ch 10. Capital market history: An overview

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  • I find that it is worth pointing out to students that it does not matter if you sell the shares at $30 or just hold, (ignoring taxes). It’s a good way to reinforce earlier discussions about opportunity cost.
  • ch 10. Capital market history: An overview

    1. 1. Chapter 10 Capital Market Theory: An Overview <ul><li>10.1 Returns </li></ul><ul><li>10.2 Holding-Period Returns </li></ul><ul><li>10.3 Return Statistics </li></ul><ul><li>10 .4 Average Stock Returns and Risk-Free Returns </li></ul><ul><li>10.5 Risk Statistics </li></ul><ul><li>10.6 Summary and Conclusions </li></ul>
    2. 2. 10.1 Returns: Example <ul><li>% return = (cash in - cash out)/(cash out) = (cash in / cash out) - 1 </li></ul><ul><li>e.g. Bought a share of XYZ at $100 a year ago. Today you received $4 dividend and just sold the share at $106. </li></ul><ul><li>Cash in = $4 + $106 Cash out = $100 </li></ul><ul><li>% return = ((4+106)/100) – 1 = 10% p.a. </li></ul><ul><li>% return= (4/100) + (106/100) – 1 </li></ul><ul><li>= (4/100) + (106 – 100)/100 </li></ul><ul><li>= dividend yield + capital gains yield </li></ul><ul><li>= 4% + 6% = 10% p.a. </li></ul><ul><li>Qu: What are two parts of (total %) return? </li></ul><ul><li>Dollar returns vs percentage returns </li></ul>
    3. 3. 10.2 Holding Period Return: Example <ul><li>Suppose your investment provides the following returns over a four-year period: </li></ul>Your holding period return = = (1.10)*(0.95)*(1.2)*(1.15) = (1 + r 1 )* (1 + r 2 )* (1 + r 3 )* (1 + r 4 ) – 1 = 44.21%
    4. 4. The Future Value of an Investment of $1 in 1957 $ 42.91 $20.69 Common Stocks Long Bonds T-Bills
    5. 5. Holding Period Return: Example <ul><li>What would be the annual return on her investment? </li></ul><ul><li>Suppose our investor made r% p.a. on her money for four years. At the end of four years, she has $1.4421: 1.4421 = (1+r%) 4 </li></ul><ul><li>Solving for r yields the geometric return: 9.58% p.a. </li></ul>
    6. 6. Holding Period Return: Example <ul><li>Note that the geometric average is not same as the arithmetic average: </li></ul>
    7. 7. 10.2 Holding-Period Returns <ul><li>The holding period return is the return that an investor would get when holding an investment over a period of n periods. </li></ul><ul><li>The holding period return is given as, where r i represents the return during period i: </li></ul><ul><li>Table 10.1 shows annual (holding period) returns on several portfolios. </li></ul><ul><li>Qu on market history. </li></ul>
    8. 8. 10.3 Return Statistics <ul><li>One can summarize the data with the average (mean), the standard deviation, and the frequency distribution of the returns. </li></ul><ul><li>Average return: What is the return that an investor could have realized during a year over the 1948-2000 period? </li></ul><ul><ul><li>Example: Annual returns for 1997-2000 are 14.98%, -1.58%, 31.71%, and 7.41%. Average return is (14.98% -1.58% + 31.71% + 7.41%)/4 =13.13%. </li></ul></ul>
    9. 9. Historical Returns, 1957-2003 Average Standard Investment Annual Return Deviation Distribution Canadian common stocks 10.64% 16.41% Long Bonds 8.96 10.36 Treasury Bills 6.80 4.11 Inflation 4.29 3.63 – 60% + 60% 0%
    10. 10. 10.4 Average Stock Returns and Risk-Free Returns <ul><li>The Risk Premium is the difference between risky and risk-free return. </li></ul><ul><li>For 1957-2003, risk premium for </li></ul><ul><ul><li>large cap common stocks: 3.84% = 10.64% – 6.8 % </li></ul></ul><ul><ul><li>long-term (corporate+gov’t) bonds: 2.16%= 8.96% – 6.8 % </li></ul></ul><ul><ul><li>One of the most significant observations of stock market data is this long-run risk premium. </li></ul></ul>
    11. 11. Risk Premia <ul><li>Suppose the current one-year Treasury bills rate is 5%. What is the expected return on the market of small-company stocks? </li></ul><ul><li>The average risk premium for small cap (capitalization) stocks for the period 1976-2000 was 5.68% </li></ul><ul><li>Given a risk-free rate of 5%, expected return on small-cap stocks is 14.8% = 5.68% + 5%. </li></ul><ul><li>Why risk premium? </li></ul>
    12. 12. Rates of Return 1948-2000
    13. 13. Why Risk Premiums? <ul><li>Rate of return on T-bills is essentially risk-free. </li></ul><ul><li>Investing in stocks is risky, but there are compensations. </li></ul><ul><li>The risk premium is the reward to bearing risk in stocks. </li></ul>
    14. 14. The Risk-Return Tradeoff (1957-2003) Long Bonds T-Bills Large-Company Stocks
    15. 15. Stock Market Volatility 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. The volatility of stocks is not constant from year to year.
    16. 16. 10.5 Risk Statistics <ul><li>There is no universally agreed-upon definition of risk. </li></ul><ul><li>We mainly use variance and standard deviation. </li></ul><ul><li>Example: Annual returns for 1997-2000 are 14.98%, -1.58%, 31.71%, and 7.41%, with an average return of 13.1%. </li></ul><ul><ul><li>var = [(14.98%-13.1%) 2 + (-1.58%-13.1%) 2 +(31.71%-13.1%) 2 + (7.41%-13.1%) 2 ]/3 = 0.019925 </li></ul></ul><ul><ul><li>stdev = sqrt (var) = sqrt (0.019925) = 0.1222 </li></ul></ul>
    17. 17. Normal Distribution <ul><li>A large sample from a normal distribution looks like a bell-shaped curve. </li></ul>Probability Return on large company common stocks 99.74% – 3  – 36.35% – 2  – 19.87% – 1  – 3.39% 0 13.09% + 1  29.57% + 2  46.05% + 3  62.53% The probability that an annual return will fall between –3.39% and 29.57% is approximately 2/3. 68.26% 95.44%
    18. 18. Normal Distribution Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™ , Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
    19. 19. 10.6 Summary and Conclusions <ul><li>Stocks have outperformed bonds over most of the twentieth century. </li></ul><ul><li>Stocks have exhibited more risk than bonds. </li></ul><ul><li>The small cap stocks have outperformed large cap stocks over most of the twentieth century, again with more risk. </li></ul><ul><li>The statistical measures in this chapter are necessary building blocks for the material of the next three chapters. </li></ul>

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