Risk Aversion and Capital Allocation Risk Tolerance Asset

Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line BUSI 186: Investments 8

Risk Premium and Risk Aversion q Risk Premium: Ø E[r] - rf It is compensation for risk Risk Measure*: q Risk Aversion coeff: q s (Std. Dev. ) A * just one of them Investments 8 2

Risk Premium and Risk Aversion q Example Ø Ø Ø Market portfolio E[r] = 12% Market portfolio s = 20% Risk-free rate (T-bill) = 4% Risk premium: E[r] - rf = 8% q Risk aversion coefficient: A = 0. 08/(0. 5*0. 20^2) = 4 q Investments 8 3

Speculation vs. Gambling q Speculation (i. e. Investing) Ø Taking risk for extra reward q Ø Risk premium: E[r] - rf > 0 q q Higher investors’ risk aversion requires higher expected returns Odds are in your favor Gambling Ø Ø Risk is the reward Risk premium: E[r] - rf < 0 q Investments 8 Odds are against you 4

Asset Allocation q How to allocate your fund among the following asset classes? Investment Funds Stock Risky Assets Investments 8 Bond T-Bills Risk-Free Asset 5

Asset Allocation q Risky and Risk-Free Assets Ø Percentage to invest in risky asset q Ø Percentage in risk-free asset q Ø Risky asset: a stock or a stock portfolio Risk-free asset: 30 -day T-bill as proxy Issues Examine risk/return tradeoff q Demonstrate how different degrees of risk aversion will affect allocations between risky and risk-free assets q Investments 8 6

Asset Allocation q Moments of asset returns q Moments of portfolio C return q Example: w = 0. 75 Investments 8 7

Capital Allocation Line q How much in risky asset … Capital Allocation Line Risky Portfolio w = 0. 75 Risk-Free Asset Investments 8 8

Capital Allocation Line q w > 1, what does that mean? Ø Find the E[rc] and SD[rc] with w = 1. 2 Ø Leverage Investing 120% of wealth in risky asset q Using margin borrowing q Higher expected return than the risky asset q Higher volatility to go with the higher return q Investments 8 9

Capital Allocation Line with Borrowing Capital Allocation Line: Borrowing at 10% Part w = 1. 2 Risky Portfolio Risk-Free Asset Investments 8 10

Capital Allocation Line q Sharpe (reward-to-variability) Ratio Investments 8 11

Capital Allocation Line q Risk Tolerance and Allocation Ø Ø Ø 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 12

How to find your portfolio allocation? Example 1 q 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 q 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 13

Wrap-up How does risk aversion affect expected returns? q Is investment a form of gambling? ? ? q What is the Capital Allocation Line? q How risk tolerance affects asset allocation? q Investments 8 14