## FMP Quiz 2

malika.aggarwal
Posts: 3
Joined: Wed Sep 12, 2012 11:54 am

### FMP Quiz 2

Hanwha Investment is underwriting a 30-year zero coupon corporate bond issue with a face value of \$50 million and a current market value of \$2,676,776 (a yield of 5% per six-month period). The firm must hold the bonds for a few days before issuing them to the public, which exposes them to interest rate risk. Hanwha Investment wishes to hedge its position by using T-bond futures contracts. The current T-bond futures price is \$90.80 per \$100 par value, and the T-bond contract will be settled using a 20-year, 8% coupon bond paying interest semiannually. The contract is due to expire in a few days, so the T-bond price and the T-bond futures price are virtually identical. Assume that the yield curve is flat and that the corporate bond will continue to yield 0.5% more that T-bond per six-month period, even if the general level of market rates should change. What hedge ratio should Hanhwa Investment use to hedge its bond holdings against possible interest rate fluctuations over the next few days?
a. 72 contracts held short to hedge
b. 85 contracts held short to hedge
c. 88 contracts held short to hedge
d. 93 contracts held short to hedge

Here the answer is option C. I want to know how did this 88 come. What values we need to consider here.

shreyas
Finance Junkie
Posts: 83
Joined: Thu Jul 19, 2012 6:49 pm

### Re: FMP Quiz 2

Assuming you know how to calculate the modified duration of treasury bond future which is 9.45,the modified duration for zero coupon bond will be Macualay duration divided by the periodic market yield, so 30/1.05= 28.57
the equation is just then hedge ratio = 30*2676776/9.45*90.80*100*10= 89.13 so the closest answer is 88 contracts

d2syh
Good Student
Posts: 21
Joined: Fri Aug 17, 2012 3:27 pm

### Re: FMP Quiz 2

Will you explain how you derive Macaulays duration i.e. 9.45? What is the purpose of calculating MD for zero coupon bond i.e. 30/1.05=28.57?

shreyas
Finance Junkie
Posts: 83
Joined: Thu Jul 19, 2012 6:49 pm

### Re: FMP Quiz 2

I am calculating the Modified duration for the treasury bond and not the Macaulay duration.
In case of hedging the duration measure should be the same. For zero coupon bond we have to calculate the modified duration as we are provided with Macaulay duration.

For the question on how we calculated the Modified duration, refer the formula from our lecture handouts.

Or you can take a look at the webinar