Answer:
In a single index model:
ri - rf = α i + β i (r M - rf ) + e i
Equivalently, using excess returns:
R i = α i + β i R M + e i
The variance of the rate of return can be decomposed into the components:
The variance due to the common market factor
Bi^2stdvm^2
The variance due to firm specific unanticipated events
STDV^2(ei)
In this model
Cov(ri,rj) =BiBjSTDV
The number of parameter estimates is:
n = 60 estimates of the mean E(ri )
n = 60 estimates of the sensitivity coefficient β i
n = 60 estimates of the firm-specific variance σ2(ei )
1 estimate of the market mean E(rM )
1 estimate of the market variance
Therefore, in total, 182 estimates.
The single index model reduces the total number of required estimates from 1,890 to 182. In general, the number of parameter estimates is reduced from:
(n^2 +3n / 2) to (3n+2)
