I would like to know how I can calculate the yield of a bond futures contract(say the 5 yr treasury "FVM05" is trading at 108.2)? I am not sure how to go about calculating the yield of the futures contract?
Need some guidance in doing so.
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There's a lot of intracacies involved and you've got several options. Let's go through an example, using the current front-month 5-year contract FVU6 (FV expiring in September 2016).
CTD Yield: The cheapest-to-deliver ("CTD") into FVU6 is the 1.625s of 11/30/2020 and its yield to maturity as of last close is 1.075%. You can simply use this as a proxy as the futures yield. This may seem dumb, but it's actually the one of the most prevalent choices in time series analyses. It works particularly well when the futures contract is fairly priced relative to cash bonds and the CTD is highly likely to be delivered into the contract (as it stands, 1.625s of 11/30/2020 has 100% delivery probability).
CTD forward yield: Given that a futures contract more closely resemble a forward, it is natural to calculate the forward yield of the CTD. You can calculate the forward price for the CTD using the cash-carry formula, assuming that the forward date = delivery date (10/5/2016 in this case). The forward price can then be converted back into a forward yield. For FVU6, we'd have 1.105%.
Futures implied yield: You can also calculate the so called futures implied yield. This is computed by assuming that the forward price of the CTD is the futures price multiplied by the conversion factor. In this case, the futures price is 121.46875, while the conversion factor for the 1.625s of 11/30/2020 is 0.8408, so you would assume that the CTD's forward price is $121.46875 \times 0.8408 = 102.130925$. Then you simply calculate the yield to maturity, assuming that the settlement date is the delivery date (10/5/2016), which nets you a yield of 1.099%.
These methods above assume that the CTD will not change between now and the delivery date. If that's not the case, you may want to calculate an average yield, weighted by CTD delivery probabilities.