Currency Risk in a Portfolio: Hedged vs Unhedged

You can price a currency pair, read a forward, recite covered interest parity in your sleep, and explain why the carry trade pays until it doesn’t. Now the practitioner’s payoff: what happens when you actually own foreign assets? The uncomfortable truth is that the moment a US investor buys a German stock, they didn’t make one bet — they made two. They’re long the stock and long the euro, whether they meant to be or not. This lesson is about finding that hidden currency bet, measuring it, and deciding what (if anything) to do about it. Everything you’ve learned — forward points, CIP, carry, safe-haven flows — comes back to do real work here.

Where currency risk hides

Analogy. Buying a foreign asset is like ordering a meal priced in a foreign currency on a credit card. The menu price (the local return) is one thing; the exchange rate your bank applies when the bill posts is another. You can love the meal and still get burned by the conversion — or get a pleasant discount. Either way, you signed up for both prices the moment you ordered.

Definition. When you hold an asset denominated in a foreign currency, your total return has two sources: the asset’s local return (how it performed in its own currency) and the FX return (how that currency moved against your home currency). A US investor in a German DAX stock is simultaneously long the stock and long the euro — if the euro weakens, part of their gain evaporates on the trip home, even if the stock did nothing wrong.

This is why “I just want exposure to European equities” is a slightly naive statement. Unless you do something about it, you’ve also taken a directional view on the euro — one you may never have intended and certainly aren’t being paid a risk premium to hold.

Decomposing the return

Analogy. Think of your foreign return as a two-stage relay. The local asset runs the first leg (its return in its own currency); the exchange rate runs the second leg (converting that result back home). Your final time is both legs combined — and a slow second leg can spoil a brilliant first.

Definition. If $r_{local}$ is the asset’s return in its own currency and $r_{fx}$ is the home-currency return on that foreign currency (how much it appreciated against your home currency), the total home-currency return is the compounding of the two:

$r_{home} = (1 + r_{local})(1 + r_{fx}) - 1$

Multiplying out:

$r_{home} = r_{local} + r_{fx} + r_{local}\cdot r_{fx}$

The first two terms are the headline story; the last term, $r_{local}\cdot r_{fx}$, is the small cross term (the return you earn on the gain itself, re-valued by the currency). For modest moves it’s tiny and the handy approximation is just:

$r_{home} \approx r_{local} + r_{fx}$

Worked example — the European stock and the falling euro

A US investor buys a European stock. Over the year it returns +10% in euros, but the euro falls 8% versus the dollar (so $r_{fx} = -0.08$). What did the US investor actually earn in dollars?

The exact dollar return is +1.2%, not the +10% the stock “earned.” The approximation (+2%) is in the right ballpark but overstates it by the 0.8% cross term — here the cross term is negative because the gain itself got marked down by the weaker euro. A double-digit local win became a barely-positive dollar year, purely on the currency leg. That gap is currency risk, made concrete.

To hedge or not

Analogy. Currency exposure is like background hiss on a recording. It rarely makes the music better — over the long run currencies have roughly zero expected return — but it definitely adds noise. Hedging is the noise-cancellation switch: flip it and the hiss drops, often without touching the melody. The catch is that the switch isn’t free, and sometimes the “hiss” is actually a useful counter-melody (more on safe havens later).

The core argument for hedging. Over long horizons, a developed-market currency has approximately zero expected return — exchange rates wander but don’t reliably trend up or down for a diversified investor. Yet currencies are volatile. So FX exposure adds variance without adding expected return — the worst trade in finance. Stripping it out via hedging can therefore reduce portfolio risk “for free” in expected-return terms. That’s the textbook case for a 100% hedge.

The arguments against. Hedging isn’t costless:

• It has a cost or carry (next section) — selling your foreign currency forward locks in the interest differential, which can bleed money.
• It creates cash-flow noise: the hedge is marked to market, so it generates gains and losses that must be settled in cash even when the underlying asset is untouched.
• It removes diversification: currency moves aren’t perfectly correlated with your assets, so some FX exposure can actually dampen total volatility — especially safe-haven currencies that rise in crises.

The conventional split. Practitioners usually resolve it by asset class:

The logic is all about relative volatility. For a low-volatility asset like a bond, currency risk dominates and is worth removing. For a high-volatility asset like equity, currency risk is a minor passenger and may even improve diversification — so many investors leave it on.

The cost (or carry) of hedging

Analogy. Remember from CIP that a forward isn’t a forecast — it’s today’s spot adjusted by the interest differential. Hedging just uses that forward, so hedging inherits the carry. It’s like renting a self-storage unit priced by your neighbourhood: hedge a “high-rent” (high-rate) currency and you pay a premium for the protection; hedge a “low-rent” (low-rate) currency and the landlord actually pays you to store there.

Definition. To hedge a foreign holding you sell the foreign currency forward (you’ll convert back home later, and the forward locks that rate now). By covered interest parity, the forward rate differs from spot by exactly the interest-rate differential — the forward points from lesson 3. So:

• Hedging a currency with a higher interest rate than your home currency means selling it forward at a discount (forward points against you) → hedging costs you carry.
• Hedging a currency with a lower interest rate means selling it forward at a premium → hedging pays you carry.

The sign is just the carry trade in reverse. The carry trade earns the differential by holding the high-rate currency; hedging that currency away gives back that same differential. There is no free lunch — and no free hedge either, but the “cost” can be negative.

