http money cnn com20170411investingunitedairlinesstockpassengerflightvideo srtw CNN 041117 unitedairlinesstockpassengerflightvideo

§ http: //money. cnn. com/2017/04/11/investing/united-airlinesstock-passenger-flight-video/? sr=tw. CNN 041117 unitedairlines-stock-passenger-flightvideo 0856 PMVODtop. Link&link. Id=36417766 Dr. Mohammad Alkhamis Kuwait University - College of Business Administration 1

Chapter 8 Risk and Rates of Return § STAND-ALONE RISK § PORTFOLIO RISK § RISK AND RETURN: CAPM/SML Dr. Mohammad Alkhamis Kuwait University - College of Business Administration © Cengage Learning 2 Modified by Dr. Bader Alhashel

What is risk? Kuwait University - College of Business Administration 3

Risk-Return Trade-off § Investors like returns and dislike risk. § There is a fundamental trade-off between risk and return: to let investors take on more risk you have to provide them with higher returns. Kuwait University - College of Business Administration 4

Dr. Mohammad Alkhamis Kuwait University - College of Business Administration 5

Investment Returns § The rate of return on an investment can be calculated as follows: § 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%. Kuwait University - College of Business Administration 6

What is investment risk? § Two types of investment risk § Stand-alone risk: the risk an investor would face if he held only one asset. § Portfolio risk: the risk an investor would face if he held the asset as one of many assets. § 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. Kuwait University - College of Business Administration 7

Probability Distributions § Probability distribution: A listing of all possible outcomes, and the probability of each occurrence. § Can be shown graphically. Firm X Firm Y -70 0 15 100 Rate of Return (%) Expected Rate of Return Kuwait University - College of Business Administration 8

Hypothetical Investment Alternatives Economy Recession Prob. T-Bills HT Coll 0. 1 5. 5% -27. 0% USR MP 6. 0% -17. 0% Below avg 0. 2 5. 5% -7. 0% 13. 0% -14. 0% -3. 0% Average 0. 4 5. 5% 15. 0% 0. 0% 3. 0% 10. 0% Above avg 0. 2 5. 5% 30. 0% -11. 0% 41. 0% 25. 0% Boom 0. 1 5. 5% 45. 0% -21. 0% 26. 0% 38. 0% Dr. Mohammad 8 -9 Alkhamis Kuwait University - College of Business Administration 9

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 5. 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. Kuwait University - College of Business Administration 10

How do the returns of High Tech and Collections behave in relation to the market? § High Tech: Moves with the economy, and has a positive correlation. This is typical. § Collections: Is countercyclical with the economy, and has a negative correlation. This is unusual. Dr. Mohammad Alkhamis 8 -11 Kuwait University - College of Business Administration 11

Calculating the Expected Return § Kuwait University - College of Business Administration 12

Summary of Expected Returns Expected Return High Tech 12. 4% Market 10. 5% US Rubber 9. 8% T-bills 5. 5% Collections 1. 0% High Tech has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk? Dr. Mohammad Alkhamis 8 -13 Kuwait University - College of Business Administration 13

Measuring Stand-Alone Risk: Standard Deviation § Kuwait University - College of Business Administration 14

Standard Deviation for Each Investment Dr. Mohammad Alkhamis 8 -15 σHT = 20% σColl = 13. 2% σM = 15. 2% σUSR = 18. 8% Kuwait University - College of Business Administration 15

Comparing Standard Deviations § The tighter the probability distribution the smaller the standard deviation and risk. Prob. T-bill USR HT 0 5. 5 9. 8 12. 4 Rate of Return (%) Kuwait University - College of Business Administration 16

Comments on Standard Deviation as a Measure of Risk § Standard deviation (σi) measures total, or stand-alone, risk. § The larger σi is, the lower the probability that actual returns will be closer to expected returns. § Larger σi is associated with a wider probability distribution of returns. Kuwait University - College of Business Administration 17

Comparing Risk and Return Kuwait University - College of Business Administration 18

§ If we had two investments with similar returns but different risk, how we choose? § Same risk but different return? § What if it was different return and different risk? Kuwait University - College of Business Administration 19

Measuring Stand-Alone Risk: Coefficient of Variation (CV) § Coefficient of Variation: A standardized measure of risk per unit of return. Kuwait University - College of Business Administration 20

