Homework #2 - 80 Points Total

Question 1 (25 points)

You are working on a currency arbitrage desk. You look up exchange rates and interest rates for the USD versus the Canadian Dollar (CAD) and find the following:

The current spot rate is 0.769 USD/CAD. The 10-month forward exchange rate is 0.713 USD/CAD (note: Canadian dollar futures contracts are 100,000 CAD each). The 10-month T-bill yield in the USA is 2.54% (assume this is continuously compounded and annualized) and the 10-month risk-free rate in Canada is 1.94% (also continuously compounded and annualized). What is the arbitrage trade, and what is your profit per futures contract?

Question 2 (25 points)

You have a short position on a Treasury bond futures contract. The most recent settlement price is 101-06, and the accrued interest is on the bond you have chosen to deliver is $0.47. The bond you have chosen to deliver is a 9% coupon bond with 19 years, 5 months and 12 days left until maturity. What will you receive at delivery?

Question 3 (20 points)

The current spot price of gold is $1,315 per ounce. The 11-month risk free rate is 0.75% (annualized, continuously compounded). Your broker quotes you an 11-month futures contract at $1,391. Assume storage costs are $0.23 monthly per ounce, paid at the end of the storage period. What is the correct theoretical futures price? What is the arbitrage trade/profit using the price you were quoted?

Question 4 (10 points)

If the Treasury bond futures price is 99-12, which of the following bonds is cheapest to deliver?

Bond Price Conversion Factor

1 99-05 0.911

2 111-01 1.029

3 135-08 1.387