 # Using CAPM, find the equity betas

Based on CAPM and using the returns on the market portfolio and the risk-free rates, estimate the equity betas for the two companies A and B. If I keep it simple and use only three months, so return for A are: -10.91% 6.52% -3.74% returns for B are: 1.13% 3.85% 10.11% S&P 500 returns: 7.04% 4.99% 0.91% and risk free rate is: 0.43% 0.39% 0.39% I know I need to use the CAPM formula but I don’t whether to average everything, or calculate the equity betas one by one and then average that, it’s baffling

1. You can find betas without needing any kind of theory, such as CAPM. 2) Three months of monthly data is not sufficient to properly calculate a beta. This is because it is built upon linear regression techniques, which typically require a larger sample size. 3) There are multiple methods to calculate the beta. Best is to regress the excess returns of the security against the market. Under some conditions, the formula for this is correlation(security-rf,mkt-rf)*stdev(security-rf)/stdev(mkt-rf). If you can’t figure out how to calculate excess returns, standard deviations, or correlations, then you should look them up on wikipedia (beta is also on wikipedia). 4) If you want to check answers, I got stdev(A-rf)=8.8%, stdev(B-rf)=4.6%, stdev(mkt-rf)=3.1%, cor(A-rf,mkt-rf)=-0.23,cor(B-rf,mkt-rf)=-1. Beta(A)=-0.64 and Beta(B)=-1.49. 5) Technically, you would regress the excess log returns against excess log returns, project out to your horizon, convert to arithmetic returns, and then recalculate for the arithmetic beta, but since you are only working with arithmetic returns over one horizon you are okay.

I know you can use a formula for beta, and I can even use the SLOPE function in excel but my specific question asks using CAPM and the risk free rates. Also there is a lot more data than the 3 months, I just wanted to keep my post looking nice. Any idea using the CAPM formula?

What is the question exactly? Portfolio Return for CAPM equation PR = RF+ Beta (MR - RF) PR is portfolio return MR is market return RF is risk free You have to multiply return in one period by another to get geometric average. Using A for example (0.8909)*(1.0652)*(0.9626) = 0.9134 Just plug in the numbers and solve for Beta. Is that what you want?

rg2005 Wrote: ------------------------------------------------------- > I know you can use a formula for beta, and I can > even use the SLOPE function in excel but my > specific question asks using CAPM and the risk > free rates. > > Also there is a lot more data than the 3 months, I > just wanted to keep my post looking nice. > > Any idea using the CAPM formula? I do it in my post with the “CAPM formula.”