G. M. Wali Ullah Lecturer, School of Business Independent University, Bangladesh (IUB) Chapter 10 Risk and Return FIN 302 (3) Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

10-1 Key Concepts and Skills  Know how to calculate the return on an investment  Know how to calculate the standard deviation of an investment’s returns  Understand the historical returns and risks on various types of investments  Understand the difference between arithmetic and geometric average returns

Dollar Returns  Dollar Returns the sum of the cash received and the change in value of the asset, in dollars. Time01 Initial investment Ending market value Dividends Percentage Returns the sum of the cash received and the change in value of the asset, divided by the initial investment.

Dollar Returns: Example  Suppose we are considering the cash flows of the investment (in Figure 10.1), showing that you purchased 100 shares of stock at the beginning of the year at a price of $37 per share. Your total investment, then, was:

Dollar Returns: Example  Suppose that over the year the stock paid a dividend of $1.85 per share. During the year, then, you received income of:  Suppose, finally, that at the end of the year the market price of the stock is $40.33 per share. Because the stock increased in price, you had a capital gain of:

Dollar Returns: Example  The total dollar return on your investment is the sum of the dividend income and the capital gain or loss on the investment:

Dollar Returns: Example  Notice that if you sold the stock at the end of the year, your total amount of cash would be the initial investment plus the total dollar return. In the preceding example you would have:

Dollar Returns: Example  Figure: 9.1

10-8 Percentage Returns  In our example, the price at the beginning of the year was $37 per share and the dividend paid during the year on each share was $1.85. Hence the percentage income return, sometimes called the dividend yield, is:

10-9 Percentage Returns  The capital gain (or loss) is the change in the price of the stock divided by the initial price. Letting P t+1 be the price of the stock at year- end, we can compute the return from capital gain as follows:

10-10 Percentage Returns  Combining these two results, we find that the total return on the investment in Video Concept stock over the year, which we will label R t+1, was:

10-11 Returns: Example  Suppose you bought 100 shares of Wal-Mart one year ago at $45. Over the last year, you received $27 in dividends (27 cents per share × 100 shares). At the end of the year, the stock sells for $48. How did you do? [calculate total return]  You invested $45 × 100 = $4,500. At the end of the year, you have stock worth $4,800 and cash dividends of $27. Your dollar gain was $327 = $27 + ($4,800 – $4,500).  Your total return for the year is: 7.3% = $4,500 $327

10-12 Returns: Example Dollar Return: $327 gain Time01 -$4,500 $300 $27 Percentage Return: 7.3% = $4,500 $327

Holding Period Return  The holding period return is the return that an investor would get when holding an investment over a period of T years, when the return during year i is given as R i :

10-14 Holding Period Return: Example  Suppose your investment provides the following returns over a four-year period:

Average Return  The historical returns can be summarized by describing the: average return

10-16 Risk 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 a sample data Its interpretation is facilitated by a discussion of the normal distribution. (Discussed Later…)

10-17 Standard Deviation the standard deviation of those returns R j : return for a particular period, j T: number of sample data

10-18 Standard Deviation: Example Analysis of the result of standard deviation will be discussed with the help of normal distribution at the end of this chapter

Average Stock Returns and Risk-Free Returns  Treasury Bill (Short Term Government Bond) return is known as Risk Free Return.  The Risk Premium is the added return (over and above the risk-free rate) resulting from bearing risk.

10-20 Historical Returns, Risk Premium & σ (STD DEV.) Source: © Stocks, Bonds, Bills, and Inflation 2008 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. Average Standard Series Annual Return Deviation Distribution Large Company Stocks12.3%20.0% Small Company Stocks Long-Term Corporate Bonds Long-Term Government Bonds U.S. Treasury Bills Inflation Return Vs Risk

Average Stock Returns and Risk-Free Returns  One of the most significant observations of stock market 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 2007 was: 8.5% = 12.3% – 3.8% The average excess return from small company common stocks for the period 1926 through 2007 was: 13.3% = 17.1% – 3.8% The average excess return from long-term corporate bonds for the period 1926 through 2007 was: 2.4% = 6.2% – 3.8%

10-22 Risk Premiums  Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills is 2%.  What is the expected return on the market of small- company stocks?  Recall that the average excess return on small company common stocks for the period 1926 through 2007 was 13.3%.  Given a risk-free rate of 2%, we have an expected return on the market of small-company stocks of 15.3% = 13.3% + 2%

10-23 The Risk-Return Tradeoff

10-24 Normal Distribution: A Brief Overview  In classical statistics, the normal distribution plays a central role, and the standard deviation is the usual way to represent the spread of a normal distribution. For the normal distribution, the probability of having a return that is above or below the mean by a certain amount depends only on the standard deviation.

10-25 Normal Distribution  For example, the probability of having a return that is within one standard deviation of the mean of the distribution is approximately 68.26%, and the probability of having a return that is within two standard deviations of the mean is approximately 95.44% and the probability of having a return that is within three standard deviations of the mean is approximately 99.74%

10-26 σ=20.2

Geometric Returns

Average Returns Vs Geometric Returns  The geometric average return answers the question, “What was your average compound return per year over a particular period?”  The arithmetic average return answers the question, “What was your return in an average year over a particular period?”

Geometric Returns  Which one is better? The geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered.