Currency Value and Momentum

Imagine two rules for picking horses to bet on. Rule one: bet on the horse that has been underpriced by the crowd for a long time and should eventually get revalued. Rule two: bet on the horse that has been winning lately, on the theory that whatever is making it win hasn't stopped yet. In currency markets these are two of the most studied systematic strategies, and they are built on opposite premises — one bets on reversal, the other on continuation — and both have earned positive average returns for decades.

Value in FX says a currency that is cheap relative to some fundamental anchor — usually purchasing power parity, comparing what a basket of goods costs in each country — will drift back toward fair value over a multi-year horizon. Momentum says a currency that has appreciated over the past several months will, on average, keep appreciating over the next few months, because trends in FX persist longer than random noise would predict, driven by slow-moving flows like central bank reserve rebalancing and gradual investor repositioning.

Building the signals

A common value signal uses real exchange rate deviation from PPP:

$$\text{value signal}_i = -\left(\ln S_i - \ln PPP_i\right)$$

Here $S_i$ is the current nominal exchange rate for currency $i$ and $PPP_i$ is the purchasing-power-parity-implied fair-value exchange rate. In words: the more the actual rate sits above the fair-value estimate (the currency is expensive), the more negative the signal — you'd rather be long the currencies that are cheap, so the sign is flipped to make a higher score mean "buy."

A common momentum signal is simply trailing return:

$$\text{momentum signal}_i = \frac{S_{i,t}}{S_{i,t-12}} - 1$$

Here $S_{i,t}$ is today's exchange rate and $S_{i,t-12}$ is the rate 12 months ago. In words: currencies that have risen the most over the past year get ranked highest, on the bet that the trend has not yet exhausted itself.

Worked example: ranking currencies on value

Three currencies trade at spot rates of 1.10, 1.30, and 0.90 (units of local currency per US dollar-equivalent basket), with PPP fair values estimated at 1.00, 1.00, and 1.00 respectively.

$$\text{signal}_1 = -\ln(1.10/1.00) = -0.0953 \quad \text{signal}_2 = -\ln(1.30/1.00) = -0.2624 \quad \text{signal}_3 = -\ln(0.90/1.00) = 0.1054$$

Currency 3, trading below fair value, gets the highest (most attractive) value score; currency 2, most overvalued, gets the lowest. A value strategy goes long currency 3 and short currency 2.

Worked example: momentum flips the ranking

Now suppose currency 3 has fallen 8 percent over the last 12 months (a weak currency getting weaker) while currency 2 has risen 6 percent (an expensive currency getting more expensive). Momentum signals are $-0.08$ and $+0.06$ respectively — momentum wants to go long currency 2 and short currency 3, the exact opposite of the value trade. A combined value-and-momentum portfolio would size these two conflicting views against each other rather than pick one blindly.

What this means in practice

Systematic FX funds typically blend value and momentum with roughly equal risk weight, because their return streams are close to uncorrelated: value tends to work when currencies are far from fundamentals and momentum tends to work during sustained macro trends (a persistent hiking cycle, a commodity boom). Combining them smooths the return profile more than either delivers alone.

Key terms

• Purchasing power parity (PPP) — the fair-value exchange rate implied by relative price levels between two countries.
• Value signal — a bet that price will converge toward a fundamental anchor over a long horizon.
• Momentum signal — a bet that a recent trend will persist over a shorter horizon.
• Signal combination — weighting multiple factors so that their independent information is used without one blindly overriding the other.