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Risk Aversion and Capital Allocation

Risk Aversion and Capital Allocation. Risk Tolerance Asset Allocation Capital Allocation Line. Risk Premium and Risk Aversion. Risk Premium: E[ r ] - r f It is compensation for risk Risk Measure*: s (Std. Dev . ) Risk Aversion coeff: A. * just one of them.

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Risk Aversion and Capital Allocation

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

  2. 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

  3. 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

  4. 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

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

  6. 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. Asset Allocation • Moments of asset returns • Moments of portfolio C return • Example: w = 0.75

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

  9. 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

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

  11. Capital Allocation Line • Sharpe (reward-to-variability) Ratio

  12. 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. 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. 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?

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