# Unit 12: Models

Unit 12: Models

The application of Markowitz’s model requires estimation of large number of co-variances.

And without having estimates of co-variances, one cannot compute the variance of portfolio returns.

This makes the task of delineating efficient set extremely difficult.

However, William Sharpe’s single-index model’ simplifies the task to a great extent.

Even with a large population of assets from which to select portfolios, the numbers of required estimates are amazingly less than what are required in Markowitz’s model.

But how accurate is the portfolio variance estimate as provided by the single-index model’s simplified formula? While the Markowitz’s model makes no assumption regarding the source of the co-variances, the single-index model does so.

Obviously, the accuracy of the latter model’s formula for portfolio variance is as good as the accuracy of its underlying assumptions.

Some other portfolio selection models that seem to hold great promises to practical applications are also looked at here.

Security Analysis and Portfolio Management Notes One such model is the multi-factor model.

There are different variants of this model and each of them is developed to capture some of the non-market influences that cause shares to move together (recall that single-index model accounts for only market-related influences).

The non-market influences, in essence, include a set of economic factors or industry (or group) characteristics that account for common movement in share prices.

While it is easy to find a set of indices that are associated with non-market effects over any period of time, it is quite another matter to find a set that is successful in predicting covariances that are not market related.

There is still a great deal of work to be done before multi-index models consistently outperform the simpler one.

Beta: The beta ( ) of a stock or portfolio is a number describing the relation of its returns with that of the financial market as a whole.

Efficient Frontier: A line created from the risk-reward graph, comprised of optimal portfolios.

Portfolio Manager: The person or persons responsible for investing a mutual, exchange-traded or closed-end fund’s assets, implementing its investment strategy and managing the day-to-day portfolio trading.