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					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                                        2
  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                              3
  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                                                    4
  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                                           5
  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                                                        6
  Asset Allocation
      Moments of asset returns


      Moments of portfolio C return


      Example: w = 0.75



Investments 8                          7
  Capital Allocation Line
      How much in risky asset …
                                              Capital Allocation Line



                                             Risky Portfolio
                                  w = 0.75




                Risk-Free Asset




Investments 8                                                  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                                                        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
      Sharpe (reward-to-variability) Ratio




Investments 8                                 11
  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                                       12
  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                                  13
  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                            14

				
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