第九章 资本市场理论综述

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1. Chapter Outline9.1 Returns 9.2 Holding-Period Returns 9.3 Return Statistics 9.4 Average Stock Returns and Risk-Free Returns 9.5 Risk Statistics 9.6 Summary and Conclusions
2. 9.1 Returns: Very ImportantDollar Returns the sum of the cash received and the change in value of the asset, in dollars.Time01Initial investmentEnding market valueDividendsPercentage Returns: the sum of the cash received and the change in value of the asset divided by the original investment. Frequently: rt = ln(1 + (pt - pt-1+dt)/pt-1) is better for modeling. Fechner’s Law: response is proportional to stimulus
3. Dollar Return = Dividend + Change in Market Value 9.1 Returns
4. 9.1 Returns: ExampleSuppose 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 – $2,500). Your percentage gain for the year is
5. 9.1 Returns: ExampleDollar Returns $520 gainTime01-$2,500$3,000$20Percentage Returns
6. 9.2 Holding-Period ReturnsThe holding period return is the return that an investor would get when holding an investment over a period of n periods, when the return during period i is given as ri:
7. Holding Period Return: ExampleSuppose your investment provides the following returns over a four-year period. [Note that this is a PV, NOT NPV
8. Holding Period Return: ExampleAn investor who held this investment would have actually realized an annual return of 9.58%:So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21%
9. Holding Period Return: ExampleNote that the geometric average is not the same thing as the arithmetic average. In finance we use the geometric average. For small changes, the arithmetic average is approximately the same as the geometric.
10. Holding Period ReturnsA famous set of studies dealing with the rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield. They present year-by-year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States: Large-Company Common Stocks Small-company Common Stocks Long-Term Corporate Bonds Long-Term U.S. Government Bonds U.S. Treasury Bills
11. The Future Value of an Investment of $1 in 1926$40.22$15.64Source: © 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.
12. 9.3 Return StatisticsThe history of capital market returns can be summarized by describing the average return the standard deviation of those returns the frequency distribution of the returns: bar graph.
13. Historical Returns, 1926-1999 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. Chart is approximate.– 90%+ 90%0% Average Standard Series Annual Return Deviation Distribution Large Company Stocks 13.0% 20.3% Small Company Stocks 17.7 33.9 Long-Term Corporate Bonds 6.1 8.7 Long-Term Government Bonds 5.6 9.2 U.S. Treasury Bills 3.8 3.2 Inflation 3.2 4.5
14. 9.4 Average Stock Returns and Risk-Free ReturnsThe Risk Premium is the additional return (over and above the risk-free rate, rF) resulting from bearing risk. One of the most significant observations of stock market data is this long-run excess of stock return over the risk-free return. The average excess return from large company common stocks for the period 1926 through 1999 was 9.2% = 13.0% – 3.8% The average excess return from small company common stocks for the period 1926 through 1999 was 13.9% = 17.7% – 3.8% The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.3% = 6.1% – 3.8%
15. Risk PremiaSuppose that The Wall Street Journal announced that the current rate for one-year Treasury bills is 5%. What is the expected return on the market of small-company stocks? Recall that the average excess return from small company common stocks for the period 1926 through 1999 was 13.9% Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of 18.9% = 13.9% + 5%
16. Risk Premia: What do they mean?Note that the calculations above are based on average performances of the various assets. Usually the risk premium for an asset is interpreted as associated with the expected variability of the expected return: rA = E(rF + risk premium for asset A) risk premium for asset A ≈ standard deviation for asset A
17. The Risk-Return Tradeoff
18. Rates of Return 1926-1999Source: © 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.
19. Risk PremiumsRate of return on T-bills is essentially risk-free: default risk-free. Investing in stocks is risky, but there are compensations. The difference between the return on T-bills and stocks is the risk premium for investing in stocks. An old saying on Wall Street is “You can either sleep well or eat well.”
20. Stock Market VolatilitySource: © 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.
21. 9.5 Risk StatisticsThere is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviation. 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. Its interpretation is facilitated by a discussion of the normal distribution.
22. Normal DistributionA large enough sample drawn from a normal distribution looks like a bell-shaped curve.ProbabilityReturn onlarge company commonstocks68%95%> 99%– 3 – 47.9%– 2 – 27.6%– 1 – 7.3%013.0%+ 1 33.3%+ 2 53.6%+ 3 73.9%the probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3. Note: returns for individual assets usually are not normally distributed.
23. Normal DistributionThe 20.1-percent standard deviation we found for stock returns from 1926 through 1999 can now be interpreted in the following way: if stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3. But asset returns are usually not symmetric!
24. Returns Distribution: Normally not normalSource: © 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.
25. 9.6 Summary and ConclusionsThis chapter presents returns for four asset classes: Large Company Stocks Small Company Stocks Long-Term Government Bonds Treasury Bills Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk. The stocks of small companies have outperformed the stocks of small companies 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.