Asset Allocation I

The goal of these simulations is to understand the mathematics of mean-variance optimization and the equilibrium pricing of risk if all investors use this rule with common information sets. Simulation A focuses on five to 10 years of monthly sector returns that are initially drawn from a known multivariate normal distribution. Mean-variance optimization is designed to produce the highest ratio of excess portfolio return to portfolio standard deviation (i.e. the highest Sharpe ratio) in this setting. Simulation B alters the setting by allowing students to determine expected returns through a simultaneous auction. We continue to have agreement over the covariance matrix, and implicitly over expected payoffs, but allow students to set market prices. The average portfolio weights across the 10 sectors is calculated and is used as the vector of market capitalization weights. With these market weights (w) and the given covariance matrix, the capital asset pricing model (CAPM) implied expected returns are calculated for each sector and compared with the student set expected returns.