chapter 10 - Chapter 10: Risk and Return: Lessons from...

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Unformatted text preview: Chapter 10: Risk and Return: Lessons from Market History Ken Seng Tan Actsc 372 Fall 2011 Chapter Outline Returns Holding-Period Returns Risk Statistics Return Statistics Risk Premium Summary and Conclusions Actsc 372-Chap. 10 Returns (Dollar vs Percentage) Dividends Dollar Returns = Dividend + Change in Market Value Time 1 0 Percentage Return Initial investment Ending market value dollar return beginning market value dividend change in market value beginning market value dividend yield capital gains yield Actsc 372-Chap. 10 Returns: Example Suppose you bought 100 shares of company X at the beginning of the year at $25/share. Over the past year, you received dividends $0.20/share. At the end of the year, the stock sells for $30/share. What is your return? Initial investment = $25 × 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Return (in dollar) = $520 = $20 + ($3,000  $2,500). $520 Return (in percentage) = 20.8% $2,500 Actsc 372-Chap. 10 Holding Period Returns The holding period return is the return that an investor would get when holding an investment over a period of n years, Suppose the return during year i is given as ri: holding period return (1 r1 ) (1 r2 ) (1 rn ) 1 Actsc 372-Chap. 10 Holding Period Return: Example Year Return 1 10% 2 -5% 3 20% 4 15% Holding period return (1 r1 ) (1 r2 ) (1 r3 ) (1 r4 ) 1 (1.10) (.95) (1.20) (1.15) 1 .4421 44.21% Geometric average return: (1 rg ) 4 rg (1 r1 ) (1 r2 ) (1 r3 ) (1 r4 ) .095844 9.58% Arithmetic average return r1 r2 r3 r4 4 10% 5% 20% 15% 10% 4 Actsc 372-Chap. 10 Arithmetic Average Return vs Geometric Average Return Example: A particular stock is bought for $100. The first year it falls to $50. The second year it rises back to $100. What is the average return on this investment? Arithmetic Ave. Return = Geometric Ave. Return = Geometric average tells you what you earned per year on average, compounded annually Arithmetic average tells you what you earned per year in a typical year. Which return is higher ? Geometric vs Arithmetic Average Returns, 19572009 Capital Market Studies A famous set of studies dealing with the rates of returns on common stocks, bonds, and Treasury bills in the U.S. was conducted by Roger Ibbotson and Rex Sinquefield. James Hatch and Robert White examined Canadian returns. The text presents year-by-year historical rates of return starting in 1948 for the following five important types of financial instruments: Large-Company Canadian Common Stocks Large-Company U.S. Common Stocks Small-Company Canadian Common Stocks Long-Term Canadian Bonds Canadian Treasury Bills Actsc 372-Chap. 10 Returns to a $1 Investment, 1957-2009 1 R1957 1 R1958 1 R2009 112.63 for S&P/TSX Rates of Return 1957-2006 50 Common Stocks Long Bonds T-bills 40 30 20 10 0 -10 -20 -30 1955 1965 1975 1985 1995 2005 Actsc 372-Chap. 10 Risk Statistics No universally agreed-upon definition of risk. Some common measures are: Standard deviation (or variance) The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. Value at risk, VaR (or quantile risk measure) Represents the maximum possible (in dollars) for a given confidence VaR min Q : Pr L Q for a given loss r.v. L Conditional tail expectation (or Tail value at risk) Actsc 372-Chap. 10 Return Statistics ˆ Let ri , i 1,..., N be the observed (historical) rate of return of a security in period i Empirical average return (sample mean) ˆ (r1 R ˆ rN ) N Sample Variance: a measure of dispersion Var R ER 1 2 N 1i N N 1 ˆ )2 ˆ (ri N1 1 ˆ ri 2 ˆ N ˆ2 ˆ2 i1 the standard deviation of those returns Std. Dev. VAR ˆ 1 N 1i N ˆ (ri ˆ )2 1 the frequency distribution of the returns. Actsc 372-Chap. 10 Average Annual Returns, 1957-2009 Risk Premium The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. One of the most significant observations of stock and bond market data is this long-run excess of security return over the risk-free return. For the period 1957 through 2009, the average excess return from Canadian large-company common stocks was 4.35% = 10.70%  6.35% from Canadian long-term bonds was 2.17% = 8.52%  6.35% Actsc 372-Chap. 10 U.S. Stock Market Volatility The volatility of stocks is not constant from year to year. 60 50 40 30 20 10 19 26 19 35 19 40 19 45 19 50 19 55 19 60 19 65 19 70 19 75 19 80 19 85 19 90 19 95 19 98 0 Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. Actsc 372-Chap. 10 The Risk-Return Tradeoff (1957-2009) 12.00 Common Stocks 11.00 Annual Return Average 10.00 9.00 Long Bonds 8.00 7.00 6.00 T-Bills 5.00 4.00 3.00 2.00 0.00 5.00 10.00 15.00 20.00 25.00 Annual Return Standard Deviation Actsc 372-Chap. 10 Summary and Conclusions This chapter presents returns for five asset classes: Canadian Large-Company Common Stocks U.S. Large-Company Common Stocks Canadian Small-Company Common Stocks Canadian Long-Term Bonds Canadian Treasury Bills Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk. The statistical measures in this chapter are necessary building blocks for the material of the next few chapters. Actsc 372-Chap. 10 ...
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This note was uploaded on 01/04/2012 for the course ACTSC 372 taught by Professor Maryhardy during the Fall '09 term at Waterloo.

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