Question

Question 1: Cooley Company's stock has a beta (b) of 1.28, the risk-free rate (rRF) is 1.25%, and the market risk premium (RPM) is 5.50%.

a. What does the beta measure? Give a short answer in 1 sentence.

b. What is market risk premium? Give a short answer in 1 sentence.

c. Calculate the firm's required rate of return? Show the step-by-step calculation and circle your answer.

(Hint: Required return = rRF + b(RPM))

Question 2: Consider the following information for Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Show the step-by-step calculation and circle your answer.

Assume that Amazon company has one-third of its funds invested in each of the three stocks. The risk-free rate (rRF) is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)

a. What is the market risk premium (RPM =rM-rRF)?

(Hint: Chose any stock, substitute the given values into the equation Required return = rRF + b(RPM)), and find RPM. Note that “Required return” is shown as “Expected return” in the table above.)

b. What is the beta of Amazon? (Hint: find portfolio beta.)

c. What is the required return of Amazon? (Hint: use the results from a and b questions and plug in to the equation of finding a Required return of the portfolio.)

d. Would you expect the standard deviation of Amazon to be less than 15%, equal to 15%, or greater than 15%? Explain. Give a short answer in 1-2 sentences.

Question 3: Use the following historical returns of stocks A and B and answer the questions. Show the step-by-step calculation and circle your answer. Then use your results from questions a, b, c, d and fill out the table for Mean, Standard Deviation (STDEV), Coefficient of variation (CV), and Portfolio.

Year

Stock A’s Returns (%), rA

Stock B’s Returns (%), rB

Portfolio (%)

2013

-18

-14.5

2014

33

21.8

2015

15

30.5

2016

-0.5

-7.6

2017

27

26.3

Mean

STDEV

CV

a. Calculate the average rate of return for each stock during the period 2013 through 2017.

b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? What would the average return on the portfolio have been during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio.

d. Calculate the coefficient of variation for each stock and for the portfolio.

e. Calculate the correlation between the returns on A and B. Are they positively or negatively correlated? Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why? Give a short answer in 1-2 sentences.

Answer 1

Answer to Q#1 (First question in the list): a) A firm's beta refers to level of risk associated with firm's capital. Higher the beta value, higher the risk associated with; Lower the beta value, lower the risk associated with; beta of value 1 indicates that the firm's stock's risk level is neutral. As Cooley Company's stock has a beta of 1.28, it has more risk associated with in the capital market. b) The term market risk premium refers to expected market return over and above risk-free rate. Here, risk-free rate refers to short-term U.S. T-Bill's coupon rate, which doesn't have any risk associated with. As Cooley Company's stock has market risk premium of 5.5%, expected market return rate is 6.75% (5.5% + 1.25%). c) Using Capital Asset Pricing Model (CAPM), Required rate of return = Risk-free Rate + (Beta x Market Risk Premium) Required rate of return = 1.25% + (1.28 x 5.5%) Required rate of return = 1.25% +7.04% Required rate of return = 8.29%