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Economics 434: The Theory of Financial Markets Professor Burton Fall 2016 Oct 11, 2016 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 P will lie to the left of the Line joining the Assets Mean Asset 2 (μ2, σ2) μ2 Asset 1 (μ1, σ1) μ1 σ1 Oct 11, 2016 ½ σ1 + ½ σ2 σ2 Main Conclusion of Markowitz Theory Mean Boundary of “feasible” portfolios “Efficient” Portfolios 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 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 = (1)212 + (2)222 + 2121,212 If one of the standard deviations is equal to zero, e.g. 1 then P2 = (2)222 Which means that: P = (2)2 Combine with Risky Assets Mean Risk Free Asset Standard Deviation Combine with Risky Assets Mean The New Feasible Set E Risk Free Asset Always combines the risk free asset With a specific asset (portfolio) E 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) CAPM – two conclusions Bill Sharpe • M – the “efficient” basket • The pricing rule based upon “beta” Capital Market Line Mean M Rf What is M ? Answer: contains all “positively” priced assets, weighted by their “market” values. STDD Security Market Line i = Rf + i [M – Rf] Mean i M Rf Security Market Line 1 Beta Oct 11, 2016