Analysis of Risk and Return

1. 5 Analysis of Risk and Return

2. Introduction • This chapter develops the risk-return relationship for individual projects (investments) and a portfolio of projects.

3. Risk and Return • Risk refers to the potential variability of returns from a project or portfolio of projects. • Returns are generated from cash flows. • Risk-free returns are known with certainty. • U.S. Treasury Securities • Check out interest rates on the following URLs • http://www.stls.frb.org/fred/data/irates.html • http://www.bloomberg.com/

4. Expected Return • Expected return is a weighted average of the individual possible returns. • The symbol for expected return, r, is called “r hat.” • r = Sum (all possible returns  their probability) ^ ^

5. Let’s Analyze Risk • Standard Deviation is an absolute measure of risk. See Tables 5.2, 5.3, and 5.4 and Figure 5.1.

6. Let’s Analyze Risk

7. Let’s Analyze Risk

8. Let’s Analyze Risk

9. Let’s Analyze Risk

10. Let’s Analyze Risk • Coefficient of variation v is a relative measure of risk. • Risk is an increasing function of time. See Figure 5.3.

11. Calculating the Z Score • Z score measures the number of standard deviations a particular rate of return r is from the expected value of r. See Figure 5.2. • Z score = ^ Target score – Expected value Standard deviation

12. Calculating the Z Score • What’s the probability of a loss (i.e., a negative return) on an investment with an expected return of 20 percent and a standard deviation of 17 percent? • (0% – 20%)/17% = –1.18 rounded • From table V = 0.1190 or 11.9 percent probability of a loss

13. Coefficient of Variation • The coefficient of variation is an appropriate measure of total risk when comparing two investment projects of different size.

14. Coefficient of Variation • Consider two assets, T and S. Asset T has expected annual returns of 25% and a standard deviation of 20%, whereas Asset S has expected annual returns of 10% and a standard deviation of 18%. Although Asset T has a higher standard deviation than Asset S, intuition tells us that Asset T is less risky, because its relative variation is smaller.

15. Coefficient of Variation • Coefficient of variation of Asset T is 0.8 (= 20%/25%) • Coefficient of variation of Asset S is 1.8 (= 18%/10%)

16. Required return = Risk-free return + Risk premium Real rate of return Risk-free rate Expected inflation premium Check out the risk-free rate at this Web site: http://www.cnnfn.com/markets/rates.html Risk-Return Relationship

17. Risk-Free Rate of Return • The real rate of return is the return that investors would required from a security having no risk of default in a period of no expected inflation. It is the return necessary to convince investors to postpone current, real consumption opportunities.

18. Risk-Free Rate of Return • The second component of the risk-free rate of return is an inflation premium or purchasing power loss premium. Investors required compensation for expected losses in purchasing power when they postpone current consumption and lend funds. Consequently, a premium for expected inflation is included in the required return on any security.

19. Risk-Free Rate of Return • The inflation premium is normally equal to investors’ expectations about future purchasing power changes. If, for example, inflation is expected to average 4 percent over some future period, the risk-free rate of return on U.S. Treasury bills (assuming a real rate of return of 3 percent) should be approximately equal to 7 percent.

20. Risk-Free Rate of Return • At any point in time, the required risk-free rate of return on any security can be estimated from the yields on short-term U.S. government securities, such as 90-day Treasury bills.

21. Risk-Free Rate of Return • When considering return requirements on all types of securities, it is important to remember that increases in expected inflation rates normally lead to increases in the required rates of return on all securities.

22. Risk Premium • A risk premium is a potential “reward” that an investor expects to receive when making a risky investment. • Investors are generally considered to be risk averse; that is, they expect, on average, to be compensated for the risk they assume when making an investment.

23. Risk Premium • The rate of return required by investors in financial assets is determined in the financial marketplace and depends on the supply of funds available as well as the demand for these funds.

24. Risk Premium • Investors who buy bonds receive interest payments and a return of principal as compensation for postponing consumption and accepting risk. • Similarly, common stock investors expect to receive dividends and price appreciation from their stocks.

25. Risk Premium • The rate of return required by investors represents a cost of capital to the firm. This required rate of return is used by a firm’s managers when computing the net present value of the cash flows expected to be generated from the company’s investment.

26. Risk Premium • The required rate of return on a security is also an important determinant of the market value of financial securities, including common stock, preferred stock, and bonds.

27. Risk Premium • The risk premium assigned by an investor to a given security in determining the required rate of return is a function of several different risk elements as you can see in the next several slides.

28. Risk Premium • Maturity risk premium • Default risk premium • Seniority risk premium • Marketability risk premium • Business risk • Financial risk

29. Maturity risk premium • The return required on a security is influenced by the maturity of that security. The term structure of interest rates is the pattern of interest rate yields (required returns) for securities that differ only in the length of time to maturity. • The longer the time to maturity, the higher the required return on the security. • See Figure 5.4.

