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Portfolio manager uses a T-bond futures

1. A portfolio manager uses a T-bond futures contract to hedge a bond portfolio over the next 4 months. The portfolio is worth $75 million and will have duration of 5 years in four months. The futures price is 118 and each contract is for $200,000. There are three bonds that can be delivered with durations 7, 8 and 9 years but it is unclear which will be the cheapest to deliver.

(a)    If you expect interest rates to rise over the next 4 months, which duration bond will likely be the cheapest to deliver?

(b)   What maturity T-bond futures contract should be used to hedge the bond portfolio?

(c)    What position of futures contrasts is required?

(d)   What adjustment is necessary in one month if you are wrong in your initial assessment that rates would rise; instead you now expect rates to fall?

(e)    How will your adjusted position effect the performance of the hedge if long term rates fall more than short term rates

2.  The futures price for the June 17, 2009 CBOT bond futures contract is 118-23.

(a)   Calculate the conversion factor for a bond maturing on Jan 1, 2025, paying a coupon rate of 9.5%.

(b)   Calculate the conversion factor for a bond maturing on Oct 1, 2030, paying a coupon rate of 7.5%.

(c)  Suppose that the quoted prices of the bonds in (a) and (b) are 167 and 134, respectively. Which bond is cheaper to deliver?

(d)   Assuming the cheapest-to-deliver bond is actually delivered, what is the cash price received for the bond?

3.   Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive the 3-month LIBOR in return on a notional principal of $50 million with payments exchanged every 3 months. The swap has a remaining life of 14 months. The current rate being swapped for 3-month LIBOR is 11.8% per annum for all maturities. The 3-month LIBOR rate 1 month ago was 12% per annum. All rates are compounded quarterly. What is the value of the swap?

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