23. The Mutual Fund Theorem and Covariance Pricing Theorems

Financial Theory (ECON 251)

This lecture continues the analysis of the Capital Asset Pricing Model, building up to two key results. One, the Mutual Fund Theorem proved by Tobin, describes the optimal portfolios for agents in the economy. It turns out that every investor should try to maximize the Sharpe ratio of his portfolio, and this is achieved by a combination of money in the bank and money invested in the "market" basket of all existing assets. The market basket can be thought of as one giant index fund or mutual fund. This theorem precisely defines optimal diversification. It led to the extraordinary growth of mutual funds like Vanguard. The second key result of CAPM is called the covariance pricing theorem because it shows that the price of an asset should be its discounted expected payoff less a multiple of its covariance with the market. The riskiness of an asset is therefore measured by its covariance with the market, rather than by its variance. We conclude with the shocking answer to a puzzle posed during the first class, about the relative valuations of a large industrial firm and a risky pharmaceutical start-up.

00:00 - Chapter 1. The Mutual Fund Theorem
03:47 - Chapter 2. Covariance Pricing Theorem and Diversification
25:19 - Chapter 3. Deriving Elements of the Capital Asset Pricing Model
40:25 - Chapter 4. Mutual Fund Theorem in Math and Its Significance
52:36 - Chapter 5. The Sharpe Ratio and Independent Risks
01:04:19 - Chapter 6. Price Dependence on Covariance, Not Variance

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

This course was recorded in Fall 2009.