1. FIN303 Vicentiu Covrig 1 Risk and return (chapter 8)

2. FIN303 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. FIN303 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. FIN303 Vicentiu Covrig 4 Selected Realized Returns, 1926 – 2004 Average Standard Return Deviation Small-company stocks17.5%33.1% Large-company stocks12.420.3 L-T corporate bonds 6.2 8.6 L-T government bonds 5.8 9.3 U.S. Treasury bills 3.8 3.1

5. FIN303 Vicentiu Covrig 5 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%

6. FIN303 Vicentiu Covrig 6 Risk: Calculating the standard deviation for each alternative Standard deviation (σ) measures total, or stand-alone, risk. Greater the σ, greater the risk. Why?

7. FIN303 Vicentiu Covrig 7 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)

8. FIN303 Vicentiu Covrig 8 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

9. FIN303 Vicentiu Covrig 9 Assume that you invested $3000 in Countrywide stock and $2,000 in Yahoo stock. The expected return of Countrywide stock is 15% and the expected return of Yahoo 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%

10. FIN303 Vicentiu Covrig 10 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.

11. FIN303 Vicentiu Covrig 11 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

12. FIN303 Vicentiu Covrig 12 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.

13. FIN303 Vicentiu Covrig 13 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

14. FIN303 Vicentiu Covrig 14 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

15. FIN303 Vicentiu Covrig 15 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%

16. FIN303 Vicentiu Covrig 16 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.

17. FIN303 Vicentiu Covrig 17 Learning objectives Know how to calculate a rate of return; historical rates of return 1926-2001 Discuss the investment risk; know that our risk measure will be the standard deviation of returns (no calculations are necessary) Know how to calculate expected return, standard deviation and coefficient of variation given probabilities of each outcome Know what is risk aversion and risk premium Know how to calculate the portfolio return Discuss the diversification effects of a portfolio; the role of correlation and its two signs and the benefits of diversification Know the two sources of risk; market and firm specific Briefly discuss what is CAPM and beta Know how to calculate required return using SML Recommended problems: ST-1, Questions 8-4,8-7,8-8, problems 8-1, 8-3,8-4