1. McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Risk and Return: Past and Prologue 5 Bodie, Kane, and Marcus Essentials of Investments, 9th Edition

2. 5-2 5.1 Rates of Return Holding-Period Return (HPR) Rate of return over given investment period HPR= [PS − PB + CF] / PB PS = Sale price PB = Buy price CF = Cash flow during holding period

3. 5-3 5.1 Rates of Return Measuring Investment Returns over Multiple Periods Arithmetic average Sum of returns in each period divided by number of periods Geometric average Single per-period return; gives same cumulative performance as sequence of actual returns Compound period-by-period returns; find per-period rate that compounds to same final value Dollar-weighted average return Internal rate of return on investment

4. 5-4 Table 5.1 Quarterly Cash Flows/Rates of Return of a Mutual Fund 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Assets under management at start of quarter ($ million) 11.220.8 Holding-period return (%)1025−2020 Total assets before net inflows1.11.51.60.96 Net inflow ($ million)0.10.5−0.80.6 Assets under management at end of quarter ($ million) 1.220.81.56

5. 5-5 5.1 Rates of Return Conventions for Annualizing Rates of Return APR = Per-period rate × Periods per year 1 + EAR = (1 + Rate per period) 1 + EAR = (1 + Rate per period) n = (1 + ) n APR = [(1 + EAR) 1/n – 1] n Continuous compounding: 1 + EAR = e APR APR n

6. 5-6 5.2 Risk and Risk Premiums Scenario Analysis and Probability Distributions Scenario analysis: Possible economic scenarios; specify likelihood and HPR Probability distribution: Possible outcomes with probabilities Expected return: Mean value of distribution of HPR Variance: Expected value of squared deviation from mean Standard deviation: Square root of variance

7. 5-7 Spreadsheet 5.1 Scenario Analysis for the Stock Market

8. 5-8 5.2 Risk and Risk Premiums

9. 5-9 Figure 5.1 Normal Distribution with Mean Return 10% and Standard Deviation 20%

10. 5-10 5.2 Risk and Risk Premiums Normality over Time When returns over very short time periods are normally distributed, HPRs up to 1 month can be treated as normal Use continuously compounded rates where normality plays crucial role

11. 5-11 5.2 Risk and Risk Premiums Deviation from Normality and Value at Risk Kurtosis: Measure of fatness of tails of probability distribution; indicates likelihood of extreme outcomes Skew: Measure of asymmetry of probability distribution Using Time Series of Return Scenario analysis derived from sample history of returns Variance and standard deviation estimates from time series of returns:

12. 5-12 Figure 5.2 Comparing Scenario Analysis to Normal Distributions with Same Mean and Standard Deviation

13. 5-13 5.2 Risk and Risk Premiums Risk Premiums and Risk Aversion Risk-free rate: Rate of return that can be earned with certainty Risk premium: Expected return in excess of that on risk-free securities Excess return: Rate of return in excess of risk- free rate Risk aversion: Reluctance to accept risk Price of risk: Ratio of risk premium to variance

14. 5-14 5.2 Risk and Risk Premiums The Sharpe (Reward-to-Volatility) Ratio Ratio of portfolio risk premium to standard deviation Mean-Variance Analysis Ranking portfolios by Sharpe ratios

15. 5-15 5.3 The Historical Record World and U.S. Risky Stock and Bond Portfolios World Large stocks: 24 developed countries, about 6000 stocks U.S. large stocks: Standard & Poor's 500 largest cap U.S. small stocks: Smallest 20% on NYSE, NASDAQ, and Amex World bonds: Same countries as World Large stocks U.S. Treasury bonds: Barclay's Long-Term Treasury Bond Index

16. 5-16 Figure 5.4 Rates of Return on Stocks, Bonds, and Bills

17. 5-17 5.4 Inflation and Real Rates of Return Equilibrium Nominal Rate of Interest Fisher Equation R = r + E(i) E(i): Current expected inflation R: Nominal interest rate r: Real interest rate

18. 5-18 5.4 Inflation and Real Rates of Return U.S. History of Interest Rates, Inflation, and Real Interest Rates Since the 1950s, nominal rates have increased roughly in tandem with inflation 1930s/1940s: Volatile inflation affects real rates of return

