Risk and Return

1. Chapter 8 Risk and Return

2. Why Study Risk and Return? • Returns to equity investments (stock) have historically been much higher than the return to debt investments • Equity returns averaged more than 10% while debt returns average between 3% and 4% • Inflation also averaged about 3% during the same time period • Returns on equity investments are much more volatile than the returns on debt instruments in the short-run

3. Why Study Risk and Return? • Since equity earns a much higher return but with higher risk, it would be nice if we could invest and earn a high return but reduce the risk associated with such investments • Investing in portfolios of securities can help manage risk • A portfolio is a collection of financial assets by investors • We wish to capture the high average returns of equity investing while limiting the associated risk as much as possible

4. The General Relationship Between Risk and Return • Risk in finance is defined as the probability of losing some or all of the money invested in a deal • Generally investments that offer higher returns involve higher risks • Suppose you could invest in a stock that would either return you 15% or a loss of everything (-100%) • Also, suppose the chance of losing everything is 1% and the chance of earning 15% is 99% • The risk associated with this investment is the 1% chance of losing everything

5. The General Relationship Between Risk and Return • Investors more or less expect to receive a positive return but they realize that there is risk associated with these investments and the chance that they can lose their money • Stocks offering a higher likely return also have higher probabilities of total loss • It is difficult to determine how much risk is associated with a given level of return • Need to define risk in a measurable way • The definition has to include all the probabilities of loss • Have to relate that measurement to return

6. Portfolio Theory—Modern Thinking about Risk and Return • Portfolio theory defines investment risk in a measurable way and relates it to the expected level of return from an investment • Has had major impact on practical investing activities

7. The Return on an Investment • The rate of return allows an investment's return to be compared with other investments • One-Year Investments • The return on a debt investment is • K = interest paid  loan amount • A return is what the investor receives divided by what is invested • The return on a stock investment is • K = D1 + (P1 – P0)  P0

8. Returns, Expected and Required • The expected return on a stock is the return investors feel is most likely to occur based on currently available information • Anticipated return based on the dividends expected as well as the future expected price • No rational person makes any investment without some expectation of return

9. Returns, Expected and Required • The required return on a stock is the minimum rate at which investors will purchase or hold a stock based on their perceptions of its risk • People will only invest in an asset if they believe the expected return is at least equal to the required return • Different people have different levels of both expected and required return • Significant investment in a stock occurs only if the expected return exceeds the required return for a substantial number of investors

10. Risk—A Preliminary Definition • A preliminary definition of investment risk is the probability that return will be less than expected • This definition includes both positive and negative returns that are lower than expected • Feelings About Risk • Most people have negative feelings about bearing risk • Risk averse investors prefer lower risk when expected returns are equal • Most people see a trade-off between risk and return • However risk isn't to be avoided, but higher risk investments must offer a higher expect return to encourage investment

11. Portfolio Theory • Review of the Concept of a Random Variable • In statistics a random variable is the outcome of a chance process and has a probability distribution • Discrete variables can take only specific variables • Continuous variables can take any value within a specified range

12. Review of the Concept of a Random Variable • The Mean or Expected Value • The most likely outcome for the random variable • For symmetrical probability distributions the mean is the center of the distribution • Statistically it is the weighted average of all possible outcomes

13. Portfolio Theory • Variance and Standard Deviation • Variability relates to how far a typical observation of the variable is likely to deviate from the mean • There's is a great deal of difference in variability around the mean for different distributions • Telephone poles don't vary much in height from pole to pole—actual pole heights are closely clustered around the mean • Office buildings do vary a great deal in terms of height—widely dispersed around the mean • The standard deviation gives an indication of how far from the mean a typical observation is likely to fall

14. Portfolio Theory • Variance and Standard Deviation • Variance Formula • Variance is the average squared deviation from the mean • Standard deviation formula

15. Q: If you toss a coin four times what is the chance of receiving heads (x)? X P(X) 0 0.0625 The mean of this distribution is 2, since it is a symmetrical distribution. Example 1 0.2500 2 0.3750 3 0.2500 4 0.0625 1.0000 Portfolio Theory—Example

16. A: The Variance and Standard Deviation of the distribution is: Xi (Xi – ) (Xi – )2 P(Xi) (Xi – )2 x P(Xi) 0 -2 4 0.0625 0.25 Since the variance is 1.0, the standard deviation is also 1.0. 1 -1 1 0.2500 0.25 Example 2 0 0 0.3750 0.00 3 1 1 0.2500 0.25 4 2 4 0.0625 0.25 Var X = 1.00 SD X = 1.00 Portfolio Theory—Example

