RSM318H1 Lecture Notes - Lecture 6: Sharpe Ratio, Risk Neutral, Expected Utility Hypothesis
Document Summary
Portfolio of one risky asset and one risk-free asset. Consider portfolio with w in risky asset and 1-w in risk-free asset. =0 for risk neutral, >0 for risk averse: if , then 100% invested in risk free asset. Suppose we know 2 but need to estimate . Uncertainty results in a significant loss in utility. Can improve estimates with longer period of data. Utility loss: utility loss is a linear function of estimated average return. Portfolios of n risky assets and a risk-free asset r is excess return of n risky asset at time t, with mean and covariance matrix . Optimal weights on risky assets rt is excess return of n risky asset at time t, with mean and covariance matrix . If portfolio invests w in risky asset and in the risk free asset, excess return is: As number of risky assets increases, utility loss also increases. In-sample optimization leads to overly optimistic forecast of true minimum-variance frontier.
