Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 September 22, 2015

The Markowitz Assumptions Every asset is a probability distribution of returns Asset X i has mean: μ i Asset X i has variance: σ 2 i Xi ~ (μ i, σ 2 i ) Assume all assets are risky: σ 2 i > 0 for all I Assume that correlation coefficients are all less than one and greater than minus one September 11, 2014

If   1 Then all the portfolios are here September 11, 2014

This Means the “boundary”of the possible portfolios looks like this: September 11, 2014

This is very convenient Standard Deviation Mean Maximizes Utility

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

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 M – the “efficient” basket The pricing rule based upon “beta”

First Conclusion What is M ? RfRf M Mean STDD Answer: contains all “positively” priced assets, weighted by their “market” values.

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:

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

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

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?

September 22, 2015