Economics 434 Theory of Financial Markets

Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

Modern Portfolio Theory • Three Significant Steps to MPT • Harry Markowitz • Mean Variance Analysis • The Concept of an “Efficient Portfolio” • James Tobin • What Happens When You Add a “Risk Free Asset” to Harry’s story • Bill Sharpe (Treynor Lintner, Mossin, etal) • Put Tobin’s Result in Equilbrium • The Rise of Beta • The Insignificance of “own variance”

Tobin’s Result • If there is a riskless asset • It changes the feasible set • All optimum portfolios contain • The risk free asset and/or • The portfolio E • …….in some combination…. • The Mutual Fund Theorem James Tobin, Prof of Economics Yale University Winner of Nobel Prize in Economics 1981

The risk free asset Mean The one with the highest mean Standard Deviation

Combine with Risky Assets Mean ? Risky Assets Risk Free Asset Standard Deviation

Recall the definition of the variance of a Portfoliowith two assets  P2 =  (P - P)2 n = {1(X1- 1) + 2(X2 - 2)}2 n

Variance with 2 Assets - Continued = (1)212 + (2)222 + 2121,2 Recall the definition of the correlation coefficient: 1,2 1,2 12 = (1)212 + (2)222 + 2121,212

If 1 is zero  P2= (1)212 + (2)222 + 2121,212 If one of the standard deviations is equal to zero, e.g. 1 then  P2 = (2)222 (2)2  P = Which means that:

Combine with Risky Assets Mean Risk Free Asset Standard Deviation

Combine with Risky Assets Mean The New Feasible Set E Always combines the risk free asset With a specific asset (portfolio) E Risk Free Asset 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 What is M ? Answer: contains all “positively” priced assets, weighted by their “market” values. Rf STDD

Second Conclusion: After all the math is over For every asset, i i = Rf + i [M – Rf] Cov (i, M)  I , M Where i =  2M Var (M) This is often called the “Capital Asset Pricing Model”

Capital Market Line Mean M What is M ? Answer: contains all “positively” priced assets, weighted by their “market” values. Rf STDD

Security Market Line i = Rf + i [M – Rf] Mean i M Rf Security Market Line Beta 1

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?

The End

Economics 434 Theory of Financial Markets