6 Analysis of Risk and Return ©2006 Thomson/South-Western

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  

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

5 Standard Deviation 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.

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7 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 = or 11.9 percent probability of a loss Target score – Expected value Standard deviation

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

10 Risk-Return Relationship Required return = Risk-free return + Risk premium Check out the risk-free rate at this Web site:

11 What Makes Up the Risk-Free Rate? The risk-free rate of return is the sum of two components: Real rate of return + expected inflation premium  The inflation premium compensates investors for the loss of purchasing power due to inflation

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13 Sources of the Risk Premium Maturity risk premium Default risk premium Seniority risk premium Marketability risk premium

14 Explaining the Maturity Premium What causes interest rates to change with the time to maturity? Expectations theory Liquidity premium theory Market segmentation theory

15 Business Risk and Financial Risk Business risk refers to the variability of operating earnings over time. Financial risk refers to the additional variability in earnings per share resulting from the use of debt financing.

16 Conceptual Risk-Return Relationship

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18 Characteristics of the Securities Comprising the Portfolio Expected return Standard deviation,  Correlation coefficient

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

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

21 Expected Return on a Portfolio A portfolio has common stock from companies A and B. Stock from A makes up 75% of the portfolio and has an expected return of 12%. Stock from B makes up 25% of the portfolio and has an expected return of 16%. r p = 0.75(12%) (16%) = 13.0% ^

22 Standard Deviation of Portfolio Return The standard deviations of returns for the securities for companies A and B are 10%(σ a ) and 20%(σ b ), respectively. With a correlation coefficient(ρ ab ) between the returns on the securities equal to +0.50, the standard deviations of return for the same portfolio is: σ p = √(.75) 2 (10) 2 + (.25) 2 (20) 2 + 2(.75)(.25)(+.50)(10)(20) = 10.90%

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24 (a) Perfect Positive Correlation for Two Investments

25 (b) Perfect Negative Correlation for Two Investments

26 (c) Zero Correlation for Two Investments

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28 CAPM: Only Systematic Risk is Relevant Systematic risk caused by factors affecting the market as a whole undiversifiable  interest rate changes  changes in purchasing power  change in business outlook Unsystematic risk caused by factors unique to the firm diversifiable  strikes  government regulations  management’s capabilities

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30 Systematic Risk is Measured by Beta,  A measure of the volatility of a securities return compared to the Market Portfolio

31 The Characteristic Line A regression line of periodic rates of return for security j and the Market Index Search for (stock beta) on this search engine: 

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33 Beta Measures Slope Return on Market Index Return on GM Slope = β

34 SML Shows the Relationship Between r and ß r SML r f  ^ ^

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37 Required Rate of Return The required return for any security j may be defined in terms of systematic risk,  j, the expected market return, r m, and the expected risk free rate, r f. ^ ^

38 Risk Premium (r m – r f ) Slope of security market line Will increase or decrease with  uncertainties about the future economic outlook  the degree of risk aversion of investors ^

39 SML ^ ^ ^ 1.0 Risk Premium = (9% – 6%) = 3% k a = 6% + 1.5(9% – 6%) = 10.5% a 10.5% r a 1.5 ^ 6% r f  r SML 9% r m

40 CAPM Assumptions 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

41 Major Problems in the Practical Application of the CAPM Estimating expected future market returns Determining an appropriate r f 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. ^

42 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

43 Risk of Failure is Not Necessarily Captured by Risk Measures 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.

44 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.

45 Ethical Issues Growth in high-risk junk bonds Savings and loan industry Insurance industry