SAMPLE EXAM QUESTIONS
TRUE/FALSE: (no explanation required, circle the correct answer)
Assume that there are no arbitrage opportunities.
TRUE / FALSE Suppose between maturities 1 yr to 10 years that the term structure
of interest rates is everywhere downward sloping (but, of
course,always positive). Then it is possible that a 10-yr zero has a
greater price than a nine-year zero.
TRUE / FALSE If, all of a sudden, government bond rates were quoted in terms of
quarterly (rather than semi-annual) compounded rates, then the prices
of treasury strips would fall. (Assume traders are rational).
TRUE / FALSE If the forward curve is upward sloping (everywhere), then the term
structure of interest rates is also everywhere upward sloping.
TRUE / FALSE Consider two U.S. gov’t bonds with the same remaining time to
maturity. One bond pays a high coupon while the other pays a
relatively low coupon. The higher coupon bond has a lower yield to
maturity. If the term structure is everywhere downward sloping, then
one can infer that the bonds are mispriced.
TRUE / FALSE For the same maturity, zeroes have more duration and convexity than
coupon bonds.
TRUE / FALSE It is possible to match both the duration and the market value of a
long-term bond using a portfolio of two short-term instruments.
The questions below represent actual questions on international finance from old exams - they are not quite representative of your testing material. You are responsible for the first two lectures on international. However, the questions below give you an indicator of the type I'm likely to ask.
TRUE/FALSE Under the rules of the European Monetary System, the dollar can
fluctuate against any individual European currencies but not against
the ECU overall.
TRUE/FALSE For a currency experiencing hyperinflation, the forward rate is probably
a more accurate predictor of the future spot rate than the present spot
rate.
TRUE/FALSE When the dollar is at a forward premium relative to the DM, it implies
that inflation in the U.S. is higher.
PROBLEM #1 (assume semi-annual compounding)
You are given the following data on two bonds:
Bond #1 $100 par of a .5-year zero has a price of $97.50
Bond #2 $100 par of a 1-year 5% coupon bond has a
price of $99.00
a) Calculate the 6-month spot rate of interest.
b) What is the price of $1 par of a 1-year zero?
c) What is the 1-year par rate, i.e., what coupon rate would make the price of a 1-year coupon bond equal to par?
d) Explain briefly (and intuitively) the following two facts:
(i) Why the 1-year par rate lies either below or above (whatever you found) the 1-year spot rate in your answer to (b) and (c) above?
(ii) Why the 1-year par rate is closer to the 1-year spot rate than the 6-month spot rate in magnitude than the 6-month spot rate?
PROBLEM #2 (assume semi-annual compounding)
For this problem, assume the 6-month and 1-year rates of interest are 6% and 8%, respectively. Today, banker Bill agrees to loan farmer George $1,000 in 6 months to be
paid back with interest in 1 year (i.e., a forward contract).
a) How much should George pay Bill?
b) What is the price value of a basis point of this forward contract? (Remember that you will have to convert dollar duration into the price value of a basis point by dividing by 10,000).
c) Explain in just a sentence or two why forward contracts are considered levered (in other words, highly risky) positions in the bond market. Do this in the context of your answer to part (b) above.
PROBLEM #3
For this problem, assume that your liabilities have a market value of $300,000; a duration of 15; and a convexity of 250.
a) What is the dollar duration of the liabilities?
b) What is the dollar convexity of the liabilities?
c) Using dollar duration alone, approximate the change in value of your liabilities if there is a parallel shift in rates of 50 basis points.
d) Using dollar duration and dollar convexity, approximate the change in value of your liabilities if there is a parallel shift in rates of 50 basis points.
e) You are given the following data on a 2-year, 5-year and 30-year zero, respectively:
Mkt. Value Duration Convexity
$1 par value of a 2-year zero: .897 1.95 4.74
$1 par value of a 5-year zero: .755 4.86 26.00
$1 par value of a 30-year zero: .150 29.07 858.97
Let represent the number of units of the 2-yr, 5-yr and 30-yr zeros, respectively. Write down but do not solve equations that determine a portfolio of the 3 assets listed below that immunizes your net position by matching the market value, duration and convexity of your liabilities.
f) Even if we put on the above duration/convexity hedge, explain briefly why this hedge may fail in practice.
PROBLEM #4
You are the assistant to the CFO of Silicon Graphics, selling hi-end workstations around the world. Your new machine costs US$500,000 to manufacture, deliver and install abroad. You have received an offer from the Mexican governments to purchase 10 of your machines for 80,000,000 Mexican Peso (MP), with payment to be made in one year's time. The current exchange rate is MP10/$. As a company policy, exposure of this type must be covered. Unfortunately, no forward market for MPs out to one year exists. Peso interest rates on secure (no credit risk) financial assets are 50%-52% p.a. to lend/borrow, while US interest rates are 5%-5.30% p.a. to lend/borrow.
(a) Is it worth accepting the bid? Assume costs ($500,000/unit) are incurred today
(b) How can you manufacture a forward contract to cover the risk?