1. GBUS502 Vicentiu Covrig 1 Risk and return (chapter 8)

2. GBUS502 Vicentiu Covrig 2 Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

3. GBUS502 Vicentiu Covrig 3 What is investment risk? Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment. Expected Rate of Return Rate of Return (%) 100 15 0-70 Firm X Firm Y Firm X (red) has a lower distribution of returns than firm Y (purple) though both have the same average return. We say that firm X’s returns are less variable/volatile (greater standard deviation  ) and thus X is a less risky investment than Y

4. GBUS502 Vicentiu Covrig 4 Selected Realized Returns, 1926-2007 Average Standard Return Deviation Small-company stocks17.1%32.6% Large-company stocks12.320.0 L-T corporate bonds 6.2 8.4 L-T government bonds 5.8 9.2 U.S. Treasury bills 3.8 3.1 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008), p28.

5. GBUS502 Vicentiu Covrig 5 Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? T-bills will return the promised 0.5%, regardless of the economy. No, T-bills do not provide a completely risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. T-bills are also risky in terms of reinvestment rate risk. T-bills are risk-free in the default sense of the word.

6. GBUS502 Vicentiu Covrig 6 Return: Calculating the expected return for each alternative OutcomeProb. of outcomeReturn in 1(recession).1-15% 2 (normal growth).615% 3 (boom).325% r ^ =expected rate of return = (.1)(-15) + (.6)(15) +(.3)(25)=15%

7. GBUS502 Vicentiu Covrig 7 Risk: Calculating the standard deviation for each alternative Standard deviation (σ) measures total, or stand-alone, risk. Greater the σ, greater the risk. Why?

8. GBUS502 Vicentiu Covrig 8 Investor attitude towards risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities Very often risk premium refers to the difference between the return on a risky asset and risk-free rate (ex. a treasury bond)

9. GBUS502 Vicentiu Covrig 9 Portfolio returns The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights. r p = W 1 r 1 + W 2 r 2 W 1 = Proportion of funds in Security 1 W 2 = Proportion of funds in Security 2 r 1 = Expected return on Security 1 r 2 = Expected return on Security 2

10. GBUS502 Vicentiu Covrig 10 Assume that you invested $3000 in IBM stock and $2,000 In Pfizer stock. The expected return of IBM stock is 15% and the expected return of Pfizer is 20%. What is the portfolio expected return? Answer: W1=3,000/(3,000+2,000)=0.6 W2=2,000/ (3,000+2,000)=0.4 Expected portfolio return = 0.6*15%+0.4*20%= 17%

11. GBUS502 Vicentiu Covrig 11 The benefits of diversification Come from the correlation between asset returns Correlation,  : a measure of the strength of the linear relationship between two variables -1.0 < r < +1.0 If r = +1.0, securities 1 and 2 are perfectly positively correlated If r = -1.0, 1 and 2 are perfectly negatively correlated If r = 0, 1 and 2 are not correlated The smaller the correlation, the greater the risk reduction potential  greater the benefit of diversification If  = +1.0, no risk reduction is possible Most stocks are positively correlated with the market (ρ  0.65)  Combining stocks and bonds in a portfolio generally lowers risk.

12. GBUS502 Vicentiu Covrig 12 Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Company-Specific Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

13. GBUS502 Vicentiu Covrig 13 Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification. If an investor chooses to hold a one-stock portfolio (exposed to more risk than a diversified investor), would the investor be compensated for the risk they bear? - NO! - Stand-alone risk is not important to a well-diversified investor. - Rational, risk-averse investors are concerned with σ p, which is based upon market risk.

14. GBUS502 Vicentiu Covrig 14 Coefficient of Variation (CV) Shows the risk per unit of return. You want to invest in a security with the highest expected return per unit of risk, and thus the lowest CV Average Standard Return DeviationCV Small-company stocks17.3%33.2%1.92 Large-company stocks12.720.21.59 L-T corporate bonds 6.1 8.61.41

15. GBUS502 Vicentiu Covrig 15 Capital Asset Pricing Model (CAPM) Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification. Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio Beta: measures a stock’s market risk Indicates how risky a stock is if the stock is held in a well- diversified portfolio Beta is calculated using regression analysis

16. GBUS502 Vicentiu Covrig 16 The Security Market Line (SML): Calculating required rates of return SML: k i = k RF + β i (k M – k RF ) SML is the empirical part of CAPM Assume k RF = 8%, k M = 15% and company’s BETA (β i ) is 1.2 The market (or equity) risk premium is RP M = k M – k RF = 15% – 8% = 7%. k i = 8% + 1.2x(15% - 8%) = 16.4%

17. GBUS502 Vicentiu Covrig 17 Comments on beta If beta = 1.0, the security is just as risky as the average stock (the market) If beta > 1.0, the security is riskier than average (the market) If beta < 1.0, the security is less risky than average (the market) Beta is greater than zero CAPM/SML concepts are based upon expectations, but betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness.