Risk Aversion and Capital Allocation Investments 8 Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Risk Premium and Risk Aversion Risk Premium: E[r] - rf It is compensation for risk Risk Measure*: s (Std. Dev.) Risk Aversion coeff: A * just one of them Investments 8

Risk Premium and Risk Aversion Example Market portfolio E[r] = 12% Market portfolio s = 20% Risk-free rate (T-bill) = 4% Risk premium: E[r] - rf = 8% Risk aversion coefficient: A = 0.08/(0.5*0.20^2) = 4 Investments 8

Speculation vs. Gambling Speculation (i.e. Investing) Taking risk for extra reward Higher investors’ risk aversion requires higher expected returns Risk premium: E[r] - rf > 0 Odds are in your favor Gambling Risk is the reward Risk premium: E[r] - rf < 0 Odds are against you Investments 8

Asset Allocation How to allocate your fund among the following asset classes? Investment Funds Stock Bond T-Bills Risk-Free Asset Risky Assets Investments 8

Asset Allocation Risky and Risk-Free Assets Percentage to invest in risky asset Risky asset: a stock or a stock portfolio Percentage in risk-free asset Risk-free asset: 30-day T-bill as proxy Issues Examine risk/return tradeoff Demonstrate how different degrees of risk aversion will affect allocations between risky and risk-free assets Investments 8

Asset Allocation Moments of asset returns Moments of portfolio C return Example: w = 0.75 Investments 8

Capital Allocation Line How much in risky asset … Capital Allocation Line Risky Portfolio w = 0.75 Risk-Free Asset Investments 8

Capital Allocation Line w > 1, what does that mean? Find the E[rc] and SD[rc] with w = 1.2 Leverage Investing 120% of wealth in risky asset Using margin borrowing Higher expected return than the risky asset Higher volatility to go with the higher return Investments 8

Capital Allocation Line with Borrowing Borrowing at 10% Part w = 1.2 Risky Portfolio Risk-Free Asset Investments 8

Capital Allocation Line Sharpe (reward-to-variability) Ratio Investments 8

Capital Allocation Line Risk Tolerance and Allocation Greater risk aversion leads to higher allocation to risk-free asset Lower risk aversion leads to greater allocation to risky asset Willingness to accept extremely higher risk for higher return may lead to leveraged position Investments 8

How to find your portfolio allocation? Example 1 You desire 12% return for your portfolio: 12% = (1-w)*7%+w*15% or w = 62.5% Std. Dev. = 62.5%*22% = 13.75% Example 2 You desire risk no more than 10% for your portfolio: w*Std. Dev. = 10% or w = 45.45% Return = (1-45.45%)*7%+45.45*15% = 10.64% Investments 8

Wrap-up How does risk aversion affect expected returns? Is investment a form of gambling??? What is the Capital Allocation Line? How risk tolerance affects asset allocation? Investments 8