17. Review of the Concept of a Random Variable • The Coefficient of Variation • A relative measure of variation—the ratio of the standard deviation of a distribution to its mean • CV = Standard Deviation  Mean • For example, if the CV = 0.5, then the typical variation is 50% the size of the mean, or ½ • Continuous Random Variable • Can take on any numerical value within some range • We talk about the probability of an actual outcome being within a range of values rather than being an exact amount

18. The Return on a Stock Investment as a Random Variable • In financial theory, the return on a stock investment is considered a random variable • Return is influenced by the future price of the stock and the expected dividends • There is an element of uncertainty in both of these variables • Return is a continuous random variable with a low value of -100% but no limit to the high value • The mean of the distribution of returns is the stock's expected return • The variance and standard deviation show how likely it is that an actual return will be some distance from the expected value • Actual return in a distribution with a large variance is likely to be different from the mean

19. Figure 8.4: Probability Distributions With Large and Small Variances

20. Risk Redefined as Variability • In financial theory risk is defined as variability in return • A risky stock has a high probability of earning a return that significantly differs from the mean of the distribution • While a low-risk stock is more like to earn a return similar to the expected return • In practical terms risk is the probability that return will be less than expected

21. Figure 8.5: Investment Risk Viewed as Variability of Return Over Time While both stocks have the same expected return, the high risk stock has a greater variability in returns.

22. Risk Aversion • Risk aversion means investors prefer lower risk when expected returns are equal • When expected returns are not equal the choice of investment depends on the investor's tolerance for risk

23. Figure 8.6: Risk Aversion

24. Q: Harold MacGregor is considering buying stocks for the first time and is looking for a single company in which he'll make a major investment. He's narrowed his search to two firms, Evanston Water Inc. (a public utility) and Astro Tech Corp. (a new high-tech company). • Public utilities are low-risk stocks because they are regulated monopolies • High tech firms are high-risk because new technical ideas can succeed tremendously, fail completely or end up in-between Harold has studied the history and prospects of both firms and their industries, and with the help of his broker has made a discrete estimate of the probability distribution of returns for each stock as follows: Example Portfolio Theory—Example

25. Evaluate Harold's options in terms of statistical concepts of risk and return. Evanston Water Astro Tech kE P(kE) kA P(kA) 6% 0.05 -100% 0.15 8 0.15 0 0.20 10 0.60 15 0.30 Example 12 0.15 30 0.20 14 0.05 130 0.15 Portfolio Theory—Example

26. A: First calculate the expected return for each stock--the mean for each distribution. Evanston Water Astro Tech kE P(kE) kE* P(kE) kA P(kA) kA* P(kA) 6% 0.05 0.3% -100% 0.15 -15.0% 8 0.15 1.2 0 0.20 0.0 Example 10 0.60 6.0 15 0.30 4.5 12 0.15 1.8 30 0.20 6.0 14 0.05 0.7 130 0.15 19.5 10.0% 15.0% Portfolio Theory—Example

27. A: Next, calculate the variance and standard deviation of the stocks' returns. kE (kE – ) (kE – )2 P(kE) (kE – )2 x P(kE) 6% -4% 16 0.05 0.8 8 -2 4 0.15 0.6 Example 10 0 0 0.60 0.0 12 2 4 0.15 0.6 14 4 16 0.05 0.8 Var kE = 2.8 SD kE = 1.7% Portfolio Theory—Example

28. kA (kA – ) (kA – )2 P(kA) (kA – )2 x P(kA) -100% -115% 13,225 0.15 1,984 0 -15 225 0.20 45 15 0 0 0.30 0 30 15 225 0.20 45 130 115 13,225 0.15 1,984 Example Var kA = 4,058 SD kA = 63.7 A: Finally, calculate the coefficient of variation for each stock's return. Portfolio Theory—Example

29. A: If Harold only considers expected return, he’ll certainly choose Astro. However, with Evanston his investment is relatively safe while with Astro there is a substantial chance he’ll lose everything. No one but Harold can make the decision as to which investment he should choose. It depends on his degree of risk aversion. Example Portfolio Theory—Example

30. Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk • Fundamental truth of the investment world • The returns on securities tend to move up and down together • Not exactly together or proportionately • Events and Conditions Causing Movement in Returns • Some things influence all stocks (market risk) • Political news, inflation, interest rates, war, etc. • Some things influence only particular firms (business-specific risk) • Earnings reports, unexpected death of key executive, etc. • Some things affect all companies within an industry • A labor dispute, shortage of a raw material