Illustrating the CV as a Measure of Relative Risk § σA = σB , but A is riskier because of a larger probability of losses. In other words, the same amount of risk (as measured by σ) for smaller returns. Prob. A B 0 Rate of Return (%) Kuwait University - College of Business Administration 21

Problem 8 -1 Kuwait University - College of Business Administration 22

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 a riskless asset, which serves as compensation for investors to hold riskier securities. Kuwait University - College of Business Administration 23

Portfolio Construction: Risk and Return § Assume a two-stock portfolio is created with $50, 000 invested in both HT and Collections. § A portfolio’s expected return is a weighted average of the returns of the portfolio’s component assets. § Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised. Kuwait University - College of Business Administration 24

Calculating Portfolio Expected Return Kuwait University - College of Business Administration 25

Calculating Portfolio Standard Deviation and CV Kuwait University - College of Business Administration 27

Comments on Portfolio Risk Measures § σp = 3. 4% is much lower than the σi of either stock (σHT = 20. 0%; σColl. = 13. 2%). § σp = 3. 4% is lower than the weighted average of HT and Coll. ’s σ (16. 6%). § Therefore, the portfolio provides the average return of component stocks, but lower than the average risk. § Why? Negative correlation between stocks. Kuwait University - College of Business Administration 28

General Comments about Risk § Kuwait University - College of Business Administration 29

Returns Distribution for Two Perfectly Negatively Correlated Stocks (ρ = -1. 0) Kuwait University - College of Business Administration 30

Returns Distribution for Two Perfectly Positively Correlated Stocks (ρ = 1. 0) Stock M’ Stock M Portfolio MM’ 25 25 25 15 15 15 0 0 0 -10 -10 § If correlation is perfectly positive, the portfolio has the same risk. § Diversification is only good when assets or stocks are not perfectly positively correlated Dr. Mohammad Alkhamis Kuwait University - College of Business Administration 31

Partial Correlation, ρ = +0. 35 Kuwait University - College of Business Administration 32

Creating a Portfolio: Beginning with One Stock and Adding Randomly Selected Stocks to Portfolio § σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. § Expected return of the portfolio would remain relatively constant. § Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σp tends to converge to 20%. Kuwait University - College of Business Administration 33

Illustrating Diversification Effects of a Stock Portfolio Kuwait University - College of Business Administration 34

Breaking Down Sources of Risk Stand-alone risk = Market risk + Diversifiable risk § Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. § Diversifiable risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification. Kuwait University - College of Business Administration 35

Failure to Diversify § If an investor chooses to hold a one-stock portfolio (doesn't diversify), would the investor be compensated for the extra risk they bear? § NO! § Stand-alone risk is not important to a well-diversified investor. § Rational, risk-averse investors are concerned with σp, which is based upon market risk. § There can be only one price (the market return) for a given security. § No compensation should be earned for holding unnecessary, diversifiable risk. Kuwait University - College of Business Administration 36

Problem 8 -18 Kuwait University - College of Business Administration 37 37

Dr. Mohammad Alkhamis Kuwait University - College of Business Administration 38

Capital Asset Pricing Model (CAPM) § Model linking risk and required returns. CAPM suggests that there is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification. ri = r. RF + (r. M – r. RF)bi § Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio. Kuwait University - College of Business Administration 39

Beta § Measures a stock’s market risk, and shows a stock’s volatility relative to the market. § Indicates how risky a stock is if the stock is held in a welldiversified portfolio. Kuwait University - College of Business Administration 40

Comments on Beta § If beta = 1. 0, the security is just as risky as the average stock. § If beta > 1. 0, the security is riskier than average. § If beta < 1. 0, the security is less risky than average. § Most stocks have betas in the range of 0. 5 to 1. 5. Kuwait University - College of Business Administration 41

Can the beta of a security be negative? § Yes, if the correlation between Stock i and the market is negative (i. e. , ρi, m < 0). § If the correlation is negative, the regression line would slope downward, and the beta would be negative. § However, a negative beta is highly unlikely. Kuwait University - College of Business Administration 42

Calculating Betas § Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future. § Without a crystal ball to predict the future, analysts are forced to rely on historical data. A typical approach to estimate beta is to run a regression of the security’s past returns against the past returns of the market. § The slope of the regression line is defined as the beta coefficient for the security. Kuwait University - College of Business Administration 43

