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FNCE 30007 DERIVATIVE SECURITIES

Tutorial Questions

Hedging with Forwards and Futures

Question 1

Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.

Question 2

Explain why a short hedger’s position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.

Question 3

Imagine you are the treasurer of a Japanese company exporting electronic equipment to the U.S. Discuss how you would design a foreign exchange hedging strategy and the arguments you would use to sell the strategy to your fellow executives.

Question 4

“For an asset where futures prices are usually less than spot prices, long hedges are likely to be particularly attractive.” Explain this statement.

Question 5

The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

Question 6

A corn farmer argues: “I don’t use futures contracts for hedging. My real risk is not the price of corn. It is my whole crop gets wiped out by the weather.” Discuss this viewpoint. Should the farmer estimate his or her expected production of corn and hedge to try to lock in a price for expected production?

Question 7

On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow?

Question 8

Derive the expression for the minimum variance hedge ratio as .

Hint: set up an expression for the hedged profit/loss and take a first order condition with respect to .

Question 9

Consider a company on October 1, 2015 seeking to hedge the purchase of 10,000 barrels of oil in the spot market on December 15, 2015. They wish to hedge by using December 2015 oil futures. The contracts expire on December 31, 2015 and each futures contract is for 100 barrels.

You are provided with the following information

October 1, 2015 spot price = $25 per barrel

October 1, 2015 futures price = $28 per barrel

December 15, 2015 spot price = $27 per barrel

December 15, 2015 futures price = $27.50 per barrel

1) Calculate the cost of the oil on December 15, 2015 using the three approaches discussed in lectures. Assume a naïve hedge ratio of 1.

a) Approach 1: Spot transaction at December 15 adjusted for futures gain/loss

b) Approach 2: Spot position at October 1 adjusted for hedged profit or loss

c) Approach 3: Futures price at October adjusted for the basis.

2) Show that the hedged profit/loss equals the change in the basis.

Question 10

Assume you are an index fund manager that has a $500M position in the Nikkei 225 index as at June 29, 2007. You are concerned about the developments in the USA (i.e the onset of the GFC) and seek to hedge your position using Nikkei 225 futures. You are provided with data on the Nikkei 225 and its futures from February 2, 1994 to July 9, 2010.

1) Consider the performance of the following strategies over the period of the GFC defined as July 2, 2007 to February 27, 2009

a. Unhedged

b. Naïve

c. MVHR using the full in sample period (February 2, 1994 to June 29, 2007)

d. MVHR using the last 3 years (July 1, 2004 to June 29, 2007)

e. Dynamic MVHR using a rolling window of 252 trading days

f. Dynamic MVHR using a rolling window of 504 trading days 

2) For each strategy, calculate the final portfolio value and the 95% confidence interval for the daily change in the portfolio value over the GFC.

3) Comment on the relative merits of each strategy.