How to Exploit Nonrandomness in Currency Returns

Currency returns are positively correlated; that is they trend. Here we describe a trading rule to exploit the nonrandomness of currency returns. For the approach to be useful, the historical presence of trends must, of course, be more than a period-specific phenomenon. One reason to believe that currencies will in fact continue to trend is the conclusion that the trending arises from central bank inteventions. The reasoning for such a conclusion is as follows. Central banks prefer stable exchange rates. Thus, whenever an economic or political shock occurs, they intervene to prevent exchange rates from moving abruptly. Generally, they do not prevent the currency from eventually reaching its market determined price, but by "leaning against the wind," they stretch out the change in a currency's value over time. They cushion its movement to the new price.

If an investor believes that central banks will continue to promote stable exchange rates and accepts the argument that central bank interventions promote currency trending, then that investor will believe a profit can be made by purchasing a currency after it rises and selling it after it falls. The rationale is that, because of the central bank's intervention, the currency's value will continue to move in the direction it has been going until underlying market forces gradually overcome the central bank's dampening efforts.

If currency returns trend, adding value to a buy-and-hold exposure may be possible by following a dynamic strategy that generates a convex payoff function. This is illustrated in the diagram below.




The horizonral axis is the exchange rate of a currency and the vertical axis represents the returns - the conditional return of a buy-and-hold exposure to the currency and the return of a dynamic strategy that produces a convex payoff function. The buy-and-hold strategy produces a straight-line payoff function with a slot of 0.5 (because it is assumed to begin with a 50% exposure to the currency); thus if the currency were to move from a value of 1.0 to 1.2, the buy-and-hold strategy would generate a return of 10%.

As can be seen, the convex strategy outperforms the buy-and-hold strategy when the exchange rate moves significantly away from its value at inception (1.0), and the direction of that move does not matter. Thus, the dynamic strategy is appealing in an environment in which currencies trend, because trending increases the likelihood that the currency's exchange rate will move to one extreme or the other rather than fluctuate within a narrow interval.

An investor can generate a convex payoff fucntion by following a linear investment rule that increases exposure to a currency as it appreciates and decreases exposure to a currency as it depreciates. For example, suppose an investor starts out with 50% exposure to a currency and the currency appreciates 1.2%. The change in the value of the currency by itself increases the buy-and-hold exposure to 50.6%. The investor can increase this exposure exposure by multiplying the currency's return by a multiple greater than 1 and then adding this value to the initial exposure. If the multiple equals 5, the new exposure to the currency would equal 56%; that is , 50% + (1.2% x 5). If the currency declines by 1.2%, the new exposure under this rule would equal 43%. As long as the currency trends, the rule produces a convex pay-off function and adds value to a buy-and-hold strategy.

The value added as the currency trends in one direction is lost, however, during turning points when the trend changes direction unless the investor imposes a ceiling and a floor to constrain the exposure to the currency. Suppose, for example, that the investor's neutral exposure is 50%. The investor may impose a 75% ceiling and 25% floor. As the currency appreicates, the investor increases exposure to the currency unltil the ceiling is reached. As the currency continues continues to trend up, the exposure remains at 75%, thus adding value relative to the buy-and-hold exposure. At some point, the currency changes direction, however, so with this rule, the investor begins to reduce exposure to the currency. During this transition, some of the profits that accrued to the strategy as the currency appreciated are lost, but because the maximum exposure was constrained to 75%, the strategy returns to a neutral exposure relatively quickly, before all of the profits are lost. It then begins to add additional value as the exposure is reduced bellow the neutral exposure. In the same fashion, as the currency's move once again changes direction, the 25% floor serves to protect some of the added value. In general if the ceiling or floor is reached before the trend changes direction, this strategy will add value beyond a buy-and-hold strategy.