FINA 5311 Chapter 12

required return

the expected return of an investment that is necessary to compensate for the risk of undertaking the investment

Which one of the following correctly describes the dividend yield?

Next year's annual dividend divided by today's stock price

Adverse selection

One party has more information than the other.

Company cost of capital

Opportunity cost of capital for investment in the firm as a whole. The company cost of capital is the appropriate discount rate for an average-risk investment project undertaken by the firm

WACC (weighted average cost of capital)

(E/V)*Re + (D/V)*Rd*(1-tc)

Economic value added (EVA)

(ROA - WACC) * Total capital

Give the definition of market index

A market index reports the value of a particular portfolio of securities.

Standard deviation measures _____ risk while beta measures _____ risk.

D. total; systematic

Which one of the following is the computation of the risk premium for an individual security? E(R) is the expected return on the security, Rf is the risk-free rate, β is the security's beta, and E(RM) is the expected rate of return on the market.

D. β[E(RM) - Rf]

Low variable costs and high gross margin

High operating leverage -> higher risk.

Expected return

R = Rf + B * (Rm-Rf)

Financial leverage

The extent to which a firm relies on debt. The firm's fixed costs of finance.

The return earned in an average year over a multiyear period is called the _____ average return.

arithmetic

Which one of the following is the best example of unsystematic risk?

B. A warehouse fire

To convince investors to accept greater volatility, you must:

increase the risk premium

What inputs do we need to estimate a firm's equity cost of capital using the CAPM?

- Construct the market portfolio, and determine its expected excess return over the risk-free interest rate - Estimate the stock's beta, or sensitivity to the market portfolio

Which one of the following statements is correct concerning market efficiency?

A firm will generally receive a fair price when it issues new shares of stock if the market is efficient.

equally weighted portfolio

A portfolio in which the same amount of money is invested in each stock.

Cyclical industry Cyclical

A type of industry that is sensitive to the business cycle. Firms do well in the expansion phase of the business cycle and do poorly in the contraction phase.

Given the following information, what is the expected return on a portfolio that is invested 30 percent in both Stocks A and C, and 40 percent in Stock B? State of Probability of Economy State of Economy Broom .05 Normal .85 Recession .10 Rate of Return if occurs Stock A Stock B Stock C 7.8% 23.6% 18.4% 9.1% 15.4% 13.7% 11.8% -12.3% 6.4%

A. 11.97 percent E(RBoom) = (0.30 × 0.078) + (0.40 × 0.236) + (0.30 × 0.184) = 0.1730 E(RNormal) = (0.30 × 0.091) + (0.40 × 0.154) + (0.30 × 0.137) = 0.1300 E(RRecession) = (0.30 × 0.118) + (0.40 × -0.123) + (0.30 × 0.064) = 0.0054 E(RPortfolio) = (0.05 × 0.1730) + (0.85 × 0.1300) + (0.10 × 0.0054) = 11.97 percent

Which one of the following describes systemic risk?

A. Risk that affects a large number of assets

How can you estimate the market risk premium?

Approach 1: E[Rmkt]-rf, historical average excess return of the market over the risk-free interest rate. Pitfall 1: standard error of the stimates are large Pitfall 2: because they are backward looking, we cannot be sure they are representative of current expectations. Approach 2: Fundamental rMkt = Div1/Po+g = Dividend Yield + Expected Dividend Growth Rate

How can we reduce estimation errors?

Averaging unlevered betas for several firms in the same industry to determine an industry asset beta.

Given the following information, what is the variance of the returns on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Broom .18 .29 Normal .77 .14 Recessiom .05 -.45

B. 0.021449 Expected return = (0.18 × 0.29) + (0.77 × 0.14) + (0.05 × -0.45) = 0.1375 Variance = 0.18(0.29 - 0.1375)2 + 0.77(0.14 - 0.1375)2 + 0.05(-0.45 - 0.1375)2 = 0.021449

What is the beta of the following portfolio? Stock Value Beta S $32,800 0.97 T 16,700 1.26 U 21,000 0.79 V 4,600 1.48

B. 1.02 Portfolio value = $32,800 + $16,700 + $21,100 + $4,600 = $75,200 βP = ($32,800/$75,200)(0.97) + ($16,700/$75,200)(1.26) + ($21,100/$75,200)(0.79) + ($4,600/$75,200)(1.48) = 1.02

The risk-free rate is 4.2 percent and the expected return on the market is 12.3 percent. Stock A has a beta of 1.2 and an expected return of 13.1 percent. Stock B has a beta of 0.75 and an expected return of 11.4 percent. Are these stocks correctly priced? Why or why not?

B. No, Stock A is overpriced and Stock B is underpriced. E(RA) = 0.042 + 1.2(0.123 - 0.042) = 13.92 percent E(RB) = 0.042 + 0.75(0.123 - 0.042) = 10.28 percent Stock A is overpriced because its expected return lies below the security market line.

Consider a portfolio comprised of four risky securities. Assume the economy has three states with varying probabilities of occurrence. Which one of the following will guarantee that the portfolio variance will equal zero?

B. The portfolio expected rate of return must be the same for each economic state.

The stock of Wiley United has a beta of 0.92. The market risk premium is 8.4 percent and the risk-free rate is 3.2 percent. What is the expected return on this stock?

C. 11.11 percent E(R) = 0.032 + 0.92(0.086) = 11.11 percent

Fiddler's Music Stores' stock has a risk premium of 9.6 percent while the inflation rate is 4.1 percent and the risk-free rate is 3.9 percent. What is the expected return on this stock?

C. 13.5 percent Expected return = 0.039 + 0.096 = 13.5 percent

Stock A has a beta of 1.47 while Stock B has a beta of 1.08 and an expected return of 13.2 percent. What is the expected return on Stock A if the risk-free rate is 4.5 percent and both stocks have equal reward-to-risk premiums?

C. 16.34 percent (RA - 0.045)/1.47 = (0.132 - 0.045)/1.08; RA = 16.34 percent

A stock has a beta of 1.47 and an expected return of 16.6 percent. The risk-free rate is 4.8 percent. What is the slope of the security market line?

