5.3 Portfolio Management Flashcards
A mature firm is operating in a very stable market. Earnings growth has averaged about 3.2% for the last dozen years, just staying in line with inflation. The firm’s weighted-average cost of capital is 8%, much lower than most firms. The new CEO wants to turn what he calls a “cash cow” into a “growth company.” The CEO wants to reduce the dividend pay-out and use the resulting retained earnings to fund the firm’s expansion into new product lines. The firm’s historical beta has been about 0.6. With the CEO’s changes, what will most likely happen to the firm’s beta and the required return on investment in its shares?
A. The beta will rise, and the required return will fall.
B. The beta will fall, and the required return will fall.
C. The beta will rise, and the required return will rise.
D. The beta will fall, and the required return will rise.
C. The beta will rise, and the required return will rise.
The required rate of return is equal to the risk-free return plus the beta times the market return less the risk-free return. If the firm starts expanding into new product lines, the historical beta will increase, as the company will be taking on more risk with these new changes and investments. This will also increase the required rate of return, as per the formula.
A measure that describes the risk of an investment project relative to other investments in general is the
A. Expected return.
B. Standard deviation.
C. Beta coefficient.
D. Coefficient of variation.
C. Beta coefficient.
The required rate of return on equity capital in the capital asset pricing model is the risk-free rate (determined by government securities), plus the product of the market risk premium times the beta coefficient (beta measures the firm’s risk). The market risk premium is the amount above the risk-free rate that will induce investment in the market. The beta coefficient of an individual stock is the correlation between the volatility (price variation) of the stock market and that of the price of the individual stock. For example, if an individual stock goes up 15% and the market only 10%, beta is 1.5.
The stock of Company Z has a beta coefficient of 2.0 and an expected return of 16% using the capital asset pricing model (CAPM). The stock of Company X has a beta coefficient that is equal to 0.80. The risk-free rate of interest is 4%. The expected return on Company X stock using the CAPM is
A. 9.6%
B. 8.0%
C. 6.4%
D. 8.8%
D. 8.8%
Under the capital asset pricing model (CAPM), the required rate of return is the risk-free rate (RF) + beta (β) multiplied by the difference between the market rate (RM) and the risk-free rate (RF), or RF + β(RM – RF). The first step is to determine the market rate using the information given for Company Z. The required rate is 16%. Therefore, the calculation is .04 + 2.0(RM – .04) = .16; or 2.0(RM – .04) = .12; or 2RM – .08 = .12; or 2RM = .20; which means RM must be equal to .10, or 10%. The second step is to solve for Company X. The calculation is .04 + .8(.10 – .04) = .088, or 8.8%.
Formula to calculate the required rate of return using CAPM
The required rate of return is the risk-free rate (RF) + beta (β) multiplied by the difference between the market rate (RM) and the risk-free rate (RF), or RF + β(RM – RF).
How is the expected rate of return calculated?
Σ (Possible rate of return × Probability)
Using the capital asset pricing model, an analyst has calculated an expected risk-adjusted return of 17% for the common stock of a company. The company’s stock has a beta of 2, and the overall expected market return for equities is 10%. The risk-free return is 3%. All else being equal, the expected risk-adjusted return for the company’s stock would increase if the
A. Beta of the company’s stock decreases.
B. Overall expected market return for equities decreases.
C. Volatility of the company’s stock decreases.
D. Risk-free return decreases.
D. Risk-free return decreases.
Required rate of return = Risk-free rate + [Beta x (Market Rate - Risk Free Return)]. If the company wants its required rate of return to increase, risk-free return should decrease.
A company’s stock has a beta of 0.50. If the current risk-free rate of return is 2%, and the market risk premium is 6%, what is the required return on the company’s stock according to the capital asset pricing model?
A. 5%
B. 8%
C. 6%
D. 3%
A. 5%
The capital asset pricing model (CAPM) is based on the idea that the investor must be compensated for his or her investment in two ways: time value of money and risk.
The CAPM quantifies the required return on equity security by relating the security’s level of risk to the average return available in the market. The required rate of return equals the risk-free rate plus the market risk premium (the difference between the market return over the return on a risk-free investment, times beta). Beta is a measure of systematic risk or the volatility of the individual security in comparison to the market as a whole. Thus, the formula to find the required return on the company’s stock is 2% + 0.5(6%) = 5%.
An investor is evaluating the common stock of a technology company which has a beta of 1.8. The expected return for the securities market as a whole is 8%. The investor could receive a risk-free return of 2% on a U.S. Treasury bill. Based on the capital asset pricing model (CAPM), what is the expected risk adjusted return of the technology company’s common stock?
