Sample exam questions

Question 1:

Jan De Nul Group is a world player in the international dredging industry. Recently, the company has

signed a contract worth $ 1 billion to dredge the port of Singapore. The entire amount will be paid at

the end of the contract, which is in one year from now. Because the company’s balance sheets are

expressed in euros, the CFO is worried about exchange rate risk. Currently, 1 euro is worth 1.25

dollars. The interest rate is 2 percent both in the euro area as in the US, so that the forward price is

equal to today’s spot price.

a. Represent graphically the cash flow (in �) of Jan de Nul group in one year as a function of the

euro-dollar (!) exchange rate. If it remains unhedged, should the company fear depreciation or

an appreciation of the US dollar.

b. Describe a position in a forward contract that would fully hedge the dollar exposure

(short/long, maturity, hedge ratio). Show graphically when the forward contract would make a

loss, and when it would make a gain.

c. How would the contract details / optimal hedge change when futures are used instead of a

forward contract?

d. Describe a position in an option that would give Jan de Nul group downward protection

(call/put, long/short, and amount). Show the payoffs of the option in a graph.

e. Make a graph that contains (1) the unhedged exposure, (2) the exposure hedged with a

forward contract, and (3) the exposure hedged with options. What are your arguments in

favour of any of the latter two strategies?

One of the main costs for Jan De Nul group is fuel (diesel) for their dredging boats. Suppose that costs

would amount to $100 million, also to be paid in 1 year from now, and that De Nul would hedge the

total exposure using crude oil futures (also maturing in 1 year from now). The relationship between

percentage price changes in diesel and crude oil are:

% change diesel = 0.79 x (% change crude oil) + error

This regression has an R-squared from 80 percent. The parameter estimate of 0.79 has a standard

error of 0.05.

f. Discuss the concept of basis risk within the context of this example.

g. Given the regression output, what is the optimal hedge ratio? Discuss the quality of this

hedge.

Until now, we assumed that De Nul hedged each exposure individually, which may not be optimal.

h. Suppose that diesel prices and the euro-dollar exchange rate are uncorrelated. How would the

optimal hedge ratios change in case De Nul hedges with forwards.

i. Suppose that the US dollar strengthens when oil prices increase (positive correlation). How

would hedge ratios change in comparison to the case where they are uncorrelated (question

a)

Question 2:

A company has outstanding debt worth $ 100 million. Interest is paid annually. The floating interest rate is reset at the end of each year, and depends on LIBOR. The interest rate at the last reset date (6 months ago) was set to 3 percent. The debt matures in 30 months (two and a half years) from now. Discuss in detail (but in maximum 2 pages) how this company can hedge this exposure by (1) treasury bill futures, (2) forward rate agreements, (3) options, and (4) swaps. Discuss in detail the characteristics of the position (short/long, hedge ratio,...). For the first three, make a payoff of the

unhedged and the hedged cash flow, as well as of the gains and losses on the derivative contract. For swaps, clearly show in a chart how interest rates are swapped. List the advantages and disadvantages of the different hedging strategies.

Question 3:

Itxassou Etxebarria has a portfolio that is invested for 60 percent in equities, 30 percent in corporate bonds, and 10 percent in a government bond fund. The total value of this portfolio is 150,000. The correlation and annualized volatilities are given in the tables below.

(a) Use these correlations and volatilities to calculate the annualized volatility of Itxassou‘s portfolio (hint: calculate first the variance-covariance matrix).

(b) Calculate the one-week Value-at-Risk at the 95 percent level. To calculate the expected return of the portfolio, assume a portfolio beta of 0.80, a riskfree rate of 2 percent, and a market risk premium (in excess of riskfree rate) of 6 percent. One year consists of 52 weeks.

Itxassou is worried about the outlook for the next three months, and considers hedging against drops in the different markets, either through a forward contract or using options.

(c) Consider a forward contract on the S&P500. Calculate the arbitrage-free three-month forward price assuming that both the riskfree rate and the annualized dividend yield on the S&P500 equal 2 percent. The spot price of the S&P500 is 1,200.

(d) Determine the optimal position in this S&P500 forward contract. Itxassou’s portfolio has a beta of 0.8 with respect to the S&P500. The current value of the index is 1200, and each contract is for 100 units of the underlying index. Show (by using the specific numbers in this exercise) that this hedge works in case the S&P500 drops with 20 percent.

Itxassou also considers hedging her portfolio using S&P500 options. She considers both buying a put option and writing a call, both with exercise prices of 1200.

(e) Price a three-month call on the S&P500 at an exercise price of 1200 assuming that the index either goes up or down with 5 percent over the next three months. Use the one-period Binomial Option Pricing model and a riskfree rate of 2 percent to price this option.

(f) Use the Put-Call Parity to price the corresponding put option. (g) Show both using real numbers and a graph how Itxassou can hedge against drops in the

portfolio value by buying a put option or by writing a call. (h) Discuss the pros and cons of the three hedging strategies (long put, short call, forward) in

detail. Tables for question 2:

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