1 Hedging with Futures (13p) (a) Table 1 shows historical futures prices for crude oil traded on the NYMEX for the firstWednesday of each month in 2015. Prices are given for different contract maturities ranging from January 2015 to December 2015.1 Prices are quoted in USD per barrel and each contract is for 1000 barrels. Give an intuitive explanation of varying price patterns in the table. (Hint: Given the current dynamics of crude oil prices, what are your expectations about the size of the convenience yield and teh storage costs? On which months is the term structure of futures prices in contango or backwardation? Is this consistent with your initial expectation of the convenience yield?) (b) Suppose that crude oil is currently priced at $37 per barrel and that the crude oil futuresprice with 4-month delivery is $38.88 per barrel. Assuming a continuously compounded interest rate of 4.5% and a convenience yield of 5.5%, what are the current implied annualized storage costs? (c) Assume, as an exporter of crude oil, that you would like to lock in the price for alarge quantity of crude oil which you will produce 18 months from now. You discover Date Delivery Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 07-Jan-15 *48.77 48.65 49.08 49.72 50.48 51.23 51.95 52.61 53.25 53.87 54.51 55.15 04-Feb-15 *48.70 48.45 49.30 50.58 51.89 53.18 54.38 55.40 56.25 57.03 57.78 04-Mar-15 *51.60 51.53 53.23 54.55 55.74 56.83 57.76 58.46 59.07 59.64 01-Apr-15 *49.55 50.09 51.75 53.06 53.98 54.74 55.44 56.11 56.74 06-May-15 *60.7 60.93 62.00 62.56 62.93 63.28 63.66 64.01 03-Jun-15 *59.61 59.64 59.93 60.14 60.31 60.59 60.93 01-Jul-15 *56.87 56.96 57.37 57.70 58.12 58.55 05-Aug-15 *45.11 45.15 45.55 46.18 46.84 02-Sep-15 *45.11 46.25 46.86 47.52 07-Oct-15 *48.13 47.81 48.40 04-Nov-15 *46.58 46.32 1 Thus, a column corresponds to one contract with prices given on different dates. A row corresponds to prices given on a particular date for different contract maturities. 2 02-Dec-15 *40.10 Table 1: NYMEX Futures prices for crude oil for the first Wednesday of each month in 2015. A * implies the spot price in the corresponding month. Source: Futures data from U.S. Energy Information Administration that the NYMEX futures crude oil contract for a 18-month delivery currently trades at $45.81 per barrel. Using the same assumptions and calculations made in (b), is there anything you would propose to do in this situation? (d) On Feb 6, 2015, as an airline company, you are concerned about a possible decreasein supply of oil over the next 6 months (i.e., August) due to tensions in the Middle East. Explain how you can use futures contracts to hedge your exposure to oil price risk. Assume the company would like to enter a position that is worth USD $3,500,000. How many contract ...

1. 1 Hedging with Futures (13p)
(a) Table 1 shows historical futures prices for crude oil traded
on the NYMEX for the
firstWednesday of each month in 2015. Prices are given for
different contract
maturities ranging from January 2015 to December 2015.1
Prices are quoted in USD
per barrel and each contract is for 1000 barrels. Give an
intuitive explanation of
varying price patterns in the table. (Hint: Given the current
dynamics of crude oil
prices, what are your expectations about the size of the
convenience yield and teh
storage costs? On which months is the term structure of futures
prices in contango or
backwardation? Is this consistent with your initial expectation
of the convenience
yield?)
(b) Suppose that crude oil is currently priced at $37 per barrel
and that the crude oil
futuresprice with 4-month delivery is $38.88 per barrel.
Assuming a continuously
compounded interest rate of 4.5% and a convenience yield of
5.5%, what are the
current implied annualized storage costs?
(c) Assume, as an exporter of crude oil, that you would like to
lock in the price for alarge

