FMP19 - Interest Rate Futures

Question 1

Identify the most commonly used day count conventions, describe which markets that each one is typically used in, and apply each to an interest rate calculation

Answer 1

1. Actual / actual used in Treasury instruments in the US
2. 30/360 used for corporate bonds in the US, 30 days in each month 360 days in the year

Count days to maturity using convention and since last coupon and apply to coupon to find accrued interest

Question 2

Differentiate between clean and dirty price for a US Treasury bond; calculate the accrued interest and dirty price on a US bond

Answer 2

Quoted price is the clean price, dirty price is that paid = clean price + accrued interest

Question 3

Explain and calculate a US Treasury bond futures contract conversion factor

Answer 3

1. calculate time to maturity from first day of delivery month to the maturity of the bond
2. round time in 1 down to nearest three months
3. calculate clean price per dollar face value for a bond with maturity in 2 and yield of 6% using semi annual compounding

If not at the start of the period, discount f

Question 4

Calculate the cost of delivering a bond into a Treasury bond futures contract

Answer 4

Cost of delivering bond = market price - price received

Question 5

Describe the impact on the level and shape of the yield curve on the cheapest-to-deliver Treasury bond decision

Answer 5

If yields > 6%, low-coupon long-maturity bonds will be cheapest to deliver, high-coupon short-maturity otherwise.

Upwards sloping yield curve favours long-maturity bonds, downwards favours short-maturity bonds.

Question 6

Calculate the theoretical futures price for a Treasury bond futures contract

Answer 6

1. Calculate dirty price of delivered bond from clean price by adding accrued interest
2. Calculate PV of coupons to be received between now and time bond will be delivered
3. 2 -1 and compound forward at risk free rate to when bond is delivered
4. 3 - accrued interest at time of delivery
5. 4 * conversion factor

Question 7

Calculate the final contract price on a Eurodollar futures contract and compare Eurodollar futures to FRAs

Answer 7

100 - R where R is 3-month Libor

Question 8

Calculate the duration-based hedge ratio and create a duration-based hedging strategy using interest rate futures

Answer 8

Number of long contracts that should be traded = -Ev / Ef

Negative indicates a short position
Ev = increase in value of one futures contract for a basis point downward parallel shift in zero curve
Ef = increase in value of traders position for a basis point downward parallel shift in zero curve

Question 9

Evaluate the limitations to a duration-based hedging strategy

Answer 9

Only considers small parallel shifts of interest rate term structure and assumes perfect correlation