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SECTION A - Answer only TWO questions
Question 1
A fund manager owns a portfolio of 10 stocks. Explain how the manager can
reduce the systematic risk of his portfolio by 10% over the next year using
futures. Will the expected return on the manager’s portfolio also drop by
10%? Is it possible for the manager to perfectly hedge his exposure to equity
risk? Explain your answers.
[15 marks]
Question 2
The Swiss National Bank (SNB) introduced a peg to the Euro in 2011. On
January 15, 2015, the SNB suddenly announced that it would no longer hold
the Swiss Franc at a fixed exchange rate to the Euro. The graph below shows
you the performance of the Swiss Franc against the Euro over the five years
leading to the peg abandonment: before 2011 there was a period of high
exchange rate volatility, followed by a period of stability while the peg was
in place (from September 2011 to January 2015), and a dramatic one-day
surge upon the peg’s abandonment.
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Explain how you would calculate the daily 95% VaR of your exposure in the
EUR/CHF currency pair while the peg was in place using the model building
approach.
[15 marks]
Question 3
At the beginning of 1995, General Motor's pension funds were under-
funded by $9.3 billion. Even though the company injected $10.4 billion during
the year, at the end of 1995 the pension funds were still underfunded.
Knowing that interest rates dropped during 1995, explain what must have
happened. Explain how GM could have hedged its risk using (i) an
immunization strategy and (ii) interest rate swaps.
[15 marks]
Question 4
a) What does the option delta refer to? For a standard European put option,
draw the graph of the delta as a function of the price of the underlying
asset.
b) You have delta hedged a long call position on a stock. The stock price
drops. Explain how you would adjust your hedge.
[15 marks]
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SECTION B - Answer ALL Questions
Question 1
Consider a 5-year bond with a face value of $100 that pays an annual coupon
of 6% and is currently rated BBB. The expected recovery rate in case of
default is 51.13%. In the table below, you are given the probabilities that in
one year (i) the bond issuer maintains its BBB rating, (ii) is upgraded to AAA,
AA or A or downgraded to BB, B or CCC and (iii) defaults.
Rating Probability (%)
AAA 0.02
AA 0.33
A 5.95
BBB 86.93
BB 5.3
B 1.17
CCC 0.12
Default 0.18
Consider also the one-year forward yield curve for zero-coupon bonds with
different maturities and credit ratings (rates are discretely compounded):
Years to Maturity
Rating 1 year 2 years 3 years 4 years
AAA 3.60% 4.17% 4.73% 5.12%
AA 3.65% 4.22% 4.78% 5.17%
A 3.72% 4.32% 4.93% 5.32%
BBB 4.10% 4.67% 5.25% 5.63%
BB 5.55% 6.02% 6.78% 7.27%
B 6.05% 7.02% 8.03% 8.52%
CCC 15.05% 15.02% 14.03% 13.52%
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a) Compute the volatility of the above bond in one year.
b) Is the volatility a coherent risk measure? Explain.
c) Compute the 1-year Value-at-Risk and Expected Shortfall of the above
bond at a 99% confidence level.
[25 marks]
Question 2
A farmer is currently growing wheat and plans to sell it in September next
year. He needs to plan his budget now, because of upcoming expenses.
Suppose that the futures price of wheat for September delivery is £100 per
ton. There is 50% probability that the spot price of wheat in September will
be £90 per ton or £110 per ton.
a) Suppose that the farmer is certain that he will need to sell 2 tons of
wheat in September. Explain how the farmer could lock in today his
future revenue.
b) Suppose now that the farmer is not certain about the quantity of wheat
he will produce and therefore will need to sell in September. For each
possible price of wheat, there are two equally likely quantities, i.e.,
there are four equally likely price-quantity pairs, which are shown in the
Table below.
Price (£) Production (tons)
90 2.5
90 1.8
110 2
110 1.5
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i. Suppose the farmer takes a futures position on his expected
production of wheat in September. Will this strategy help him
reduce his risk? Explain why.
ii. Design a hedging strategy that minimizes the variance of the
farmer’s revenue in September.
