现代企业资本市场理论分析

1、McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-0Chapter Outline9.1Returns9.2Holding-Period Returns9.3Return Statistics9.4Average Stock Returns and Risk-Free Returns9.5Risk Statistics9.6Summary and ConclusionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill

2、 Companies, Inc. All rights reserved.9-19.1 Returns: Very Important Dollar 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 d

3、ivided by the original investment. Frequently: rt = ln(1 + (pt - pt-1+dt)/pt-1) is better for modeling. Fechners Law: response is proportional to stimulusMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-2Dollar Return = Dividend + Change in Market Value9.1 Ret

4、urnspercentage return dollar returnbeginning market valuedividend change in market valuebeginning market value dividend yield capital gains yieldThis is not statutory (tax law) capital gainsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-39.1 Returns: Example

5、 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 h

6、ave 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 is500, 2$520$%8 .20McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-49.1 Returns: Example Dollar Returns $520 gainTime01-$2,5

7、00$3,000$20Percentage Returns500, 2$520$%8 .20McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-59.2 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, when the return

8、 during period i is given as ri: holding period return (1 r1)(1 r2)L(1 rn)1sometimescalledbuy and hold returnfor the 4 year periodMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-6Holding Period Return: Example Suppose your investment provides the following re

9、turns over a four-year period. Note that this is a PV, NOT NPVYear Return110%2-5%320%415%21.444421.1)15. 1 ()20. 1 ()95(.)10. 1 (1)1 ()1 ()1 ()1 (return period holdingYour 4321rrrrMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-7Holding Period Return: Example

10、 An investor who held this investment would have actually realized an annual return of 9.58%:Year Return110%2-5%320%415%58. 9095844.1)15. 1 ()20. 1 ()95(.)10. 1 ()1 ()1 ()1 ()1 ()1 (return average Geometric443214ggrrrrrr So, our investor made 9.58% on his money for four years, realizing a holding pe

11、riod return of 44.21%4)095844. 1 (4421. 1McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-8Holding Period Return: Example Note that the geometric average is not the same thing as the arithmetic average. In finance we use the geometric average. For small change

12、s, the arithmetic average is approximately the same as the geometric.Year Return110%2-5%320%415%104%15%20%5%104return average Arithmetic4321rrrrMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-9Holding Period Returns A famous set of studies dealing with the ra

13、tes 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 Smal

14、l-company Common Stocks Long-Term Corporate Bonds Long-Term U.S. Government Bonds U.S. Treasury BillsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-10The Future Value of an Investment of $1 in 19260.110100019301940195019601970198019902000Common StocksLong T-

15、BondsT-Bills$40.22$15.6463.845, 2$)1 ()1 ()1 (1$199919271926rrrLSource: 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/IrwinCopyright 2002 by The McGraw-Hill Co

16、mpanies, Inc. All rights reserved.9-119.3 Return Statistics The 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.TRRRT)(1L1)()()(22221TRRRRRRVARSDTLMcGraw-Hill/IrwinCopyri

17、ght 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-12Historical 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 approxima

18、te. 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 Bills3.83.2Inflation3.24.5McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc

19、. All rights reserved.9-139.4 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-f

20、ree 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 fo

21、r the period 1926 through 1999 was 2.3% = 6.1% 3.8%McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-14Risk 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

22、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%McGraw-Hill/IrwinCopyright 2002 by The McGraw

23、-Hill Companies, Inc. All rights reserved.9-15Risk 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 +

24、 risk premium for asset A) risk premium for asset A standard deviation for asset AMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-16The Risk-Return Tradeoff2%4%6%8%10%12%14%16%18%0%5%10%15%20%25%30%35%Annual Return Standard DeviationAnnual Return AverageT-Bon

25、dsT-BillsLarge-Company StocksSmall-Company StocksMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-17Rates of Return 1926-1999-60-40-200204060263035404550556065707580859095Common StocksLong T-BondsT-BillsSource: Stocks, Bonds, Bills, and Inflation 2000 Yearbook

26、, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-18Risk Premiums Rate of return on T-bills is essentially risk-free: default risk-free

27、. 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.”McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc.

28、 All rights reserved.9-19Stock Market Volatility0102030405060192619351940194519501955196019651970197519801985199019951998Source: Stocks, Bonds, Bills, and Inflation 2000 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reser

29、ved.The volatility of stocks is not constant from year to year.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-209.5 Risk Statistics There is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviati

30、on. 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.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights re

31、served.9-21Normal Distribution A 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 t

32、he mean of 13.3 percent will be approximately 2/3. Note: returns for individual assets usually are not normally distributed.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.9-22Normal Distribution The 20.1-percent standard deviation we found for stock returns fr

33、om 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!McGraw-Hill/IrwinCop