A portfolio management organization analyzes 56 stocks and constructs a mean-var

Question

A portfolio management organization analyzes 56 stocks and constructs a mean-variance efficient portfolio using only these 56 securities.

b. If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed?a. How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio?

estimates =

How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio? Estimates of expected returns Estimates of variances Estimates of covariances Total estimates

Explanation / Answer

a.
Estimates of mean =n =56
Estimates of variance=n=56
Estimates of co-variances = [(56)^2– 56] / 2 = 1,540
Total estimates = 56+56+1540=1652

b.
ri– rf=i+ i(rM– rf) + ei
i=stock’s expected return when market’s excess return = 0
i(rM-ri) =Market movement return component
ei=unexpected firm-specific events returnc component
rf= Risk free rate
E(rM) =Expected return on market
=Beta

Variance of return on each stock is decomposed into :i) Variance due to common market factor = i
ii) Variance due to unanticiapted firm specific events= Cov(ri,rj) =ij*standard deviation
Estimates of mean =n =56
Estimates of sensitivty coefficient beta=n=56
Estimates of firm specific varaince=n=56
Estiamtes of market mean=1
Estimates of market variance=1
Total estimates = 56+56+56+1+1=170

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