Solutions to the problems in the supplement are found at the end of the supplement

Transcription

1 FIN 301 Exam 2 Chapter 12 Supplement Solutions to the problems in the supplement are found at the end of the supplement Chapter 12 The Capital Asset Pricing Model Risk and Return Higher returns require taking more risk If you want to earn big returns, you have to take a lot of risk o Risk The uncertainty associated with the expected future returns of an asset. Risk is the part of an asset s price movement that is caused by an unexpected event Risk is measured by the range of possible returns based around an expected return for an investment Low risk stocks = Utilities High risk stocks = Technology, large banks o Standard deviation is used as a measurement of risk An assets risk is measured by the variability of returns Standard deviation measures how wildly or tightly observed stock returns cluster around the average stock return Greater standard deviation = Increased risk o Unsystematic risk or firm-specific risk (FSR) Risk related to a surprise event that affects a single company The effects of unsystematic risk can be greatly reduced or eliminated through diversification. The stock market does not reward investors for taking on unsystematic risk because it is risk that can be diversified away. o Systematic risk Risk related to a surprise event that affects the entire economy and all assets to some degree Examples of systematic risk are an increase in the interest rate, a terrorist attack, or a declaration of war. It is not possible to reduce systematic risk through diversification. The capital asset pricing model (CAPM) assumes that the expected return on an asset depends only on systematic risk because it is possible to eliminate unsystematic risk through diversification.

2 Return on an investment = (Change in price + Cash payment) / Purchase price o Change in price Capital gain or capital loss from the investment Capital gain An increase in the price of a stock, bond, or other asset Capital loss A decrease in the price of a stock, bond, or other asset Realized gains or losses Gaines or losses are realized when the asset is sold Long-term gains are taxed at a lower rate than short-term gains Unrealized gains or losses Term used for gains or losses when you still own the asset If the price of a stock you own falls and you still own the stock, the loss is considered an unrealized loss until you sell the stock Definitions Related to Returns Expected return on a risky asset E(R i ) The rate of return an investor expects to earn on an asset over time based on the asset s risk level Expected return on the market E(R m ) The average return of the stock market or the return on a stock market index o In the U.S., investors usually use the return on the S&P 500 Index or the Wilshire 5000 Index as a measure of market performance. Return on the risk-free asset R f The return that an investor receives on a safe asset that is free from credit risk o In the U.S., investors usually use the rate of return on U.S. Treasury bills as the risk-free rate because there is an underlying assumption that the U.S. government will always meets its financial obligations. Definitions Related to Risk Beta B i A measure of an asset s systematic risk o Indicates how responsive a stock s return is to changes in the expected return on the market o The overall stock market is said to have a beta of 1. o If an asset has a beta greater than 1, it is riskier than the market. o If an asset has a beta less than 1, it is less risky than the market. Market risk premium [E(R m ) R f ] The expected return of the stock market minus the risk-free rate o The market risk premium can be thought of as the additional return an investor will receive if he purchases an average-risk stock (beta = 1), as opposed to a Treasury bill. o The market risk premium is an important part of the capital asset pricing model (CAPM), which will be covered shortly. Firm-specific risk (FSR) A measure of unsystematic risk of an asset o Extra return (or loss) received by a firm due to some event affecting only that firm Standard deviation of return (σ) Measures the risk of an asset o Measures how wildly or tightly observed stock returns cluster around the average stock return o A higher standard deviation means greater risk. o A lower standard deviation means less risk.

