Midterm exam
This midterm is taken under the honor code. This means that the exam is to be
done individually; no help can be accepted, solicited or given during the exam, and
you may not discuss the exam with classmates of yours that have not yet taken
it. The exam is an open book, take-home exam. You should submit online on
Canvas a MS Excel spreadsheet by January 30th at 10pm EST.
For the multiple choice questions, please indicate the correct answer clearly in the
MS Excel spreadsheet. There is only one correct answer. No partial credit will be
given for these questions.
For the short answer questions, be sure to show all of your work. You will not
receive credit unless work is shown in the excel spreadsheet, but you will receive
most of the credit if your methodology is correct even if your final answer is not.
The exam has a total of 150 points plus 10 bonus points.
Solutions will be posted on Canvas.
Multiple choice questions (7 points each; 70 points total)
Assumptions: Unless specified otherwise, assume bonds have a par value of $100 and pay
coupons semi-annually. Assume interest rates are annualized but compounded semi-annually.
Assume there is no risk-free arbitrage unless otherwise stated. No information needs to be
extracted from the Bloomberg screenshots.
1. Suppose the price of a 6-year Zero (e.g., Treasury STRIP) is $90.95. What is the yield of this
Zero rounded to the nearest basis point?
a. The yield is negative
b. 0.79%
c. 1.59%
d. 3.19%
e. 19.90%
f. None of the above
2. Consider the Gamestop Inc. (GME) bond in the Bloomberg screenshot below (note that you
do not have to extract any information from this screenshot) featuring a 10% annualized coupon
rate and maturing in 2 years. Abstracting from GME default risk, which portfolio replicates the
cash flows of 20 of these bonds?
a. Long 105 2-year Treasury STRIPS
b. Long 200 2-year T-notes with a 1% coupon rate
c. Long 100 2-year T-notes with a 2% coupon rate
d. Long 200 2-year T-notes with a 1% coupon rate and short 180 2-year Treasury STRIPS
e. Long 100 2-year T-notes with a 2% coupon rate and short 200 2-year Treasury STRIPS
3. The current yield of the GME bond equals 9.67%, whereas the current yield of the 2-year Tnote with a 1% coupon rate is 0.87% and the current yield of the 2-year Treasury STRIPS are
0.89%. What is the credit spread of the GME bond rounded to the nearest basis point?
a. 8.52%
b. 8.78%
c. 8.80%
d. 8.96%
e. 9.31%
f. 9.48%
g. None of the above
4. The Bloomberg screenshot shows the price path of the GME bond, why do you think the
bond’s price is so volatile?
a. Mostly because of time-varying interest rate risk
b. Mostly because of time-varying default risk
c. In equal parts because of both time-varying interest and default risk
d. Bond prices are generally not very volatile
e. None of the above statements are correct
5. The current 2-year Zero yield is 0.89% whereas the yield of a 2-year Inflation-Protected
Treasury Security (TIPS) is 0.44% (see Bloomberg screenshot below). What is the expected
inflation rate of investors in the bond market?
a. -0.45%
b. 0.25%
c. 0.45%
d. 6.81%
e. We cannot infer the expected inflation from these two yields
f. None of the above
6. Current inflation is 6.81% in the US (and around 5% in the Eurozone), what would be
plausible reasons that this high inflation is transitory and expected inflation is not as high?
a. Current inflation is concentrated in goods (gas, used cars, hotel rooms, and meat) that
may be subject to supply-chain constraints
b. The current medium- and long-term interest rates have not increased
c. The Fed moved to tighten monetary policy, reducing its bond purchases and indicating
that it expects to raise interest rates at least modestly next year
d. There is a lot of pent-up demand, especially for durable goods like automobiles, after a
year of pandemic rationing, which might be transitory
e. Maybe there is some unwillingness of many Americans idled by the pandemic to return
to work, which might be transitory
f. All of the above are plausible reasons
7. Consider the GM bond displayed in the Bloomberg screenshot below. The bond’s annualized
coupon rate is 1.25%, its yield is 1.49%, and it matures in 5 years. What is the bond’s Modified
duration?
a. 4.83
b. 4.86
c. 5.92
d. 5.00
e. None of the above
8. Suppose that your portfolio consists of a $200K long position in the GM bond and a $100K
cash position and suppose the bond’s Macaulay duration is 4.8. Additionally, you can invest into
the Italian government bond displayed in the Bloomberg screenshot below that matures in 2039,
has a yield of -0.14%, and a modified duration of 16 years. Suppose you think that this Italian
bond is a terrible deal. Which trade would bet against the bond and immunize your portfolio
against a parallel shift in interest rates today?