C. 8.03 percent Slope = (0.166 - 0.048)/1.47 = 8.03 percent

Julie wants to create a $5,000 portfolio. She also wants to invest as much as possible in a high risk stock with the hope of earning a high rate of return. However, she wants her portfolio to have no more risk than the overall market. Which one of the following portfolios is most apt to meet all of her objectives?

C. Invest $2,500 in a risk-free asset and $2,500 in a stock with a beta of 2.0

Stock A comprises 28 percent of Susan's portfolio. Which one of the following terms applies to the 28 percent?

C. Portfolio weight

Which one of the following best exemplifies unsystematic risk?

C. Unexpected increase in the variable costs for a firm

The capital asset pricing model:

C. considers the time value of money.

The addition of a risky security to a fully diversified portfolio:

C. may or may not affect the portfolio beta.

Connection between Beta and the CAPM

CAPM calculates the expected return of an asset based on its beta and expected market returns.

Advantages and criticisms of EVA

Capital costs cannot be ignored. It is stark, the number is eigher positive or negative. EVA only focuses on current earnings, no use for capital budgeting. It may increase the shortsightedness of managers.

Factors or determinants of beta

Cyclicality of revenues Operating leverage Financial leverage

You own a $222,000,000 portfolio that is invested in Stocks A and B. The portfolio beta is equal to the market beta. Stock A has an expected return of 18.7 percent and has a beta of 1.42. Stock B has a beta of 0.88. What is the value of your investment in Stock A?

D. $49,333 βP = 1.0 = 1.42A + [0.88 × (1 - A)]; A = 0.222222 Investment in Stock A = $222,000 × 0.222222 = $49,333

Currently, you own a portfolio comprised of the following three securities. How much of the riskiest security should you sell and replace with risk-free securities if you want your portfolio beta to equal 90 percent of the market beta? Stock Value Beta A $16,400 1.06 B 20,500 1.32 C 18,200 0.98

D. $9,613.64 Portfolio value = $16,400 + $20,500 + $18,200 = $55,100 βP = (0.90)(1.00) = [$16,400/$55,100][1.06] + [($20,500 - x)/55,100)(1.32) + [$18,200/$55,100)(0.98) + ($x/$55,100)(0) x = $9,613.64

Given the following information, what is the variance of the returns on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Broom .30 .18 Normal .65 .11 Recession .05 -.06

D. 0.002759 Expected return = (0.30 × 0.18) + (0.65 × 0.11) + (0.05 × -0.06) = 0.1225 Variance = 0.30(0.18 - 0.1225)2 + 0.65(0.11 - 0.1225)2 + 0.05(-0.06 - 0.1225)2 = 0.002759

Given the following information, what is the variance of the returns on a portfolio that is invested 40 percent in both Stocks A and B, and 20 percent in Stock C? State of Probability of Economy State of Economy Normal .87 Recession .13 Rate of Return if occurs Stock A Stock B Stock C 13.4% 17.6% 9.3% 2.2.% -28.5% 11.2%

D. 0.005746 E(RNormal) = (0.40 × 0.134) + (0.40 × .0.176) + (0.20 × 0.093) = 0.1426 E(RRecession) = (0.40 × 0.022) + (0.40 × -0.285) + (0.20 × 0.112) = -0.0828 E(RPortfolio) = (0.87 × 0.1426) + (0.13 × -0.0828) = 0.113298 Variance = 0.87(0.1426 - 0.113298)2 + 0.13(-0.0828 - 0.113298)2 = 0.005746

Sugar and Spice stock is expected to produce the following returns given the various states of the economy. What is the expected return on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Recession 0.05 0.05 Normal 0.7 0.09 Boom 0.25 0.14

D. 10.05 percent Expected return = (0.05 × 0.05) + (0.70 × 0.09) + (0.25 × 0.14) = 10.05 percent

What is the expected return on a security given the following information? State.Of.Economy Prob Of S.O.E RateOfReturn Recession 0.14 0.18 Normal 0.75 0.11 Boom 0.11 -0.05

D. 10.22 percent Expected return = (0.14 × 0.18) + (0.75 × 0.11) + (0.11 × -0.05) = 10.22 percent

Stock J has a beta of 1.17 and an expected return of 14.4 percent, while Stock K has a beta of 0.68 and an expected return of 7.6 percent. You want a portfolio with the same risk as the market. What is the expected return of your portfolio?

D. 12.04 percent βP = 1.0 = 1.17x + 0.68(1 - x) x = 0.653061 E(RP) = 0.653061(0.144) + (1 - 0.653061)(0.076) = 12.04 percent

Bama Entertainment has common stock with a beta of 1.46. The market risk premium is 9.3 percent and the risk-free rate is 4.6 percent. What is the expected return on this stock?

D. 18.03 percent E(R) = 0.046 + 1.46(0.092) = 18.03 percent

A stock is expected to return 13 percent in an economic boom, 10 percent in a normal economy, and 3 percent in a recessionary economy. Which one of the following will lower the overall expected rate of return on this stock?

D. A decrease in the probability of an economic boom

Based on the capital asset pricing model, investors are compensated based on which of the following? I. Market risk premium II. Portfolio standard deviation III. Portfolio beta IV. Risk-free rate

D. I, III, and IV only

The systematic risk principle states that the expected return on a risky asset depends only on which one of the following?

D. Market risk

You are assigned the task of computing the expected return on a portfolio containing several individual stocks. Which one of the following statements is correct concerning this task?

D. The summation of the return deviation from the portfolio expected return for each economic state must equal zero.

The expected rate of return on Delaware Shores, Inc. stock is based on three possible states of the economy. These states are boom, normal, and recession which have probabilities of occurrence of 20 percent, 75 percent, and 5 percent, respectively. Which one of the following statements is correct concerning the variance of the returns on this stock?

D. The variance must be positive provided that each state of the economy produces a different expected rate of return.

Portfolio diversification eliminates which one of the following?

