# Treasury futures basis & calendar spd [multiple questions]

How do I determine if a bond will become CTD in a futures contract and how likely there a CTD switch is?

Also, how do you use implied repo/actual repo to assess richness/cheapness of two calendar spreads (June vs September)

• A good way to identify CTD is by computing each deliverable's implied repo rate minus its actual repo rate. The deliverable with the highest implied-to-actual repo spread is usually taken as the CTD. (Some investors use the bond with the lowest net basis as CTD. Don't – this can occasionally be unreliable!)
• To identify CTD switches, perform scenario analysis as @dm63 suggested. Popular scenarios include: 1) bump all yields in a parallel way by $x$ basis points; 2) bump the on-the-run/CTD yield by $x$ basis points, and bump the yields of other issues based on their yield beta to on-the-run/CTD; and 3) build a 2D grid that separates shifts in yield levels and curve reshaping. Computing the probabilities of CTD switches require a delivery option model (see below).
• Typically, if implied repo rate is greater than actual repo, futures are rich. However, if implied repo is less than repo, futures are cheap ONLY IF you ignore the switch option. As a result, using implied repo rates to assess richness/cheapness can be misleading.
• Instead, you should build a delivery option model that properly prices your contracts (an outline is available here). The futures/calendar spread rich/cheapness can be ascertained from these models. These models also allow you to properly account for potential CTDs that haven't been auctioned yet. (At the time of this writing, the TY calendar spread faces this exact issue, since a highly likely CTD for the back contract, TYM2018, has yet to be auctioned.)
• Thanks, how were you able to quickly determine that the yet to be issued bond is likely the CTD for the TYM2018. – VanillaCall Feb 18 '18 at 13:22
• A follow up question would be how does this potential switch affect the price of the TYM2018 (back contract). My thought would be that the future price would be lower and the net basis (current CTD bond minus futures price) would be larger due to this uncertainty/risk..... – VanillaCall Feb 18 '18 at 14:23
• You need to make assumptions about its coupon rate, yield spread, and term repo rates; it's not difficult to make educated guesses about these quantities. Then you simply introduce this hypothetical bond into the deliverable basket and compare it against others. More complex models can be devised to account for uncertainties in these quantities (should be easy if you have a delivery option model). Assuming that switches can happen between this unauctioned note and other deliverable, then yes, futures price would reflect that. – Helin Feb 20 '18 at 4:03
• Why is using net basis unreliable? I've been checking this on Bloomberg and the trader next to me just looks at the lowest net basis to get the CTD of the security. Also, if implied repo is less than repo, then futures are cheap only if you ignore the switch option. Is this because if there is a switch option, this optionality results in a lower futures price (to compensate the longs) and the implied repo is higher? – VanillaCall Aug 18 '18 at 12:27

To answer the first question, many people like to use scenario analysis. Check what is the CTD if rates move up or down 50bp for example. That will give you a sense of the likelihood. Sometimes the CTD switches on a curve move, so you should also check flatteners and steepeners.

For the second question, I think you should calculate the net basis of each contract using the actual repo, then the contract with the highest net basis is the expensive one.

Implied repo is the return you get by shorting the futures and buying the underlying security (cheapest-to-deliver). In order for you to buy the security, you have to finance it in the repo market and this cost is the repo rate you pay buy borrowing cash against the collateral that you post. If implied repo is greater than actual repo rate, your return from the cash/carry trade (buy buy, sell futures) is higher than the cost of financing. In this scenario, futures are rich and the CTD is cheap.

Implied repo is your return for shorting the future and buying the deliverable bond. At the same time, the CTD is determined by the lowest net basis, which is your cost adjusted for carry. The bond with the highest implied repo and the lowest net basis is your CTD.

You can use scenarios to determine a switch (-10bp, +10bp, -20bp, +20bp etc).