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Capital Allocation Between the Risky Asset and the Risk-Free Asset

Capital Allocation Between the Risky Asset and the Risk-Free Asset. Allocating Capital Between Risky & Risk Free Assets. It’s possible to split investment funds between safe and risky assets. Risk free asset: proxy; T-bills Risky asset: stock (or a portfolio).

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Capital Allocation Between the Risky Asset and the Risk-Free Asset

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  1. Capital Allocation Between the Risky Asset and the Risk-Free Asset

  2. Allocating Capital Between Risky & Risk Free Assets • It’s possible to split investment funds between safe and risky assets. • Risk free asset: proxy; T-bills • Risky asset: stock (or a portfolio)

  3. Allocating Capital Between Risky & Risk Free Assets (cont.) Issues • Examine risk/return tradeoff. • Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets.

  4. rf = 7% rf = 0% E(rp) = 15% p = 22% w = % in p (1-w) = % in rf Example

  5. E(rc) = wE(rp) + (1 - w)rf rc = complete or combined portfolio For example, w = .75 E(rc) = .75(.15) + .25(.07) = .13 or 13% Expected Returns for Combinations

  6. Possible Combinations E(r) E(rp) = 15% P E(rc) = 13% C rf = 7% F  0 c 22%

  7. Since = 0, then rf = w c p Variance on the Possible Combined Portfolios *  

  8. If w = .75, then = .75(.22) = .165 or 16.5% c If w = 1 = 1(.22) = .22 or 22% c If w = 0 = (.22) = .00 or 0% c Combinations Without Leverage   

  9. Using Leverage with Capital Allocation Line Borrow at the Risk-Free Rate and invest in stock. Using 50% Leverage, rc = (-.5) (.07) + (1.5) (.15) = .19 c = (1.5) (.22) = .33

  10. CAL (Capital Allocation Line) E(r) P E(rp) = 15% E(rp) - rf = 8% ) S = 8/22 rf = 7% F  0 p = 22%

  11. Risk Aversion and Allocation • Greater levels of risk aversion lead to larger proportions of the risk free rate. • Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets. • Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations.

  12. rf = 7% rf = 0% E(rp) = 15% p = 22% w = % in p (1-w) = % in rf Example • 1. Given the above data, suppose you want to achieve 10% of rate of return, how much do you want to invest in the risky asset p? • 2. Again, suppose you want to maintain your risk level with standard deviation at 11%, what’s the maximum return you can achieve?

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