2. quantity of crude oil which you will produce 18 months from
now. You discover
Date Delivery Month
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
07-Jan-15 *48.77 48.65 49.08 49.72 50.48 51.23 51.95 52.61
53.25 53.87 54.51 55.15
04-Feb-15 *48.70 48.45 49.30 50.58 51.89 53.18 54.38 55.40
56.25 57.03 57.78
04-Mar-15 *51.60 51.53 53.23 54.55 55.74 56.83 57.76 58.46
59.07 59.64
01-Apr-15 *49.55 50.09 51.75 53.06 53.98 54.74 55.44 56.11
56.74
06-May-15 *60.7 60.93 62.00 62.56 62.93 63.28 63.66 64.01
03-Jun-15 *59.61 59.64 59.93 60.14 60.31 60.59 60.93
01-Jul-15 *56.87 56.96 57.37 57.70 58.12 58.55
05-Aug-15 *45.11 45.15 45.55 46.18 46.84
02-Sep-15 *45.11 46.25 46.86 47.52
07-Oct-15 *48.13 47.81 48.40
04-Nov-15 *46.58 46.32
1 Thus, a column corresponds to one contract with prices given
on different dates. A row corresponds to

3. prices given on a particular date for different contract
maturities.
2
02-Dec-15 *40.10
Table 1: NYMEX Futures prices for crude oil for the first
Wednesday of each month in 2015.
A * implies the spot price in the corresponding month. Source:
Futures data from U.S.
Energy Information Administration
that the NYMEX futures crude oil contract for a 18-month
delivery currently trades at
$45.81 per barrel. Using the same assumptions and calculations
made in (b), is there
anything you would propose to do in this situation?
(d) On Feb 6, 2015, as an airline company, you are concerned
about a possible decreasein
supply of oil over the next 6 months (i.e., August) due to
tensions in the Middle East.
Explain how you can use futures contracts to hedge your
exposure to oil price risk.
Assume the company would like to enter a position that is worth
USD $3,500,000. How
many contracts do you need to buy/sell?
(e) Go to the web site of CME Group2 and find the historical
margin requirements for Light
Sweet Crude Oil (WTI) on Feb 6, 2015 for the contract maturity
traded in part (d).
Assuming the airline company is a hedger, what is the total

4. initial margin required for
this position? What is the total maintenance margin?
2 Duration Hedging with Futures (16p)
Liability-driven investment policies (LDI) have come to
prominence in the UK and the U.S. as
a result of recent changes in the regulatory and accounting
frameworks. As a result, the Office
of the Superintendent of Financial Institutions of Canada
decided to implement LDI policies
in its federal pension plan. LDI aims to address the duration
mismatch between assets and
liabilities, which has become a non-negligible risk to the
funding status of pension plans
around the world. Assume that the Canada Pension Plan
Investment Board (CPPIB) has the
balance sheet illustrated in Table 2, in which all numbers are
expressed in million $CAD.
Assets Liabilities
Equity 600 Liabilities 1,050
Fixed Income 400 Liabilities 1,050
Total 1,000 Total 1,050
Table 2: Balance Sheet of Canada Pension Plan Investment
Board.
2 http://www.cmegroup.com/clearing/risk-
management/historical-margins.html

5. 3
(a) Is the CPPIB currently under- or overfunded? By how much?
(b) What is the total asset duration of CPPIB’s investment
portfolio, assuming that
equityhas a duration of zero years, and the fixed income
portfolio a duration of 5 years?
(c) Assume a 10% decrease in global equity markets. How will
this affect CPPIB’s
fundingratio?
(d) Assume that the liabilities have a duration of 12 years.
Given an independent
decreasein interest rates of 100 basis points (i.e., a decrease by
one percentage point),
how will CPPIB’s funding ratio change? Explain duration risk
in relation to your
findings. (Hint: By independent, I mean that you should ignore
your answer from
question (c)).
(e) Assume that CPPIB wants to hedge 70% of its liabilities
against interest rate
fluctuations over the following year. It therefore decides to
hedge its exposure by
investing into bond futures contracts as the LDI solution. If the
bond futures is
currently priced at 109.4823 percent, and the underlying bond
has a duration of 22
years and a par value of $CAD 1 million, how many contracts
are needed in order to be
fully immunized? You need indicate whether the fund needs to