A. 12.8%
B. 20.0%
C. 10.8%
D. 16.4%
A. 12.8%
The CAPM formula quantifies the required return on an equity security by relating the security’s level of risk to the average return available in the market. The beta value is a measure of the systematic risk or volatility of the individual security in comparison to the market. The formula is
Required rate of return = Risk-free return + beta x (Market return - risk free return)
= 2% + 1.8 x (8% - 2%)
= 12.8%
The state of the economy has a strong effect on expected returns as shown below:
State of the economy, Probability, Stock Returns
Recession, 0.35, (10)%
Stable, 0.40, 10%
Expansion, 0.25, 30%
What is the expected rate of return?
A. 15%
B. 30%
C. 10%
D. 8%
D. 8%
The expected rate of return on an investment is the sum of the weighted averages of the possible outcomes weighted by their probabilities. The computation is performed as follows:
Recession, 0.35 x (10)% = (3.5)%
Stable, 0.40 x 10% = 4.0%
Expansion, 0.25 x 30% = 7.5%
= Expected rate of return = 8.0%
Based on the assumptions of the Capital Asset Pricing Model, the risk premium on an investment with a beta of 0.5 is equal to
A. The risk premium on the market.
B. Half the risk premium on the market.
C. Twice the risk premium on the market.
D. The risk-free rate.
B. Half the risk premium on the market.
Required rate of return = Risk-free rate + Risk Premium = Risk-free rate + (Beta x Market risk premium).
Risk Premium = Beta x Market Risk premium.
Thus, if beta is 0.5, the risk premium on the investment is half the market risk premium.
For a firm engaged in risk management, value-at-risk is defined as the
A. Worst possible outcome given the distribution of outcomes.
B. Maximum loss within a certain time period at a given level of confidence.
C. Maximum value a company can lose.
D. Most likely negative outcome at a given level of confidence.
B. Maximum loss within a certain time period at a given level of confidence.
Value-at-risk (VaR) is defined as the maiximum loss within a certain time period at a given level of confidence. VaR is a technique that employs the statistical phenomenon known as the normal distribution (bell curve). The potential gain or loss resulting from a given occurrence can be determined with statistical precision.
Stock J has a beta of 1.2 and an expected return of 15.6%, and stock K has a beta of 0.8 and an expected return of 12.4%. What is the expected return on the market and the risk-free rate of return, consistent with the capital asset pricing model?
A. Market is 14%; risk free is 4%.
B. Market is 14%; risk free is 6%.
C. Market is 12.4%; risk free is 0%.
D. Market is 14%; risk free is 1.6%.
B. Market is 14%; risk free is 6%.
This problem requires the use of simultaneous equations. Set up a CAPM formula for each stock:
Stock J: 15.6 = Rf + 1.2(Rm-Rf)
Stock K: 12.4 = Rf + 0.8(Rm-Rf)
Removing the parentheses and combining terms, you get
Stock J: 15.6 =1.2Rm - 0.2Rf
Stock K: 12.4 = 0.8Rm + 0.2Rf
Since one equation has a positive 0.2Rf term and the other has a negative 0.2Rf term, we can add the equations together to eliminate the 0.2Rf term.
(15.6 + 12.4) = (1.2Rm + 0.8Rm) + (-0.2Rf + 0.2Rf)
28 = 2Rm
14 = Rm
Substitute 14 for M in the second equation:
12.4 = Rf + 0.8(14 - Rf)
12.4 = 0.2Rf + 11.2
1.2 = 0.2Rf or Rf = 6
The difference between the required rate of return on a given risky investment and that on a riskless investment with the same expected utility is the
A. Beta coefficient.
B. Coefficient of variation.
C. Standard deviation.
D. Risk premium.
D. Risk premium.
The required rate of return on equity capital asset pricing model is the risk-free rate (determined by government securities) plus the product of the market risk premium times the beta coefficient (beta measures the firm’s risk). The market risk premium is the amount above the risk-free rate that will induce investment in the market. The beta coefficient of an individual stock is the correlation between the volatility (price variation) of the stock market and that of the price of the individual stock.
DQZ Telecom is considering a project for the coming year that will cost $50 million. DQZ plans to use the following combination of debt and equity to finance the investment.
* Issue $15 million of 20-year bonds at a price of $101, with a coupon rate of 8%, and flotation costs of 2% of par.
* Use $35 million of funds generated from earnings.
