FIN 353 - CH 12 hw, iq, and concepts
True or False: the most important characteristic in deterring the expected return of a well-diversified portfolio is the standard deviations of the individual assets in the portfolio. explain.
False. Expected returns depend on systematic risk, not total risk.
You own a stock portfolio invested 25 percent in Stock Q, 18 percent in Stock R, 10 percent in Stock S, and 47 percent in Stock T. The betas for these four stocks are 1.3, .5, 1.4, and .8, respectively. What is the portfolio beta?
Beta of portfolio is weighted average of the beta of constituents within portfolio. Beta of portfolio = Weight1 * Beta1 + Weight2 * Beta2 + ........ Beta of portfolio = 25% * 1.3 + 18% * 0.5 + 10% * 1.4 + 47% * 0.8 Beta of portfolio = 0.325 + 0.09 + 0.14 + 0.376 Beta of portfolio = 0.931
hw: A stock has an expected return of 13.5 percent, the risk-free rate is 3.3 percent, and the market risk premium is 8.8 percent. What must the beta of this stock be?
CAPM = Rf + Beta*(Rm-Rf) E(r)= 13.5% Rf= 3.3% Beta = ? Rm-Rf = also known as market risk premium = 8.8% 13.5%= 3.3+beta (8.8%) 13.5% - 3.3% = beta (8.8%) 10.2% = beta (8.8%) Beta = 10.2%/8.8% =1.15909
as indicated by exmaples in this chapter, earning announcements by companies are closely followed by, and frequently result in, share price revisions. two issues should come to mind. first, earnings announcements concern past periods. if the market values stocks based on expectations of the future, why are numbers summarizing past performance relevant? second, these announcements concern accounting earnings. such earnings may have little to do with cash flow, so, again, why are they relevant?
Earnings contain information about recent sales and costs. This information is useful for projecting future growth rates and cash flows. Thus, unexpectedly low earnings lead market participants to reduce estimates of future growth rates and cash flows; price drops are the result. The reverse is often true for unexpectedly high earnings
A stock has a beta of .50, the expected return on the market is 12 percent, and the risk-free rate is 3.10 percent. What must the expected return on this stock be?
Expected Return =Risk Free Rate + Beta * Market Risk Premium = 3.10% + 0.50 * (12%-3.1%) = 3.10% + 0.50 * 8.90% = 7.55%
A stock has a beta of 1.2 and an expected return of 15.0 percent. If the risk-free rate is 5.3 percent, what is the market risk premium?
Expected Return =Risk Free Rate+ Beta* Market Risk Premium 15 = 5.3 + Market Risk Premium * 1.2 Market Premium (15-5.3)/1.2 8.083333 The Market Premium is 8.08%
suppose the government announces that, based on a just-completed survey, the growth rate in the economy is likely to be 2 percent in the coming year, compared to 5 percent for the year just completed. will security prices increase, decrease, or stay the same following the announcement? does it make any difference whether the 2 percent figure was anticipate by the market? explain.
If the market expected the growth rate in the coming year to be 2 percent, then there would be no change in security prices if this expectation had been fully anticipated and priced. However, if the market had been expecting a growth rate different than 2 percent and the expectation was incorporated into security prices, then the government's announcement would most likely cause security prices in general to change; prices would drop if the anticipated growth rate had been more than 2 percent, and prices would rise if the anticipated growth rate had been less than 2 percent.
Landon Stevens is evaluating the expected performance of two common stocks, Furhman Labs, Inc., and Garten Testing, Inc. The risk-free rate is 4.0 percent, the expected return on the market is 12.1 percent, and the betas of the two stocks are 1.2 and .9, respectively. Landon's own forecasts of the returns on the two stocks are 14.40 percent for Furhman Labs and 11.10 percent for Garten. a. Calculate the required return for each stock. b. Is each stock undervalued, fairly valued, or overvalued?
Rf = 4% Rm = 12.10% Rm - Rf = 8.10% beta furhman = 1.2 garten = 0.9 Expected Return furhman = 14.4% garten 11.10% Rf + beta(Rm-Rf) furhman = 4% + 1.2(8.10%) = 13.72% based on expected return of 14.40%, furhman is undervalued Rf + beta(Rm-Rf) garten = 4% + 0.9(8.10%) = 11.29% based on expected return of 11.10%, furhman is overvalued
concepts: book in broad terms, why is some risk diversifiable? why are some risks nondiversifiable? does it follow that an investor can control the level of unsystematic risk in a portfolio but not the level of systematic risk?
Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique portion of the total risk can be almost completely eliminated at little cost. On the other hand, there are some risks that affect all investments. This portion of the total risk of an asset cannot be costlessly eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in expected returns.
Stock Y has a beta of .91 and an expected return of 7.01 percent. Stock Z has a beta of .90 and an expected return of 7 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other?
Stock Y Beta = 0.91 Expected return = 7.01% Risk free rate = rf According to CAPM model: Expected return = rf + risk premium × beta 7.01% = rf + risk premium × 0.91 .................................. (1) Again Stock Z Beta = 0.90 Expected return = 7.00% Risk free rate = rf According to CAPM model: Expected return = rf + risk premium × beta 7.00% = rf + risk premium × 0.90 .................................. (1) Solving equation 1 and 2 7.00% × 0.91 - 7.01% × 0.90 = .91rf - 0.9rf 6.37% - 6.309% = 0.01rf Rf = 6.1% Hence, Risk free rate is 6.1%.
suppose you identify a situation in which one security is overvalued relative to another. how would you go about exploiting this opportunity? does it matter if the two securities are both overvalued relative to some third security? are your profits certain in this case?
The rule is always "buy low, sell high." In this case, we buy the undervalued asset and sell (short) the overvalued one. It does not matter whether the two securities are incorrectly valued with regard to some third security; all that matters is their relative value. In other words, the trade will be profitable if the relative misvaluation disappears; however, there is no guarantee that the relative misvaluation will disappear, so the profits are not certain.
A stock has a beta of 1.2 and an expected return of 14 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .20, what are the portfolio weights? stock: risk free asset: c. If a portfolio of the two assets has an expected return of 12.50 percent, what is its beta? d. If a portfolio of the two assets has a beta of 1.29, what are the portfolio weights? stock: risk free asset:
a. Expected return = (0.14 + 0.038)/2 = 0.089 or 8.9%. b. Beta of portfolio of two assets = 0.20 beta = 0.20 0.20 = weight of stock(1.2) Weight of stock (Xs) = 0.20 / 1.2 = 0.1666 or 16.67% Weight of risk free asset (Xrf) = (1- weight of stock) = ( 1 - 0.1666) = 0.8334 or 83.34%. c. expected return = 12.50% or 0.125 weight of stock = 0.14 weight of risk free asset (Xrf) = 0.038 0.125 = 0.14(Xs) + 0.038(1-Xs) 0.125 = 0.14Xs + 0.038+0.038Xs 0.087 = 0.102Xs Xs = 0.8529. beta of portfolio = 0.8529 (1.2) + (1-0.8528(0) = 1.02348. d. beta = 1.29 Weight of stock (Xs) = 1.29 / 1.2 = 1.075 Weight of Risk free asset (Xrf) = (1 - Xs) = ( 1 - 1.075 ) = - 0.075 Weight of stock is 107.5% Weight of risk free asset = - 7.5%.
indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price a. the government announces that inflation unexpectedly jumped by 2 percent last month b. big widget's quarterly earnings report, just issued, generally fell in line with analysts' expectations c. the government reports that economic growth last year was at 3 percent, which generally agreed with most economists' forecasts d. the directors of big widget die in a plane crash e. congress approves change to the tax code that will increase the top marginal corporate tax rate. the legislation had been debated for the previous six months
a. An unexpected, systematic event occurred; market prices in general will most likely decline. b. No unexpected event occurred; company price will most likely stay constant. c. No unexpected, systematic event occurred; market prices in general will most likely stay constant. d. An unexpected, unsystematic event occurred; company price will most likely decline. e. No unexpected, systematic event occurred unless the outcome was a surprise; market prices in general will most likely stay constant.
dudley trudy, CFA, recently met with one of his clients. trudy typically invests in a master list of 30 securities drawn from several industries. after the meeting concluded, the client made the following statement: "I trust your stock-picking ability and believe that you should invest my funds in your five best ideas. why invest in 30 campaniles when you obviously have stronger opinions on a few of them?" trudy plans to respond to his client within the context of modern portfolio theory. a. contrast the concepts of systematic and firm-specific risk and give one examples of each b. critique the client's suggestion. discuss the impact of systematic risk and firm-specific risk on portfolio risk as the number of securities in a portfolio is increased.
