# Impact on DV01 of cbot bond futures by changing coupon from 6% to 4%

CBOT has been asking customers lately what their thoughts would be on coupon change from 6% to 4% on all bond futures. I believe the last time this was done was in 2000 where the coupon was changed from 8% to 6%.

My question is, how would this impact the DV01 of the contracts themselves? I believe it reduces the DV01 (requires more contracts to be traded vs same number of actual cash bonds) but not 100% sure.

Thanks!

• Super interesting news... do you have a reference at all (a quick google search has failed me...)? Oct 22 '20 at 1:03
• There is an article about it on risk.net but unfortunately, I do not have a subscription. Oct 22 '20 at 1:42
• risk.net/derivatives/7695186/… this one? Oct 22 '20 at 6:01

## 1 Answer

It's complicated.

Assuming there is no CTD switches, then yes, the theoretical modified duration should be unchanged and the DV01 will be lower.

For simplicity, imagine that there is only one bond eligible for delivery into the contract. We'll also ignore all the other complications (e.g., variation margins), then the theoretical futures price is simply the converted forward price of the bond: $$f = \frac{\text{Bond forward price}}{\text{Bond conversion factor}}.$$

Recall that the conversion factor is approximately the price of a bond assuming its yield to maturity as of the first delivery date is 6%. If we change this to 4%, then the conversion factor will increase, resulting in a decline in $$f$$, as well as its dollar sensitivity.

For a numerical example, I took the current TY contract (TYZ2020 as of 10/21/2020) and ran some simulations. The left column below shows the current market pricing; the right column shows the model price and duration metrics if the notional coupon is changed to 4% today.

The next table shows the individual deliverables for TYZ2020, including their current conversion factors as well as the theoretical conversion factors at a 4% notional coupon. Notice that the converted forward DV01s are lower, as expected.

However, it's completely plausible that a lower notional coupon does result in a CTD switch. Right now, because yields are so low and curve is upward sloping, CTDs tend to be the higher coupon, lower duration issues. If yields were to rise (meaningfully from current levels) AND notional coupon is adjusted lower, then it's completely plausible for CTDs to move to longer maturity issues, actually increasing both the duration & DV01 of the contracts.

To see this, I shocked the yield curve by 400 bps. The table below shows the delivery probabilities and converted forward DV01s. As you can see, at a much higher yield level, changing the notional coupon actually causes a significant CTD switch into longer maturity bonds, increasing duration.

• I believe this would also reduce the value of the wild card option, which has attained significant value on longer contracts such as WN in recent months. Do you agree?
– dm63
Oct 22 '20 at 10:20
• A higher conversion factor would reduce the amount of tails you’d have to sell out of if CF<1 and market rallies post 3pm so I would agree it would reduce the wildcard value. Oct 22 '20 at 10:45
• For example, you'd have to sell 1-CF worth of tails (either in the form of futures or equivalent bonds) out to hedge your DV01 post 3pm in the case where CF<1 and the market rallies(higher bond px) post 3pm. You want 1-CF to be as large as possible to lower your breakeven wildcard level, if that makes sense. Oct 22 '20 at 10:54