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Fundamentals of Currency Management

2011 July 14
by Jarrod

For some years I managed what was then a good-sized currency fund, attempting both to reduce the volatility of client stock holdings in other countries (the passive component) and to add value in terms of extra return (the active management component).  This unpublished article outlines a basic understanding of currency management.  If I wrote it today, I would modify the Markowitz mean-variance optimization to take greater cognizance of “black swans,” and talk more about changing return correlations in turbulent times.  Nevertheless, you may find it useful, because the basic principles haven’t changed.



Jarrod Wilcox

January 29, 1999




International diversification of stocks is greatly advantaged by at least a rudimentary knowledge of currency.  Many asset managers feel relatively comfortable in translating their knowledge of how to invest in their own home country to investing in other countries.  But they feel uncomfortable with the currency portion of their investment.  This paper introduces basic currency ideas that can provide a solid foundation for understanding currency and the opportunities it presents for enhancing return and reducing risk in international diversification.


Currency return is the percentage change in the spot exchange rate. For example, if the price  of a dollar quoted in yen rate moves from 100 to 120 as the yen weakens, one calculates the dollar currency return as 20%.  (The yen currency return is -16.67%.)  There is also a forward rate for delivery of currency at a time a few months in the future.  If you own a foreign security, you could imagine hedging against changes in its currency by selling short an amount of currency equivalent to the security’s current value.  In practice, this is done by entering into a contract to sell the foreign currency at a fixed rate in terms of the home currency at some definite point in the future.  There is an active futures market for currency; however, most hedging transactions are done on a customized basis with bank counter-parties.


It is usually not possible to precisely offset currency returns by hedging.  Instead, one receives a hedging return that reflects the difference between the current forward rate, say 90 days out, and the future spot rate.  Arbitrage with short-term interest rates makes this the percentage change in the spot rate plus the interest-rate differential in favor of the home country.  Thus, an accurate measure of the performance of currency management must be based on hedging return rather than on currency return.  Assume you are a US investor in Japanese securities for a year and US interest rates were 4% higher than Japanese rates.  Then a move in the yen from 100 to 120 would create a hedging return of approximately 24%.


Suppose you hedge all foreign currency exposure.  The return that results is the total foreign return including currency, plus the hedging return.  The currency return cancels out, and you are left with the home country interest rate plus the excess of the foreign stock return over the foreign interest rate.


Currency volatility is often a significant part of foreign equity investment returns.  Exhibit 1 shows a history of the dollar priced in Japanese yen (lighter line) and German D-marks (darker line).  The price changes have been significant, both up and down.

Dollar Exchange Rate History

Some in the investment community assume that growing globalization is making currency less important.  That is, as nations come closer together, the volatility based on currency movements should decline.  For example, consider the advent of the European Currency Union and its common currency, the Euro.  Exhibit 2 plots weekly standard deviation of currency hedging returns as seen by the US investor across two groups:  21 currencies in the EAFE index plus Canada (darker line), and the subset of those countries joining the European Currency Union, commonly known as Euroland (lighter line).  This perspective excludes entirely the volatility of the US dollar with respect to these baskets of currencies.  It measures only the within-basket return dispersion.  Note that while the volatility within the Euroland group has declined to essentially zero, the overall volatility of the larger currency basket has actually increased.  If currency volatility is going away, this is not yet apparent.


Convergence of European Currencies

Having established that currency is important, let us go over what the investor needs to know to deal with it.  In the remainder of the chapter we will discuss the following topics:


1. The source of currency hedging returns

2.  Typical strategic mistakes

3.  Currency return statistical characteristics

4.  Optimally hedged asset allocation

5.  Ideas for active currency management.

The Source of Currency Hedging Returns


Currency returns are fundamentally different from either stock or bond returns.  Stock and bond returns each relate to a single economic unit.  Currency returns, on the other hand, relate to the differential performance of two entities, the differential value between the script of two governments.