6. buy or to sell the futures
contracts.
(f) Once the LDI duration hedging solution is implemented, will
the plan remain
immunized against changes in interest rates? Why or why not?
Explain.
3 Swap Pricing (18p)
A Brazilian Software company (KondZilla) plans to expand its
business to the U.S. market
and requires USD$15 million to fund the expansion. The
Brazilian company faces the
following borrowing opportunities: obtain a 11.25% Brazilian
real (BRL)-denominated loan
in Brazil, or a 8.5% USD-denominated loan in the U.S.
Meanwhile, a U.S. based minerals
extraction company plans to expand its operations to Brazil and
requires 60 million BRL to
finance its project. The U.S. based company can secure either a
10.75% BRL-denominated
loan in Brazil or a 7.5% USD-denominated loan in the U.S.
(a) Which company has an absolute borrowing advantage, which
company has a
comparative borrowing advantage (and in which market)? Why?
Which company
would you consider to have a higher credit risk?
(b) As an alternative option to paying fixed rate loans, both
companies approach
DeutscheBank, who acts as an intermediary by suggesting to
broker a currency swap
between the two companies. Essentially, Deutsche Bank
engages into a 4-year fixed-

7. for-fixed currency-swap with both companies:
4
• The Brazilian company borrows 60 million BRL at 11.25%
and swaps it with
Deutsche Bank for a $15 million USD loan at 8.25%.
• The U.S. based company borrows $15 million USD at 7.5%
and swaps it with
Deutsche Bank for $60 million BRL at 10.5%.
Assuming a flat term structure of interest rates in both
countries, 4% in the U.S. and
8% in the Brazil and the spot exchange rate of 4 BRL per USD.
All interest rates are
expressed in continuous compounding. Draw a sketch of the
cash flows for the three
stages in the transaction: initial cash flow, annual interest cash
flow, principal payment
at maturity. How much does Deutsche Bank make in USD from
the annual exchange of
interest cash flows (annual profit)?
(c) Calculate the present value of the swap from the perspective
of the U.S. based
andBrazilian companies in USD. Explain whether entering into
the swap contract is
beneficial to both companies compared to directly borrowing in
the financial markets?
(d) Calculate the duration of the swap from the perspective of
the Brazilian company.(Use
continuous discounting!)

8. (e) How would your answer to (d) change if Deutsche Bank
were to use the floating
annualrate of 4%+LIBOR instead of the fixed rate of 8.25% in
its swap with the
Brazilian Company?
(f) On January 8, 2016, almost 2 years into the swap contract,
the inflation rate shoots
upto 10% in Brazil as Standard & Poor’s downgraded Brazil’s
credit rating to junk
earlier in September. Being concerned about the Brazilian
company ability to honor
the swap contract, Deutsche Bank decides to cancel the
Brazilian leg of the swap
transaction. How would this affect Deutsche Bank’s overall risk
profile? Give a
qualitative answer.
(g) In the above situation, what would happen if the spot
exchange rate increases to 4.5
BRL per USD after Deutsche Bank cancels the contract of the
Brazilian leg of the swap
transaction? Do you think the cancellation of the contract was a
good idea? (Hint: think
about the credit risk and market risk of Deutsche Bank, and how
the remaining cash
flows would change with the new exchange rate.)
4 Currencies and Forward Pricing (19p)
Table 3 lists the daily spot and forward quotes for the
Euro/USD exchange rates in December
2015. The currency is quoted as the number of USD per Euro.

9. (a) December 3 and December 17 represent the two days with
the largest price
movementsin December 2015, measured by the percentage
change in spot prices. Go
to the website of the European Central Bank (ECB,
https://www.ecb.europa.eu/press)
5
and the U.S. Federal Reserve Bank (FED,
http://www.federalreserve.gov/monetarypolicy) to see whether
there were any
major monetary policy changes responsible for the price
movements on these days.
(b) The spot EUR/USD exchange rate has fallen to around 1.09
by the end of 2015
from1.20 at the beginning of 2015. What is the intuition behind
the exchange rate
movement? After the news of an interest rate hike has been
released, assuming that no
further interest rate hike is expected in the United States, and
assuming that uncovered
interest rate parity holds, in what direction would you expect
the future spot exchange
rate to move?
(c) Given your findings in (a), was the subsequent price
movement consistent with
thechange in monetary policy news? Do you think the monetary
policy change
surprised the market?
(d) Describe the currency forward patterns across different