D. Unsystematic risk

Systematic risk is:

D. measured by beta.

A stock has an expected return of 15.0 percent, the risk-free rate is 3.2 percent, and the market risk premium is 8.1 percent. What must the beta of this stock be?

E. 1.46 E(R) = 0.15 = 0.032 + β(0.081) β = 1.46

Currently, the risk-free rate is 4.0 percent. Stock A has an expected return of 9.6 percent and a beta of 1.08. Stock B has an expected return of 13.5 percent. The stocks have equal reward-to-risk ratios. What is the beta of Stock B?

E. 1.83 (0.096 - 0.04)/1.08 = (0.135 - 0.04)/βB; βB = 1.83

You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.15. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market?

E. 1.85 1/3(0) + 1/3(1.15) + 1/3(x) = 1.0 x = 1.85

You own a portfolio of two stocks, A and B. Stock A is valued at $6,500 and has an expected return of 11.2 percent. Stock B has an expected return of 8.1 percent. What is the expected return on the portfolio if the portfolio value is $9,500?

E. 10.22 percent ValueB = $9,500 - $6,500 = $3,000 Expected return = [($6,500/$9,500) × 0.112] + [($3,000/$9,500) × 0.081] = 10.22 percent

Which one of the following represents the amount of compensation an investor should expect to receive for accepting the unsystematic risk associated with an individual security?

E. Zero

You own a portfolio consisting of the securities listed below. The expected return for each security is as shown. What is the expected return on the portfolio? Number Price Expected Stock Of Shares Per Share Return W 300 $11 8.9% X 450 19 11.6% Y 100 48 28.4% Z 575 33 12.7%

E. 14.20 percent ValueW = 300 × $11 = $3,300 ValueX = 450 × $19 = $8,550 ValueY = 100 × $48 = $4,800 ValueZ = 575 × $33 = $18,975 ValuePort = $3,300 + $8,550 + $4,800 + $18,975 = $35,625 Expected return = [($3,300/$35,625) × 0.089] + [($8,550/$35,625) × 0.116] + [($4,800/$35,625) × 0.284] + [($18,975/$35,625) × 0.127] = 14.20 percent

A stock has a beta of 1.86, the expected return on the market is 14.72, and the risk-free rate is 4.65. What must the expected return on this stock be?

E. 23.38 percent E(R) = 0.0465 + 1.86(0.1472 - 0.0465) = 23.38 percent

Given the following information, what is the standard deviation of the returns on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Broom .04 .26 Normal .74 .17 Recession .22 -.44

E. 25.52 percent Expected return = (0.04 × 0.26) + (0.74 × 0.17) + (0.22 × -0.44) = 0.0394 Variance = 0.04(0.26 - 0.0394)2 + 0.74(0.17 - 0.0394)2 + 0.22 (-0.44 - 0.0394)2 = 0.065130 Standard deviation = √0.065130 = 25.52 percent

Ben & Terry's has an expected return of 12.9 percent and a beta of 1.25. The expected return on the market is 11.7 percent. What is the risk-free rate?

E. 6.92 percent E(R) = 0.129 = Rf + 1.25(0.117 - Rf) Rf = 6.92 percent

A portfolio is comprised of 35 securities with varying betas. The lowest beta for an individual security is 0.74 and the highest of the security betas of 1.51. Given this information, you know that the portfolio beta:

E. will be greater than or equal to 0.74 but less than or equal to 1.51.

How do we identify the best-fitting line if we assume E[εi]=0?

E[Ri]=rf+βi(E[Rmkt]-rf)+αi rf+βi(E[rmkt]-rf) = expected return for i from the SML αi = distance above/below the SML

Why might projects within the same firm have different cost of capital?

Firm or industry asset betas reflect the market risk of the average project in that firm or industry. Individual project may be more or less sensitive to the overall market.

According to the CAPM, we can determine the cost of capital of an investment by comparing it to what portfolio?

Given a security's beta, we can estimate its cost of capital using the CAPM equation for the security market line: ri = rf+βi*(E[Rmkt]-rf)

Why does the equity beta of a levered firm differ from the beta of its assets?

If the comparable firm has debt, the returns of the firm's equity alone are not representative of the underlying assets; in fact, because of the firm's leverage, the equity will often be much riskier

Volatility of a Portfolio

Investors care about return but also risk. - When we combine stocks in a portfolio, some return is eliminated through diversification. Remaining risk depends upon the degree to which the stokcs share common risl. - Vo

What to do with extra cash?

Pay out immediately as dividend. Invest extra cash in a project, future cash flows as dividends.

Market portfolio

Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market

Security market line

Relationship between expected return and beta

Which one of the following best defines the variance of an investment's annual returns over a number of years?

The average squared difference between the actual returns and the arithmetic average return

Liquidity

The costs of buying and selling: Brokerage fees = pay to a broker to execute a trade. Bid-ask spread = loss you are making on a round-trip transaction. Market impact costs = the price drop associated with a large sale and the price rise associated with a large purchase.

Beta

The covariance of a security with the market, divided by the variance of the market.

market portfolio

The portfolio of all risky investments, held in proportion to their value.

Security Market Line (SML)

The pricing implication of the CAPM; it specifies a linear relation between the risk premium of a security and its beta with the market portfolio.

Give the definition of operating leverage.

The relative proportion of fixed versus variable costs. Holding fixed the cyclicality of the project's revenues, a higher proportion of fixed costs will increase the sensitivity of the project's cash flows to market risk and raise the beta. Operating leverage is one factor that can increase a project's market risk.

What is the effect from execution risk on the cost of capital?

The risk that due to missteps in the firm's execution the project may fail to generate the forecasted cash flows. Firms sometimes try to adjust for this risk by assigining a higher cost of capital (incorrect diversifiable risk, because it is firm-specific).

Beta is a measure of

The vitality, or systematic risk, of a security or a portfolio in comparison to the market as a whole.

expected return of a portfolio

The weighted average of the expected returns of the investments in a portfolio, where the weights correspond to the portfolio weights.

return of a portfolio

The weighted average of the returns on the investments in a portfolio, where the weights correspond to the portfolio weights.

How do we calculate the firm's unlevered cost of capital?

