Rolling Regression to Calculate Abnormal Returns

[Hoa Phan]

Hi there,
I used the rolling regression with window 12 months to calculate expected Beta and then I calculate expected returns. After that, I calculate abnormal returns = Real returns - Expected returns.
My codes is as the following:

asreg excessR MarpreCSI SmB HmL MOM , wind( Month 12)

gen expectedALPHA4= Riskfreerate3monthdeposit + _b_MarpreCSI * MarpreCSI +_b_SmB * SmB + _b_HmL * HmL +_b_MOM * MOM

gen ALPHA4= rp- expectedALPHA4

and I also calulate the residuals as:

gen resid4= excessR - _b_cons - _b_MarpreCSI * MarpreCSI - _b_SmB * SmB - _b_HmL * HmL - _b_MOM * MOM

So, I wonder my code is correct or not?

Thank you in advance!

[Joro Kolev]

Is there a question, or you are reporting on your success?

[Hoa Phan]

Is there a question, or you are reporting on your success?

This is a question? Please let me know whether is correct or not or could you please suggest me another way!

[Joro Kolev]

-asreg- is a user written command with which I am not familiar, so I cannot comment on this part. You should just read the help file to see whether -asreg- is doing what you think it is doing.

As for the finance part of what you are doing, the constant in a regression of excess returns on the risk factors is the alpha. So your code

gen expectedALPHA4= Riskfreerate3monthdeposit + _b_MarpreCSI * MarpreCSI +_b_SmB * SmB + _b_HmL * HmL +_b_MOM * MOM

gen ALPHA4= rp- expectedALPHA4

is at best redundant, or at worst incorrect.

I think these two lines should be replaced by the single line

gen ALPHA4= _b_cons

The last line is correct, but -asreg- might be able to directly generate residual, or predicted values, and then if so, you can simplify.

This is a question? Please let me know whether is correct or not or could you please suggest me another way!

[Hoa Phan]

At first, I aslo think that ALPHA4=_b_cons

However, on the paper of Journal of Finance, they estimate coefficients (beta), then they calculate expected returns. After that, Alpha (abnormal returns) = real returns - expected returns.
That's why I code like this:

gen expectedALPHA4= Riskfreerate3monthdeposit + _b_MarpreCSI * MarpreCSI +_b_SmB * SmB + _b_HmL * HmL +_b_MOM * MOM
gen ALPHA4= rp- expectedALPHA4

[Joro Kolev]

The CAPM, and the multifactor generalisations work just as the CAPM, is

1) E(Ri) = Rf + b*(Mkt - Rf).

I can rewrite this as

2) E(Ri - Rf) = a + b*(Mkt - Rf), and observe that the CAPM eq.1 predicts that my a has to be 0.

Therefore it is not what I thought or you thought, the CAPM says that anything in E(Ri - Rf) which is not explained by b*(Mkt - Rf) is excess return. The parameter a is the constant in your regression and it is the excess return.

You can also use eq.1 directly, but then you need to be careful, the term is (Mkt - Rf) -- this is the excess return of the market over the risk free rate -- and you are using a term _b_MarpreCSI * MarpreCSI which does not look like an excess return at all, MarpreCSI looks like a raw return.

[Hoa Phan]

MarpreCSI is equal = Market returns - rf. So, I think you are correct, the b_cons is the ALPHA.
Thank you so much!

You can also use eq.1 directly, but then you need to be careful, the term is (Mkt - Rf) -- this is the excess return of the market over the risk free rate -- and you are using a term _b_MarpreCSI * MarpreCSI which does not look like an excess return at all, MarpreCSI looks like a raw return.

[Hoa Phan]

I double check again and I found that you have to use the expected beta.

So, the first steps:

asreg excessR MarpreCSI SmB HmL MOM , wind( Month 12)

to estimate beta

The second step I have to calcuate the expected returns from expected beta, and then I calculate abnormal returns = actual returns - expectect returns.

after run the regression:

asreg excessR MarpreCSI SmB HmL MOM , wind( Month 12)

I try by use: predict yhat,xb

However, this is does not work

So, I think that my below code may be correct:

gen expectedALPHA4= Riskfreerate3monthdeposit + _b_MarpreCSI * MarpreCSI +_b_SmB * SmB + _b_HmL * HmL +_b_MOM * MOM
gen ALPHA4= rp- expectedALPHA4

[Hoa Phan]

Thank Joro. I got it. You are right, ALPHA4 =_b_cons.

The CAPM, and the multifactor generalisations work just as the CAPM, is

1) E(Ri) = Rf + b*(Mkt - Rf).

I can rewrite this as

2) E(Ri - Rf) = a + b*(Mkt - Rf), and observe that the CAPM eq.1 predicts that my a has to be 0.

Therefore it is not what I thought or you thought, the CAPM says that anything in E(Ri - Rf) which is not explained by b*(Mkt - Rf) is excess return. The parameter a is the constant in your regression and it is the excess return.

You can also use eq.1 directly, but then you need to be careful, the term is (Mkt - Rf) -- this is the excess return of the market over the risk free rate -- and you are using a term _b_MarpreCSI * MarpreCSI which does not look like an excess return at all, MarpreCSI looks like a raw return.