EUR-hedged ETFs

For some indices (the S&P 500, for instance) and for global ETFs, a monthly EUR hedged historical series is constructed. The model simulates a euro-based investor hedging currency risk through FX forward contracts on a basket of currencies, extending the simulation back before UCITS ETFs with built-in hedging existed.

The pipeline in 3 steps

1. Starting point: local currency

Start from monthly returns in EUR quotation and remove realised FX, weighted across each leg of the basket (historical end-of-month FX rates), yielding a local-neutral return $R_{\text{asset}}$. For baskets that are entirely USD this is equivalent to a EUR→USD conversion. Only then is the synthetic carry applied.

2. Carry from interest rates

Each month, weighted carry based on Covered Interest Rate Parity (CIP) is added, with a one-month lag. If the basket is 100% a single currency, the calculation matches the textbook EUR–currency differential.

3. Frictions and roll costs

An annual hedging cost is subtracted, set by default at ~1% to cover cross-currency basis swaps, forward spreads and structural frictions, plus a roll cost where requested. The result is a cumulative euro index comparable with real ETFs.

The monthly formula

Monthly return of the hedged index, in monthly percentage points:

$r_t = R_{\text{asset}} + \sum_i w_i \frac{r^{c_i} - r_{\text{EUR}}}{12} - \frac{c_{\text{hedge}} + c_{\text{roll}}}{12}$

Legend:

• $R_{\text{asset}}$: local-neutral return (EUR quotation minus basket-weighted realised FX).
• $w_i$: weights of individual currencies in the FX basket ($\sum_i w_i = 1$). In the platform these can derive from the ETF's real currency exposure.
• $r^{c_i}$ and $r_{\text{EUR}}$: annualised short-term rates for the foreign currency and the euro.
• $c_{\text{hedge}}$ and $c_{\text{roll}}$: annual drag costs, in decimals.

Why carry isn't just the rate spread

In pure theory (CIP), the price of an FX forward depends solely on the interest rate differential between the two currencies. In real markets the cross-currency basis swap intervenes: a structural premium tied to asymmetric funding demand, which became particularly pronounced and persistent for the dollar after the 2008 crisis.

That premium almost always translates into an additional cost for euro holders hedging foreign currencies. To reflect this structural inefficiency, the model includes the fixed parameter $c_{\text{hedge}}$ (~1% by default) on top of official rates, calibrating it against real listed hedged ETFs as soon as data becomes available.

Data sources: rates and FX

Short-term rates used for carry come from public rate databases and the OECD, selected according to historical availability.

Historical continuity: since the euro did not exist before 1999, the German mark (DEM) is used as the euro-area benchmark and proxy for discount and interbank rates across that earlier history. See also The euro before 1999.

How to read the result

Hedging doesn't remove risk, it swaps it. Three things to keep in mind when comparing a hedged version with an unhedged one:

• Carry can be positive or negative. When foreign rates exceed euro rates, hedging costs; in the opposite situation it can actually add return. It isn't a fixed-premium insurance policy.
• The hedge is on the currency, not the asset. A hedged S&P 500 ETF remains fully exposed to the US equity market.
• Over very long horizons the currency effect tends to wash out, while the hedging cost is paid every month. That's why hedging long-horizon equities has historically rarely paid off, whereas on bonds, where currency can dominate the return, the logic runs the other way.