We can estimate a project's cost of capital based on the aset or unlevered cost of capital of comparable firms in the same line of business. Given a target leverage ratio based on the market value of the firm's equity and debt, the firm's unlevered cost of capital is: ru=E/(E+D)re+D/(E+D)rd

What data can we use to estimate the beta of a project?

We can estimate the beta of a project as the unlevered beta of comparable firm: βu=E/(E+D)βe+D/(E+D)βd

Give the definition of equal-owernership portfolio.

We hold an equal fraction of the total number of shares outstanding of each security in the portfolio.

Even if the CAPM is not perfect, why might we continue to use it in corporate finance?

While the CAPM is not perfect, it is straightforward to use, relatively robust, hard to manipulate, and correctly emphasizes the importance of market risk. As a result, it is the mmost popular and best available method to use for capital budgeting. CAPM gets managers to think about risk in the correct way.

value-weighted portfolio

a portfolio in which each security is held in proportion to its market capitalization

Beta- definition and formula

beta formula Beta measures a security's sensitivity to market risk. Specifically, beta is the expected change (in%) in the return of a security given a 1% change in the return of the market portfolio.

You are aware that your neighbor trades stocks based on confidential information he overhears at his workplace. This information is not available to the general public. This neighbor continually brags to you about the profits he earns on these trades. Given this, you would tend to argue that the financial markets are at best _____ form efficient.

semistrong

The U.S. Securities and Exchange Commission periodically charges individuals with insider trading and claims those individuals have made unfair profits. Given this, you would be most apt to argue that the markets are less than _____ form efficient.

strong

Inside information has the least value when financial markets are:

strong form efficient.

market risk premium (equity risk premium)

the historical average excess returns on the market portfolio

Standard deviation is a measure of which one of the following?

volatility *differ from the mean over a period of time

Which form of market efficiency would most likely offer the greatest profit potential to an outstanding professional stock analyst?

weak

How do you determine the weight of a stock in the market portfolio?

xi = Market Value of i / Total Market Value of All securities in the portfolio = MVi/∑jMVj = (Number of shares of i outstanding)*(price of i per share)/Total market value of all securities in the portfolio

Volatility of portfolio

- Negative correltation between stocks; always move oppositely - 0 No correlation between stocks - +1 correlation between stocks - 0-1 tend to correlate - 0- -1 tend to move oppostitely

Describe two methods that can be used to estimate a firm's debt cost of capital.

1. Given annual default and expected loss rates, the debt cost of capital can be estimated as: rd = Yield to Maturity - Prob(default)*Expected Loss Rate rd = (1-p)y+p(y-L)=y-pL 2. We can also estimate the expected return for debt based on its beta using the CAPM. However, beta estimates for individual debt securities are hard to obtain. In practice, estimates based on the debt's rating may be used.

Review the key distinctions between unlevered cost of capital and wacc.

1. unlevered cost of capital (pretax wacc) is the expected return investors will earn holding the firm's assets. In a world with taxes, it can be used to evaluate an all-equity financed project with the same risk as the firm. 2. The WACC is the effective after-tax cost of capital to the firm. In a world with taxes, the WACC can be used to evaluate a project with the same risk and the same financing as the firm itself.

Correlation

A measure of the degree to which returns share common risk. It is calculated as the covariance of the returns divided by the product of the standard deviations of each return.

Give the definition of price-weighted portfolio.

A price-weighted portfolio holds an equal number of shares of each stock, independent of their size.

Beasley Enterprises stock has an expected return of 11.5 percent. Given the information below, what is the expected return if the economy is in a recession? State.Of.Economy Prob Of S.O.E RateOfReturn Recession 0.18 ? Normal 0.65 .13 Boom 0.17 .24

A. -5.72 percent E(R) = 0.115 = (0.18 × x) + (0.65 × 0.13) + (0.17 × 0.24) x = -5.72 percent

Consider the following information: State of Probability of Economy State of Economy Boom .72 Bust .28 Rate of Return if occurs Stock A Stock B Stock C .06 .11 .17 .19 -.04 .23 What is the variance of a portfolio invested 30 percent each in Stocks A and B and 40 percent in Stock C?

A. 0.000065 E(RBoom) = (0.30 × 0.06) + (0.30 × 0.11) + (0.40 × 0.17) = 0.119 E(RBust) = (0.30 × 0.19) + (0.30 × -0.04) + (0.40 × 0.23) = 0.137 E(RPortfolio) = (0.72 × 0.119) + (0.28 × 0.137) = 0.12404 Variance = 0.72(0.119 - 0.12404)2 + 0.28(0.137 - 0.12404)2 = 0.000065

You currently own a portfolio valued at $56,000 that has a beta of 1.28. You have another $10,000 to invest and would like to invest it in a manner such that the portfolio beta decreases to 1.20. What does the beta of the new investment have to be?

A. 0.75 βP = 1.20 = ($56,000/$66,000)(1.28) + ($10,000/$66,000)x x = 0.75

What is the beta of the following portfolio? Stock Value Beta J $21,600 1.48 K 13,000 1.13 L 46,000 0.99 M 19,800 1.08

A. 1.13 Portfolio value = $21,600 + $13,000 + $46,000 + $19,800 = $100,400 βP = ($21,600/$100,400)(1.48) + ($13,000/$100,400)(1.13) + ($46,000/$100,400)(0.99) + ($19,800/$100,400)(1.08) = 1.13

Stock A has an expected return of 15.6 percent and a beta of 1.27. Stock B has an expected return of 11.4 percent and a beta of 0.89. Both stocks have the same reward-to-risk ratio. What is the risk-free rate?

A. 1.56 percent (0.156 - Rf)/1.27 = (0.114 - Rf)/0.95 Rf = 1.56 percent

Given the following information, what is the standard deviation of the returns on a portfolio that is invested 40 percent in Stock A, 35 percent in Stock B, and the remainder in Stock C? State of Probability of Economy State of Economy Normal .65 Recession .35 Rate of Return if occurs Stock A Stock B Stock C 14.3% 16.7% 18.2% -9.8% 5.4% -26.9%

A. 11.86 percent E(RNormal) = (0.40 × 0.143) + (0.35 × 0.167) + (0.25 × 0.182) = 0.16115 E(RRecession) = (0.40 × -0.098) + (0.35 × 0.054 + (0.25 × -0.269) = -0.08755 E(RPortfolio) = (0.65 × 0.16115) + (0.35 × -0.08755) = 0.074105 Variance = 0.65(0.16115 - 0.074105)2 + 0.35(-0.08755 - 0.074105)2 = 0.014071 Standard deviation = Ö0.014071 = 11.86 percent

Stock J has a beta of 1.47 and an expected return of 15.8 percent. Stock K has a beta of 1.05 and an expected return of 11.9 percent. What is the risk-free rate if these securities both plot on the security market line?

A. 2.15 percent (0.158 - Rf)/1.47 = (0.119 - Rf)/1.05 Rf = 2.15 percent

Stock Y has a beta of 1.28 and an expected return of 13.7 percent. Stock Z has a beta of 1.02 and an expected return of 11.4 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other?

A. 2.38 percent (0.137 - Rf)/1.28 = (0.114 - Rf)/1.02 Rf = 2.38 percent

Given the following information, what is the standard deviation of the returns on a portfolio that is invested 35 percent in both Stocks A and C, and 30 percent in Stock B? State of Probability of Economy State of Economy Broom .20 Normal .80 Rate of Return if occurs Stock A Stock B Stock C 16.4% 31.8% 11.4% 11.2% 19.6% 7.3%

A. 2.77 percent E(RBoom) = (0.35 × 0.164) + (0.30 × 0.318) + (0.35 × 0.114) = 0.1927 E(RNormal) = (0.35 × 0.112) + (0.30 × 0.196) + (0.35 × 0.073) = 0.12355 E(RPortfolio) = (0.20 × 0.1927) + (0.80 × 0.12355) = 0.13738 Variance = 0.20(0.1927 - 0.13738)2 + 0.80(0.12355 - 0.13738)2 = 0.000765 Standard deviation = √0.000765 = 2.77 percent

58. You own a $46,000 portfolio comprised of four stocks. The values of Stocks A, B, and C are $5,600, $16,700, and $11,400, respectively. What is the portfolio weight of Stock D?

A. 24.57 percent ValueD = $46,000 - $6,600 - $16,700 - $11,400 = $11,300 WeightD = $11,300/$46,000 = 24.57 percent

Noah's Landing stock is expected to produce the following returns given the various states of the economy. What is the expected return on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Recession 0.3 -0.27 Normal 0.65 0.16 Boom 0.05 0.35

A. 4.05 percent Expected return = (0.3 × -0.27) + (0.65 × 0.16) + (0.05 × 0.35) = 4.05 percent

Consider the following information on a portfolio of three stocks: State of Probability of Economy State of Economy Broom .15 Normal .80 Recession .05 Rate of Return if occurs Stock A Stock B Stock .05 .21 .18 .08 .15 .07 .12 .22 -.02 The portfolio is invested 35 percent in each Stock A and Stock B and 30 percent in Stock C. If the expected T-bill rate is 3.90 percent, what is the expected risk premium on the portfolio

A. 6.19 percent E(RBoom) = (0.35 × 0.05) + (0.35 × 0.21) + (0.30 × 0.18) = 0.1450 E(RNormal) = (0.35 × 0.08) + (0.35 × 0.15) + (0.30 × 0.07) = 0.1015 E(RBust) = (0.35 × 0.12) + (0.35 × -0.22) + (0.30 × -0.02) = -0.0410 E(RP) = (0.15 × 0.1450) + (0.80 × 0.1015) (0.05 × -0.0410) = 0.1009 E(RPP) = 0.1009 - 0.039 = 6.19 percent

A stock has a beta of 1.24, an expected return of 13.68 percent, and lies on the security market line. A risk-free asset is yielding 2.8 percent. You want to create a $6,000 portfolio consisting of Stock A and the risk-free security such that the portfolio beta is 0.65. What rate of return should you expect to earn on your portfolio?

A. 8.50 percent E(R) = 0.1368 = 0.028 + 1.24(MRP) MRP = 0.087742 E(RP) = 0.028 + 0.65(0.087742) = 8.50 percent

Mary owns a risky stock and anticipates earning 16.5 percent on her investment in that stock. Which one of the following best describes the 16.5 percent rate?

A. Expected return

The expected return on a security depends on which of the following? I. Risk-free rate of return II. Amount of the security's unique risk III Market rate of return IV. Standard deviation of returns

A. I and III only

If a security plots to the right and below the security market line, then the security has ____ systematic risk than the market and is ____.

A. more; overpriced

Expected return of a portfolio

Aka the realized return on a Portfolio, Rp. - Weighed return on the investmetns in the portfolio: Rp=w1R1 + w2R2....+wnRn

Which one of the following statements best defines the efficient market hypothesis?

All securities in an efficient market are zero net present value investments.

How do we define a stock's alpha, and what is its interpretation?

Alpha measures the historical performance of the security relative to the expected return predicted by the security market line. Thus, we can inpret alpha as a risk-adjusted measure of the stock's historical performance.

Capital Asset Pricing Model (CAPM)

An equilibrium model of the relationship between risk and return that characterizes a security's expected return based on its beta with the market portfolio.

Under what conditions can we evaluate a project using the firm's weighted average cost of capital?

An unlevered cost of capital can be used to evaluate an equity-financed project. If the project will be financed in part with debt, the firm's effective after-tax cost of debt is less than its expected return to investors. In that case, the weighted average cost of capital can be used: rwacc = E/(E+D)re+D/(E+D)rd(1-tc)

A stock has annual returns of 5 percent, 21 percent, −12 percent, 7 percent, and 6 percent for the past five years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Arithmetic average = (.05 + .21 − .12 + .07 + .06)/5 Arithmetic average = .054, or 5.4% Geometric return = [1.05 (1.21) (.88) (1.07) (1.06)]^.20 − 1 Geometric return = .0486, or 4.86%

A stock had annual returns of 5.1 percent, 12.2 percent, −3.8 percent, and 9.4 percent for the past four years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Arithmetic average = (.051 + .122 − .038 + .094)/4 Arithmetic average = .0573, or 5.73% Geometric return = [1.051 (1.122) (.962) (1.094)]^.25 − 1 Geometric return = .0555, or 5.55%

A stock had returns of 5 percent, 14 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns?