* The equity market is expected to earn 12%. U.S Treasury bonds are currently yielding 5%. The beta coefficient for DQZ is estimated as .60. DQZ is subject to an effective corporate income tax rate of 40%.
The capital asset pricing model (CAPM) computes the expected return on a security by adding the risk-free rate of return to the incremental yield of the expected market return, which is adjusted by the company’s beta. Compute DQZ’s expected rate of return.
A. 9.20%
B. 12.20%
C. 7.20%
D. 12.00%
A. 9.20%
The market return, given as 12%, minus the risk-free rate, given as 5%, is the market risk premium. It is the rate at which investors must be compensated to induce them to invest in the market. The beta coefficient of an individual stock, given as 60%, is the correlation between volatility (price variation) of the stock market and the volatility of the price of the individual stock. Consequently, the expected rate of return is 9.20%
Rf + beta(Rm-Rf) = 0.05 + 0.6(.12-.05)
The betas and expected returns for three investments being considered are given below.
Investment A
Beta: 1.4, Expected Return 12%
Investment B
Beta: 0.8, Expected Return: 11%
Investment C
Beta: 1.5, Expected Return: 13%
The return on the market is 11% and the risk-free rate is 6%. If the capital asset pricing model (CAPM) is used for calculating the required rate of return, which investments should management make?
A. B and C only.
B. A and C only.
C. A, B, and C.
D. B only.
D. B only.
The risk premium is 5% (11% - 6%)
The CAPM can be applied to each of the three investments as follows:
Investment A: 6% + (1.4 x 5%) = 13.00 %
Investment B: 6% + (0.8 x 5%) = 10.00 %
Investment C: 6% + (1.5 x 5%) = 13.5 %
These required rates of return can be compared to the expected rates to evaluate which investments should be accepted and which should be rejected.
Investment A: Reject
required rate: 13%
Expected rate: 12%
Investment B: Accept
required rate: 10%
Expected rate: 11%
Investment C: Reject
required rate: 13.5%
Expected rate: 13%
Based on the following information about stock price increases and decreases, make an estimate of the stock’s beta: July = Stock +1.5%, Market +1.1%; August = Stock +2.0%, Market +1.4%; September = Stock –2.5%, Market –2.0%.
A. Beta equals 1.0.
B. Beta is greater than 1.0
C. There is no consistent pattern of returns.
D. Beta is less than 1.0.
B. Beta is greater than 1.0.
Beta measures the volatility of the return of a security relative to the returns on the market portfolio. In each case, the stock price increase or decreases was a greater percentage than the market change. Thus, the beta (stock change over market change) is greater than 1.0.
An analyst of common stock estimates the following information for next year:
Expected return on the market portfolio 12%
Expected return on Treasury securities 5%
Expected beta of stock 2.2
Using the CAPM, the analyst’s estimate of next year’s risk premium for the stock is closest to
A. 7.0%
B. 15.4%
C. 10.4%
D. 21.4%
B. 15.4%
The capital asset pricing model derives the risk premium of a particular stock (that is, the excess of the rate of return on the stock over the risk-free rate) by multiplying the stock’s beta by the excess of the market rate of return over the risk free rate. Mathematically, this is expressed as
(Rstock - Rrisk-free) = Beta x (Rmakret x Rrisk-free)
This calculation looks like this?:
(Rstock - 5%) = 2.2 x (12% - 5%)
(Rstock - 5%) = 2.2 x 7%
(Rstock - 5%) = 15.4%
Rstock = 20.4%
Therefore, the risk premium is 15.4 (20.4% - 5%).
If the return on the market portfolio is 10% and the risk-free rate is 5%, what is the effect on a company’s required rate of return on its stock of an increase in the beta coefficient from 1.2 to 1.5?
A. 1.5% increase.
B. 1.5% decrease.
C. No change.
D. 3% increase.
A. 1.5% increase.
The required rate of return on equity capital can be estimated with the capital asset pricing model (CAPM). CAPM consists of adding the risk-free rate (i.e., the return on government securities, denoted RF) to the product of the beta coefficient (a measure of the issuer’s risk) and the difference between the market return and the risk-free rate (denoted RM – RF, referred to as the risk premium). Below is the basic equilibrium equation for the CAPM:
Required rate of return = RF + β(RM – RF)
In this situation, the risk premium is 5% (10% – 5%). Thus, the required rate of return when the beta coefficient is 1.2 is 11% [5% + (1.2 × 5%)], and when the beta coefficient is 1.5, the required rate is 12.5% [5% + (1.5 × 5%)]. This is an increase of 1.5% (12.5% – 11%).
