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Annalena
Fluorite | Level 6

Hello everybody,

 

I am doing an event study based on the constant mean return model and I'm stuck with regressing the model parameters.

The constant mean return model assumes that expected asset returns can differ by company, but are constant over time. The constant mean return model is:

R_{i,\tau}=\mu_{i}+\epsilon_{i,\tau}

 

where

 \hat{\mu_{i}}=\frac{1}M_i \sum_{i=T_{0+1}}^{T_1} R_{i,\tau} = the average of the estimation window returns.

 

I have the code to estimate the parameters if the market model was used, but i am stuck on changing it. The market model is based on the assumption of a constant and linear relation between individual asset returns and the return of a market index:

 R_{i,\tau}=\alpha_i+\beta_i R_{M,\tau}+\epsilon_{i,\tau}

 

This is the code for the market model:

 

proc reg data=estper outtest=mmparam;

by firm;

model ret = mrktret;

quit;

 

The problem with the standard regression procedure for the constant mean return model is now that I technically have alpha = 0 and beta = 1 fixed but i don't know how to this. I need to do a regression because I need  the standard error for testing.

 

I'd greatly appreciate it if anybody could help me with this! 🙂

4 REPLIES 4
WarrenKuhfeld
Rhodochrosite | Level 12

Have you tried the restrict statement?  Sounds like it does exactly what you want.

proc reg data=sashelp.class;
  model weight = height;
  restrict intercept=0;
  restrict height=1;
quit;
PGStats
Opal | Level 21

How about:

 

proc glm data=estper;
class firm;
model ret = firm;
lsmeans firm;
run; quit;
PG
Annalena
Fluorite | Level 6

Both your solutions didn't completely do what I need. I can't use GLM because it's not recommended by the theoretical foundations I am using in my thesis. This is the solution I found now:

/*Computing the constant mean return model parameters in estimation period*/

PROC MEANS data = estper MEAN NOPRINT;
VAR ret;
BY Firm ;
OUTPUT OUT= cmparameter(drop=_type_ _freq_)
MEAN(ret)=mu;
RUN; QUIT;

/*Computing of AR and its var in estimation period*/

Data AR;
	merge estper cmparameter;
	by firm;
	ar = ret - mu;
Run;Quit;

Proc Means data=AR var noprint;
	by firm;
	output out = AR (drop=_type_ _freq_)
	var(ar)=varar_est;
Run;

I guess there probably is a shorter way to do this.

PGStats
Opal | Level 21

Yes:

 

proc means data=esper /* vardef=n */ noprint;
by firm;
var ret;
output out=mv(drop=_type_ _freq_) mean=mu var=varar_est;
run;

uncomment vardef=n if you want to match your procedure above exactly. 

 

PG

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