1. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Economics 434 Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

2. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 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. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 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. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 The risk free asset Mean Standard Deviation The one with the highest mean

5. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Combine with Risky Assets Mean Standard Deviation Risky Assets Risk Free Asset ?

6. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Recall the definition of the variance of a Portfolio with two assets  P 2 =  (P -  P ) 2 n =  {  1 (X 1 -  1 ) +  2 (X 2 -  2 )} 2 n

7. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Variance with 2 Assets - Continued = (  1 ) 2  1 2 + (  2 ) 2  2 2 + 2  1  2  1,2 Recall the definition of the correlation coefficient:  1,2   1,2 1212 = (  1 ) 2  1 2 + (  2 ) 2  2 2 + 2  1  2  1,2  1  2

8. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012  P 2 = (  1 ) 2  1 2 + (  2 ) 2  2 2 + 2  1  2  1,2  1  2 If one of the standard deviations is equal to zero, e.g.  1 then  P 2 = (2)222 (2)222 Which means that: (2)2 (2)2  P = If  1 is zero

9. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Combine with Risky Assets Mean Standard Deviation Risk Free Asset

10. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Combine with Risky Assets Mean Standard Deviation Risk Free Asset The New Feasible Set Always combines the risk free asset With a specific asset (portfolio) E E

11. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Tobin’s Result Mean Standard Deviation Risk Free Asset Use of Leverage E

12. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 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)

13. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 CAPM – two conclusions M – the “efficient” basket The pricing rule based upon “beta”

14. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 First Conclusion What is M ? RfRf M Mean STDD Answer: contains all “positively” priced assets, weighted by their “market” values.

15. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 After all the math is over For every asset, i  i = R f +  i [  M – R f ] This is often called the “Capital Asset Pricing Model” Where  i = Cov (i, M) Var (M)   I, M 2M2M Second Conclusion:

16. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Capital Market Line What is M ? RfRf M Mean STDD Answer: contains all “positively” priced assets, weighted by their “market” values.

17. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 Security Market Line  i = R f +  i [  M – R f ] Rf Beta Mean MM 1 Security Market Line ii

18. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 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?

19. Economics 434 – Financial Market Theory Thursday, August 25, 2009 Thursday, August 24,Thursday, September 21, Thursday, Oct 18, 2012 The End