a. Long $48K of the Italian bond
b. Long $60K of the Italian bond
c. Short $48K of the Italian bond
d. Short $60K of the Italian bond
e. None of the above would immunize my portfolio and bet against the Italian bond
9. Roku IPO’d in September 2017 with a first-day-of-trading closing price of $26.54 and it is
currently trading at $117.56. Using our DDM model, we value Roku at $21.54 per share, its beta
is 2.13, the equity premium is 5% and the risk-free rate is 0.66%. If you expect Roku’s stock
price to converge to the firm’s expected value in one year, what is the 1-year expected return
(annualized, rounded to the nearest 0.01%)?
a. -95.77%
b. -81.67%
c. -79.61%
d. 445.78%
e. None of the above
10. Suppose BABA’s stock has a total return volatility of 56.32%. The stock’s market beta is
1.71, and market return volatility is 18%. What is BABA stock’s idiosyncratic volatility?
a. 30.78%
b. 47.16%
c. 62.43%
d. 75.31%
e. None of the above
Short answer question 1 (35 points plus 5 bonus points total)
The term structure as of January 8, 2022 (see Bloomberg snapshot below, but note that you do
not need to extract information from this screenshot to do the question) is given by
Year (n) rn (annualized)
0.5 0.25%
1.0 0.46%
1.5 0.67%
2.0 0.89%
2.5 1.03%
3.0 1.17%
3.5 1.27%
4.0 1.38%
4.5 1.45%
5.0 1.56%
Assume interest rates are annualized but compounded semi-annually. Consider the 4.5-year
AAPL bond (see Bloomberg screenshot below, but note that you do not need to extract
information from this screenshot to do the question) with a face value of $100 and an annualized
coupon rate of 3.60%.
a. (5 points) What is the price and yield-to-maturity of the AAPL bond?
b. (12 points) Calculate the Macaulay and modified durations of the AAPL bond in years.
c. (8 points) Suppose the yield curve shifts up in parallel by 0.25%. Use the AAPL bond’s
modified duration to predict its new price. How does the duration-predicted price
compare to the actual new price of the bond?
d. (10 points) Suppose you short-sell the AAPL bond and you want to immunize this
position against parallel shifts in the yield curve using a position in shorter-term (1-year)
and longer-term (5-year) Zeros—i.e., using a “barbell hedge.” In which weights should
you buy or sell-short the 1-year and 5-year Zeros to immunize your overall portfolio
against parallel shifts in the yield curve?
e. (5 bonus points) Suppose the yield curve now flattens at 0.72%. Would that increase or
decrease the value of your portfolio consisting only of the positions in the 1- and 5-year
Zeros as well as the Treasury note? Explain in one or two sentences.
Short answer question 2 (45 points plus 5 bonus points)
Download the excel file Midterm Spring 2022 Data.xlsx. You will find daily price data of the
Vanguard Total Stock Market ETF (VTI), Coinbase Global Inc. (COIN), and the price of one
Bitcoin in USD (BTC) from April 2021 to Jaunary 2022. Suppose that the risk-free rate is
constant and equals 0.22% (the current 3-month LIBOR rate), history will repeat itself, and that
these are the only risky assets you can invest into in the economy.
a. (15 points) Calculate daily returns as well as annualized means, volatilities, and the
Sharpe ratios of each of the three assets (e.g., you annualize a daily return by multiplying
with 252). If you can only invest into one asset. Which asset should be combined with the
risk-free asset to give any investor with mean-variance preferences the highest utility?
b. (10 points) Calculate monthly returns as well as the annualized mean, volatility, and
Sharpe ratio of a portfolio consisting of 70% VTI, 20% COIN, and 10% BTC.
c. (10 points) Assume that the risky portfolio is the maximum Sharpe ratio portfolio,
determine the weight of the risky portfolio and the risk-free asset in the optimal complete
portfolio for an investor with mean-variance utility and a coefficient of risk aversion A =
2.
d. (5 points) Test whether the “market” as proxied for by VTI is the maximum Sharpe ratio
(MVE) portfolio by running a regression of COIN returns on VTI to see whether its
(annualized) alpha is zero.
e. (5 points) Find the optimal portfolio weights using Solver of the actual maximum Sharpe
ratio (MVE) portfolio.
f. (5 bonus points) Test whether you found the optimal portfolio weights using Solver by
running a regression of COIN returns on the MVE portfolio to see whether the alpha is
closer to zero now.