19. 5-19 Figure 5.5 Interest Rates, Inflation, and Real Interest Rates 1926-2010

20. 5-20 5.5 Asset Allocation across Portfolios Asset Allocation Portfolio choice among broad investment classes Complete Portfolio Entire portfolio, including risky and risk-free assets Capital Allocation Choice between risky and risk-free assets

21. 5-21 The Risk-Free Asset Treasury bonds (still affected by inflation) Price-indexed government bonds Money market instruments effectively risk-free Risk of CDs and commercial paper is miniscule compared to most assets 5.5 Asset Allocation across Portfolios

22. 5-22 Portfolio Expected Return and Risk P: portfolio composition y: proportion of investment budget r f : rate of return on risk-free asset r p : actual rate of return E(r p ): expected rate of return σ p : standard deviation E(r C ): return on complete portfolio E(r C ) = yE(r p ) + (1 − y)r f σ C = yσ rp + (1 − y) σ rf 5.5 Asset Allocation Across Portfolios

23. 5-23 Figure 5.6 Investment Opportunity Set

24. 5-24 Capital Allocation Line (CAL) Plot of risk-return combinations available by varying allocation between risky and risk-free Risk Aversion and Capital Allocation y: Preferred capital allocation 5.5 Asset Allocation across Portfolios

25. 5-25 5.6 Passive Strategies and the Capital Market Line Passive Strategy Investment policy that avoids security analysis Capital Market Line (CML) Capital allocation line using market-index portfolio as risky asset

26. 5-26 Table 5.4 Excess Return Statistics for S&P 500 Excess Return (%) AverageStd DevSharpe Ratio5% VaR 1926-20108.0020.70.39−36.86 1926-195511.6725.40.46−53.43 1956-19855.0117.58.28−30.51 1986-20107.1917.83.40−42.28

27. 5-27 Cost and Benefits of Passive Investing Passive investing is inexpensive and simple Expense ratio of active mutual fund averages 1% Expense ratio of hedge fund averages 1%-2%, plus 10% of returns above risk-free rate Active management offers potential for higher returns 5.6 Passive Strategies and the Capital Market Line

28. Selected Problems 5-28

29. Problem 1 V (12/31/2004) = V (1/1/1998) x (1 + GAR) 7 = $100,000 x (1.05) 7 = $140,710.04 5-29

30. Problem 2 a. The holding period returns for the three scenarios are: Boom: Normal: Recession: E(HPR) =  2 (HPR) (50 – 40 + 2)/40 = 0.30 = 30.00% (43 – 40 + 1)/40 = 0.10 = 10.00% (34 – 40 + 0.50)/40 = –0.1375 = –13.75% [(1/3) x 30%] + [(1/3) x 10%] + [(1/3) x (–13.75%)] = 8.75% 0.031979 5-30

31. Problem 2 Cont. b. E(r) =  = (0.5 x 8.75%) + (0.5 x 4%) = 6.375% 0.5 x 17.88% = 8.94% Risky E[r p ] = 8.75% Risky  p = 17.88% 5-31

32. Problems 3 & 4 3. For each portfolio: Utility = E(r) – (0.5  4   2 ) We choose the portfolio with the highest utility value, which is Investment 3. InvestmentE(r)  U 10.120.30-0.0600 20.150.50-0.3500 30.210.16 0.1588 40.240.21 0.1518 5-32

33. Problems 3 & 4 Cont. 4. When an investor is risk neutral, A = _ so that the portfolio with the highest utility is the portfolio with the _______________________. So choose ____________. highest expected return 0 Investment 4 5-33

34. Problem 5 (95 – 90 + 4)/90 = 10.00% 2004-2005 (90 – 110 + 4)/110 = –14.55% 2003-2004 (110 – 100 + 4)/100 = 14.00% 2002-2003 Return = [(capital gains + dividend) / price] a. TWR Year Dividends on four shares, plus sale of four shares at $95 per share 396 Dividends on five shares, plus sale of one share at $90 110 Purchase of two shares at $110, plus dividend income on three shares held -208 Purchase of three shares at $100 per share -300 3 2 1 0 Explanation Cash flow Time b. DWR a. TWR 2.33% 3.15% -0.1661% 5-34