Estimating Treasury Futures Gross Basis from a Forward Bond Price

Summary

The document explains how to estimate a Treasury futures contract’s gross basis at a future date when the forward bond price is known. Gross basis is the bond’s clean price minus the futures price multiplied by the bond’s conversion factor. Since the conversion factor is fixed, the estimate also requires an assumption about the futures price; the response holds it unchanged for the estimate. The forward bond price is calculated from today’s bond price using the repo rate and the fraction of a year to the forecast date.

The note distinguishes this forward gross basis from net basis. Net basis compares prices at settlement, so a forward gross basis is not necessarily the forward net basis unless the forward bond price used corresponds to the delivery settlement price. The explanation gives a simple framework rather than a complete forecast model: it does not model changes in futures prices, repo rates, delivery options, or other market conditions that could affect the basis estimate.

Key ideas

• Gross basis equals the bond’s clean price minus the futures price multiplied by its conversion factor.
• A forward gross basis estimate needs a forward bond price and an assumption for the futures price.
• The conversion factor is treated as constant over the forecast horizon.
• The forward bond price can be estimated by applying the repo rate over the relevant time fraction.
• Forward gross basis and forward net basis differ unless the forward price reflects delivery settlement.

Tags

# How do you calculate or estimate the future gross basis of a treasury future?


# How do you calculate or estimate the future gross basis of a treasury future?












Gross Basis for treasury futures = clean price - future price* conversion factor

Is there a way to estimate the gross basis, say 10 days from now, given that you know what the forward bond price is?

Conversion factor is constant as well.

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/44382

Gross basis today is as your formula: $$GB_{today} = P_{today} - F*C_f$$ Forward gross basis depends on the future price of the bond: $$GB_{forward} = P_{forward} - F*C_f$$ The important part being the futures price is not expected to change. You stated you know what forward price is but for clarity it is: $$P_{forward} = P_{today} * (1 + dayfrac * reporate)$$

Net basis is the difference between the two prices measured at settlement, so the forward net basis does not equal the forward gross basis unless your forward price is the delivery settlement price.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.