8/17/2009 1 1 Chapter 9 Characterizing Risk and Return 2 Chapter 9 Learning Goals LG1: Compute an investment’s dollar and percentage return LG2: Find information about the historical returns and volatility for the stock, bond, and cash markets LG3: Measure and evaluate the total risk of an investment using several methods LG4: Recognize the risk / return relationship and its implications LG5: Plan investments that take advantage of diversification and its impact on total risk LG6: Find efficient and optimal portfolios LG7: Compute a portfolio’s return 3 Introduction • The relationship between risk and return is fundamental to finance theory • You can invest very safely in a bank or in Treasury bills. Why would you invest in risky stocks and bonds? – If you want the chance of earning higher returns, it requires that you take on higher risk investments • There is a positive relationship between risk and return 8/17/2009 2 4 Historical Returns • Computing Returns Dollar Return = (Capital gain or loss) + Income = (Ending Value – Beginning Value) + Income • We can convert from dollar returns to percentage returns by dividing by the Beginning Value 5 • Percentage Returns Value Beginning Income Value Beginning - Value Ending Return Percentage += 6 • Let’s assume we are considering an investment in stock. The income piece of this equation would be in the form of dividends. We can break this equation into two parts to reflect the capital gains yield and the dividend yield Price Beginning Dividend Price Beginning Price Beginning - Price Ending Return Percentage += YieldDivident Yield Gains Capital Return Percentage += 8/17/2009 3 7 • Example: You held 250 shares of Hilton Hotel’s common stock. The company’s share price was $24.11 at the beginning of the year. During the year, the company paid a dividend of $0.16 per share, and ended the year at a price of $34.90. What is the dollar return, the percentage return, the capital gains yield, and the dividend yield for Hilton? 8 Dollar return = 250 x ($34.90-$24.11+$0.16) = $2,737.50 Percent return = ($34.90-$24.11+$0.16)/$24.11 = 45.42% Capital gains yield = ($34.90 - $24.11)/$24.11 = 44.75% Dividend yield = $0.16/$24.11 = 0.66% 9 • Average Return – The arithmetic average return provides an estimate for how an investment has performed over long periods of time N Return Return Average N 1t t∑ == 8/17/2009 4 10 Performance of Asset Classes • Over long periods of time, how do stocks, bonds, and cash securities (e.g. T-bills) perform? • Historically, stocks have earned higher returns than either bonds or cash • [insert Table 9.2] 11 Historical Risks • When you purchase a U.S. Treasury bill, you know exactly what your returns are going to be, i.e. there is no uncertainty, or risk • On the other hand, when you invest in stocks you do not know what your returns will be, i.e. stock investing is risky • It is useful to be able to quantify the uncertainty of various asset classes 12 • Computing Volatility – High volatility in historical returns are an indication that future returns will be volatile – One popular way of quantifying volatility is to compute the standard deviation of percentage returns • Standard deviation is the square root of the variance • Standard deviation is a measure of total risk 1-N Return) Average - (Return Deviation Standard 1 2 t∑ == N t 8/17/2009 5 13 • A large standard deviation indicates greater return variability, or high risk • The standard deviation is in the same units as the data, i.e. in this case percent – The variance is in percentage squared – not very useful 14 Example: Using the following returns, calculate the average return, the variance, and the standard deviation for Acme stock. Year Acme 1 10% 2 4 3 - 8 4 13 5 5 15 Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80% σ2Acme = [(10 – 4.8)2 + (4 – 4.8)2 (- 8 – 4.8)2 + (13 – 4.8)2 + (5 – 4.8)2 ] / (5 - 1) σ2Acme = 258.8 / 4 = 64.70 σAcme = (64.70)1/2 = 8.04% 8/17/2009 6 16 • Risk of Asset Classes • [insert Table 9.4] 17 – The volatility of stocks is much higher than the volatility of bonds and T-bills – While the stock market as averaged a 13.2% return since 1950, that return comes with high volatility, with a standard deviation of 17.0% 18 • Risk versus Return – There is a tradeoff between risk and return – One way to measure this risk-vs.