1 Bodie Kane Marcus Essentials of Investments Fourth
1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 6 Risk and Return: Past and Prologue Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
2 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Rates of Return: Single Period HPR = Holding Period Return P 1 = Ending price P 0 = Beginning price D 1 = Dividend during period one Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
3 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Rates of Return: Single Period Example Ending Price = Beginning Price = Dividend = 24 20 1 HPR = ( 24 - 20 + 1 )/ ( 20) = 25% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
4 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Data from Text Example p. 154 1 1. 0. 10 Assets(Beg. ) HPR TA (Before Net Flows 1. 1 Net Flows 0. 1 End Assets 1. 2 Irwin / Mc. Graw-Hill 2 1. 2. 25 3 2. 0 (. 20) 4. 8. 25 1. 5 0. 5 2. 0 1. 6 (0. 8). 8 1. 0 0. 0 1. 0 © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
5 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Returns Using Arithmetic and Geometric Averaging Arithmetic ra = (r 1 + r 2 + r 3 +. . . rn) / n ra = (. 10 +. 25 -. 20 +. 25) / 4 =. 10 or 10% Geometric rg = {[(1+r 1) (1+r 2). . (1+rn)]} 1/n - 1 rg = {[(1. 1) (1. 25) (. 8) (1. 25)]} 1/4 - 1 = (1. 5150) 1/4 -1 =. 0829 = 8. 29% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
6 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Dollar Weighted Returns Internal Rate of Return (IRR) - the discount rate that results present value of the future cash flows being equal to the investment amount • • • Considers changes in investment Initial Investment is an outflow Ending value is considered as an inflow Additional investment is a negative flow Reduced investment is a positive flow Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
7 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Dollar Weighted Average Using Text Example Net CFs $ (mil) 1 2 -. 1 -. 5 3. 8 4 1. 0 Solving for IRR 1. 0 = -. 1/(1+r)1 + -. 5/(1+r)2 +. 8/(1+r)3 + 1. 0/(1+r)4 r =. 0417 or 4. 17% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
8 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Quoting Conventions APR = annual percentage rate (periods in year) X (rate for period) EAR = effective annual rate ( 1+ rate for period)Periods per yr - 1 Example: monthly return of 1% APR = 1% X 12 = 12% EAR = (1. 01)12 - 1 = 12. 68% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
9 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Characteristics of Probability Distributions 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
10 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Normal Distribution s. d. r Symmetric distribution Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
11 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Skewed Distribution: Large Negative Returns Possible Median Negative Irwin / Mc. Graw-Hill r Positive © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
12 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Skewed Distribution: Large Positive Returns Possible Median Negative Irwin / Mc. Graw-Hill r Positive © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
13 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Measuring Mean: Scenario or Subjective Returns Subjective returns E(r) = S p(s) r(s) s p(s) = probability of a state r(s) = return if a state occurs 1 to s states Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
14 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Numerical Example: Subjective or Scenario Distributions State Prob. of State rin State 1. 1 -. 05 2. 2. 05 3. 4. 15 4. 2. 25 5. 1. 35 E(r) = (. 1)(-. 05) + (. 2)(. 05). . . + (. 1)(. 35) E(r) =. 15 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
15 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Measuring Variance or Dispersion of Returns Subjective or Scenario Variance = S p(s) [rs - E(r)] 2 s Standard deviation = [variance]1/2 Using Our Example: Var =[(. 1)(-. 05 -. 15)2+(. 2)(. 05 -. 15)2. . . +. 1(. 35 -. 15)2] Var=. 01199 S. D. = [. 01199] 1/2 =. 1095 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
16 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Real vs. Nominal Rates Fisher effect: Approximation nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (R - i) / (1 + i) 2. 83% = (9%-6%) / (1. 06) Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
17 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Annual Holding Period Returns From Figure 6. 1 of Text Series Lg Stk Sm Stk LT Gov T-Bills Inflation Irwin / Mc. Graw-Hill Geom Mean% 11. 01 12. 46 5. 26 3. 75 3. 08 Arith Stan. Mean% Dev. % 13. 00 20. 33 18. 77 39. 95 5. 54 7. 99 3. 80 3. 31 3. 18 4. 49 © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
18 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Annual Holding Period Risk Premiums and Real Returns Series Lg Stk Sm Stk LT Gov T-Bills Inflation Irwin / Mc. Graw-Hill Risk Premiums% 9. 2 14. 97 1. 74 ----- Real Returns% 9. 82 15. 59 2. 36 0. 62 --- © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
19 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 (or a portfolio) Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
20 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
21 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Example Using the Numbers in Chapter 6 (pp 171 -173) rf = 7% srf = 0% E(rp) = 15% sp = 22% y = % in p (1 -y) = % in rf Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
22 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Expected Returns for Combinations E(rc) = y. E(rp) + (1 - y)rf rc = complete or combined portfolio For example, y =. 75 E(rc) =. 75(. 15) +. 25(. 07) =. 13 or 13% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
23 Essentials of Investments Bodie • Kane • Marcus E(r) E(rp) = 15% rf = 7% 0 Irwin / Mc. Graw-Hill Possible Combinations Fourth Edition P F 22% s © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
24 Bodie • Kane • Marcus Essentials of Investments Variance on the Possible Combined Portfolios Since Fourth Edition s r = 0, then f sc = y s p Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
25 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Combinations Without Leverage If y =. 75, then s c =. 75(. 22) =. 165 or 16. 5% If y = 1 s c = 1(. 22) =. 22 or 22% If y = 0 sc = 0(. 22) =. 00 or 0% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
26 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
27 Essentials of Investments Bodie • Kane • Marcus Fourth Edition CAL (Capital Allocation Line) E(r) P E(rp) = 15% E(rp) - rf = 8% rf = 7% 0 Irwin / Mc. Graw-Hill ) S = 8/22 F P = 22% s © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
28 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
29 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Quantifying Risk Aversion E(rp) = Expected return on portfolio p rf = the risk free rate. 005 = Scale factor A x sp = Proportional risk premium The larger A is, the larger will be the added return required for risk Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
30 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Quantifying Risk Aversion Rearranging the equation and solving for A Many studies have concluded that investors’ average risk aversion is between 2 and 4 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
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