# Equations in PM (market model and FMCAR)

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!