Eurodollar futures and duration based hedges

[RaamZen]

Hello,

Can you explain how did the solution below arrived to short the contracts. I was thinking other way round ie., long the contracts and couldn't get it whether it should be long / short.

Question:
173.2. A portfolio manager wants to hedge her bond portfolio this is worth $30 million and will have a duration of 6.0 years at maturity of the hedge in a few months. The relevant U.S. Treasury bond futures price is 95-12 and the cheapest-to-delivery (CTD) bond will have a duration of 9.1 years at hedge maturity. What is the trade that hedges against interest rate movements? a) Long 57 contracts b) Long 207 contracts c) Short 57 contracts d) Short 207 contracts

Answer:
Number of contracts (N*) = (Portfolio value * duration of portfolio) / (futures contract price * duration of futures contract underlying bond). In this case, N* = (30,000,000 * 6.0 ) / (95,375 * 9.1) = 207.39; i.e., short 207 contracts

 

[Deepak Chitnis]

Hi @RaamZen, I am not 100% sure but, portfolio manager own the bond of $30 million, so need to hedge against decline of the price. Whenever you own the portfolio with shares or bonds you need to short the position because you are hedging downsides. I think this link will help you https://forum.bionicturtle.com/...portfolio-beta-with-stock-index-futures.4449/. I hope that helps. Thank you

 

[Dr. Jayanthi Sankaran]

Hi @RaamZen,

Question:

173.2. A portfolio manager wants to hedge her bond portfolio this is worth $30 million and will have a duration of 6.0 years at maturity of the hedge in a few months. The relevant U.S. Treasury bond futures price is 95-12 and the cheapest-to-delivery (CTD) bond will have a duration of 9.1 years at hedge maturity. What is the trade that hedges against interest rate movements? a) Long 57 contracts b) Long 207 contracts c) Short 57 contracts d) Short 207 contracts

If V(F) = Contract price for one US T-bond futures price contract
D(F) = Duration of the bond portfolio underlying the futures contract at the maturity of the futures contract
P = Forward value of the bond portfolio being hedged at the maturity of the hedge (in practice, this usually assumed to be the same as the value of the portfolio today)
D(P) = Duration of the portfolio at the maturity of the hedge

If we assume that the change in the yield, dP/dY is the same for all maturities, which means that only parallel shifts in the yield curve can occur, it is approximately true that

dP = -P*D(p)*dY

It is also approximately true that

d(V(F)) = -V(F)*D(F)*dY

The number of contracts required to hedge against an uncertain dY therefore is

N* = P*D(p)/V(F)*D(F) = $30,000,000*6.0/95, 375*9.1 = 207.39 ie. short 207 contracts. Since the portfolio manager is long the bond portfolio of $30,000,000, in order to hedge, she must short 207 T-bond futures contracts.

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.

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Thanks for the help here @Deepak Chitnis and @Jayanthi Sankaran
FYI, there is additional discussion in the source at https://forum.bionicturtle.com/threads/l1-t3-173-eurodollar-futures-and-duration-based-hedges.4570/

 

[RaamZen]

Thanks much for the detailed explanation, that makes clear.