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Capital Asset Pricing Model (CAPM)

We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available to all. In addition we have a risk-free asset (for borrowing and/or lending in unlimited quantities) with interest rate rf . We assume that all information is available to all such as covariances, variances, mean rates of return of stocks and so on. We also assume that everyone is a risk-averse rational investor who uses the same financial engineering mean-variance portfolio theory from Markowitz. A little thought leads us to conclude that since everyone has the same assets to choose from, the same information about them, 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 fund F (of risky assets). In other words, everyone sets up the same optimization problem, does the same calculation, gets the same answer and chooses a portfolio accordingly. This efficient fund used by all is called the market portfolio and is denoted by M . The fact that it is the same for all leads us to conclude that it should be computable without using all the optimization methods from Markowitz: The market has already reached an equilibrium so that the weight for any asset in the market portfolio is given by its capital value (total worth of its shares) divided by the total capital value of the whole market (all assets together). If, for example, asset i refers to shares of stock in Company A, and this company has 10,000 shares outstanding, each worth $20.00, then the captital value for asset i is Vi = (10, 000)($20) = $200, 000. Computing this value for each asset and summing over all n (total number of assets) yields the total capital value of the whole market, V =

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