How Bond Carry Can Offset Rising Yields in Monthly Returns
Summary
A bond can earn a positive total return over a month even when its yield rises. The explanation separates a bond’s return into the value gained as its cash flows get closer, price changes caused by yield movements, and coupon payments. The first effect is approximately proportional to bond price, yield, and elapsed time; the yield effect depends on modified duration and the yield change.
If the gain from time passing exceeds the price loss from a modest yield increase, total return can remain positive. Lower-duration bonds are less sensitive to yield changes, making this outcome more plausible. Coupon receipts also contribute to total return, although the bond price drops by the coupon amount on the payment date. These are approximations and a component-based explanation; the document gives no numerical market example or method for estimating returns under changing curves.
Key ideas
- A bond gains value as its remaining cash flows move closer, even if its yield does not change.
- A yield increase generally reduces bond price, with the effect scaled by modified duration.
- Coupon receipts contribute to total return, while the bond price falls by the coupon amount when paid.
- Time-related gains can exceed losses from a small yield rise, especially for a low-duration bond.
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Full text
# Positive bond returns and positive yield change in the same month # Positive bond returns and positive yield change in the same month Can a bond return over a month be positive while the bond also has a positive yield change for the month? How does this occur? ## Answer by Dom (score 1) https://quant.stackexchange.com/a/29750 The price change of a bond over a time period $dt$ is composed of: 1) An increase in value due to all coupons and principal repayment getting closer in time and so increasing their PV (assuming no yield change). This price change is roughly equal to $P .y . dt$ where $y$ is the bond yield and $P$ is the bond price. 2) An increase/decrease in value due to a decrease/increase in bond yields. This may be due to market moves. It will also include a component due to "roll-down" i.e. the tendency of the yield curve to be upward sloping such that as time passes, the corresponding yield declines. The size of the price change is $D . P . dy$ where $D$ is the modified duration of the bond. 3) Coupon payments when an amount $c/f$ is paid (coupon $c$ paid with frequency $f$). The bond price will fall by exactly $c/f$ across the coupon payment date. The coupon is a received payment that forms part of the period return and may be reinvested. A single period total return will take into account all of these. It is possible that the positive contribution of (1) can exceed the negative contribution of (2) if the yield increase is small and the bond duration is low, thereby resulting in a positive total return.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.