An Active Hedge for the EUR Investor

Part 2 of the Hedging Series

Static currency hedging is a coin toss with predictable losers. The investor either pays the interest-rate differential as carry every month for years, or accepts the full drawdown when the dollar reverses. A trend-following forecast on EUR/USD, combined with carry treated honestly as a cost rather than a feature, sizes the hedge dynamically and finishes ahead of the US-domiciled investor over forty-six years.

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A European investor holding the IVOL strategy in dollars carries a second risk book they did not ask for: a short EUR/USD position equal to the strategy’s notional. Article 1 measured what this cost over fifty-six years, using EUR/USD from 1999 onward and a synthetic series anchored to DEM/USD before that — a reasonable proxy that lets the analysis stretch back through the Volcker and Plaza periods. Either extreme — hedge everything, hedge nothing — wins in one regime and bleeds in the opposite. The hedger pays carry every month for years on end. The unhedged investor takes a forty-five percent drawdown the first time the currency turns hostile. Neither feels like advice you would give yourself.

The middle position needs a rule. What signal predicts the next month’s currency move, what threshold separates action from inaction, and how should the carry cost enter that decision. The rest of this article works through one answer based on a trend feature ensemble.

The asymmetry that simplifies everything

The two policies are not symmetric. Staying unhedged costs nothing. The natural short EUR/USD position pays no carry, no spread, no insurance premium. Hedging requires a synthetic FX position via forward or futures, and that position pays the interest differential between the two currencies for as long as it is held. When US rates exceed European rates, which describes most of the last thirty years, the hedge bleeds money every month it is on.

This matters for how a forecast should be combined with carry. If the signal predicts EUR/USD will rise next month, the natural short position is expected to lose. The investor can accept that loss or pay carry to neutralize. The question is whether the expected loss is large enough to justify the carry. If the signal predicts EUR/USD will fall, the natural short is expected to gain. Hedging would forfeit those gains andpay carry. There is no decision to make. Carry enters on one side of the prediction, not both.

Decision rule

Where the forecast comes from

The forecast is a time-series signal. One class of signals that has held up across asset classes for decades is trend following — the past direction of a price predicts its near-future direction. The mechanism is not chart-pattern mysticism. Central banks adjust policy with lags. Capital flows have inertia. And market participants update their views slowly when regimes change. Each creates persistence on a multi-month horizon. The currency-specific evidence is well documented (Moskowitz, Ooi and Pedersen 2012; Menkhoff, Sarno, Schmeling and Schrimpf 2012).

The construction is standard: take the monthly EUR/USD spot rate, compute four cumulative returns over one, three, six, and twelve months, standardize each by its expanding-window mean and standard deviation, and average the four z-scores into a single signal. This trend feature ensemble follows the pattern Carver (2015) describes. Lagged by one month so it cannot contain information about the move it is predicting, it feeds an ordinary least-squares regression on the next-month spot return.

Figure 1. Construction of the signal and the trading decision. Spot prices feed four lookback returns. Each is standardized into a z-score. The four are averaged into a single trend signal. An OLS regression turns that signal into a predicted price move α̂. The carry hurdle is observed at decision time and applied asymmetrically. The output is a monthly hedge ratio in {0, 0.5, 1}.

The three views below show what the regression is fit on and how well it works. The scatter on the left is the raw data — each dot a month, the horizontal axis the lagged trend signal, the vertical the realized price move. The middle and right panels summarize the same data into ten deciles, plotted on the z-score axis and on a uniform rank index respectively. The OLS slope is positive and significant, decile means line up cleanly along it, and the deciles trace a clear monotonic gradient from the lowest signal to the highest.

Figure 2. Three views of the same data. Left: raw scatter of lagged trend z-score versus next-month price move on the short EUR/USD position. Middle: decile means plotted on the z-score axis with bar widths matching each decile’s span. Right: the same decile means plotted on the equal-spacing rank index. The OLS line is straight in z-space and curves into an S-shape on the rank axis purely because the trend signal’s density is highest near zero.

The signal is real but noisy. The OLS slope is plus 0.68 percent per standard deviation of trend, the R-squared is 7.2 percent, and the residual standard deviation is 2.06 percent per month. Most of any single month’s move is unexplained. The signal captures a drift across many decisions, not a deterministic outcome on any one of them. This R-squared is in the range that the time-series momentum literature reports for currency markets; trend signals at the monthly horizon do not explain large fractions of variance, they accumulate small expectational edges over many trades.

