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Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 September 22, 2015 The Markowitz Assumptions • Every asset is a probability distribution of returns • • • • • Asset Xi has mean: μi Asset Xi has variance: σ2i Xi ~ (μi , σ2i ) Assume all assets are risky: σ2i > 0 for all I Assume that correlation coefficients are all less than one and greater than minus one September 11, 2014 If 1 Then all the portfolios are here September 11, 2014 This Means the “boundary”of the possible portfolios looks like this: September 11, 2014 This is very convenient Mean Maximizes Utility Standard Deviation Tobin’s Result Mean Use of Leverage E Risk Free Asset Standard Deviation Capital Asset Pricing Model • Makes all the same assumptions as Tobin model • But Tobin’s model is about “one person” • CAPM puts Tobin’s model in equilibrium, by assuming that everyone faces the same portfolio choice problem as in Tobin’s problem • Only difference between people in CAPM is that each has their own preferences (utility function) CAPM – two conclusions • M – the “efficient” basket • The pricing rule based upon “beta” First Conclusion Mean M Rf What is M ? Answer: contains all “positively” priced assets, weighted by their “market” values. STDD Second Conclusion: After all the math is over For every asset, i i = Rf + i [M – Rf] Where i = Cov (i, M) Var (M) I,M 2 M This is often called the “Capital Asset Pricing Model” Capital Market Line Mean M Rf What is M ? Answer: contains all “positively” priced assets, weighted by their “market” values. STDD Security Market Line i = Rf + i [M – Rf] Mean i M Rf Security Market Line 1 Beta Random Questions • What is the beta of the market? • Why not just buy one stock with the beta of the market? • Can betas be negative? What does it mean? • Is this model testable? September 22, 2015