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# Long hedge versus short hedge

#### akrushn2

##### Member
1. Posting this here. About long and short hedges. https://www.bionicturtle.com/forum/...short-hedges-hull-chapter-3.10546/#post-77932
2. As per this thread short hedge means long basis which means that if the basis strengthens we gain. I.e. the logic is that b/c i go long the spot and sell the futures this means that I will gain if spot goes up. This isn't really true though. Lets think of it from a treasury futures contract. If I am short a treasury futures I have a treasury bond that I need to deliver. If the spot price of this bond goes up I need to deliver a higher priced bond in exchange for a lower priced futures invoice price. How am I gaining from this?

If someone could clarify this point that would be much appreciated.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @akrushn2 The cheapest to deliver (CTD) option is a complication but I think the basic idea that a "long (short) hedge is long (short) the basis" still applies in T-bonds. If you are a bond manager with a long position in long-duration bonds then your exposure is to an increase in interest rates so you might short T-bond futures contracts (which will increase in value if the interest rate drops). Your net position is: long bond + short T-bond futures contacts; aka, short hedge. This is long the basis because your still (stylistically only, okay?) B = +S - F. If rates drop, then bond price increases; and a basis strengthening would be (eg) if the future price decreases less than the bond increases. Or, if rates increases so your bonds drop, but say your futures increased more than expected (aka, overhedge) such that you do better by way of the unexpected basis strengthening. The linked thread concerns commodity basis, wherease the T-bond basis is more complicated due to the CTD. Here is a good resource https://www.dropbox.com/s/t0l1ecfilezequa/understanding-treasury-futures.pdf?dl=0

#### akrushn2

##### Member
Hi David,

"So you might short T-bond futures contracts (which will increase in value if the interest rate drops)". I just want to be careful about the arrangement of this sentence to make sure I am understanding you properly. The increase in value if interest rate drops pertains to your position of long duration bonds and not shorting of t bond futures right? Because short futures contracts will only have benefit to the short party if interest rates increase. Just want to be careful about the wording here.

It sounds like you are saying that this idea of basis is more relevant to commodities than treasury bond futures? even then I still have trouble trying to understand how a higher priced spot than I am going to need to give up at some point in the future to receive a lower priced futures is a good thing for me. I guess it kind of makes sense if I think about it as basis strengthening as meaning that my futures doesnt decrease by too much or basis weakening as futures not increasing by as much as I expected. can I know what situations in the commodity world would cause this to happen?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @akrushn2 No, I'm including T-bonds which are an investment asset commodity, so they should fit the logic along with all the consumption commodities. Basis risk is firstly a mark-to-market risk. Basis strengthening/weakening is a dynamic over time, from today until maturity. I'm saying: say you are the bond manager who is long $10.0 million (e.g., similar to Hull's EOC Q 6.17) and, for convenience's sake, the T-bond future contract happens to be exactly$100.00. At the hedge horizon, your portfolio's duration is estimated (will be) to be 9.0 years. Your hedge will estimate the cheapest-to-deliver bond (by definition, it isn't known with certainty when you put on the hedge) will have duration of 10.0 years. Per the duration-based hedge, you will short \$10,000,000/100,000 * (9 yrs/10 yrs) = 90.0 T-bond contracts. You have a value on the underlying exposure and a (dynamic) price on the T-bond that hedges. What happens if:
• Interest rates increase (the risk to the exposure): value of portfolio and price of futures contract decreases, but you are short the futures contract so your T-bond short position increases in value, thereby hedging.
• Interest rates decrease: value of long portfolio and price of futures contract both increase, but you are short the futures contract so the value of your short position decreases. As far as I can see, B = S - F still applies. In this rate decrease scenario, an unexpected basis strengthening would include when (for whatever reason) the futures T-bond contract price dropped less than anticipated, so you lost less on the hedging contract here.
Indeed there is another "basis risk" with respect to the cheapest-to-deliver "option" in the futures contract but I think that's second order (e.g., if the anticipated CTD bond were to change along the way, we could expect this to create strengthening/weakening) and i don't see how it can be analyzed if we aren't clear firstly on the ordinary basis risk between the exposure (in this example, long a bond portfolio) and the hedge (in this case, short T-bond futures contracts). I hope that helps,

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#### akrushn2

##### Member
Thanks David, I think I understand this better now.