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Optimal Capital Allocation Strategies for Risky and Risk-Free Assets

Explore the dynamics of dividing investment funds between safe T-bills and volatile stocks, analyzing risk-return tradeoffs and impact of risk aversion on asset allocations. Understand leveraging and risk preferences through utility functions.

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Optimal Capital Allocation Strategies for Risky and Risk-Free Assets

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  1. Chapter 7 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% y = % in p (1-y) = % in rf Example Using the Numbers in Chapter 7.2

  5. E(rc) = yE(rp) + (1 - y)rf rc = complete or combined portfolio For example, y = .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 = y c p Variance on the Possible Combined Portfolios *   * Rule 4 in Chapter 6

  8. If y = .75, then = .75(.22) = .165 or 16.5% c If y = 1 = 1(.22) = .22 or 22% c If y = 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. CAL with Higher Borrowing Rate E(r) P ) S = .27 9% 7% ) S = .36  p = 22%

  12. 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.

  13. Utility Function U = E ( r ) - .005 A s2 Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion s2 = variance of returns

  14. CAL with Risk Preferences E(r) The lender has a larger A when compared to the borrower P Borrower 7% Lender  p = 22%

  15. Home Assignment • Required: • problems 1, 2, 5, 6, 7, 8, 9, 19 (3rd ed). • problems 1, 2, 5, 6, 7, 8, 9, 22 (5rd ed). • closely follow financial news!

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