Worked example — hedging cost from the rate differential

A US investor (home rate 5%) holds a UK equity position worth £1,000,000 and decides to hedge the pound. The UK rate is 6% (higher than the US). They sell £1,000,000 forward one year. Spot is $1.2500 per pound. By CIP, the one-year forward is roughly:

$F \approx S \times \frac{1 + r_{home}}{1 + r_{foreign}} = 1.2500 \times \frac{1.05}{1.06}$

Because the pound is the higher-rate currency, the investor must sell it forward at a discount — locking in a price about 0.94% below spot, almost exactly the −1% rate differential ($5\% - 6\%$). That’s a roughly 1%/year drag on the hedged position: the price of removing GBP risk. Flip the rates (hedge a low-rate currency like the yen from a high-rate home base) and the same arithmetic turns the drag into a pickup — the hedge pays you the differential.

When to weigh the cost

If hedging a currency pays you carry (low-rate foreign currency), the decision is easy — you reduce risk and get paid, so hedge. If hedging costs carry (high-rate foreign currency), you must judge whether the volatility reduction is worth the drag. For a low-vol bond portfolio the drag is almost always worth eating; for a high-vol equity portfolio where FX is a minor passenger, a 1–2%/yr hedging cost can be a poor trade — another reason equities are often left unhedged.

The hedge ratio

Analogy. The hedge ratio is the volume knob on your currency exposure: 0% (unhedged, full hiss), 100% (fully hedged, dead silent), or anywhere in between. The interesting setting is rarely either extreme — it’s the spot where total portfolio noise is lowest, which depends on whether the currency’s wobble adds to or cancels the asset’s wobble.

Definition. The hedge ratio is the fraction of your foreign-currency exposure you offset with forwards:

• 0% — unhedged: keep the full currency bet (and any diversification it brings).
• 100% — fully hedged: sell all the foreign currency forward; only local asset risk remains.
• Minimum-variance hedge ratio — a level between (or even beyond) those that minimises the variance of the combined position. It depends on the correlation between the asset’s local return and the FX rate. The variance-minimising intuition: $h^* \propto$ how much of the FX move co-varies with the asset. If the currency and the asset move together (positive correlation), the currency amplifies risk and you want to hedge more; if they move oppositely (negative correlation), the currency is already cushioning your asset, so you want to hedge less — sometimes even keep it entirely.

Safe-haven currencies — the free equity hedge

Some currencies — the US dollar, Japanese yen, and Swiss franc — tend to rise during crises, when investors flee to safety. That makes their FX return negatively correlated with risky-asset returns: exactly when your equities crater, these currencies appreciate, partly offsetting the loss. For a non-USD investor holding US equities, the unhedged dollar exposure can therefore act as a built-in equity hedge — the currency rallies in the sell-off that’s hammering the stocks. Hedging it away would remove that cushion and could raise total portfolio risk.

Worked example — min-variance intuition

A European (EUR-based) investor holds US equities. Consider two correlation regimes between the S&P’s local (USD) return and the USD/EUR rate:

The variance-minimising hedge isn’t a fixed number — it’s wherever the currency’s contribution to total portfolio variance is smallest, and that hinges on correlation, not on the currency’s expected direction. For safe-haven currencies, that often argues for less hedging than the naive “hedge everything” rule.

Doing it in practice

Analogy. Running a currency hedge is less like flipping a switch once and more like steering a ship — small, continuous corrections. The forwards you sell expire; you must keep rolling them, settling the cash each time, and re-sizing as your asset value drifts. It’s maintenance, not a one-off.

The mechanics. A real-world FX hedge involves several moving parts:

• Rolling forward hedges. Forwards expire, so a continuous hedge is maintained by rolling — closing the expiring forward and opening a new one, typically via an FX swap (the spot-plus-forward package from lesson 2). Each roll re-prices at the current interest differential, so the hedge’s carry can change over time as rate gaps move.
• Mark-to-market cash-flow risk. A forward hedge is revalued continuously. If the foreign currency rises, your hedge (which is short that currency) shows a loss that must be funded in cash — even though the underlying asset is perfectly fine and has risen in value too. The asset gain may be unrealised (paper), but the hedge loss is a real cash outflow. This cash-flow / margin mismatch is the operational headache of hedging: a hedge can demand cash exactly when nothing is “wrong.”
• Hedging cost drag. The carry (the rate differential) is a recurring drag or pickup that compounds over time — small per period, but meaningful over years, and it must be budgeted into expected returns.
• Choosing a strategic hedge ratio. Rather than re-optimising daily, most institutions set a strategic (long-run policy) hedge ratio per asset class — e.g. hedge bonds 100%, equities 0–50% — and may tilt tactically around it based on carry (hedge more when the currency pays you) or valuation.

Putting it together

Owning a foreign asset is always two bets: the asset’s local return and the currency’s move home — a US investor in a German stock is long the stock and the euro. You decompose the home return by compounding the two legs, $(1+r_{local})(1+r_{fx})-1$, keeping the cross term for big moves. Because developed-market currencies have ~zero expected return but real volatility, hedging can cut risk “for free” — which is why bonds are usually hedged (FX vol swamps bond vol) while equities are often left partly unhedged (FX vol is small beside equity vol and adds diversification). The hedge’s cost is pure CIP: selling the foreign currency forward locks the interest differential, so hedging a high-rate currency bleeds carry and hedging a low-rate one pays — the carry trade in reverse. The hedge ratio runs 0% to 100% (or beyond), with the minimum-variance point set by the asset–FX correlation — and safe-haven currencies (USD, JPY, CHF), negatively correlated with risky assets, can hedge your equities for you, arguing for less hedging. In practice you roll the forwards (FX swaps), live with mark-to-market cash-flow demands, budget the cost drag, and pick a strategic ratio. Here’s the whole picture on one card:

One last mixed recap before the final exam:

Key Takeaways