# CAPM and Market Model & Multifactor models

I know the formulas for both and understand that CAPM is logical extension from CML line. So if everybody has same market expectations then everybody ends up with the same CAL which is then the SML as everybody holds same assets(=market). If that’s the case then people only get rewarded for systematic risk and the expected return for an indiviudual security is estimated with CAPM. So far so good.

Market Model: Return=a+B(Market Return) +e. Apparently first factor Model? and it’s not returning E® but R… so how is that related to CAPM? Furthermore: MultiFactor models are probably only an extension of market model? Then what about APM Model which looks similar to Multifactor Model but apparently only used to estimate inputs of multifactor models?

Just had a thought. CAPM based on efficient markets so Alpha (mispricing) doesn’t exist. Market Model: obviously includes Alpha so does this model work for efficent and not so efficient markets?

Market model is not a factor model. Market model is simply a model for estimating mean variance analysis inputs such as:

a) Expected return of asset b) Variance of return of asset c) Covariance of return between assets

The relationship with CAPM is that you can use market model’s Beta for calulcation in CAPM. But since this Beta is derived from historical regression, you will need to calculate the adjusted or forecasted Beta for greater accuracy of required return calculation.

It is a factor model in the sense that the market return determines the return of the stock. The expected return on the stock depends only on the expected return of the market portfolio, E(RM), the sensitivity of the returns of stock to movements in the market, and “alpha” which is the average return of stock when the market return is zero.

Thanks g3r41d. That together with Drearys comments makes sense. One more question though: Macroeconomic Factor Models intercept a would be the expected return if there’s no surprises according to Multifactor reading in Portfolio Analysis. It seems though as not all macroeconomic Models are structured that way. The Birr model introduced in Equity Book for example seems to have risk free rate as intercept so without any surprises the return would the RF rate?

Well in that case, APT is a multifactor model with Rf as the intercept! If the factors are surprises then the model has “a” as the expected return, whereas, if factors are risk premiums, then it’s Rf.

What about BIRR Model? that’s clearly a macroeconomic model, uses surprise factors BUT RF rate as min. return if no surprises?

I don’t recall BIRR now, but I think it is similiar to FFm and PSM, so it shouldn’t have surprises…are you sure?

Yes, just checked again. Page 86-87 Equity book. Uses RF and surprises so I suppose we just have to remember specs of model and then work with them. It just seemed strange that a macro model that uses surprises has RF as “no surprises” result. Doesn’t make sense to me as one risk adverse investor would then prefer RF investments without volatility ?

You really can’t have “surprises” as input if you have Rf {risk free rate} as the intercept, as you do in APT. If there were no surprises, you couldn’t earn more than Rf…

For macroeconomic models, however, you have the expected return as intercept combined with sensitivities to various “surprises”. If there are no surprises, you get what you expected to get according to this other model.

APT, however, is an equilibrium asset pricing model, like CAPM. Since it’s an equilibrium model, the sensitivities are actual risk premiums to whatever that particular sensitivity is measuring.

BIRR stands for Burmeister, Ibbotson, Roll and Ross. The BIRR core model works with domestic macroeconomic surprises. The BIRR model consists of five factors, macroeconomic factors that is. It’s an equity risk model. The company actually has it’s own web page, and on their page (at www.birr.com) they’ve posted some interesting material on the topic. Non-diversifiable surprises affect all equities: interest rates, inflation, economic growth, market sentiment, and it seems the core factors are based on these: confidence risk, time-horizon risk, inflation, business cycle risk, market sentiment risk. The two first risks (confidence and time-horizon) belongs to the interest rate category and are based on government and coroporate bond and bill returns. A boom in the business cycle triggers economic growth, and finally “sentiment” which has to do with market timing and bull/bear markets etc.