How do I hedge yield spread?

We'd like to offer a product in which a notional amount $$(N)$$ is given, and the underlying is spread $$(s)$$ defined as, say, 30Y yield minus 10Y yield (both from treasury YTM yield curve). At the end of the trade, we give the client $$N \cdot(s_t-s_0)$$ in exchange for a transaction fee equal $$N$$ times some bps.

How can I hedge my position?

More detials: our product is likely to be casted into a total return swap (TRS) form. And we also offer early termination option but based on mutual negotiation and usually incur a punishiment fee for client if it happened(i.e., makewhole). Another termination condition is when the spread is moving in opposite direction, e,g, if the investor makes a bet the spread will widen, but it siginificantly narrows after entering the contract, then we will early terminate (or asking for more collateral, but I guess the design of such is again based on the hedging part).

• So just a CMT steepener structured note? Or this is on specific bonds? – user42108 Mar 31 at 15:10
• @user42108 Hey my friend, I added some details to my question. For now, the underlying is the spread of two key rates on yield curve and with a single notional to calcculate return. It's fine I guess to use specific bonds (on-the-run/ctd I guess) to hedge our position, but i've also heard products that offer two notionals with underlying as two specifc treasuy bonds in the market. I feel like in the latter case, the investor need to balance dv01, I dunno. – Nicholas Apr 1 at 1:12
• You might want to have a look at Howard Corb's book which has a chapter on structured notes, including range accruals / non-inversion notes (related to what you want to do). cupola.columbia.edu/978-0-231-15964-7. – user42108 Apr 1 at 14:39
• Really appreciated@user42108 – Nicholas Apr 2 at 1:55

Is this all that there is to this product, no early termination, no embedded caps, floors, minimums, maxiumums, or any other optionality? If the curve inverts so much that 10Y>30Y at time t, will the client pay you instead?

As currently described, the cash flow at t simply has sensitivities to two yields that no one knows now: 10Y+t and 30Y+t.

To hedge the 10Y+t sensitivity, you can short some 10+t cash treasuries to exactly offset it.

To hedge the 30Y+t sensitivity, you can buy now some 30Y cash treasuries (because this is the longest maturity available). If t is far enough in the future, you occasionally sell this and buy the on the run 30Y when they are issued.

You could also use exchange-listed futures instead of cash treasuries.

All these transactions have costs, not exactly predictable, that your fees should cover.

• Hey Dimitri, firstly thanks for the answer. For more details: our product is casted into a total return swap (TRS) form. And we also offer early termination option but based on mutual negotiation and usually incur a punishiment fee (i.e., makewhole). Another termination condition is when the spread is moving in opposite direction, e,g, if the investor makes a bet the spread will widen, but it siginificantly narrows after entering the contract, then we will early terminate. – Nicholas Apr 1 at 0:58
• And yes the final return is two-way for the investor since the difference of $s_t$ and $s_0$ can be positive as well as negative, however, as mentioned above, if it gets very negative, it might trigger early termination (or the investor needs to provide collateral for the trade to continue). – Nicholas Apr 1 at 1:17
• Could you elaborate on the trade direction a bit? Why long 30Y and short 10Y given that we pay our client $N \cdot(s_t-s_0)$? If the curve steepens, say, 30Y goes up, bond price goes down, shouldn't we short 30Y instead, similarly, long 10Y? BTW, why enter 10+t treasury? How is it related to $N$ times the absolute drop amount of 10Y rate? Lastly, how do I decide the size of long and short position? – Nicholas Apr 1 at 5:05
• "how do I decide the size of long and short position?" - you're paying the client \$N per bp so you trade the same DV01 in 10s and 30s to offset. – user42108 Apr 1 at 14:44
• don't forget about convexity! – Edward Watson May 2 at 0:05