31. Market reopens after World Trade Center collapses. Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk

32. Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk • Movement in Return as Risk • The total movement in a stock's return is the total risk inherent in the stock • Separating Movement/Risk into Two Parts • A stock's risk can be separated into systematic or market risk and unsystematic or business-specific risk

33. Portfolios • A portfolio is an investor's total stock holding • Risk and Return for a Portfolio • Each stock in a portfolio has its own expected return and its own risk • Portfolios have their own risks and returns • The return on a portfolio is a weighted average of the returns of the individual stocks in the portfolio • The risk is the variance or standard deviation of the probability distribution of the portfolio's return • Not the same as the weighted average of the standard deviations or variances of the individual stocks within the portfolio

34. Portfolios • The Goal of the Investor/Portfolio Owner • Goal of investors: to capture the high average returns of equities while avoiding as much risk as possible • Generally done by constructing diversified portfolios to minimize portfolio risk for a given return • Investors are concerned with how stocks impact portfolio performance, not with the stocks' stand-alone characteristics

35. Diversification—How Portfolio Risk Is Affected When Stocks Are Added • Diversification means adding different (diverse) stocks to a portfolio • Can reduce (but not eliminate) risk in a portfolio • Business-Specific Risk and Diversification • Business-specific risk is a series of essentially random events that push the returns of individual stocks up or down • Their effects simply cancel when added together over a substantial number of stocks • Is essentially random and can be diversified away • For this to work, the stocks within the portfolio must be from fundamentally different industries

36. Diversification—How Portfolio Risk Is Affected When Stocks Are Added • Systematic (Market) Risk and Diversification • If the returns of all stocks move up and down more or less together, it's not possible to reduce risk completely • Systematic risk can be reduced but never entirely eliminated • The Portfolio • If we have a portfolio that is as diversified as the market, its return will move in tandem with the market • The Impact on Portfolio Risk of Adding New Stocks • If we add a stock to the portfolio which has returns perfectly positively correlated with the portfolio, it will generally add risk to the diversified portfolio • If we add a stock that is perfectly negatively correlated with the portfolio, it will decrease the risk of the portfolio

37. Diversification—How Portfolio Risk Is Affected When Stocks Are Added • The Risk of the New Additions By Themselves and in Portfolios • Stocks with equal stand-alone risk can have opposite risk impacts on a portfolio because of the timing of the variation in their returns • A stock's risk in a portfolio sense is its market risk • Choosing Stocks to Diversify for Market Risk • How do we diversify to reduce market risk in a portfolio • Theoretically it's simple: just add stocks that move counter cyclically with the market • Unfortunately it's difficult to find stocks that move in that direction • However numerous stocks exist that have returns that are less than positively correlated with the market • Adding these stocks to the portfolio will generally reduce risk somewhat, but will not eliminate it

38. Diversification—How Portfolio Risk Is Affected When Stocks Are Added • The Importance of Market Risk • Modern portfolio theory is based on the assumption that investors focus on portfolios rather than on individual stocks • How stocks affect portfolios depends only on market risk • For the small investor with a limited portfolio, these concepts do not apply

39. Measuring Market Risk—The Concept of Beta • Market risk is a crucial concept in investing, so we need a way to measure it for individual stocks • A stock's beta measures its market risk • It measures the variation of a stock's return which accompanies the market's variation in return • Developing Beta • Beta is developed by determining the historical relationship between a stock's return and the return on a market index, such as the S&P500 • The stock's characteristic line reflects the average relationship between its return and the market • Beta is the slope of the characteristic line • Projecting Returns with Beta • Knowing a stock's beta enables us to estimate changes in its return given changes in the market's return

40. IBM’s beta Measuring Market Risk—The Concept of Beta Characteristic line determined using data from Slide 31.

41. Q: Conroy Corp. has a beta of 1.8 and is currently earning its owners a return of 14%. The stock market in general is reacting negatively to a new crisis in the Middle East that threatens world oil supplies. Experts estimate that the return on an average stock will drop from 12% to 8% because of investor concerns over the economic impact of a potential oil shortage as well as the threat of a limited war. Estimate the change in the return on Conroy shares and its new price. A: Beta represents the past average change in Conroy’s return relative to changes in the market’s return. The new return can be estimated as kConroy = 14% - 7.2% = 6.8% Example Measuring Market Risk—The Concept of Beta