a. Systematic risk refers to fluctuations in asset prices caused by macroeconomic factors that are common to all risky assets; hence systematic risk is often referred to as market risk. Examples of systematic risk include the business cycle, inflation, monetary policy, and technological changes. Firm-specific risk refers to fluctuations in asset prices caused by factors that are independent of the market such as industry characteristics or firm characteristics. Examples of firm-specific risk include litigation, patents, management, and financial leverage. b. Trudy should explain to the client that picking only the top five best ideas would most likely result in the client holding a much riskier portfolio. The total risk of the portfolio, or portfolio variance, is the combination of systematic risk and firm-specific risk. i.) The systematic component depends on the sensitivity of the individual assets to market movements as measured by beta. Assuming the portfolio is well-diversified, the number of assets will not affect the systematic risk component of portfolio variance. The portfolio beta depends on the individual security betas and the portfolio weights of those securities. ii.) On the other hand, the components of the firm-specific risk (sometimes called nonsystematic risk) are not perfectly positively correlated with each other and as more assets are added to the portfolio those additional assets tend to reduce portfolio risk. Hence, increasing the number of securities in a portfolio reduces firm-specific risk. For example, a patent expiring for one company would not affect the other securities in the portfolio. An increase in oil prices might hurt an airline stock but aid an energy stock. As the number of randomly selected securities increases, the total risk (variance) of the portfolio approaches its systematic variance.
The return on a stock is said to have which two of the following basic parts? a. an expected return and an unexpected return b. a measurable return and an unmeasurable return c. a predicted return and a forecast return d. a total return and a partial return
a. an expected return and an unexpected return
in the context of capital market theory, unsystematic risk: a. is described as unique risk b. refers to nondiversifiable risk c. remains in the market portfolio d. refers to the variability in all risky assets caused by macroeconomic factors and other aggregate market-related variables?
a. is described as unique risk
classify the following events as mostly systematic or mostly unsystematic. is the distinction clear in every case? a. short-term interest rate increase unexpectedly b. the interest rate on a company pays on its short-term debt borrowing is increased by its bank c. oil prices unexpectedly decline d. an oil tanker ruptures, creating a large oil spill e. a manufacturer loses a multimillion-dollar product liability suit f. a Supreme Court decision substantially boarders producer liability for injuries suffered by product users
a. systematic b. unsystematic c. both; probably mostly systematic d. unsystematic e. unsystematic f. systematic
a financial market's security marker line (SML) describes: a. the relationship between systematic risk and expected returns b. the relationship between unsystematic risk and expected returns c. the relationship between systematic risk and unexpected return d. the relationship between unsystematic risk and unexpected return
a. the relationship between systematic risk and expected returns
a company announces that its earnings have decreased 25 percent form the previous year, but analysts' expected a small increase. what is the likely effect on the stock price? a. the stock price will increase b. the stock price will decrease 'c. the stock price will rise and then fall after an overreaction. d. the stock price will not be affected
b. the stock price will decrease
a company announces that its earnings have increased 25 percent over the previous year, but analysts actually expected a 50 percent increase. what is the likely effect on the stock price? a. the stock price will increase b. the stock price will decrease 'c. the stock price will rise and then fall after an overreaction. d. the stock price will not be affected
b. the stock price will decrease
the systematic risk of a security is also called its: a. perceived risk b. unique or asset-specific risk c. market risk d. fundamental risk
c. market risk
the systematic risk principle states that: a. systematic risk doesn't matter to investors b. systematic risk can be essentially eliminated by diversification c. the reward for bearing risk is independent of the systematic risk of an investment d. the reward for bearing risk depends only on the systematic risk of an investment
d. the reward for bearing risk depends only on the systematic risk of an investment
a company announces that its earnings have increased 50 percent over the previous year, which matches analysts' expectations. what is the likely effect on the stock price? a. the stock price will increase b. the stock price will decrease 'c. the stock price will rise and then fall after an overreaction. d. the stock price will not be affected
d. the stock price will not be affected
You are given the following information concerning a stock and the market: ------Returns year; market; stock 2014; 19%; 31% 2015; 10; 16 2016; 19; 3 2017; -15; -28 2018; 37; 16 2019; 15; 15 a. Calculate the average return and standard deviation for the market and the stock b. Calculate the correlation between the stock and the market, as well as the stock's beta.
excel
Suppose you observe the following situation: security; beta; expected return peat co.: 1.40; 12.2 re-peat co.: 0.70; 10.1 Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk-free rate?
(.122 − Rf) / 1.40 = (.101 − Rf) / .70 .70(.122 − Rf) = 1.40(.101 − Rf) Rf = .0800, or 8.00% .122 = .0800 + 1.40(RM − .0800) RM = .1100, or 11.00% .101 = .0800 + .70(RM − .0800) RM = .1100, or 11.00%
A stock has an expected return of 11.2 percent, its beta is .90, and the risk-free rate is 3.6 percent. What must the expected return on the market be?