3 Problem #1 Estimate the beta for the company below given the following information. Year 1: Stock return = 20%; market return = 10% Year 2: Stock return = 8%; market return = 4% a) 2.0 b) 0.5 c) 0.5 d) 2.0 e) 1.5 Problem #2 Estimate the beta for the company below given the following information. Year 1: Stock return = 5%; market return = 5% Year 2: Stock return = 9%; market return = 9% a) 0.5 b) 1.0 c) 2.5 d) 1.0 e) 0.5 Problem #3 Which of the following companies is most risky? a) Company ABC Standard deviation = 40% b) Company CDE Standard deviation = 32% c) Company EFG Standard deviation = 24% d) Company GHI Standard deviation = 18% e) Company IJK Standard deviation = 12% Problem #4 Given the following information, which statement is true? Stock Beta Average return A % B % a) Stock A s expected return is greater than stock B s expected return. b) Stock A outperformed stock B. c) Stock A has more risk than stock B. d) Both A and B e) Both B and C

4 Asset Classes in Order of Risk 1. U.S. Treasury bills (Least risky) 2. U.S. government bonds 3. Corporate bonds 4. Large company stocks 5. Small company stocks (most risky) Average Return Risk Premium = Security Return T-bill Return Treasury Bills 4% 4% 4% = 0% Government Bonds 5% 5% 4% = 1% Corporate Bonds 6% 6% 4% = 2% Average Common Stock 12% 12% 4% = 8% The Capital Asset Pricing Model (CAPM) The capital asset pricing model (CAPM) Theory used to price risky assets o Focuses on the tradeoff between the risk of an asset and the expected return associated with that asset E(R i ) = (R f ) + (B i )[E(R m ) (R f )] + FSR Problem #5 Calculate the expected return of a company with the following information using CAPM. Beta = 1.5 Treasury Bill rate = 2% S&P 500 averaged return rate = 6% a) 5% b) 9% c) 8% d) 3% e) 4% Problem #6 Calculate the expected return of a company with the following information using CAPM. Beta = 0.8 Treasury Bill rate = 3% S&P 500 averaged return rate = 8% a) 5% b) 9% c) 7% d) 3% e) 8%

5 CAPM and Portfolios Portfolio The specific securities (stocks, bonds, mutual funds) owned by an investor o The return on a portfolio is calculated by multiplying the return on a specific security by the percent of the portfolio the security represents and then adding the result for each security together. o If you own a portfolio where stock X makes up 60% of the portfolio and stock Y makes up the other 40% of the portfolio, you would calculate the return on the portfolio using the following equation: R portfolio = (0.60)(R X ) + (0.40)(R Y ) Investors who hold large portfolios are not concerned about unsystematic (firm-specific) risk. Investors can use diversification to virtually eliminate firm-specific risk (FSR). o A well-diversified portfolio will have an FSR component that is so small that it is considered to be insignificant. o This is why we say that asset diversification reduces risk. CAPM and well-diversified portfolios When using the CAPM equation to calculate the expected return on a well-diversified portfolio, the FSR term is dropped off because diversification has reduced the FSR to virtually zero. o The only uncertainty associated with a well-diversified portfolio is uncertainty over the performance of the market in general, which is referred to as systematic risk. E(R portfolio ) = (R f ) + (B portfolio )[E(R m ) (R f )] Well-diversified portfolios are identical to one another, except for their betas. A portfolio s beta measures the systematic risk of the portfolio. o When adding an additional stock to a well-diversified portfolio, the stock s only effect on the portfolio is its effect on the portfolio s beta. o A stock with a beta greater than the portfolio s beta will increase the portfolio s beta, and a stock with a beta lower than the portfolio s beta will reduce the portfolio s beta. o For any investment, beta is the appropriate measure of risk.

6 CAPM and Alpha Alpha = Observed return Expected return o When alpha is positive, the security outperformed the returns expected under the CAPM benchmark. o When alpha is negative, the security underperformed compared to the returns expected under the CAPM benchmark. Make sure to note we are comparing the actual return on a portfolio to the expected return on the portfolio using CAPM. It is common for people to compare the actual return on the portfolio to the actual return on the market. o The portfolio s beta is taken into account by finding the expected return on the portfolio using CAPM. o It is possible for a portfolio with a beta less than 1 to have a positive alpha even if it has a return lower than the market return because the portfolio was less risky than the market. o It is also possible for a portfolio with a beta greater than 1 to have a negative alpha even if it has a return greater than the market return because the portfolio was riskier than the market. o A portfolio s level of risk needs to be taken into account when evaluating its performance. Problem #7 Calculate the alpha of the following portfolio: Beta = 0.6 S&P 500 averaged return = 10% T-bill rate = 2.0% Portfolio actual return = 8% a) 3.0% b) 1.2% c) 2.0% d) 5.1% e) 2.0% Problem #8 Determine the actual return for LionTutors stock using the information below. Alpha = 4% Beta = 1.1 Market return = 8.2% T-Bill rate = 2.5% a) 4.8% b) 8.8% c) 10.2% d) 12.8%

