Transcription of 1 Capital Asset Pricing Model (CAPM)
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1 Capital Asset Pricing Model (CAPM)
Copyrightc 2005 by Karl Sigman1 Capital Asset Pricing Model (CAPM)We now assume an idealized framework for an open market place, where all the risky assetsrefer to (say) all the tradeable stocks available to all. In addition we have a risk-free Asset (forborrowing and/or lending in unlimited quantities) with interest raterf. We assume that allinformation is available to all such as covariances, variances, mean rates of return of stocksand so on. We also assume that everyone is a risk-averse rational investor who uses the samefinancial engineering mean-variance portfolio theory from Markowitz. A little thought leads usto conclude that since everyone has the same assets to choose from, the same information aboutthem, and the same decision methods,everyone has a portfolio on the same efficient frontier,and hence has a portfolio that is a mixture of the risk-free Asset and a unique efficient fundF(of risky assets).In other words, everyone sets up the same optimization problem, does thesame calculation, gets the same answer and chooses a portfolio efficient fund used by all is called themarket portfolioand is denoted byM.
Note that when β p = 1 then r p = r M; the expected rate of return is the same as for the market portfolio. When β p > 1, then r p > r M; when β p < 1, then r p < r M. Also note that if an asset i is negatively correlated with M, σ M,i < 0, then β i < 0 and r i < r f; the expected rate of return is less than the risk-free rate.Effectively, such a negatively
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