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Chapter 5

Chapter 5. Risk and Return, Capital Allocation to Risky Assets. Outline. Return Hold Period Return Expected Return Risk Allocating Capital Between Risky & Risk-Free Assets. I: Return. Rates of Return: Single Period. HPR = Holding Period Return P 1 = Ending price

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Chapter 5

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  1. Chapter 5 Risk and Return, Capital Allocation to Risky Assets

  2. Outline • Return • Hold Period Return • Expected Return • Risk • Allocating Capital Between Risky & Risk-Free Assets

  3. I: Return

  4. Rates of Return: Single Period HPR = Holding Period Return P1 = Ending price P0 = Beginning price D1 = Dividend during period one Define return? Your gain per dollar investment

  5. Rates of Return: Single Period Example Ending Price = 24 Beginning Price = 20 Dividend = 1 HPR = ( 24 - 20 + 1 )/ ( 20) = 25%

  6. Expected Return • Future means uncertainty: More than one possible outcome (returns) • Expected return measure the average of possible future returns • Example: a stock with two possible returns

  7. Calculating the expected return

  8. Investment alternatives

  9. Calculating the expected return

  10. Summary of expected returns Expected return HT 12.4% Market 10.5% USR 9.8% T-bill 5.5% Coll. 1.0% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

  11. II. Risk

  12. Calculating standard deviation

  13. Standard deviation for each investment

  14. Comparing risk and return ^ * Seem out of place.

  15. III.Allocating Capital Between Risky & Risk-Free Assets

  16. Allocating Capital Between Risky & Risk-Free Assets • Possible to split investment funds between safe and risky assets • Risk free asset: proxy; T-bills • Risky asset: stock portfolio

  17. 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

  18. rf = 7% srf = 0% E(rp) = 15% sp = 22% y = % in p (1-y) = % in rf Example rp = return of risky portfolio or risky individual stock

  19. 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

  20. s Since = 0, then rf = y c p risk on the Possible Combined Portfolios s s

  21. If y = .75, then = .75(.22) = .165 or 16.5% c If y = 1 = 1(.22) = .22 or 22% c If y = 0 = 0(.22) = .00 or 0% c Examples: risk on the Possible Combined Portfolios s s s

  22. 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 sc = (1.5) (.22) = .33

  23. CAL (Capital Allocation Line) E(r) P E(rp) = 15% E(rp) - rf = 8% Slope(reward-to-volatility ratio) = 8/22 rf = 7% F s 0 P = 22%

  24. Reaching your financial goal by allocating assets • Set return as goal • Set risk as goal

  25. 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

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