-reward relationship is the coefficient of variation – A smaller CoV indicates a better risk-reward relationship Return Average Deviation Standard Variation oft Coefficien = 8/17/2009 7 19 Forming Portfolios • Individual stocks have high standard deviations • The standard deviations of large portfolios are much smaller – Diversification reduces risk 20 • Diversifying to Reduce Risk – A stock’s total risk has two components: • Firm specific risk • Market risk Total Risk = Firm Specific Risk + Market Risk – Firm specific risk is specific to the company and common to other companies in the same industry – Market risk affects all firms 21 • Standard deviation measures total risk • We can reduce firm specific risk by combining stocks into a portfolio – For this reason, firm specific risk is also called diversifiable risk • On the other hand, macroeconomic events such as changes in interest rates, affect all companies 8/17/2009 8 22 • How does diversification lower risk? – If an investor holds one stock, the portfolio is very risky (it rises and falls based on what happens to the firm). – When stocks are added to the portfolio, the companies’ firm-specific risk tends to offset each other • As investors add stocks to their portfolio, the firm-specific portion of the risk declines, and all that is left is the systematic (or market) risk. The remaining risk is therefore due to overall movements in the market. • After a portfolio is fully diversified, the portfolio carries only market risk – For this reason, market risk is also called non- 23 • [Insert Figure 9.1] 24 • Modern Portfolio Theory – The concept that diversification reduces risk was formalized in the 1950s by Harry Markowitz when he was a doctoral student at the University of Chicago. He eventually won the Nobel Prize for his work. – In addition to showing how risk reduction occurs when securities are combined, Markowitz’s modern portfolio theory also describes how to combine stocks to achieve the lowest total risk possible for a given expected return. This is called an optimal portfolio. 8/17/2009 9 25 • [insert Figure 9.3] 26 • Portfolios with the highest return possible for each risk level are called efficient portfolios • If we added all available securities to the graph in Figure 9.3, then all of the efficient portfolios of those securities form the efficient frontier • Efficient frontier portfolios dominate all other possible stock portfolios 27 • How Does Diversification Work? – Diversification comes when stocks are subject to different kinds of events such that their returns differ over time, i.e. the stock’s returns are not perfectly correlated. Their price movements often counteract each other – If two stocks are perfectly positively correlated, diversification has no effect on risk. 8/17/2009 10 28 • Correlation measures the tendency of two stock’s returns to move together, and is represented by ρA,B -1.0 ≤ ρ ≤ +1.0 • Perfect positive correlation means ρA,B = +1.0 – Returns from two stocks are perfectly in sync • Perfect negative correlation means ρA,B = -1.0 – Returns from two stocks move exactly opposite • Perfect positive correlation gives no risk reduction • Correlation between -1.0 and +1.0 gives some, but not all, risk reduction 29 • Portfolio Return – A portfolio return is a weighted average of the returns of the individual components of the portfolio • Weighted by the proportion invested in each security )R x (w ..... )R x (w )R x (w R nn2211p +++= i n i R∑ = = 1 i p w R 30 • Example: At the beginning of 2007 you owned $5,000 of Disney stock, $10,000 of Bank of New York stock, and $15,000 of IBM stock. In 2007, the three company's returns were -4.8 percent, 19.4 percent, and 12.8 percent respectively. What is your portfolio return? Stock Amount invested Weight Calculation Weight Disney $5,000 5,000/30,000 0.1667 Bank of New York $10,000 10,000/30,000 0.3333 IBM $15,000 15,000/30,000 0.50 8/17/2009 11 31 Rp = (0.1667 x -4.8%) + (.3333 x 19.4%) + (.50 x 12.8%) Rp = 12.07% fitc Chapter 9