Question

Assume you have a total number of 50 shares available, and that you construct an optimal portfolio using the Single Index Model (SIM) with these 50 securities. Compute the number of estimates needed to construct the portfolio:

A. The number of estimates is as high as 1,325.
B. The number of estimates is as high as 1,225.
C. The number of estimates is as high as 152.
D. The number of estimates is as high as 150.

Answer 1

Answer is c.the number of estimates is as high as 152.

In Single Index Model, for N securities, estimates would be 3N+2. Thus, for 50 securities it would be 152. In the Single Index model, only three estimates are required for each security i.e. specific return, measure of systematic risk and variance of the residual return. In addition to it two estimates of the market index is required that is market return and variance of the market return. Thus, required estimates would be 3N+2.