BUS 330 Corporate Finance
Spring 2015
HW 2
Due Thursday, March 19, 2015 in-class
1. Suppose asset M (the market portfolio) pays a -5% (minus five percent) return 50% of the time,
and a +15% return 50% of the time.
When asset M pays the -5% return; then there is then a 50% chance that asset X pays an return
of -12%, and a 50% chance that asset X pays a return of 0%. When asset M pays the +15%
return, then there is a 50% asset X will pay a return of 0%, and a 50% chance that asset X will
pay a return of 40%.
a. What is the value of “beta” for asset X?
b. If the Capital Asset Pricing Model (CAPM) correctly describes the relationship of risk and
return for assets M and X, then what is the risk-free interest rate RF?
c. If (instead of your answer to part b), the risk-free interest rate is 1%, describe the outline of
your strategy to make yourself filthy rich by exploiting the arbitrage opportunity.
2. Suppose asset M (the market portfolio) pays a -5% (minus five percent) return 50% of the time,
and a +15% return 50% of the time. You are considering purchasing asset Z at price Pz. If you sell
the asset in one year, your return will be RETz = (future selling price)/Pz – 1. Your analysis of the
likely outcome from owning Z in comparison with the market return is as described below:
If the market return is -5%, then there is a 50% chance that the price of Z in one year will be $20, and a
50% chance that the price of Z in one year will be $40.
If the market return is 15%, then there is a 50% chance that the price of Z in one year will be $60, and a
50% chance that the price of Z in one year will be $80.
a. If the risk-free interest rate RF is 2% (0.02), then what value Pz would satisfy the CAPM?
b. If Pz happens to be exactly the value you calculate in part a, then what is the value of beta for
asset Z?
c. If (instead of your answer to part a, you observe a price Pz = $45, describe the outline of your
strategy to make yourself filthy rich by exploiting the arbitrage opportunity.
HINT: On this problem, you might find it advantageous to use the following (equivalent) statement
of the CAPM:
1+RETz = 1+RF + BETAz∙(RM – RF)
3. On the spreadsheet also loaded onto elearn titled “mcd spy data”, you will find in column B the
monthly returns from owning McDonald’s Corporation stock (MCD), and in column C you will
find the monthly return from owning an exchange-traded fund (ETF) that includes all the shares
in the S&P 500 index. (data from Yahoo.com) This fund trades under the symbol SPY, and can be
considered a good approximation for “the market”. The data goes back a little over 20 years.
Using this data, what value of beta would you estimate for McDonald’s stock?
HINT: On this problem, you might find it advantageous to use the excel function:
=LINEST(known_y’s, known_x’s, constant, stats). The “=LINEST” function returns the regression
coefficient beta from an ordinary least squares regression of the Y variable on the X variable.
DOUBLE HINT: You will NOT get exactly the same value of beta that is reported on the Yahoo page
(or any other financial data provider). You can’t do this correctly just by looking it up.
TRIPLE HINT: If you want to see the actual regression results (including constants, standard errors, rsquared, etc.) you must select “1” for stats, and enter the formula as an “array formula”. This means
that you select an array of cells 2 columns wide and 5 rows high, with the “=linest” must be in the
upper left cell of the array. Then you hit “F2”, then “Control + Shift + Enter”.