Estimating Bond Carry and Returns from Par-Yield Curves

Summary

The note outlines an approximate way to estimate bond forward prices and carry when the available inputs are government yields by maturity. It proposes treating the observed yields as par yields, so each yield also serves as the coupon rate for a hypothetical bond priced at par. With short-term interest rates, that bond can be used to calculate a forward price as a proxy for a futures price, with conversion-factor effects still requiring attention. Under this setup, carry is the difference between the assumed spot price and the forward price.

To estimate a holding-period return, reprice the hypothetical bond at the next period’s yield, keeping its coupon rate fixed while reducing its remaining maturity. The note gives no numerical example or empirical validation. Its approach depends on strong assumptions: par yields must be a reasonable proxy for the bonds of interest, and the simplified futures proxy does not capture all contract features, including delivery-option effects. Treat the resulting carry and return estimates as approximations rather than observed futures performance.

Key ideas

• Treat observed government yields as par yields to define hypothetical par bonds.
• Use short-term rates to estimate a forward price for the hypothetical bond.
• Approximate carry as the difference between spot and forward prices.
• Estimate holding-period return by repricing at the next yield with a shorter maturity and unchanged coupon.

Tags

# Calculation of Bond Carry from Synthetic future prices


# Calculation of Bond Carry from Synthetic future prices












I have only government bond yields with different maturities. How can I obtain sythetic future prices on bonds? After obtained the future prices, I am supposed to compute the return and carry returns.

## Answer by Helin (score 1, accepted)

https://quant.stackexchange.com/a/25559

This is pretty much impossible to do, but if you must, you'll have to make some assumptions.

You can assume that the yields given are par yields. In other words, they represent both the yield AND the coupon rates of bonds trading at par. And assuming you also have short-term interest rates, you can compute forward price on this hypothetical par bond and use that as the basis for futures price (you won't need to worry about delivery option, but you still have to account for the conversion factor). Carry is simply the difference between spot price (assumed to be 100) and forward price.

To compute returns, you take this bond and reprice at at the next period (i.e., holding coupon rate constant and reducing time to maturity, you reprice it at the new yield). That allows you to compute returns.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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