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 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 • 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. • Z score measures the number of standard deviations a particular rate of return r is from the expected value of r. See table V page T5 and slide 6 • Coefficient of variation v is a relative measure of risk. • Risk is an increasing function of time. ^

6. Calculating the Z Score • Z score = • What’s the probability of a loss on an investment with an expected return of 20 percent and a standard deviation of 7 percent? • (0% – 20%)/17% = –1.18 rounded • From table V = 0.1190 or 11.9 percent probability of a loss Target score – Expected value Standard deviation

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

8. 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

9. Expected Inflation Premium • Compensates investors for the loss of purchasing power due to inflation

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

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

12. Characteristics of the Securities Comprising the Portfolio • Expected return • Standard deviation,  • Correlation coefficient • Efficient portfolio

13. r a c b Risk a and c are preferred to b a and c are efficient ^ Efficient Portfolio • Has the highest possible return for a given  • Has the lowest possible  for a given expected return

14. The Portfolio effect is the risk reduction accompanying diversification. Systematic Risk Unsystematic Diversifiable Diversification

15. Systematic risk caused by factors affecting the market as a wholeundiversifiable interest rate changes changes in purchasing power change in business outlook Unsystematic risk caused by factors unique to the firmdiversifiable strikes government regulations management’s capabilities CAPM: Only Systematic Risk is Relevant

16. Systematic Risk is Measured by Beta,  • A measure of the volatility of a securities return compared to the Market Portfolio • A regression line of periodic rates of return for security j and the Market Portfolio • Search for (stock beta) on this search engine: • http://www.altavista.digital.com/

17. ^ rSML rf  ^ SML Shows the Relationship Between r and ß ^

18. Required Rate of Return • The required return for any security j may be defined in terms of systematic risk, j, the expected market return, rm, and the expected risk free rate, rf. ^ ^

19. Risk Premium ^ • (rm – rf) • Slope of security market line • Will increase or decrease with • uncertainties about the future economic outlook • the degree of risk aversion of investors ^

20. SML r ^ SML a ^ 10.5% ra ^ 9% rm ^ 6%rf 1.0 1.5  Risk Premium = (9% – 6%) = 3% ka = 6% + 1.5(9% – 6%) = 10.5%

21. Investors hold well-diversified portfolios Competitive markets Borrow and lend at the risk-free rate Investors are risk averse No taxes Investors are influenced by systematic risk Freely available information Investors have homogeneous expectations No brokerage charges CAPM Assumptions

22. Major Problems in the Practical Application of the CAPM • Estimating expected future market returns • Determining an appropriate rf • Determining the best estimate of  • Investors don’t totally ignore unsystematic risk. • Betas are frequently unstable over time. • Required returns are determined by macroeconomic factors. ^

23. International Investing • Appears to offer diversification benefits • Returns from DMCs tend to have high positive correlations. • Returns from MNCs tend to have lower correlations. • Obtains the benefits of international diversification by investing in MNCs or DMCs operating in other countries

24. Risk of Failure is Not Necessarily Captured by Risk Measurers • Risk of failure especially relevant • For undiversified investor • Costs of bankruptcy • Loss of funds when assets are sold at distressed prices • Legal fees and selling costs incurred • Opportunity costs of funds unavailable to investors during bankruptcy proceedings.

25. High-Yield Securities • Sometimes called “Junk Bonds” • Bonds with credit ratings below investment-grade securities • Have high returns relative to the returns available from investment-grade securities • Higher returns achieved only by assuming greater risk. • Ethical Issues next slide

26. Ethical Issues • Growth in high-risk junk bonds • Savings and loan industry • Insurance industry