10. maturities. Are the
forwardcontracts trading at a premium or a discount? Are the
patterns consistent with
the theory of covered interest rate parity?
(e) Given the spot, 1-month, 3-month, 6-month and 1-year
forward rates for the
Euroagainst the USD on December 30, 2015, compute the
annualized interest rate
differential implied by each forward contract.
(f) Repeat part (e) for December 2 and December 3. Compute
and contrast the
impliedinterest rate differentials before and after the news is
released. How are the
implied interest rate differentials related to actual interest rate
differentials? Briefly
Comment.
(g) Go to Bloomberg’s website and look up the level of the
German stock index (DAX) on
December 16, 2015. What is the level of the DAX 30 futures
contract with March 2016
delivery on the same day? Hint: Bloomberg’s website does not
have historical data; but
you can read the data from the historical data plot.3
(i) The March 2016 contract of the three-month Euribor futures
traded at 100.165
onDecember 16, 2015. Given the spot and futures prices in (g),
what was the annualized
implied dividend yield on December 16, 2015?
(j) Global markets fell in response to turmoil in the Chinese
market on January 4, 2016.

11. The DAX index fell more than 4%. Find the closing level of the
DAX on January 4, 2016.
Assuming the same interest rate and dividend yield as in (i),
what should be the new
price of a DAX futures price with March 2016 delivery?
3 You will find information for the spot price at
http://www.bloomberg.com/quote/DAX:IND, and
information for the futures price at
http://www.bloomberg.com/quote/GX1:IND.
6
Spot 1 month 3 month 6 month 1 year
01/12/2015 1.0608 1.0619 1.0636 1.0668 1.0748
02/12/2015 1.0573 1.0584 1.0602 1.0635 1.0716
03/12/2015 1.0852 1.0861 1.0877 1.0908 1.0984
04/12/2015 1.0889 1.0898 1.0914 1.0943 1.1017
07/12/2015 1.0853 1.0863 1.0878 1.0908 1.0985
08/12/2015 1.0871 1.0881 1.0897 1.0927 1.1005
09/12/2015 1.0963 1.0973 1.0988 1.1020 1.1098
10/12/2015 1.0937 1.0948 1.0965 1.0996 1.1074
11/12/2015 1.0997 1.1009 1.1025 1.1056 1.1134

12. 14/12/2015 1.1028 1.1040 1.1056 1.1087 1.1166
15/12/2015 1.0921 1.0934 1.0950 1.0981 1.1060
16/12/2015 1.0944 1.0956 1.0972 1.1004 1.1081
17/12/2015 1.0834 1.0846 1.0862 1.0893 1.0972
18/12/2015 1.0845 1.0856 1.0872 1.0903 1.0982
21/12/2015 1.0918 1.0930 1.0946 1.0977 1.1057
22/12/2015 1.0967 1.0979 1.0995 1.1027 1.1108
23/12/2015 1.0880 1.0890 1.0907 1.0939 1.1018
24/12/2015 1.0959 1.0969 1.0986 1.1018 1.1098
25/12/2015 1.0959 1.0969 1.0986 1.1018 1.1098
28/12/2015 1.0972 1.0982 1.0999 1.1031 1.1113
29/12/2015 1.0906 1.0915 1.0933 1.0965 1.1047
30/12/2015 1.0914 1.0922 1.0939 1.0972 1.1057
31/12/2015 1.0863 1.0871 1.0889 1.0921 1.1004
Source: Datastream.
Table 3: Euro/USD Spot and Forward Rates, December 2015.
5 Futures Arbitrage (12p)
Anheuser-Busch InBev NV, the Belgium giant for beverages and

13. brewing products, issued a
mammoth $46bn bond on January 15, 2016 to fund its
acquisition of the UK’s SAB-Miller.
The company received a record subscription of $110 billion
from investors, allowing it to tap
the bond market at a fairly low yield, thereby reducing its
annual interest costs. This bond
issue is the second-largest corporate debt sale on record and
proves the strong demand for
high-quality corporate bonds in light of the current weak
performance in global equity
markets. One of the issued bonds has a maturity of 10 years, a
yield of 1.6 percentage points
above the benchmark U.S. Treasury rate. Hint: you can ignore
the accrued interest rate.
7
(a) Suppose the 10-year benchmark Treasury bond yield is
2.07% on January 15, 2016.
The bond of AB InBev has a coupon rate of 5%, and the coupon
is paid semi-annually.
What is the cash price of the AB Inbev bond for a notional
value of $10,000?
(b) The interest rate curve is upward sloping, with a 6-month
USD interest rate of
0.4%,and a 9-month USD interest rate of 0.6%. What is the fair
value of a futures
contract on AB Inbev’s bond with delivery on October 15, 2016,
assuming no default
risk? Hint: the futures price is quoted with a notional value of
100.

