do we need to know formulas for variance and covariance in market model
and how to calculate FMCAR?
Hi,
The LOS says: EXPLAIN the market model, STATE and INTERPPRET the market model’s predictions with respect to asset return, variances and covariances.
_ First - WHY is the market model so useful? _
It simplyfies the estimation procedures for conducting a mean-variance analysis.
Note: For a mean-variance analysis we need n expected returns, n variances and n*(n-1)/2 covariances forecasts.
=> By using the market model, we “only” need 3n+2 parameters to derive these required forecasts.
Why 3n+2?
Example: n=100
We need 100 expected returns, 100 variances and 100*(100-1)/2=4.950 covariance forecasts.
With the market model, we can derive these forecats with 100 alpha estimates, 100 ß estimates, 100 regression error variance estimates, 1 estimate of expected R(m) and 1 estimate of variance of market variance: 100+100+100+1+1=302
or: 3*n +2 = 300+2 = 302.
A) Premise of market model: there are 2 sources of risk:
a.1) systematic risk (=unanticipated macroeconomic events) > ß(i) x R(m)
a.2) unsystematic risk (=firm-specific events) > e(i)
B) There are 3 assumptions:
b.1) E(V) of error term = 0
b.2) errors are NOT correlated with R(m)
b.3) firm-specific surprises are NOT correlated across assets
C) There are 3 predictiions:
The market model predicts
c.1) E(Ri) = expected return for asset i = alpha(i) + ß(i) x E(Rm)
c.2) sigma(i)² = variance of asset i = ß(i)² x sigma(m)² + sigma(e)²
where ß(i)² x sigma(m)² = systematic component and sigma(e)² = unsystematic component
c.3) Cov(i,j) = covariance btw assets i and j = ß(i) x ß(j) x sigma(m)²
Thanks!
what about FMCAR?
To which LOS does FMCAR refer to in your opinion?
I would just try and remember it anyway 