Average return = (.05 + .14 + .11 − .08 + .06)/5 Average return = .056 σ = {[1/(5 − 1)] [(.05 − .056^)2 + (.14 − .056)^2 + (.11 − .056)^2 + (−.08 − .056)^2 + (.06 − .056)^2]}.5 σ = .0844, or 8.44%

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 7 percent, 13 percent, 19 percent, −8 percent, and 15 percent. Suppose the average inflation rate over this time period was 2.6 percent and the average T-bill rate was 3.1 percent. Based on this information, what was the average nominal risk premium?

Average return = (.07 + .13 + .19 − .08 + .15)/5 Average return = .092, or 9.2% Average nominal risk premium = 9.2% − 3.1% Average nominal risk premium = 6.1%

You would like to invest $19,000 and have a portfolio expected return of 12.3 percent. You are considering two securities, A and B. Stock A has an expected return of 15.6 percent and B has an expected return of 10.3 percent. How much should you invest in Stock A if you invest the balance in Stock B?

B. $7,170 E(RP) = 0.123 = 0.156x + 0.103(1 - x) x = 0.377358 InvestmentA = 0.377358 × $19,000 = $7,170

Given the following information, what is the expected return on a portfolio that is invested 35 percent in Stock A, 45 percent in Stock B, and the balance in Stock C? State of Probability of Economy State of Economy Broom .20 Normal .75 Recession .05 Rate of Return if occurs Stock A Stock B Stock C 11.4% 31.2% 7.3% 8.7% 17.6% 8.1% -3.4% -37.6% 9.9%

B. 12.53 percent E(RBoom)= (0.35 × 0.114) + (0.45 × 0.312) + (0.20 × 0.073) = 0.1949 E(RNormal) = (0.35 × 0.087) + (0.45 × .0.176) + (0.20 × 0.081) = 0.12585 E(RRecession) = (0.35 × -0.034) + (0.45 × -0.376) + (0.20 × 0.099) = -0.1613 E(RPortfolio) = (0.20 × 0.1949) + (0.75 × 0.12585) + (0.05 × -0.1613) = 12.53 percent

You own a stock that has an expected return of 16.00 percent and a beta of 1.33. The U.S. Treasury bill is yielding 3.65 percent and the inflation rate is 2.95 percent. What is the expected rate of return on the market?

B. 12.94 percent E(R) = 0.1600 = 0.0365 + 1.33(Rm - 0.0365) Rm = 12.94 percent

You own a portfolio that is invested as follows: $11,400 of Stock A, $8,800 of Stock B, $14,900 of Stock C, and $3,200 of Stock D. What is the portfolio weight of Stock C?

B. 38.90 percent WeightC = $14,900/($11,400 + $8,800 + $14,900 + $3,200) = 38.90 percent

A stock has an expected return of 17.2 percent and a beta of 1.65. The risk-free rate is 5.1 percent. What is the slope of the security market line?

B. 7.33 percent Slope = (0.172 - 0.051)/1.65 = 7.33 percent

You have compiled the following information on your investments. What rate of return should you expect to earn on this portfolio? Number Price Expected Stock Of Shares Per Share Return A 150 $23 12.8% B 400 37 3.6% C 200 42 9.4% D 350 16 24.5%

B. 9.83 percent ValueA = 150 × $23 = $3,450 ValueB = 400 × $37 = $14,800 ValueC = 200 × $42 = $8,400 ValueD = 350 × $16 = $5,600 ValuePort = $3,450 + $14,800 + $8,400 + $5,600 = $32,250 Expected return = [($3,450/$32,250) × 0.128] + [($14,800/$32,250) × 0.036] + [($8,400/$32,250) × 0.098] + [($5,600/$32,250) × 0.245] = 9.83 percent

A risky security has less risk than the overall market. What must the beta of this security be?

B. > 0 but < 1

Which one of the following statements related to the security market line is correct?

B. A security with a beta of 1.54 will plot on the security market line if it is correctly priced.

Which one of the following measures the amount of systematic risk present in a particular risky asset relative to that in an average risky asset?

B. Beta coefficient

Which one of the following is an example of systematic risk?

B. Increase in consumption created by a reduction in personal tax rates

Which one of the following is the slope of the security market line?

B. Market risk premium

What other method is used?

Because cash holding will reduce a firm's equity beta, when unlevering betas we can use the firm's net debt, which is debt less excess cash.

Why does the yield to maturity of a firm's debt generally overestimate its debt cost of capital?

Because of default risk, the debt cost of capital, which is its expected return to investors, is less than its yield to maturity, which is its promised return.

What is a market proxy?

Because the true market portfolio is difficult if not impossible to constuct, in practice we use a proxy for the market portfolio, such as the S&P 500 or Wilshire 5000 indices.

How can you estimate a stock's beta from historical returns?

Beta corresponds to the slope of the best-fitting line in the plot of a security's excess returns versus the market's excess returns.

Give the definition of beta.

Beta measures a security's sensitivity to market risk. Specifically, beta is the expected change (in%) in the return of a security given a 1% change in the return of the market portfolio.

How a corporation can higher liquidity (decrease trading costs)

Bring in more uninformed investors. Reduction adverse selection costs -> lower bid-ask spreads. Disclose more information.

A $36,000 portfolio is invested in a risk-free security and two stocks. The beta of Stock A is 1.29 while the beta of Stock B is 0.90. One-half of the portfolio is invested in the risk-free security. How much is invested in Stock A if the beta of the portfolio is 0.58?

