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1、Risk and Return Lessons from Market History,Chapter 10,Key Concepts and Skills,Know how to calculate the return on an investment Know how to calculate the standard deviation of an investments returns Understand the historical returns and risks on various types of investments Understand the importanc
2、e of the normal distribution Understand the difference between arithmetic and geometric average returns,Chapter Outline,10.1Returns 10.2Holding-Period Returns 10.3Return Statistics 10.4Average Stock Returns and Risk-Free Returns 10.5Risk Statistics 10.6More on Average Returns,10.1Returns,Dollar Retu
3、rns the sum of the cash received and the change in value of the asset, in dollars.,Percentage Returns the sum of the cash received and the change in value of the asset divided by the initial investment.,Dollar Return = Dividend + Change in Market Value,Returns,Returns: Example,Suppose you bought 100
4、 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
5、cash dividends of $20. Your dollar gain was $520 = $20 + ($3,000 $2,500). Your percentage gain for the year is:,Returns: Example,Dollar Return: $520 gain,Percentage Return:,10.2 Holding-Period Returns,The holding period return is the return that an investor would get when holding an investment over
6、a period of n years, when the return during year i is given as ri:,Holding-Period Return: Example,Suppose your investment provides the following returns over a four-year period:,Holding-Period Returns,A famous set of studies dealing with rates of returns on common stocks, bonds, and Treasury bills w
7、as 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
8、U.S. Government Bonds U.S. Treasury Bills,10.3 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,Historical Returns, 1926-2004,Source: Stocks, Bonds, Bills, and
9、 Inflation 2005 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved., 90%,+ 90%,0%,Average Standard Series Annual Return DeviationDistribution Large Company Stocks12.4%20.3% Small Company Stocks17.533.1 Long-Term Corpo
10、rate Bonds6.28.6 Long-Term Government Bonds5.89.3 U.S. Treasury Bills3.83.1 Inflation3.14.3,10.4 Average Stock Returns and Risk-Free Returns,The Risk Premium is the added return (over and above the risk-free rate) resulting from bearing risk. One of the most significant observations of stock market
11、data is the 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 2004 was: 8.6% = 12.4% 3.8% The average excess return from small company common stocks for the period 1926 through 2004 was: 13.7% = 17.5% 3.8
12、% The average excess return from long-term corporate bonds for the period 1926 through 2004 was: 2.4% = 6.2% 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? Rec
13、all that the average excess return on small company common stocks for the period 1926 through 2004 was 13.7%. Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of 18.7% = 13.7% + 5%,The Risk-Return Tradeoff,10.5 Risk Statistics,There is no universally agr
14、eed-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 n
15、ormal distribution.,Normal Distribution,A large enough sample drawn from a normal distribution looks like a bell-shaped curve.,Probability,Return onlarge company commonstocks,99.74%, 3s 48.5%, 2s 28.2%, 1s 7.9%,012.4%,+ 1s 32.7%,+ 2s 53.0%,+ 3s 73.3%,The probability that a yearly return will fall wi
16、thin 20.3 percent of the mean of 12.4 percent will be approximately 2/3.,68.26%,95.44%,Normal Distribution,The 20.3% standard deviation we found for large stock returns from 1926 through 2004 can now be interpreted in the following way: if stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.3 percent of the mean of 12.4% will be approximately 2/3.,Example Return and Variance,Variance = .0045 / (
