Category Archives: CAPM and Beta

Recap of the Capital Asset Pricing Model (CAPM)

The CAPM states the following:

E(R) = Rf + β(E(Rm) – Rf)

where R is the return on the asset of interest, Rf is the risk-free rate of return, Rm is the rate of return for the entire market (the market portfolio) and β is a parameter that describes the sensitivity of the asset’s return to the market’s return.

To estimate a stock’s β, you therefore need historical data on a stock’s returns, the market’s returns, and the risk-free interest rate. You can calculate returns from an asset’s prices as follows:

Rt = (Pt + Dt – Pt-1) / (Pt-1)

Where Rt is the asset’s return in period t, Pt is the asset’s price in period t, and Dt is the dividend on the stock in period t (usually 0). It is customary to use a broad-based market index (such as the S&P 500 or the Wilshire 5000) to estimate the returns on the market portfolio and to use the returns on short term US Treasury bills to estimate the risk-free rate of return.

The following regression model can then be used to estimate a stock’s β:

Rt – Rft = α + β(Rmt – Rft) + ut

If the CAPM holds, α = 0, and the regression output allows you to test this hypothesis (as well as other hypotheses related to α and β.

Some Links about CAPM

http://finance.wharton.upenn.edu/~mrrobert/Teaching/LectureSlides/Class9_Leverage_Slides_Handout.pdf

http://www.12manage.com/methods_capm.html

http://www.quickmba.com/finance/cf/

http://www.12manage.com/methods_capm.html

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/AppldCF/derivn/ch4deriv.html

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/AppldCF/derivn/ch4deriv.html

http://www.ibankingfaq.com/interviewing-technical-questions/why-do-you-have-to-unlever-and-then-relever-beta/

These links has examples of unleveraging beta:

http://www.washburn.edu/sobu/rhull/cf10.html

The Hamada Equation for Unlevering Beta