C. $12,000 βP = 0.58 = [A/$36,000][1.29] + [($36,000 - A - $18,000)/$36,000)][0.90] + [0][0.50] A = $12,000

You want to create a $65,000 portfolio comprised of two stocks plus a risk-free security. Stock A has an expected return of 14.2 percent and Stock B has an expected return of 17.8 percent. You want to own $20,000 of Stock B. The risk-free rate is 4.8 percent and the expected return on the market is 13.1 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest in the risk-free security?

C. $15,266

A portfolio has an expected return of 12.3 percent. This portfolio contains two stocks and one risk-free security. The expected return on Stock X is 9.7 percent and on Stock Y it is 17.7 percent. The risk-free rate is 3.8 percent. The portfolio value is $78,000 of which $18,000 is the risk-free security. How much is invested in Stock X?

C. $21,375

You currently own a portfolio valued at $80,000 that is equally as risky as the market. Given the information below, what is the beta of Stock C? Stock Value Beta A $24,600 1.14 B 17,500 1.06 C 32,000 ? Risk-free asset ? ?

C. 1.04 Value of risk-free asset = $80,000 - $24,600 - $17,500 - $32,000 = $5,900 βP = 1 = ($24,600/$80,000)(1.14) + ($17,500/$80,000)(1.06) + ($32,000/$80,000)(βC) + ($5,900/$80,000)(0) βC = 1.04

BJB, Inc. stock has an expected return of 15.15 percent. The risk-free rate is 3.8 percent and the market risk premium is 8.6 percent. What is the stock's beta?

C. 1.32 E(R) = 0.1515 = 0.038 + β(0.086) β = 1.32

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.12 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

C. 1.88 βP = 1 = (1/3)(0) + (1/3)(1.12) + (1/3)(x) x = 1.88

Southern Wear stock has an expected return of 14.6 percent. Given the information below, what is the expected return on this stock if the economy is normal? Round your answer to the nearest whole percentage. State.Of.Economy Prob Of S.O.E RateOfReturn Recession 0.15 -0.05 Normal 0.8 ? Boom 0.05 0.2

C. 18 percent E(R) = 0.146 = (0.15 × -0.05) + (0.80 × x) + (0.05 × 0.20) x = 17.94 percent

Given the following information, what is the standard deviation of the returns on this stock? State.Of.Economy Prob Of S.O.E RateOfReturn Broom .20 .21 Normal .70 .13 Recession .10 -.09

C. 7.80 percent Expected return = (0.20 × 0.21) + (0.70 × 0.13) + (0.10 × -0.09) = 0.124 Variance = 0.20(0.21 - 0.124)2 + 0.70(0.13 - 0.124)2 + 0.10(-0.09 - 0.124)2 = 0.006084 Standard deviation = √0.006084 = 7.80 percent

Which one of the following portfolios will have a beta of zero?

C. A portfolio comprised solely of U. S. Treasury bills

Which one of the following terms best refers to the practice of investing in a variety of diverse assets as a means of reducing risk?

C. Diversification

Which of the following terms can be used to describe unsystematic risk? I. Asset-specific risk II. Diversifiable risk III. Market risk IV. Unique risk

C. I, II, and IV only

The expected return on a security is currently based on a 22 percent chance of a 15 percent return given an economic boom and a 78 percent chance of a 12 percent return given a normal economy. Which of the following changes will decrease the expected return on this security? I. An increase in the probability of an economic boom II. A decrease in the rate of return given a normal economy III. An increase in the probability of a normal economy IV. An increase in the rate of return given an economic boom

C. II and III only

Which of the following yields on a stock can be negative?

Capital gains yield and total return

You own a portfolio that is invested 38 percent in Stock A, 43 percent in Stock B, and the remainder in Stock C. The expected returns on these stocks are 10.9 percent, 15.4 percent, and 9.1 percent, respectively. What is the expected return on the portfolio?

D. 12.49 percent Expected return = [0.38 × 0.109] + [0.43 × 0.154] + [(1 - 0.38 - 0.43) × 0.091] = 12.49 percent

You own a portfolio that has $1,900 invested in Stock A and $2,700 invested in Stock B. If the expected returns on these stocks are 9 percent and 15 percent, respectively, what is the expected return on the portfolio?

D. 12.52 percent E(R) = [1,900/($1,900 + $2,700)][0.09] + [$2,700/($1,900 + $2,700)][0.15] = 12.52 percent

You want to create a $48,000 portfolio that consists of three stocks and has an expected return of 14.5 percent. Currently, you own $16,700 of Stock A and $24,200 of Stock B. The expected return for Stock A is 18.7 percent, and for Stock B it is 11.2 percent. What is the expected rate of return for Stock C?

D. 15.87 percent Value Stock C = $48,000 - $16,700 - $24,200 = $7,100 E(RP) = 0.145 = [($16,700/$48,000) × 0.187] + [($24,200/$48,000) × 0.112] + [($7,100/$48,000) × E(RC)]; E(RC) = 15.87 percent

Which one of the following is the best example of systematic risk?

D. Decrease in gross domestic product

The security market line is defined as a positively sloped straight line that displays the relationship between which two of the following variables?

D. Expected return and beta

Which one of the following best describes a portfolio?

D. Group of assets held by an investor

Which one of the following statements is correct?

D. If a risky security is correctly priced, its expected risk premium will be positive.

World United stock currently plots on the security market line and has a beta of 1.04. Which one of the following will increase that stock's rate of return without affecting the risk level of the stock, all else constant?

D. Increase in the market risk-to-reward ratio

Which one of the following is the best example of an announcement that is most apt to result in an unexpected return?

D. Statement by a firm that it has just discovered a manufacturing defect and is recalling its product

A stock has a beta of 1.56 and an expected return of 17.3 percent. A risk-free asset currently earns 5.1 percent. If a portfolio of the two assets has a beta of 1.06, what are the portfolio weights?

D. Stock weight = 0.68; risk-free weight = 0.32 βP = 1.06 = x(1.56) + (1 - x)(0) x = 0.68 Stock weight is 0.68 and the risk-free weight is 0.32

The risk premium for an individual security is based on which one of the following types of risk?

