The document discusses risk and return in investing. It explains that equity investments like stocks historically have higher average returns of over 10% compared to debt investments like bonds that return 3-4%, but stocks are also more volatile. It defines risk as the variability of returns, and introduces the concepts of systematic risk that affects all stocks equally and unsystematic risk that is specific to individual stocks. Diversification can reduce unsystematic risk but not systematic risk. It also discusses measuring market risk through a stock's beta value, which represents its volatility relative to the overall market.

1. Risk and Return Chapter 8

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

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

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

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.

23. Figure 8.6: Risk Aversion

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

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

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

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

29. Portfolio Theory—Example 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

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

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

41. Measuring Market Risk—The Concept of Beta 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 k Conroy = 14% - 7.2% = 6.8% Example

49. The Security Market Line (SML)—Example 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: k Kelvin = 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

50. The Security Market Line (SML)—Example 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

51. The Security Market Line (SML)—Example The new required rate of return will be: k Kelvin = 6 + (10 – 6)2.3 = 15.2% Plugging this new required rate of return along with the higher growth rate of 9% into the Gordon model gives us the new estimated price: Thus, the venture looks like a good idea. Example