7 Problem #9 Determine the expected return for LionTutors stock using the information below. Alpha = 6% Beta = 0.9 Market return = 5.5% T-Bill rate = 1.3% a) 0.9% b) 5.1% c) 5.8% d) 6.9% e) 11.1% Problem #10 Select the true statement about CAPM below. a) Alpha is used in the CAPM calculation b) CAPM gives you the value of the market risk premium c) As beta decreases, CAPM will decrease as well d) CAPM does not take the risk free rate into account e) CAPM is used to find the observed return Solutions 1. D Positive 2.0 because the return for the stock is double the market return in both years 1 and B Negative 1.0 because the return for the stock is the market return multiplied by A Company ABC because standard deviation is our measurement of risk. 4. B Stock A outperformed Stock B. Stock B is riskier than Stock A. So we will require a higher rate of return on Stock B. Since Stock A was able to give the same return as Stock B while having less risk, we say Stock A outperformed Stock B.

8 5. C 8% To solve this problem, you will need to use the CAPM equation. You can use the Treasury bill rate as the risk-free rate and the return on the S&P 500 as the expected return on the market. If you are not given any information about the firm-specific risk (FSR) for the company, you can assume that the FSR is zero. E(R i ) = (R f ) + (B i )[E(R m ) (R f )] + FSR E(R i ) = 2% + (1.5)(6% - 2%) + 0% E(R i ) = 8% 6. C 7% To solve this problem, you will need to use the CAPM equation. You can use the Treasury bill rate as the risk-free rate and the return on the S&P 500 as the expected return on the market. If you are not given any information about the firm-specific risk (FSR) for the company, you can assume that the FSR is zero. E(R i ) = (R f ) + (B i )[E(R m ) (R f )] + FSR E(R i ) = 3% + (0.8)(8% - 3%) + 0% E(R i ) = 7%

9 7. B Positive 1.2% The most common mistake that people make on these problems is to compare the S&P 500 return, which represents the return on the market, to the portfolio s actual return. You need to compare the portfolio s actual return to the expected return on the portfolio. You are given the portfolio s actual return, and you can use the CAPM equation to solve for the expected return on the portfolio. E(R portfolio ) = (R f ) + (B portfolio )[E(R m ) (R f )] E(R portfolio ) = 2% + (0.6)(10% - 2%) E(R portfolio ) = 6.8% Alpha = Observed return Expected return Alpha = 8% 6.8% Alpha = 1.2% A positive alpha of 1.2% means that this portfolio performed 1.2% better than it was expected to perform. At first, this might seem confusing because the portfolio s actual return was less than the S&P 500 s return; however, the beta on this portfolio was less than 1. Since the portfolio s beta was less than 1, the portfolio was not expected to perform as well as the market because this portfolio was less risky than the market. This is why you need to make sure to always compare the portfolio s actual return to the portfolio s expected return, not to the market s return. 8. D 12.8% Expected return = 2.5% + (1.1)(8.2% 2.5%) = 8.8% Alpha = Actual return Expected return 4% = Actual return 8.8% Actual return = 12.8%

10 9. B 5.1% For this problem all we need to do is plug into the CAPM equation to find the expected return. We don t need to use the value of alpha for anything for this problem. A problem like this appeared on a past exam. Many students solved for the actual return instead of the expected return because simply finding the expected return seemed too easy. Expected return = 1.3% + (0.9)(5.5% 1.3%) = 5.1% 10. C As beta decreases, CAPM will decrease as well. Beta is our measurement of risk. Decreasing risk will decrease an investor s expected return on an investment.