Illustrating the Calculation of Beta _ ri . 20 15 . 10 Year r. M ri 1 15% 18% 2 -5 -10 3 12 16 5 -5 . 0 5 -5 -10 10 15 20 r. M Regression line: ^ ri = -2. 59 + 1. 44 r. M ^ Kuwait University - College of Business Administration 44

Beta Coefficients for HT, Coll, and T-Bills HT: b = 1. 32 ri 40 20 T-bills: b = 0 -20 0 20 40 r. M Coll: b = -0. 87 -20 Kuwait University - College of Business Administration 45

Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a correlation coefficient with the market of -0. 3, and a beta coefficient of -0. 5. Stock B has an expected return of 12%, a standard deviation of expected returns of 10%, a correlation coefficient with the market of 0. 7, and a beta coefficient of 1. 0. Which security is riskier? Why? Kuwait University - College of Business Administration 46

Calculating Portfolio Beta Kuwait University - College of Business Administration 47

Problem 8 -2 Kuwait University - College of Business Administration 48

Problem 8 -14 Kuwait University - College of Business Administration 49

The Security Market Line (SML): Calculating Required Rates of Return SML: ri = r. RF + (r. M – r. RF)bi ri = r. RF + (RPM)bi § Assume the yield curve is flat and that r. RF = 5. 5% and RPM = 5. 0%. Kuwait University - College of Business Administration 50

What is the market risk premium? § Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. § Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion. § Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year. Kuwait University - College of Business Administration 51

Illustrating the Security Market Line SML: ri = 5. 5% + (5. 0%)bi ri (%) SML . . . HT r. M = 10. 5 r. RF = 5. 5 -1 . Coll. 0 . USR T-bills 1 2 Risk, bi Kuwait University - College of Business Administration 53

Problem 8 -9 Kuwait University - College of Business Administration 54

Problem 8 -19 Kuwait University - College of Business Administration 55

An Example: Equally-Weighted Two-Stock Portfolio § Create a portfolio with 50% invested in HT and 50% invested in Collections. § The beta of a portfolio is the weighted average of each of the stock’s betas. b. P = w. HTb. HT + w. Collb. Coll b. P = 0. 5(1. 32) + 0. 5(-0. 87) b. P = 0. 225 Kuwait University - College of Business Administration 56

Calculating Portfolio Required Returns § The required return of a portfolio is the weighted average of each of the stock’s required returns. r. P = w. HTr. HT + w. Collr. Coll r. P = 0. 5(12. 10%) + 0. 5(1. 15%) r. P = 6. 625% § Or, using the portfolio’s beta, CAPM can be used to solve for expected return. r. P = r. RF + (RPM)b. P r. P = 5. 5% + (5. 0%)(0. 225) r. P = 6. 625% Kuwait University - College of Business Administration 57

Is it possible to construct a portfolio of real-world stocks that has a required rate if return equal to the risk-free rate? Kuwait University - College of Business Administration 58

Factors That Change the SML § What if investors raise inflation expectations by 3%, what would happen to the SML? ri (%) ΔI = 3% 13. 5 10. 5 SML 2 SML 1 8. 5 5. 5 Risk, bi 0 0. 5 1. 0 1. 5 Kuwait University - College of Business Administration 59

Factors That Change the SML § What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? ri (%) ΔRPM = 3% SML 2 SML 1 13. 5 10. 5 5. 5 Risk, bi 0 0. 5 1. 0 1. 5 Kuwait University - College of Business Administration 60

Problem 8 -15 Kuwait University - College of Business Administration 61

Verifying the CAPM Empirically § The CAPM has not been verified completely. § Statistical tests have problems that make verification almost impossible. § Some argue that there additional risk factors, other than the market risk premium, that must be considered. Kuwait University - College of Business Administration 62

More Thoughts on the CAPM § Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of ri. ri = r. RF + (r. M – r. RF)bi + ? ? ? § 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. Kuwait University - College of Business Administration 63

Some Concluding Thoughts § There is a trade-off between risk and return. To achieve a higher expected return, an investors needs to take higher risk. § Diversification is crucial. § Real returns are what matters, not nominal returns. § The risk of an investment depends how long you plan to hold it. Stocks are very risky on the short-term but their risk is reduced if you hold them over the long-run. Kuwait University - College of Business Administration 64

Some Concluding Thoughts § While historical data can be helpful in telling us about the risks and returns of investments, there is no guarantee that the past will repeat itself. Kuwait University - College of Business Administration 65