14. (c) If the futures contract on AB Inbev’s bond is trading at
$109, is there an
arbitrageopportunity? If yes, what is the portfolio strategy to
exploit this arbitrage
opportunity?
(d) If one institutional investor faces a flat (same rate for all
maturities) borrowing cost
of0.8%, and a flat lending rate of 0.6%, what is range of futures
prices that provide no
arbitrage opportunity?
6 Futures Pricing, Hedging and Margin Requirements
(22p)
Go to the web site of the Montreal Exchange (TMX)
(https://www.m-x.ca/accueil en.php)
and find information related to the Five-Year Government of
Canada Bond Futures contract,
commonly referred to as the “CGF” contract.
(a) What are the standardized contract terms of the CGF futures
contract
(Underlying,Contract size, tick size, initial margin ...)?
Describe the contract!
(b) Table 4 shows daily settlement prices, open interest and
volume, for CGF contractswith
delivery in March 2016, as well as P&L of an existing margin
account that was entered
on Dec. 1, 2015. Does the counterparty to the clearing house
have a long or a short
position in the CGF futures? How many contracts are held by
the counterparty? Does

15. the existing margin account belong to a speculator or hedger?
What is the percentage
of the maintenance margin over the initial margin? Hint: you
can find historical margin
requirements for speculators and hedgers from the website of
the TMX.
(c) Calculate the daily P&L and the value at the end of each day
for this margin
accountfrom December 1 to December 7. You can assume the
initial margin and
maintenance margin are constant and given by the requirements
on Dec. 1, 2015. How
many margin calls are made?
(d) Which of the margin requirements for hedgers and
speculators is higher? Why?
Sincemargin requirements change on a daily basis, could you
think of at least two
determinants of margin requirements?
8
(e) Examine the relationship between volume and open interest?
What does this tell
youabout the liquidity in this market? Is it possible that volume
is greater than open
interest?
(f) Go to the website of the TMX (https://www.m-x.ca/nego fin
jour en.php) and find the
daily settlement price of the CGF contract in December, 2015

16. (the TMX website only
allows for downloading data of 5 days; but you could change
the initial date several
times to access the whole December data.) At the same time, go
the web site of Bank of
Canada (www.bankofcanada.ca/rates/interest-rates/lookup-bond-
yields/) and find
the benchmark 5-year bond yields (selling at par) in December,
2015. In excel, compute
the underlying prices of 5-year Canadian deliverable bonds (you
should check the
definition of the underlying in CGF’s contract specification; for
simplicity, you can treat
the coupon rate as an annual payment). Calculate the optimal
hedge ratio! (Note that
for this question, you need to have the Data Analysis ToolPak
installed in Excel: open
Excel, go to “Files,” choose “Options,” then choose “Add-ins,”
click on “Analysis
ToolPak,” then click on the “Go” button next to Manage Excel
Add-ins). The Data
Analysis icon should now show on your Excel Toolbar.
(g) How can you determine the hedge effectiveness?
(h) Compare the cash prices and futures prices in (f). Which one
is higher? Given that
thetheoretical futures price is determined by the cash price
multiplied by the cost of
carry as S0er−c, explain how the shape of yield (interest rate)
curve influences the
futures price.
(i) Consider the spot and the futures prices on December 15,
2015. If futures prices

17. aredetermined according to S0er−c, what is the implied
financing rate?
(j) Go back to the web site of the Montreal Exchange and
browse the available
CGFcontracts with different maturities. Assume you would like
to hedge a 5-year
Canadian Government bond with nominal amount of
$1,000,000, which comes due in
August 2016. Which contract maturity would you choose to
hedge your exposure?
Why? How many contracts would you buy/sell?
(k) The delivery standard of CGF contract requires 5-year
Government of Canada
Bondswhich have an outstanding amount of at least C$3.5
billion nominal value.
Explain the intuition behind this requirement.
Settl. price Open int. Vol. Daily P&L Initial Margin
Maitainence Margin
Dec-01 124.81 4,810 100 38040 34236
Dec-02 124.72 4,571 103 -3600
Dec-03 124.20 4,521 259
9
Dec-04 124.49 4,643 263
Dec-07 124.85 4,634 250

18. Table 4: Margin Account