42. Measuring Market Risk—The Concept of Beta • Betas are developed from historical data • May not be accurate if a fundamental change in the business environment occurs • Small investors should remember that beta doesn't measure total risk • A beta > (<) 1.0 implies the stock moves more (less) than the market • Beta < 0 means the stock tends to move against the market • Stocks in gold mining companies are a real-world example of negative beta stocks • Beta for a Portfolio • Beta for a portfolio is the weighted average of the betas of the individual stocks within the portfolio

43. Using Beta—The Capital Asset Pricing Model (CAPM) • The CAPM helps us determine how stock prices are set in the market • Developed in 1950s and 1960s by Harry Markowitz and William Sharpe • The CAPM's Approach • People won't invest unless a stock's expected return is at least equal to their required return • The CAPM attempts to explain how investors' required returns are determined

44. Using Beta—The Capital Asset Pricing Model (CAPM) • Rates of Return, The Risk-Free Rate and Risk Premiums • The risk-free rate (kRF) is a rate for which there is no chance of receiving less than what is expected • Returns on federally insured bank accounts and short-term Treasury debt are examples of risk-free investments • Investing in any other investment is a risky venture; thus investors will require a return greater than the risk-free rate • Investors want to be compensated for the extra risk taken via a rate known as the risk premium (KRP) • The CAPM purports to explain how the risk premium in required rates of return are formed • The Security Market Line (SML) is the heart of the CAPM

45. The Security Market Line (SML) • The SML proposes that required rates of return are determined by: • The Market Risk Premium • Is a reflection of the investment community's level of risk aversion • It is the risk premium for an investment in the market as a whole • The Risk Premium for Stock X • The beta for Stock X times the risk premium of the market • Says that the risk premium for a stock is determined only by the stock's relationship with the market as measured by beta

46. The Security Market Line (SML) • The SML as a Portrayal of the Securities Market • The standard equation of a straight line is • y = mx + b • Where: y is the vertical axis variable; x is the horizontal axis variable; m is the slope of the line and b is the y intercept • The SML can be viewed as a straight line: • The slope of the SML plotted in risk-return space reflects the general level of risk aversion • The vertical intercept of the SML represents investment in short-term government securities

47. The Security Market Line (SML) • The SML as a Line of Market Equilibrium • If, for every stock, its expected return equals its required return, the SML represents equilibrium • Suppose that a stock's expected return now becomes less than its required return • Investors would no longer desire that stock and owners of the stock would sell while potential buyers would no longer be interested • The stock price would drop because supply would exceed demand • Since the stock price is dropping, its expected return is increasing, driving it back toward equilibrium • The SML represents a condition of stable equilibrium

48. The Security Market Line (SML) • Valuation Using Risk-Return Concepts • The SML allows us to calculate the minimum required rate of return for a stock • This return can then be used in the Gordon model to determine an intrinsic value for a stock • The Impact of Management Decisions on Stock Prices • Since managers can influence a stock's beta and future growth rates, management's decisions impact the price of the stock

49. Q: The Kelvin Company paid an annual dividend of $1.50 recently, and is expected to grow at 7% into the indefinite future. Short-term treasury bills are currently yielding 6%, and an average stock yields its owner 10%. Kelvin stock is relatively volatile. Its return tends to move in response to political and economic changes about twice as much as does the return on the average stock. What should Kelvin sell for today? A: The required rate of return using the SML is: kKelvin = 6 + (10 – 6)2.0 = 14% Plugging this required rate of return along with the growth rate of 7% into the Gordon model gives us the estimated price: Example The Security Market Line (SML)—Example

50. Q: The Kelvin Company has an exciting new opportunity. The firm has identified a new field into which it can expand using technology it already possesses. The venture promises to increase the firm's growth rate to 9% from the current 7%. However, the project is new and unproven, so there's a chance it will fail and cause a considerable loss. As a result, there's some concern that the stock market won't react favorably to the additional risk. Management estimates that undertaking the venture will raise the firm's beta to 2.3 from its current level of 2.0. Should Kelvin undertake the new project if the firm’s current stock price is $22.93? A: The objective of the firm’s management should be to maximize shareholder wealth. If growth is expected to increase, this will have a positive impact on stock price; however, if an increase in beta is expected, stockholders will demand a higher rate of return which will cause an offsetting drop in the stock price. The expected price of the stock given both the increase in the growth rate and the increase in the firm’s beta must be calculated. Example The Security Market Line (SML)—Example