Economics 434 Theory of Financial Markets

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

2. 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”

3. 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

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

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

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

7. 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

8. 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:

9. Combine with Risky Assets Mean Risk Free Asset Standard Deviation

10. 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

11. Tobin’s Result Mean Use of Leverage E Risk Free Asset Standard Deviation

12. The End