do we need to know formulas for variance and covariance in market model

and how to calculate 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!

what about FMCAR?

To which LOS does FMCAR refer to in your opinion?

I would just try and remember it anyway