1、Chapter Outline,9.1Returns9.2Holding-Period Returns9.3Return Statistics9.4Average Stock Returns and Risk-Free Returns9.5Risk Statistics9.6Summary and Conclusions,9.1Returns: Very Important,Dollar Returnsthe sum of the cash received and the change in value of the asset, in dollars.,Percentage Returns
2、: 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. Fechners Law: response is proportional to stimulus,Dollar Return = Dividend + Change in Market Value,9.1Returns,9.1Returns: Exa
3、mple,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, yo
4、u 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,9.1Returns: Example,Dollar Returns$520 gain,Percentage Returns,9.2Holding-Period Returns,The holding period return is the return that an investor would get when
5、 holding an investment over a period of n periods, when the return during period i is given as ri:,Holding Period Return: Example,Suppose your investment provides the following returns over a four-year period. Note that this is a PV, NOT NPV,Holding Period Return: Example,An investor who held this i
6、nvestment 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%,Holding Period Return: Example,Note that the geometric average is not the same thing as the arithmetic average. In finance we use the
7、 geometric average. For small changes, the arithmetic average is approximately the same as the geometric.,Holding Period Returns,A 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
8、-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 StocksSmall-company Common StocksLong-Term Corporate BondsLong-Term U.S. Government BondsU.S. Treasury Bills,The Future Value of an Investmen
9、t of $1 in 1926,$40.22,$15.64,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.,9.3Return Statistics,The history of capital market returns can be summarized by descri
10、bing the average return the standard deviation of those returns the frequency distribution of the returns: bar graph.,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. Sin
11、quefield). All rights reserved. Chart is approximate., 90%,+ 90%,0%,Average Standard Series Annual Return DeviationDistributionLarge Company Stocks13.0%20.3%Small Company Stocks17.733.9Long-Term Corporate Bonds6.18.7Long-Term Government Bonds5.69.2U.S. Treasury Bills3.83.2Inflation3.24.5,9.4 Average
12、 Stock Returns and Risk-Free Returns,The 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
13、 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%
14、 = 6.1% 3.8%,Risk Premia,Suppose 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 w
15、as 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%,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 a
16、s 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,The Risk-Return Tradeoff,Rates of Return 1926-1999,Source: Stocks, Bonds, Bills, and Inflation 2000 Yearbook, Ibbotson Associates, Inc., Chi
17、cago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.,Risk Premiums,Rate 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
18、risk premium for investing in stocks.An old saying on Wall Street is “You can either sleep well or eat well.”,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
19、 rights reserved.,The volatility of stocks is not constant from year to year.,9.5Risk Statistics,There 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
20、 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.,Normal Distribution,A large enough sample drawn from a normal distribution looks like a bell-shaped curve.,Return onlarge company commonstocks,68%,95%, 99%, 3
21、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.,Normal Distribution,The 20.1-percent standar
22、d 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 retur
23、ns are usually not symmetric!,Returns Distribution: Normally not normal,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.,9.6 Summary and Conclusions,This chapter pre
24、sents returns for four asset classes:Large Company StocksSmall Company StocksLong-Term Government BondsTreasury BillsStocks 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.,
