APT vs CAPM sensivities estimation

[ryzhiy]

Hi guys,
In contrast to CAPM where one would regress the times series in order to estimate the market beta, the book says that in the APT the betas are to be estimated from cross section analysis? Could someone elaborate on this and tell how to precisely estimate those betas in the ATP model?
Thanks

 

[Aether]

Can you cite your source? Page# etc.?

 

[ryzhiy]

Let me rephrase, how one would estimate the betas in an Arbitrage Pricing Theory model?

 

[Aether]

Your original post threw me off - I don’t remember reading “cross-sectional analysis for estimating betas in APT” in the CFAI curriculum. You estimate the betas the same way you’d under CAPM… regression.

 

[whatsyourgovt]

isnt it just 1/3 + 2/3(historic b) but written as a AR model?

 

[Aether]

whatsyourgovt wrote:
isnt it just 1/3 + 2/3(historic b) but written as a AR model?

The betas we’re talking about has nothing to do with “adjusted beta” that you’re talking about.

 

[S2000magician]

ryzhiy wrote:Hi guys …

Howdy!

ryzhiy wrote:Hi guys,
In contrast to CAPM where one would regress the times series in order to estimate the market beta, the book says that in the APT the betas are to be estimated from cross section analysis? Could someone elaborate on this and tell how to precisely estimate those betas in the ATP model?
Thanks

The estimation is done via regression as with CAPM. The difference is that, as you say, the analysis is done cross-sectionally. Thus, they’ll look at, say, 100 firms (or 1,000 firms) and compare their returns over the same period to whatever factors they’ve included in the model (GDP growth, interest rates, industry size, geographical location, company’s net sales, who won the Super Bowl, whatever) and use those data to do their regression.

 

[Aether]

S2000magician wrote:
The estimation is done via regression as with CAPM. The difference is that, as you say, the analysis is done cross-sectionally. Thus, they’ll look at, say, 100 firms (or 1,000 firms) and compare their returns over the same period to whatever factors they’ve included in the model (GDP growth, interest rates, industry size, geographical location, company’s net sales, who won the Super Bowl, whatever) and use those data to do their regression.

Ummm, how do you compare the “GDP” of one firm to another? Also, when one of your factors is the market risk premium, there’s no “cross-sectional analysis.” I have never regressed S&P 500 returns, cross-sectionally, with Russell 2000 returns.
For all intents and purposes, the regression is based on historical data of the factor itself.
Unless you’re saying, ex-post, it’s the output of the model - let’s say the APT-based returns of company A and company B - that is compared cross-sectionally?

 

[S2000magician]

Aether wrote:

S2000magician wrote:The estimation is done via regression as with CAPM. The difference is that, as you say, the analysis is done cross-sectionally. Thus, they’ll look at, say, 100 firms (or 1,000 firms) and compare their returns over the same period to whatever factors they’ve included in the model (GDP growth, interest rates, industry size, geographical location, company’s net sales, who won the Super Bowl, whatever) and use those data to do their regression.

Ummm, how do you compare the “GDP” of one firm to another? Also, when one of your factors is the market risk premium, there’s no “cross-sectional analysis.” I have never regressed S&P 500 returns, cross-sectionally, with Russell 2000 returns.
For all intents and purposes, the regression is based on historical data of the factor itself.
Unless you’re saying, ex-post, it’s the output of the model - let’s say the APT-based returns of company A and company B - that is compared cross-sectionally?

Good point: I wrote those examples too hastily. I should have written that the factors are firm-specific: P/E ratio, size, profit margin, whatever.
Then sensitivities are calculated something like a z-statistic: (Factor-i – Factor-avg) / Factor-sigma.
Finally, the returns associated with each factor are calculated using regression analysis. You then multiply the firm-specific factor sensitivity by the regression-estimated factor return to get the firm-specific factor return for that factor; add up all of the firm-specific factor returns, plus the regression constant, to get the estimated return for firm i.

 

[CMLSML]

APT model uses only the returns data for stocks (or assets if the database has them). Actually, it only needs the variance covariance matrix to find the ‘factors’. The factors are themselves not known (nor revealed). Hence the relative futility of using it for estimating expected returns.

 

[ryzhiy]

magician: you are talking about fundamental factor model. I still don’t get whether FFM and APT is the same thing?
BTW, I’ve started this topic, cause I could not understand the following phrase from one of the Schweser’s questions:
APT is a cross-sectional equilibrium pricing model that explains the variation across assets’ expected returns during a single time period. Multi-factor model is a time serise regression that explains variation over time in returns for one asset.
I still don’t get it. Assume you have three companies A,B,C with the expected returns derived from the copmany specific projections (fundamental attributes) 7%, 9%, 14% respectively. Let’s assume that you are trying to follow the APT and you build a model as follows: E(R) = Rf + beta1*GDPrp + beta2*INFLrp + beta3*ROErp. How would you estimate the betas in this case?

 

[ryzhiy]

bump. anyone?