Government Bond Futures

[Bester]

Hi, can you please explain why the value of government bond futures decline when interest rates increase.

Following question from the GARP 2015 practice exam.


A German housing corporation needs to hedge against rising interest rates. It has chosen to use futures on

10-year German government bonds. Which position in the futures should the corporation take, and why?

a. Take a long position in the futures because rising interest rates lead to rising futures prices.

b. Take a short position in the futures because rising interest rates lead to rising futures prices.

c. Take a short position in the futures because rising interest rates lead to declining futures prices.

d. Take a long position in the futures because rising interest rates lead to declining futures prices.

Correct Answer: c

Government bond futures decline in value when interest rates rise, so the housing corporation should

short futures to hedge against rising interest rates.

 

[David Harper CFA FRM]

Hi @Bester The government bond futures contract is quoted with a price just like the underlying bond is priced; i.e., the futures contract generally does not quote the rate but rather the price. In this way, the futures contract reacts directionally just like the bond that it hedges. The most fundamental bond relationship we need to know is that higher (lower) rates imply lower (higher) bond prices, simply because a higher (lower) discount rate gives us a lower (higher) present value for a given stream of cash flows (i.e., coupons). I hope that explains, thanks,

 

[Bester]

Thanks for the help.

 

[HPASI2304]

Hey @David Harper CFA FRM

Could you please explain why in this case the correlation between interest rate and the future price is positive and in this example, the relationship changes?

Regards!

 

[David Harper CFA FRM]

Hi @HPASI2304 What I wrote above is the more fundamental, relevant relationship ....

The government bond futures contract is quoted with a price just like the underlying bond is priced; i.e., the futures contract generally does not quote the rate but rather the price. In this way, the futures contract reacts directionally just like the bond that it hedges. The most fundamental bond relationship we need to know is that higher (lower) rates imply lower (higher) bond prices, simply because a higher (lower) discount rate gives us a lower (higher) present value for a given stream of cash flows (i.e., coupons). I hope that explains, thanks,

... because we hedge interest rate increases with a short position in interest rate futures. The Eurodollar futures contract typifies this because the quote price is 100 minus the rate. Or as Hull explains,

"When hedges are constructed using interest rate futures, it is important to bear in mind that interest rates and futures prices move in opposite directions. When interest rates go up, an interest rate futures price goes down. When interest rates go down, the reverse happens, and the interest rate futures price goes up. Thus, a company in a position to lose money if interest rates drop should hedge by taking a long futures position. Similarly, a company in a position to lose money if interest rates rise should hedge by taking a short futures position." -- Hull, John C.. Options, Futures, and Other Derivatives (2-downloads) (p. 144). Pearson Education. Kindle Edition.

On the other hand, the conversation over here is a "narrow" application of the cost of carry (COC) to retrieve the theoretical price of a T-bond futures contract. That exercise is just different and it's good to understand the difference! In cost of carry, the F(0) is an increasing function of the risk-free rate. But to use the contract, you'd still hedge a long (underlying) bond position with a short T-bond futures contract and its price would react per the fundamental dynamics. Thanks!