# Regression giving the return on a stock

I have this regression equation:

$$R_{stock} = 3,28\% + 1,65*R_{market}$$

Where $R_{stock}$ is the expected return on a stock and $R_{market}$ being the market risk premium.

I have a one-year T-bill rate of 4,8% and a 30-year T-bond rate of 6,4%.

1. What is the expected return on the stock the nearest year?
2. Would the expected return change if we were to compute the discount rate to value cash flow, and if so, how?

I do not know if I just assume an $R_{market}$ rate?

Swap the 3,28% for the T-bill rate in (1) and the T-bond rate in (2) to get an expected return.

So how do you estimate $R_{market}$, just by assuming or is there a way to find out? And do I let $\beta$ (1,65) go to 1 as we calculate with a T-bond rate for 30 years and $\beta$ is assumed to fluctuate around 1 in the long term.

• this smells awfully like homework. And by the way your setup is not clearly outlined at all. You make people assume the risk free rate is 3.28% although later on you state it is 4.8%. I guess you copied the first equation from somewhere and 3.28% only constitutes an example? And I thought we all learned in middle school that one equation with two unknowns cannot be pinpoint to one solution. – Matt Feb 20 '13 at 2:49

## 1 Answer

The basic CAPM - which is what your regression estimates - says $$R_S = R_f + \beta_S (R_{Market}-R_f)$$ where $$\beta_S = \frac{Cov(R_M,R_S)}{Var(R_M)}$$ i.e. the return of a certain stock depends only on the correlation with the market portfolio.

For your pricing equation to work, you will need to have an idea about the expected market (excess) return. In practice, often the historical mean return of an index (such as S&P 500, ...) is used, but that is very far from perfect. Only that assuming seems like an even worse idea to me...

Keep in mind that, if you want to estimate the regression, you need to use excess returns for the market, otherwise your intercept will be the wrong one (though beta should be fine).