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

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

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

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

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

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

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 one with the highest mean 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

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:

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

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

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

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)

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

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

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

Oct 11, 2016