1. Empirical Financial Economics 4. Asset pricing and Mean Variance Efficiency Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June 19-21 2006

2. Mean variance facts

3. The geometry of mean variance Note: returns are in excess of the risk free rate

4. Tests of Mean Variance Efficiency  Mean variance efficiency implies CAPM  For Normal with mean and covariance matrix, is distributed as noncentral Chi Square with degrees of freedom and noncentrality

5. MacBeth T 2 test  Regress excess return on market excess return  Define orthogonal return  Market efficiency implies, estimate.

6. MacBeth T 2 test (continued)  The T 2 test statistic is distributed as noncentral Chi Square with m degrees of freedom and noncentrality parameter  The quadratic form is interpreted as the Sharpe ratio of the optimal orthogonal portfolio  This is interpreted as a test of Mean Variance Efficiency  Gibbons Ross and Shanken adjust for unknown

7. Multiple period consumption- investment problem  Multiperiod problem:  First order conditions:  Stochastic discount factor interpretation:

8. Stochastic discount factor and the asset pricing model  If there is a risk free asset:  which yields the basic pricing relationship

9. Stochastic discount factor and mean variance efficiency  Consider the regression model  The coefficients are proportional to the negative of minimum variance portfolio weights, so

10. The geometry of mean variance Note: returns are in excess of the risk free rate

11. Hansen Jagannathan Bounds  Risk aversion times standard deviation of consumption is given by:  “Equity premium puzzle”: Sharpe ratio of market implies a risk aversion coefficient of about 50  Consider

12. Non negative discount factors  Negative discount rates possible when market returns are high  Consider a positive discount rate constraint: