1. Economics 434: The Theory of Financial Markets
Professor Burton
Fall 2016
Oct 11, 2016

2. Chapters 8 and 9 – available on Collab
Readings
Chapters 8 and 9 – available on Collab
Chapter 8 – Tobin
Chapter 9 – CAPM
So far, all 9 chapters plus “Random Walk Down Wall Street”
Oct 11, 2016

3. The Capital Asset Pricing Model
Markowitz – mean, variance analysis
Tobin – the role of the risk free rate
Sharpe (and others) – beta and the market basket
September 15, 17, 2015

4. If σ < 1 σ1 ½ σ1 + ½ σ2 σ2 Asset 2 (μ2, σ2) Asset 1 (μ1, σ1)
P will lie to the left of the
Line joining the Assets
Mean μ2
Asset 2 (μ2, σ2)
Asset 1 (μ1, σ1) μ1 σ1
½ σ1 + ½ σ2 σ2
Oct 11, 2016

5. Main Conclusion of Markowitz Theory
Mean
Boundary of “feasible” portfolios
“Efficient” Portfolios σ σ
September 15, 17, 2015

6. Today: Tobin Adds a Risk-Free Asset
Oct 11, 2016

7. 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

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

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

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

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

12. 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

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

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

15. The Capital Asset Pricing Model
Markowitz – mean, variance analysis
Tobin – the role of the risk free rate
Sharpe (and others) – beta and the market basket

16. 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)

17. M – the “efficient” basket The pricing rule based upon “beta”
CAPM – two conclusions
M – the “efficient” basket
The pricing rule based upon “beta”
Bill Sharpe

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

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

20. Oct 11, 2016