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Lesson 4. Capital market theory: an overview Prof. Beatriz de Blas May 2006 4. Capital market theory: an overview Introduction Previous lessons: discount rate for risk-free assets Next: determine discount rate for risky projects Need to measure risk – measure risk of an asset (Chapter 9) – measure risk of a portfolio (Chapter 10) Plan of the lesson: 8 > < 1. Returns 2. Holding-period returns > : 3. Return statistics 2 4. Capital market theory: an overview 1. Returns 1. 1. Dollar returns The return got on an investment % & Dividend to shareholders (income component) Capital gain (or capital loss): change in market value Total dollar return = Dividend income + Capital gain (or loss) 3 4. Capital market theory: an overview 4 2. 1. Percentage returns Summarize information about returns in percentage terms than in dollars. How much return do we get for each $ invested? Let Pt be the beginning market value Dividend yield = Divt+1 Pt (Pt+1 Pt) Capital gains yield = Pt Divt+1 (Pt+1 Pt) Total percentage return: Rt+1 = + Pt Pt 4. Capital market theory: an overview 5 Example: Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25: Over the last year, you received $20 in dividends (= 20 cents per share 100 shares). At the end of the year, the stock sells for $30: How did you do? 4. Capital market theory: an overview 6 Example: Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25: Over the last year, you received $20 in dividends (= 20 cents per share 100 shares). At the end of the year, the stock sells for $30: How did you do? Quite well. You invested $25 100 = $2; 500 At the end of the year, you have stock worth $3; 000 and cash dividends of $20: Your dollar gain was $520 = $20 + ($3; 000 What is your percentage gain? $2; 500) 4. Capital market theory: an overview 7 Example: Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25: Over the last year, you received $20 in dividends (= 20 cents per share 100 shares). At the end of the year, the stock sells for $30: How did you do? Quite well. You invested $25 100 = $2; 500 At the end of the year, you have stock worth $3; 000 and cash dividends of $20: Your dollar gain was $520 = $20 + ($3; 000 Your percentage gain for the year is 20:8% = $2; 500) $520 $2; 500 4. Capital market theory: an overview 8 2. 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, when the return during year i is given as ri : holding period return = (1 + r1) (1 + r2) ::: (1 + rn) 1 4. Capital market theory: an overview 9 Example: Suppose your investment provides the following returns over a fouryear period: Year Return 1 10% 2 5% 3 20% 4 15% then, your holding period return is 4. Capital market theory: an overview 10 Example: Suppose your investment provides the following returns over a fouryear period: Year Return 1 10% 2 5% 3 20% 4 15% then, your holding period return is (1 + r1) (1:10) (0:95) (1 + r2) (1:20) (1 + r3) (1:15) (1 + r4) 1= 1 = 0:4421 = 44:21% 4. Capital market theory: an overview 11 An investor who held this investment would have actually realized an annual return of 9:58% : (1 + rg )4 = (1 + r1) q 4 (1:10) (0:95) (1 + r2) (1:20) (1:15) (1 + r3) (1 + r4) = 1 = 0:0958 = 9:58% So, our investor made 9:58% on his money for four years, realizing a total period return of 44:21% 1:4421 = (1:095844)4 9-11 The Future Value of an Investment of $1 in 1925 $1,775.34 1000 $59.70 $17.48 10 Common Stocks Long T-Bonds T-Bills 0.1 1930 1940 1950 1960 1970 1980 1990 2000 Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 9-13 Historical Returns, 1926-2002 Series Average Annual Return Standard Deviation Large Company Stocks 12.2% 20.5% Small Company Stocks 16.9 33.2 Long-Term Corporate Bonds 6.2 8.7 Long-Term Government Bonds 5.8 9.4 U.S. Treasury Bills 3.8 3.2 Inflation 3.1 4.4 Distribution – 90% 0% + 90% Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 4. Capital market theory: an overview 12 3. Return statistics The history of capital market returns can be summarized by describing average stock return (R1 + ::: + RT ) R= T the std. deviation of those returns std:dev: = p var = s (R1 frequency distribution of the returns R)2 + ::: + (RT T 1 R )2 4. Capital market theory: an overview 13 Risk premium: average stock returns and risk-free returns The risk premium is the additional return (over and above the risk-free rate) resulting from bearing risk. In the data (1926-1999): long-run excess of stock return over the risk-free return. Rate of return on T-bills is essentially risk-free. The di¤erence between the return on T-bills and stocks is the risk premium for investing in stocks. The risk-return tradeo¤ 9-16 The Risk-Return Tradeoff 18% Small-Company Stocks Annual Return Average 16% 14% Large-Company Stocks 12% 10% 8% 6% T-Bonds 4% T-Bills 2% 0% 5% 10% 15% 20% 25% 30% Annual Return Standard Deviation McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 35% 9-17 Rates of Return 1926-2002 60 40 20 0 -20 Common Stocks Long T-Bonds T-Bills -40 -60 26 30 35 40 45 50 55 60 65 70 75 80 85 90 95 2000 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. McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.