Adding the carry hurdle

With a forecast in hand, the trading rule follows from the asymmetry stated earlier. The forecast α̂ is compared against the negative of the current monthly carry, observed at decision time as the prior-month interest differential divided by twelve. The carry hurdle varies considerably across the sample — over one percent per month in the Volcker era, close to zero through the late 2010s, around fifteen basis points per month today.

To avoid acting on noise, a small margin is added on each side of the hurdle in units of OLS residual standard deviation. A margin of zero produces a binary toggle: hedge fully or not at all. A margin of half a residual sigma creates a middle band where the rule sits at fifty percent because the forecast is not confident enough either way. The two variants below test both.

The active hedge in practice

With OLS coefficients refit every month on expanding data, the trend signal recomputed without look-ahead, and the asymmetric carry rule applied at each decision point, the policy generates a monthly hedge ratio sequence for the full sample. The same calculation is applied to four static benchmarks for comparison: the US investor running the strategy in dollars with no FX exposure, the EUR investor unhedged, the EUR investor fully hedged, and the EUR investor running a static fifty-percent hedge. All assets are USD-denominated, including gold; the operational variant with EUR-traded gold appears at the end.

The numbers below cover 1980 onward. The trend feature ensemble needs a seven-year warm-up before its expanding-window z-scores stabilize and the OLS coefficients become meaningful, which trims off the early-1970s data. That trimming also removes the most extreme drawdown the unhedged EUR investor took in the entire fifty-six-year sample — the late-1970s dollar collapse that Article 1 documented. Including it would penalize the static unhedged comparator disproportionately and make the active rule’s advantage look larger than it really is. Starting in 1980 is the more honest comparison.

Figure 3. Cumulative equity (log scale) and drawdown across six policies, 1980–2026, monthly compounded. The two active variants both finish above the US investor, with shallower drawdowns and roughly the same volatility. The static EUR policies span a wide range — unhedged tracks the US investor’s CAGR with much worse drawdowns, fully hedged ends about half the final equity.

The numbers behind the figure:

Both active variants land above the US investor on CAGR and Sharpe and well below all static EUR policies on drawdown. The half-sigma variant gives back roughly ninety basis points of annual return relative to the binary variant in exchange for somewhat lower turnover. The binary variant is the more aggressive expression of the rule and the harder to run cleanly without transaction costs eating into it.

This is not the result of taking more risk. The realized volatility of the half-sigma variant matches the US investor’s almost exactly. The active EUR investor captures a return advantage by converting a forced FX exposure into a partially predictable one and declining to pay carry when the forecast says it is not worth it.

Isolating the FX leg

The cleanest way to see what the hedging decision actually contributes is to strip out the strategy returns entirely and look only at the FX-leg P&L. Per unit notional, the fully hedged investor pays the carry differential every month and accumulates a smooth, near-deterministic decline. The unhedged investor takes the spot price move each month and accumulates a random walk that ends roughly where it started, near one. The two active variants make money on the FX leg alone over the same window.

Figure 4. Standalone FX-leg P&L per unit notional, separated from the underlying strategy returns. Fully hedged (black) loses 1.7 percent per year just on carry. Unhedged (grey) ends roughly flat with the dollar’s long round-trip. The active 0.0σ variant (red) and the 0.5σ variant (green) both end positive, with materially shallower drawdowns than either static path. The hedge decision itself is generating a positive return stream, not just diversifying the asset book.

Over forty-six years, the binary active variant compounds the FX leg to plus 1.85 percent per year with a maximum drawdown of 25 percent. The half-sigma variant compounds at plus 0.96 percent per year. Both deliver this on a leg that the static unhedged investor finishes flat on and the fully hedged investor loses on. The active rule is not hedging in the insurance sense — it is trading the FX exposure, sized between zero and one, in a direction informed by the trend signal and disciplined by the carry hurdle.

What this does not solve

The rule earns its keep over the full sample. It does not earn it in every sub-period.

