the inputs to the portfolio selection problem. Each of these models makes an assumption about why stocks covary together. Each leads to a simplified structure for the correlation matrix or covariance matrix between securities. These models were developed to cut down on the number of inputs and simplify the nature of the inputs needed to forecast correlations between securities. The use of these models was expected to lead to some loss of accuracy in forecasting correlations, but the ease of using the models was expected to compensate for this loss of accuracy. However, we have seen in Chapters 7 and 8 that when fitted to historical data, these simplifying models result in an increase, not a decrease, in forecasting accuracy. The models are of major interest because they both reduce and simplify the inputs needed to perform portfolio analysis *and* increase the accuracy with which correlations and covariances can be forecast.

In this chapter we see that there is yet another advantage to these models. Each allows the development of a system for computing the composition of optimum portfolios that is so simple it can often be performed without the use of a computer. Perhaps even more important than the ease of computation is the fact that the methods of portfolio selection described in this chapter make it very clear why a stock does or does not enter ...

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