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Index models - Portfolio construction and the single index model

5 important questions on Index models - Portfolio construction and the single index model

Why don't you just hold the market index?

Security analysis gives us the chance to uncover securities with a nonzero alpha and to take a differ- ential position in those securities. The cost of that differential position is a departure from efficient diversification, in other words, the assumption of unnecessary firm-specific risk. The model shows us that the optimal risky portfolio trades off the search for alpha against the departure from efficient diversification.

What is the active portfolio?

An active portfolio, denoted by A, comprised of the n analyzed securities (we call this the active portfolio because it follows from active security analysis).

What is the passive portfolio?

The market- index portfolio, the (n + 1)th asset we include to aid in diversification, which we call the passive portfolio and denote by M.

What is the relation between the correlation and active and passive portfolio for any level of variance A?

For any level of Variance A, the correlation between the active and passive portfolios is greater when the beta of the active portfolio is higher. This implies less diversification benefit from the passive portfolio and a lower position in it. Correspondingly, the position in the active portfolio increases.

What happens when a security's alpha is negative?

The security will assume a short position in the optimal risky portfolio. If short positions are prohibited, a negative- alpha security would simply be taken out of the optimization program and assigned a port- folio weight of zero.