The 2020s have been a single-regime decade for the natural short EUR/USD position. The dollar has strengthened, European rates have lagged US rates, and the unhedged EUR investor has accumulated a small return advantage over both the US investor and the static fifty-percent hedge. Against this regime, the active rule has been roughly half hedged on average and has consequently underperformed the static unhedged path by about one percent of CAGR over six years.

Figure 5. The 2020s, in detail. USD investor in navy, EUR unhedged in grey, EUR active 0.5σ in green. Drawdown panel below and the active hedge ratio history at the bottom. In single-regime periods favoring the natural short, the active rule pays a small premium for its diversification across regimes. This is the honest characteristic of any signal-based rule at this signal strength: not free, not always winning.

The same property runs in reverse. Between 1985 and 1995, after the Plaza Accord weakened the dollar, the static unhedged position lost over twenty percent against the active rule. Different decades reward different static policies. The active rule sits between them, and across decades the diversification compounds into the advantage shown in Figure 3.

Three caveats on the backtest. Transaction costs on FX-forward rolls are real and would shave twenty to forty basis points per year off the binary variant’s headline CAGR; the half-sigma variant is less affected because it changes hedge ratio less often. The OLS slope itself is refit monthly on expanding data, but the choice of trend as the feature was informed by full-sample diagnostics — a soft form of in-sample bias common to all backtest research, and one that a strict held-out test would degrade modestly without overturning. The 7.2 percent R-squared is small enough that a single bad month can swing any short-window evaluation; the rule needs decades to earn its alpha.

Other signals, briefly

Trend is not the only forecast available. The forward-premium puzzle implies that the carry level itself has predictive content for FX returns, concentrated at extreme positionings (Fama 1984; Asness, Moskowitz and Pedersen 2013). Purchasing-power-parity gaps mean-revert over multi-year horizons (Engel and West 2005), suggesting a value signal. Commitment-of-traders positioning at multi-year extremes shows weak-to-modest predictive power per Klitgaard and Weir (2004), better as confirmation than primary signal. Real-rate differentials and growth differentials matter at longer horizons.

These are not used here for two reasons. This article is about hedging, not about a standalone FX trend system, so the action space is bounded between zero and one — going synthetic long is not a hedge but a directional bet. Within those bounds, one good signal is enough. The second reason is editorial discipline: more features mean more in-sample levers, where the headline performance grows but out-of-sample reliability does not. The same framework, extended to a long-short FX sleeve trading futures or CFDs across many pairs, naturally accommodates carry alongside trend.

Where this lands

The active hedge is one signal, one cost, and one explicit asymmetry. No regime overlays, no parameter tuning beyond the choice of margin band, no feature zoo. The first article ended at the choice between two unsatisfactory extremes. This article fills the space between them with a rule that compounds an investor-specific disadvantage into something close to parity with the US-based version of the same strategy. The numbers are not magic — over six-year windows the rule will sometimes underperform whichever static policy happens to fit the regime. Over multiple decades, in a sample that includes Volcker, Plaza, the euro launch, the GFC, and the post-2020 dollar repricing, the active variant compounds faster and bleeds shallower. That is the kind of edge an active hedge can deliver. Not a promise of perfect timing, just a structural improvement over paying for hedging whether the forecast supports it or not.

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References

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2. Carver, R. (2015). Systematic Trading: A unique new method for designing trading and investing systems. Harriman House.

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4. Fama, E. (1984). Forward and spot exchange rates. Journal of Monetary Economics, 14(3), 319–338.

5. Klitgaard, T. and Weir, L. (2004). Exchange rate changes and net positions of speculators in the futures market. Federal Reserve Bank of New York Economic Policy Review, May 2004, 17–28.

6. Menkhoff, L., Sarno, L., Schmeling, M. and Schrimpf, A. (2012). Currency momentum strategies. Journal of Financial Economics, 106(3), 660–684.

7. Moskowitz, T., Ooi, Y. and Pedersen, L. (2012). Time series momentum. Journal of Financial Economics, 104(2), 228–250.

8. Quantpedia (2019). Currency hedging — a cost or a benefit? Quantpedia blog. quantpedia.com/currency-hedging-a-cost-or-a-benefit

9. S&P Dow Jones Indices (2019). Currency Hedged Returns: Cost or Benefit? Research note.

10. Stulz, R. (1996). Rethinking risk management. Journal of Applied Corporate Finance, 9(3), 8–25.