According to capm, 0.112 = 0.036+0.9(Rm-0.036) Rm = 0.1204 = 12.04%
You have $112,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 12 percent and that has only 76 percent of the risk of the overall market. If X has an expected return of 31 percent and a beta of 2.1, Y has an expected return of 18 percent and a beta of 1.3, and the risk-free rate is 6 percent, how much money will you invest in Stock Y?
As total amount for investment is 112000 Let amount invested in Stock X be x, Stock Y be y and risk free asset be 112000-x-y Beta of risk free asset=0 Beta of market=1 Expected return=w1*r1+W2*r2+w3*r3 =>x/112000*31%+y/112000*18%+(112000-x-y)/112000*6%=12% Beta=w1*b1+w2*b2+w3*b3 =>x/112000*2.1+y/112000*1.3+(112000-x-y)/112000*0=76%*1 Amount invested in Stock Y y=98192
Asset W has an expected return of 18.8 percent and a beta of 2.00. If the risk-free rate is 5.1 percent, what is the market risk premium?
Expected return = Risk free rate + beta * (market risk premium) 18.8 = 5.1 + 2 * (market risk premium) market risk premium = 6.85%
explain what it means for all assets to have the same reward-to-risk ratio. how can you increase your return if this holds true? why would we expect that all assets have the same reward-to-risk ratio in liquid, well-functioning markets?
If every asset has the same reward-to-risk ratio, the implication is that every asset provides the same risk premium for each unit of risk. In other words, the only way to increase your return (reward) is to accept more risk. Investors will only take more risk if the reward is higher, and a constant reward-to-risk ratio ensures this will happen. We would expect every asset in a liquid, well-functioning market to have the same reward-to-risk ratio due to competition and investor risk aversion. If an asset has a reward-to-risk ratio that is lower than all other assets, investors will avoid that asset, thereby driving the price down, increasing the expected return and the reward-to-risk ratio. Similarly, if an asset has a reward-to-risk ratio that is higher than other assets, investors will flock to the asset, increasing the price, and decreasing the expected return and the reward-to-risk ratio.
You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.31 and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio?
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market, it must have the same beta as the market. Since the beta of the market is one, we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk. Setting up the equation for the beta of our portfolio, we get: βp = 1.0 = 1/3(0) + 1/3(1.31) + 1/3(βX) Solving for the beta of Stock X, we get: βX = 1.69
You own 400 shares of Stock A at a price of $75 per share, 490 shares of Stock B at $90 per share, and 750 shares of Stock C at $32 per share. The betas for the stocks are 1.2, 1.7, and .6, respectively. What is the beta of your portfolio?
The beta of the portfolio is computed as shown below: Value of stock A is computed as follows: = 400 x $ 75 = $ 30,000 Value of stock B is computed as follows: = 490 x $ 90 = $ 44,100 Value of stock C is computed as follows: = 750 x $ 32 = $ 24,000 So the total value of stock A, B and C will be: = $ 30,000 + $ 44,100 + $ 24,000 = $ 98,100 So the beta of the portfolio will be: Beta of A x Value of stock A / Total value of Stock A, B and C + Beta of B x Value of stock B / Total value of Stock A, B and C + Beta of C x Value of stock C / Total value of Stock A, B and C = 1.2 x $ 30,000 / $ 98,100 + 1.7 x $ 44,100 / $ 98,100 + 0.6 x $ 24,000 / $ 98,100 = 1.28 Approximately
A stock has an expected return of 15.1 percent and a beta of 1.60, and the expected return on the market is 11.40 percent. What must the risk-free rate be?
To calculate risk free rate we should use CAPM method, which is as follows Expected rate of retun of stock = Risk free rate + (Market rate of retun - risk free rate)Beta Suppose risk free rate = X 15.1 = X + (11.40 - X) 1.60 15.1 = X + 18.24 - 1.60X 15.1 - 18.24 = 0.60X 3.14 = 0.60X 3.14/0.60 = X 5.23% = X = Risk free rate
is it possible that a risky asset could have a beta of zero? explain. Based on the CAPM, what is the expected return on such an asset? is it possibly that a risky asset could have a negative beta? what does the CAPM predict about the expected return on such an asset? can you give an explanation for your answer?
Yes. It is possible, in theory, for a risky asset to have a beta of zero. Such an asset's return is uncorrelated with the overall market. Based on the CAPM, this asset's expected return would be equal to the risk‑free rate. It is also possible to have a negative beta; the return would be less than the risk‑free rate. A negative beta asset would carry a negative risk premium because of its value as a diversification instrument. A negative beta asset can be created by shorting an asset with a positive beta. A portfolio with a zero beta can always be created by combining long and short positions.
Consider the following information on Stocks I and II: The market risk premium is 13 percent and the risk-free rate is 5 percent. a-1. What is the beta of each stock? a-2. Which stock has the most systematic risk? b-1. What is the standard deviation of each stock? b-2. Which one has the most unsystematic risk? c. Which stock is "riskier"?
a. stock 1 beta = (expected return - risk free rate) / market risk premium = (17.15% - 5%) / 13% = 0.9346 stock 2 beta = (expected return - risk free rate) / market risk premium = (13.25% - 5%) / 13% = 0.6346 expected returns = sum of stock * prob for each state of economy a-2. stock 1 b-1. stock 1: 2nd data x01 = 0.05 y01 =25 x02 = 0.24 y02 = 40 x03 = 0.18 y03 = 35 2nd stat 1-v; down to standard deviation x (not Sx) = 0.0747 (STANDARD DEVIATION) stock 1: 2nd data x01 = -0.17 y01 =25 x02 = 0.14 y02 = 40 x03 = 0.34 y03 = 35 2nd stat 1-v; down to standard deviation x (not Sx) = 0.19486 (STANDARD DEVIATION) b-2. stock 2 c. stock 1
a news announcement about a stock is said to have which two of the following parts? a. an expected part and a surprise b. public information and private information c. financial information and product information d. a good part and a bad part
a. an expected part and a surprise
an investor completed a factor analysis to evaluate the impact of earnings growth and cash flow yield on stock price performance. The factor analysis model provides estimates of the impacts of theses factors. We refer tot else estimated impacts as: a. relational boundaries b. factor loadings c. factor efficiencies d. contradictory anomalies
b. factor loadings
which of the following statements about the security market line (SML) is false? a. properly values assets plot exactly on the SML b. the SML leads all investors to invest in the same portfolio of risky assets c. the SML provides a benchmark for evaluating expected investment performance d. the SML is a graphic representation of the relationship between expected return and beta
b. the SML leads all investors to invest in the same portfolio of risky assets
which of the following is not an implication of risk aversion for the investment process? a. the security market line is upward sloping b. the promised yield on AAA-rated bonds is higher than on A- rated bonds c. investors expect a positive relationship between expected return and risk d. investors prefer portfolios that lie on the efficient frontier to others portfolios with equal rates of return
b. the promised yield on AAA-rated bonds is higher than on A- rated bonds
the systematic risk principle has na important implication, which is: a. systematic risk is preferred to unsystematic risk b. systematic risk is the only risk that can be reduced by diversification c. the expected return on an asset is independent of its systematic risk d. the expect return on an asset depends only on its systematic risk
d. the expect return on an asset depends only on its systematic risk
iq: according to the CAPM what is the rate of return of a portfolio with a beta of 1? a. between Rm and Rf b. the risk free rate Rf c. Beta * (Rm - Rf) d. the return on the market Rm
d. the return on the market Rm
which type of risk is essentially eliminated by diversification? a. perceived risk b. market risk c. systematic risk d. unsystematic risk
d. unsystematic risk
A share of stock sells for $39 today. The beta of the stock is 1.1 and the expected return on the market is 20 percent. The stock is expected to pay a dividend of $1.20 in one year. If the risk-free rate is 3.8 percent, what should the share price be in one year?
elow are the given data Share price today39Beta1.1Market Return (Rm)20%Risk free rate (Rf)3.80% As we know the return of a stock is equal to Re = Rf + β * (Rm - Rf)) Hence for this stock the return should be 3.8+1.1*(20-3.8) = 21.62% But Return = (change in stock price + dividend) / previous stock price So 21.62 = (Change in stock price+1.20)/39 So change in stock price = 7.23 So after one year the stock price will be 39+7.23 = 46.23
Stock Y has a beta of .95 and an expected return of 15.80 percent. Stock Z has a beta of .90 and an expected return of 7 percent. If the risk-free rate is 6.0 percent and the market risk premium is 9.8 percent, what are the reward-to-risk ratios of Y and Z?
reward to risk ratio = (average return - risk free rate) / beta Y = (.1580 - .06) / 0.95 = 10.32% Z = (0.07 - 0.06) / 0.90 = 1.11%
