1. A banks assets and liabilities both have a duration of 5 years. Is the bank hedged against interest rate movements? Explain carefully any limitations of the hedging scheme it has chosen.

2. Explain what is meant by basis risk in the situation where a company knows it will be purchasing a certain asset in two months and uses a three-month futures contract to hedge its risk.

3. A trader takes the long position and a hedge fund takes a short position on ten 1-month S&P 500 futures contracts at 1300. A single S&P 500 futures contract equals ($250) x (Index Value). The initial margin is $325,000 and the maintenance margin is $245,000 for both accounts. Ten trading days later, the futures price of the index drops to 1,260 triggering a margin call for the trader. What is the change margin account balance (indicate gain or loss) for: a) the trader and b) the hedge fund? What is the margin call for the trader?

4. A speculator sells a July 2013 wheat futures contract at 721 cents per bushel. Each futures contract is for 5,000 bushels. The futures price drops to 676 on December 31, 2012 and rises to 712 in May 2013 when she closes the contract. What is the gain or loss for accounting purposes in 2013?

5. In December 2011, a company expects to buy 100,000 MMBtu of natural gas before the end of March 2012, but does not know exactly when. To hedge against volatile gas prices, it implements a rolling forward hedge by taking a long position on 10 two-month natural gas futures (only held for 1 month). One futures contract is for 10,000 MMBtu and is quoted in $ per MMBtu. The commodity is purchased in March 2012. What is total dollar gain/loss from the rolling hedge? Assume a hedge ratio of 0.8.

Date	Dec 2011	Jan 2012	Feb 2012	Mar 2012
Feb 2012 Futures Price	3.65	3.00	-	-
Mar 2012 Futures Price	-	2.95	2.70	-
Apr 2012 Futures Price	-	-	2.65	2.50
Spot Price	3.67			2.50

6. A trader owns 55,000 troy oz of silver and decides to hedge with 6-month silver futures contracts. Each futures contract is on 5,000 troy oz. The standard deviation of the change in the spot price of silver is 0.43. The standard deviation of the change in silver futures prices is 0.40. The coefficient of correlation between the two is 0.95.

a. What is the minimum variance hedge ratio?

b. What is the optimal number of futures contracts without tailing the hedge?

c. What is the optimal number of futures contracts with tailing the hedge?

7. For an interest rate compounded annually of 7%, what is the equivalent interest rate compounded:

a. Semi-annually

b. Quarterly

c. Monthly

d. Weekly

e. Daily

8. Given the zero rates and cash flows for a bond (see table below):

a. What is the theoretical price?

b. What is the bond yield?

Maturity(Years)	Treasury Zero Rates (%)	Coupon Payments	Principal
0.5	2.0%	$10	-
1.0	2.3%	$15	-
1.5	2.7%	$10	-
2.0	3.2%	$15	$1000

9. A US investor sees an arbitrage opportunity in the currency markets. The spot exchange rate between the Swiss Franc and US Dollar is 1.0404 ($ per CHF). Assume the continuously compounded interest rates in the US and Switzerland are 0.25% and 0%, respectively. The 3-month currency forward price is 1.0300 ($ per CHF). What is the theoretically correct forward price. What is the investors total profit (in CHF), assuming she begins by borrowing 1,000 CHF?

10. A stock provides a dividend yield of 5.0% paid semi-annually (equivalent to 4.94% continuously compounded). The spot price of the stock is currently $500, and the risk-free rate is 7.5% with continuous compounding.

a. What is the two-year forward price for a stock?

b. What is the continuously compounded cost of carry for the stock?