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# 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 overviewPresentation Transcript

• Chapter 10 Capital Market Theory: An Overview
• 10.1 Returns
• 10.2 Holding-Period Returns
• 10.3 Return Statistics
• 10 .4 Average Stock Returns and Risk-Free Returns
• 10.5 Risk Statistics
• 10.6 Summary and Conclusions
• 10.1 Returns: Example
• % return = (cash in - cash out)/(cash out) = (cash in / cash out) - 1
• e.g. Bought a share of XYZ at \$100 a year ago. Today you received \$4 dividend and just sold the share at \$106.
• Cash in = \$4 + \$106 Cash out = \$100
• % return = ((4+106)/100) – 1 = 10% p.a.
• % return= (4/100) + (106/100) – 1
• = (4/100) + (106 – 100)/100
• = dividend yield + capital gains yield
• = 4% + 6% = 10% p.a.
• Qu: What are two parts of (total %) return?
• Dollar returns vs percentage returns
• 10.2 Holding Period Return: Example
• Suppose your investment provides the following returns over a four-year period:
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%
• The Future Value of an Investment of \$1 in 1957 \$ 42.91 \$20.69 Common Stocks Long Bonds T-Bills
• Holding Period Return: Example
• What would be the annual return on her investment?
• 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
• Solving for r yields the geometric return: 9.58% p.a.
• Holding Period Return: Example
• Note that the geometric average is not same as the arithmetic average:
• 10.2 Holding-Period Returns
• The holding period return is the return that an investor would get when holding an investment over a period of n periods.
• The holding period return is given as, where r i represents the return during period i:
• Table 10.1 shows annual (holding period) returns on several portfolios.
• Qu on market history.
• 10.3 Return Statistics
• One can summarize the data with the average (mean), the standard deviation, and the frequency distribution of the returns.
• Average return: What is the return that an investor could have realized during a year over the 1948-2000 period?
• 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%.
• 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%
• 10.4 Average Stock Returns and Risk-Free Returns
• The Risk Premium is the difference between risky and risk-free return.
• For 1957-2003, risk premium for
• large cap common stocks: 3.84% = 10.64% – 6.8 %
• long-term (corporate+gov’t) bonds: 2.16%= 8.96% – 6.8 %
• One of the most significant observations of stock market data is this long-run risk premium.
• Risk Premia
• Suppose the current one-year Treasury bills rate is 5%. What is the expected return on the market of small-company stocks?
• The average risk premium for small cap (capitalization) stocks for the period 1976-2000 was 5.68%
• Given a risk-free rate of 5%, expected return on small-cap stocks is 14.8% = 5.68% + 5%.
• Rates of Return 1948-2000
• Rate of return on T-bills is essentially risk-free.
• Investing in stocks is risky, but there are compensations.
• The risk premium is the reward to bearing risk in stocks.
• The Risk-Return Tradeoff (1957-2003) Long Bonds T-Bills Large-Company Stocks
• 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.
• 10.5 Risk Statistics
• There is no universally agreed-upon definition of risk.
• We mainly use variance and standard deviation.
• Example: Annual returns for 1997-2000 are 14.98%, -1.58%, 31.71%, and 7.41%, with an average return of 13.1%.
• var = [(14.98%-13.1%) 2 + (-1.58%-13.1%) 2 +(31.71%-13.1%) 2 + (7.41%-13.1%) 2 ]/3 = 0.019925
• stdev = sqrt (var) = sqrt (0.019925) = 0.1222
• Normal Distribution
• A large sample from a normal distribution looks like a bell-shaped curve.
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%
• 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.
• 10.6 Summary and Conclusions
• Stocks have outperformed bonds over most of the twentieth century.
• Stocks have exhibited more risk than bonds.
• The small cap stocks have outperformed large cap stocks over most of the twentieth century, again with more risk.
• The statistical measures in this chapter are necessary building blocks for the material of the next three chapters.