# Treasury Bond Futures

I’ve thought about this some and rather than continue to rack my head I thought I would ask on here. There is probably a reason and I’m not thinking of it.

I’m using schweser to study and they present the the formula to obtain a futures price of a treasury bond future as this:

FP=bond price x (1+riskfree)^T - FVC

The formula makes sense to me and I understand the reason for adjusting for the future value of the coupon payments. But why can’t the formula be rewritten this way:

FP=(bond price - PVC) x (1+riskfree)^T

When calculating stock futures (of individual stocks and indexes) and forwards the text presents an option of doing it either way. It even presents using this second format when calculating forward prices for treasury bonds. Am I missing something right in front of me? I checked the CFA material and they only present the equation one way as well (the first formula). Thanks.

Clay

I think you can use both. Either way they are the same thing.

PVC * (1+rf)^t = FVC so Bond Price * (1+rf)^t - FVC = (BondPrice-PVC) * (1+rf)^t both are the same, and either can be used, depending on what you have been given in the problem statement.

There is one thing to understand which I forgot to mention. In case of stocks the dividend schedule is given. If you are using PVD then you need to discount the dividends to the date of valuation while if you are using FVD then you need to calculate the dividend value from the date when they will be realized to the contract expiration date. The time horizon is different sometimes for calculating PVD and FVD. If dividend is going to be realized 3 months from now then PVD is calculated by discounting the dividend for 3 months time. Whereas if the contract will expire in 9 months from now then the FVD will be calculated by compounding the dividend for 6 months time. This is the thing which I found tricky and even did a mistake while doing such questions. Same could be applied to Coupons.