Interpreting Fixed-Income Carry Through Bond Roll-Down and Coupons
Summary
The discussion explains how a carry expression based on the spot and forward prices of a fully funded position relates to a bond’s one-period return. Under the simplifying assumption that yield to maturity stays unchanged, the bond’s value at the next date reflects its shorter remaining maturity and, when scheduled, a coupon payment. This gives the intuition for comparing the forward value with today’s bond price when defining carry.
The answer also connects carry to funding and cash flows in other markets: under its stated parity assumptions, a non-dividend-paying asset’s carry is associated with funding, while dividends or foreign interest income adjust that relationship. These are explanatory identities, not a general forecast of realized returns. The reasoning depends on the assumptions used in the cited paper, including unchanged asset prices or yields for the carry calculation, and does not examine risk premia, changing yields, or practical bond-market conventions.
Key ideas
- Bond carry can be interpreted through the change in value as maturity shortens and coupons are received.
- The explanation assumes the bond’s yield to maturity remains unchanged over the period.
- A coupon paid during the period contributes to the bond holder’s one-period value.
- Parity relationships connect carry to funding costs and, where applicable, dividends or foreign interest income.
- The stated relationships are assumption-dependent and do not account for changing yields or realized market risk.
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# understanding carry for Fixed Income Securities in Pedersen
# understanding carry for Fixed Income Securities in Pedersen
I'm following the famous paper Carry of Pedersen et al. I have a particular question about the section Global Fixed Income Carry.
My main questions are around equation 15. They define Carry as
$$C_t:=\frac{S_t-F_t}{F_t} (1)$$
for a fully funded position. My first question, why is this equivalent to for fixed income securities?
$$\frac{P_{t+1}^{T-1}+D\cdot 1_{[t+1\in \text{coupon dates}]}-P_t^T}{P_t^T} (2)$$
## Answer by Magic is in the chain (score 2, accepted)
https://quant.stackexchange.com/a/58990
As per the definition:
$C_t:=\frac{S_t-F_t}{F_t}$
Per the article, it should actually be: (tomorrow minus today ) divided by today:
$C_t=\frac{F_{t+1}-F_t}{F_t}$
but they assume price does not change so $S_{t+1}=S_t$. An equivalent assumption for the bond would be that the YTM does not change. But there are two predictable (model free) characteristics of bonds: it pays coupon and its maturity shrinks as time progresses. So tomorrow (t+1) the same bond will have one fewer day to maturity, and if tomorrow happened to be a coupon date, then the bond holder will get coupon as well, so the equivalent of $F_ {t+1}$ is $P^{T-1}_{t+1}+D (\,\mathrm{if}\; t+1 \;\mathrm{is \,coupon \,date}\,)$
Re-comment, the price of the asset or exchange rate is a random process so it will vary over time, and then there is the arbitrage/parity type relationship between the current price and the forward/future price. In the calculation of their carry, they assumed that the price remains constant over time, but the parity relationships are deterministic so they hold. If you have a non-dividend paying stock, then $F_t=S_t (1+r)$. If you substitute into the carry equation:
$C_t:=\frac{S_t-F_t}{F_t}=\frac{S_t-S_t (1+r^f)}{F_t}=-r^f \frac{S_t}{F_t}$
So the carry is minus funding rate. And if you have a dividend paying stock or FX, then $F_t=S_t (1+r)-E[D]$,so carry will be dividend minus the funding rate:
$C_t:=\frac{S_t-F_t}{F_t}=\frac{S_t-S_t (1+r^f)+E[D]}{F_t}=\left(\frac{E[D]}{S_t}-r^f \right)\frac{S_t}{F_t}$
So essentially they assume the price is not random over time, but parity type relationships hold.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.