30. Term Structure of Interest Rates • Expectations theory • Liquidity premium theory • Market segmentation theory

31. Expectations Theory • According to the expectations theory, long-term interest rates are a function of expected future (that is, forward) short-term interest rates. • If future short-term interest rates are expected to rise, the yield curve will tend to be upward sloping. In contrast, a down-sloping yield curve reflects an expectation of declining future short-term interest rates.

32. Expectations Theory • According to the expectations theory, current and expected future interest rates are dependent on expectations about future rates of inflation. • Many economic and political conditions can cause expected future inflation and interest rates to rise or fall. • These conditions include expected future government deficits (or surplus), changes in Federal Reserve monetary policy and cyclical business conditions.

33. Liquidity Premium Theory • The liquidity (or maturity) premium theory of the yield curve holds that required returns on long-term securities tend to be greater the longer the time to maturity. • The maturity premium reflects a preference by many lenders for shorter maturities because the interest rate risk associated with these securities is less than longer-term securities.

34. Liquidity Premium Theory • As we shall see in Chapter 6, the value of a bond tends to vary more as interest rates change, the longer the term to maturity. Thus, if interest rates rise, the holder of a long-term bond will find that the value of the investment has declined substantially more than that of the holder of a short-term bond.

35. Liquidity Premium Theory • In addition, the short-term bondholders has the option of holding the bond for the short time remaining to maturity and then reinvesting the proceeds from that bond at the new higher interest rate. The long-term bondholder must wait much longer before this opportunity is available.

36. Liquidity Premium Theory • Accordingly, it is argued that whatever the shape of the yield curve, a liquidity (or maturity) premium is reflected in it. The liquidity premium is larger for long-term bonds than for short-term bonds.

37. Market Segmentation Theory • According to market segmentation theory, the securities markets are segmented by maturity. Furthermore, interest rates within each maturity segment are determined to a certain extent by the supply and demand interactions of the segment’s borrowers and lenders.

38. Market Segmentation Theory • If strong borrower demand exists for long-term funds and these funds are in short supply, the yield curve will upward sloping. Conversely, if strong borrower demand exists for short-term funds and these funds are in short supply, the yield curve will be downward sloping.

39. Limitation of the choice of Maturities • Several factors limit the choice of maturities by lender. One such factor is the legal regulations that limit the types of investments commercial banks, savings and loan associations, insurance companies, and other financial institutions are permitted to make.

40. Limitation of the choice of Maturities • Another limitation faced by lenders is the desire (or need) to match the maturity structure of their liabilities with assets of equivalent maturity.

41. Limitation of the choice of Maturities • For example, insurance companies and pension funds, because of the long-term nature of their contractual obligations to clients, are interested primarily in making long-term investments. Commercial banks and money market funds, in contrast, are primarily short-term lenders because a large proportion of their liabilities is in the form of deposits that can be withdraw on demand.

42. Default risk premium • U.S. government securities are generally considered to be free of default risk. That is, the risk that interest and principal will not be paid as promised in the bond indenture. • In contrast, corporate bonds are subject to varying degrees of default risk. Investors require higher rates of return on securities subject to default risk.

43. Default risk premium • Bond rating agencies, such as Moody’s and Standard & Poor’s, provide evaluations of the default risk of many corporate bonds in the form of bond ratings. • The yields on bonds increases as the risk of default increases, reflecting the positive relationship between risk and required return.

44. Default risk premium • Over time, the spread between the required returns on bonds having various levels of default risk varies, reflecting the economic prospects and the resulting probability of default.

45. Seniority risk premium • Corporations issue different types of securities. These securities differ with respect to their claim on the cash flows generated by company and the claim on company’s assets in the case of default.

46. Seniority risk premium • A partial listing of these securities, from the least senior (that is, from the security having the lowest priority claim on cash flows and assets) to the most senior, includes common stock, preferred stocks, income bonds, subordinated debentures, debentures, second mortgage bonds, and first mortgage bonds.

47. Seniority risk premium • Generally, the less senior the claims of security holder, the greater the required rate of return demanded by investors in that security.

48. Seniority risk premium • For example, the holders of bonds issued by ExxonMobil are assured that they will receive interest and principal payments on these bonds except in the highly unlikely event that the company faces bankruptcy. In contrast, ExxonMobil common stockholders have no such assurance regarding dividend payments.

49. Seniority risk premium • In the case of bankruptcy, all senior claim holders must be paid before common stockholders receive any proceeds from the liquidation of the firm. Accordingly, common stockholders require a higher rate of return on their investment in ExxonMobil stock than do the company’s bondholders.

50. Marketability risk premium • Marketability risk refers to the ability of an investor to buy and sell a company’s securities quickly and without a significant loss of value.