1. Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

2. Investments 82 Risk Premium and Risk Aversion  Risk Premium: E[r] - r f  It is compensation for risk  Risk Measure*:   (Std. Dev. )  Risk Aversion coeff: A * just one of them

3. Investments 83 Risk Premium and Risk Aversion  Example  Market portfolio E[r] = 12%  Market portfolio  = 20%  Risk-free rate (T-bill) = 4%  Risk premium: E[r] - r f = 8%  Risk aversion coefficient: A = 0.08/(0.5*0.20^2) = 4

4. Investments 84 Speculation vs. Gambling  Speculation (i.e. Investing)  Taking risk for extra reward  Higher investors’ risk aversion requires higher expected returns  Risk premium: E[r] - r f > 0  Odds are in your favor  Gambling  Risk is the reward  Risk premium: E[r] - r f < 0  Odds are against you

5. Investments 85 Asset Allocation  How to allocate your fund among the following asset classes? Investment Funds StockBondT - Bills Risky Assets Risk-Free Asset

6. Investments 86 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

7. Investments 87 Asset Allocation  Moments of asset returns  Moments of portfolio C return  Example: w = 0.75

8. Investments 88 Capital Allocation Line  How much in risky asset … Capital Allocation Line Risky Portfolio w = 0.75 Risk-Free Asset

9. Investments 89 Capital Allocation Line  w > 1, what does that mean?  Find the E[r c ] and SD[r c ] 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

10. Investments 810 Capital Allocation Line with Borrowing Capital Allocation Line: Borrowing at 10% Part Risky Portfolio w = 1.2 Risk-Free Asset

11. Investments 811 Capital Allocation Line  Sharpe (reward-to-variability) Ratio

12. Investments 812 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

13. Investments 813 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%

14. Investments 814 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?