D. Systematic

You own 850 shares of Western Feed Mills stock valued at $53.15 per share. What is the dividend yield if your total annual dividend income is $1,256?

Dividend yield = ($1,256/850)/$53.15 Dividend yield = .0278, or 2.78%

Based on the capital asset pricing model, which one of the following must increase the expected return on an individual security, all else constant?

E. A decrease in the risk-free rate given a security beta of 1.06

Which one of the following statements is correct?

E. An underpriced security will plot above the security market line.

Which one of the following is the minimum required rate of return on a new investment that makes that investment attractive?

E. Cost of capital

The security market line is a linear function that is graphed by plotting data points based on the relationship between which two of the following variables?

E. Expected return and beta

Diversifying a portfolio across various sectors and industries might do more than one of the following. However, this diversification must do which one of the following?

E. Reduce the portfolio's unique risks

Which one of the following is the vertical intercept of the security market line?

E. Risk-free rate

Assume you own a portfolio of diverse securities which are each correctly priced. Given this, the reward-to-risk ratio:

E. of each security must equal the slope of the security market line.

The beta of a risky portfolio cannot be less than _____ nor greater than ____.

E. the lowest individual beta in the portfolio; the highest individual beta in the portfolio

Generally speaking, which of the following best correspond to a wide frequency distribution?

High standard deviation, large risk premium

Highly cyclical securities have ... betas

High.

When should projects be undertaken?

If its expected return is greater than that of a financial asset of comparable risk.

Stock split

Increase of the number of shares outstanding. Share price should fall.

Project cost of capital

Minimum acceptable expected rate of return on a project given its risk

You find a certain stock that had returns of 8 percent, −3 percent, 12 percent, and 17 percent for four of the last five years. The average return of the stock for the past five-year period was 6 percent. What is the standard deviation of the stock's returns for the five-year period?

Return5 = .06 (5) − (.08 - .03 + .12 + .17) Return5 = −.04, or −4% σ = {[1/(5 − 1)] [(.08 − .06)^2 + (−.03 − .06)^2 + (.12 − .06)^2 + (.17 − .06)^2 + (−.04 − .06)^2]}.5 σ = .0925, or 9.25%

Assume that last year T-bills returned 2.8 percent while your investment in large-company stocks earned an average of 7.6 percent. Which one of the following terms refers to the difference between these two rates of return?

Risk premium

Market risk premium

Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.

Beta

Sensitivity of a stock's return to the return on the market portfolio.

Give the definition of debt cost of capital.

The cost of capital that a firm must pay on its debt.

Operating leverage

The degree to which a firm or project can increase operating income by increasing revenue.

Which errors in the capital budgeting process are likely to be more important than discrepancies in the cost of capital estimate?

The errors in estimating project cash flows are likely to have a far greater impact than small discrepancies in the cost of capital.

beta (B)

The expected percentage change in the excess return of a security for a 1% change in the excess return of the market (or other benchmark) portfolio.

Give the definition of unlevered cost of capital / asset cost of capital.

The expected return required by the firm's investors to hold the firm's underlying assets, is the weighted average of the firm's equity and debt costs of capital: Asset or unlevered cost of capital = (fraction of firm value financed by equity)*(equity cost of capital)+(fraction of firm value financed by debt)*(debt cost of capital)

portfolio weights

The fraction of the total invest- ment in a portfolio held in each individual investment in the portfolio.

Portfolio weights

The fraction of the total portfolio held in each investment in the portfolio. Wi=value of investment (i)/total value of portfolio - Portoflio weights for a portfolio of 200 shares of Apple at 200 per share and 1,000 shares of Coke at 60 per share. W(apple)=200X200/100,000=40%. W (coke) 1,000 X 60/100,000=60%

Give the definition of value-weighted portfolio.

The market portfolio is a value-weighted portfolio of all securities traded in the market. According to the CAPM, the market portfolio is efficient. In a value-weighted portfolio, the amount invested in each security is proportional to its market capitalization.

Market Capitalization

The total market value of a firm's equity; equals the market price per share times the number of shares.

Capital assets pricing model (CAPM)

Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

Give the definition of passive portfolio.

Thus, it is a passive portfolio, meaning no rebalancing is necessary due to daily price chanes.

One year ago, you purchased 200 shares of SL Industries stock at a price of $18.97 a share. The stock pays an annual dividend of $1.42 per share. Today, you sold all of your shares for $17.86 per share. What is your total dollar return on this investment?

Total dollar return = ($17.86 − 18.97 + 1.42) (200) Total dollar return = $62

Ex. Suppose you invest 10,000 in Boeing stock and 30,000 in Merck stock. You expect a return of 10% for Boeing and 16% for Merck. What is the expected return of your porfolio going foward.

Total of 40,000 invested. - 10,000/40,000=25% in Boeing: E[Rba]=10% - 30,000/40,000=75% in Merck: Exepected return is 16%. - Expeted return of portfolio: 0.25 X 10% + 0.75 X 16%=14.5%

What is the difference between alpha and beta?

Unlike estimating an average return, reliable beta estimates can be obtained with just a few years of data. Betas tend to remain stable over time, whereas alphas do not seem to be persistent.

The average compound return earned per year over a multiyear period is called the _____ average return.

geometric

Give the definition of index funds and exchange-traded fund (ETF).

index funds = many mutual fund companies offer funds that invest in these portfolios. ETF = a security that trades directly on an exchange, like a stock, but represents ownership in a portfolio of stocks.

How do we identify the best-fitting line through a set of points?

linear regression (Ri-rf)=αi+βi(Rmkt-rf)+εi αi = constant / intercept; βi(Rmkt-rf) = sensitivity of the stock to market risk; εi = error term (deviation from best-fitting line) = diversifical risk of the stock

Individual investors who continually monitor the financial markets seeking mispriced securities:

make the markets increasingly more efficient.

The excess return is computed as the:

return on a risky security minus the risk-free rate.

How can we calculate the WACC using industry asset betas?

rwacc = ru-D/(E+D)*tc*rd

market index

the market value of a broad-based portfolio of securities

volatility of a portfolio

the total risk, measured as standard deviation, of a portfolio