Use Case — FX Hedge

PM question

A USD-based fund holds €10,000,000 of EUR-denominated bonds. Should the currency exposure be hedged back to USD, and what does that hedge cost?

Concepts

covered interest parity, FX forward rate, FX carry, hedge sizing.

First exercise

Spot = 1.10 (USD/EUR), r_USD = 5%, r_EUR = 3%, hedge horizon = 1 year.

Hand-calculate: 1. the 1-year forward rate (pm.fx.fx_forward_rate) 2. the carry given up by hedging (pm.fx.fx_carry) — is it positive or negative for a USD investor here, and why? 3. the forward notional needed to fully hedge the €10,000,000 exposure (reuse pm.fixed_income.duration.hedge_ratio — for a 1:1 forward contract, the "hedge instrument DV01" is just 1 unit of notional, so the hedge ratio reduces to the exposure itself)

Extend

Reprice the hedge if r_EUR rises to 4.5% (EUR rates catching up to USD) — does the forward rate move toward or away from spot, and what happens to the cost of staying hedged? See reference/fx/spot_and_forward.md and fx_carry.md.