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Estimating FX-Hedged Bond Yield from Forward Carry

Article Quant Q&A · Author: VanillaCall
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Summary

The document outlines a practical estimate for the yield on a US Treasury bond hedged into euros. For a quarterly hedge, the notional is set slightly above the bond’s current value to reflect the expected increase in bond value over the hedge period. The hedge carry is then estimated from the forward premium or discount relative to spot, scaled by that projected notional. Subtracting this cost from the bond yield gives a rough hedged-yield estimate, with care needed when converting quarterly amounts to annual terms.

If forward rates are unavailable, the forward can be inferred from the interest-rate differential between the two currencies, adjusted for the cross-currency basis. A more exact approach converts every bond cash flow into euros using corresponding FX forward rates and computes yield from those converted cash flows. The rough estimate can leave residual currency exposure because the bond return used to size the hedge is uncertain; the document gives no market data or worked valuation beyond an illustrative notional adjustment.

Key ideas

  • A hedge notional can account for the bond’s estimated value at the end of the hedge period.
  • Forward carry relative to spot provides an estimate of the FX hedging cost.
  • Subtract estimated hedge carry from the bond yield, using consistent annualization.
  • Interest-rate differentials and cross-currency basis can help infer a forward rate.
  • Converting all bond cash flows at their matching forward rates gives a more exact hedged yield.

Tags

Fixed incomeForexCarryDerivatives pricing
Full text
# How to calculate FX hedged bond yield?


# How to calculate FX hedged bond yield?












How does one go about calculating a 10 year US treasury yield hedged back to EUR? I vaguely understand this but I think there's two methods

1) Calculate 3-month annualized hedging cost 2) Calculate the difference between 3-month USD libor and 3-month EUR and then add in the cross currency???

## Answer by Alex C (score 0, accepted)

https://quant.stackexchange.com/a/37407

When you hedge 1 million in bonds, you do not enter into a 1 million forward, but a slightly larger number H, where H = 1 + estimated return on the bond in next 3 months. (I.e. you have to hedge now based on what the bond position will be worth 3 months from now). The bond return, in turn, is usually estimated from the bond yield. (If the bond yield is 2% then $H\approx 1+0.02/4=1.005$

The "carry from the hedge" i.e. essentially the cost of hedging is ex ante equal to $H*\frac{FWD-SPOT}{SPOT}$ where FWD and SPOT are the forward and spot rates now (at the beginning) of the quarter. The ex-post cost will also include an error term because the H you used will turn out to be not quite correct, so you had a small exposure to FX after all.

In any case a rough and ready estimate for the hedged yield can be had by subtracting $H*\frac{FWD-SPOT}{SPOT}$ from the yield of the bond, having care to convert between quarterly and annual figures.

If you don't have $FWD$ then you can calculate it as you mention from the difference of the two Libors plus the cross currency basis, but that is a more roundabout way.

## Answer by gavbrennan (score 2)

https://quant.stackexchange.com/a/37258

An exact approach would be to calculate all the cash flows in USD, calculate their EUR equivalent using forward fx rates and then compute a yield from the EUR flows

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.