Using CAPM to Estimate a Stock’s Expected Return
Summary
The document explains how to interpret a stock-return regression through the Capital Asset Pricing Model. Under CAPM, expected stock return is the risk-free rate plus the stock’s beta multiplied by the market’s expected excess return. Beta is defined as the covariance of market and stock returns divided by the variance of market returns, linking the estimate to the stock’s sensitivity to market movements.
To apply the model, an investor needs an estimate of the market risk premium; the response notes that historical index returns are often used, while warning that this estimate is imperfect. It also cautions that a regression intended to estimate CAPM should use market excess returns. Using raw market returns can distort the intercept, though the response says beta should remain valid. The discussion does not provide a market-premium estimate or resolve which risk-free maturity suits a particular forecast or valuation horizon.
Key ideas
- CAPM expresses expected stock return as the risk-free rate plus beta times the market risk premium.
- Beta measures the covariance of stock and market returns relative to market return variance.
- Historical index returns are one common but imperfect basis for estimating the market premium.
- A CAPM regression should use market excess returns to avoid distorting the intercept.
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Full text
# Regression giving the return on a stock
# 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%.
- What is the expected return on the stock the nearest year?
- 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.
## Answer by zuiqo (score 2)
https://quant.stackexchange.com/a/7333
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).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.