1. Risk Aversion and Capital Allocation
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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
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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
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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
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5. Asset Allocation
How to allocate your fund among the following asset classes?
Investment Funds
Stock
Bond
T-Bills
Risk-Free Asset
Risky Assets
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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
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7. Asset Allocation Moments of asset returns
Moments of portfolio C return
Example: w = 0.75
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8. Capital Allocation Line
How much in risky asset …
Capital Allocation Line
Risky Portfolio
w = 0.75
Risk-Free Asset
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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
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10. Capital Allocation Line with Borrowing
Borrowing at 10% Part
w = 1.2
Risky Portfolio
Risk-Free Asset
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11. Capital Allocation Line
Sharpe (reward-to-variability) Ratio
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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
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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 = ( %)*7%+45.45*15% = 10.64%
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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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