Let us relate to something more familiar.  Suppose shares in Microsoft were your currency.  You could spend it on real things, or exchange it for shares in Intel.  The rate of exchange between Microsoft shares and Intel shares fluctuates every day.  Assume the exchange ratio begins at 1 Intel/Microsoft.  Over a period of time it may fall to 0.1 or rise to 10.0.  On the other hand, if both companies do equally well, there will be no movement in their exchange rate.  Suppose someone were to agree with you to exchange Intel shares for Microsoft shares at a fixed rate 90 days in the future.  Consider how the value of that contract would vary over the next three months.  Its expected return would be zero.  It’s standard deviation of returns would be different from that of the return of either Microsoft or Intel.  The risk of the differential would be lower than the average of their individual risks if the correlation of their returns were more than one-half.


Now let us come back to the currency impact of buying a foreign stock and not hedging.  You give up possession of your own currency, an obligation of your government, and take possession of a foreign currency, an obligation of a foreign government.  If you intend eventually to sell the stock and convert the proceeds back to your home currency, and do not hedge, it is as though you borrowed money from your own government and lent it to a foreign government.


Even if there should be no difference in interest rate, you will still take a credit risk on the loan.  Suppose the foreign government returns you a depreciated currency because it has created too much money during the period of the investment.  This is analogous to a partial default on a loan.  You should be concerned about the borrower’s ability and motivation to repay.


In practice, things are more complicated because each government that sponsors a currency stimulates conditions that create international interest rate differentials.  The forward exchange rate will approximate the current spot rate adjusted for these interest rate differentials.  Otherwise there would be profitable riskless arbitrage as follows.  Borrow money in the low interest rate country, exchange it at the spot rate, lend it in the other country, and buy a forward contract entitling you to convert it back to the original currency.


Factoring in interest rate differentials, you should think like a very good banker.  You must balance the excess interest rate paid by the foreign government against the excess credit risk of the foreign government over your own government.  Note that this can work in either direction, because the foreign currency may be either a better or a worse deal than your own home currency in terms of future ability to buy real goods.


Suppose, on the other hand, that you are considering hedging.  The decision to hedge will reflect the same ingredients, but with reversed signs.  That is, you should hedge if the excess credit risk of the foreign government’s script overbalances whatever excess exists in interest rates.


Hedging profits come when the market recognizes that the foreign country is falling in creditworthiness or your home country is rising in creditworthiness.  They also come when your home interest rate rises, resulting in a higher current value of your home currency so that it can be expected to depreciate, or when the foreign interest rate falls.

Although there are many individual sources of differential demand and supply for currency pairs, including trade balances, arbitrage with short-term interest rates means that the key uncertainty is market’s perception of creditworthiness.


Typical Strategic Mistakes

In our experience as currency managers, we have found that currency is little understood and that investors frequently make strategic mistakes in dealing with it.


Inadequate  international diversification:


The usual practice is to decide on how much foreign investment you want, and only later decide how much of it should be hedged against foreign currency risk.  Two different securities will always have equal or higher optimal allocation than one of them individually.  The choice of hedging a foreign holding creates a second security.  Consequently, the optimal degree of foreign diversification would generally be larger if the option to hedge were considered from the beginning.


The sub-optimality that thus results from sequential rather than simultaneous asset allocation has modest consequence for US investors.  However, it overlooks a major opportunity for investors whose home countries are a smaller part of the global market and who thereby derive greater benefit from international diversification.  The benefit of a proper Markowitz asset allocation study incorporating currency from the beginning can be quite large and economically significant for an investor from a smaller country.


Inappropriate passive hedging benchmarks:

The best way to derive long-term strategic hedging ratios is to conduct a Markowitz optimal asset allocation in which both hedged and unhedged assets are represented.  This should be done separately for stocks and bonds.  For the typical US investor in stocks with 20% of his or her portfolio placed outside the US, the resulting stock hedging ratio is likely to be between 20% and 50%.  (However, in practice one often sees 0% or 100% hedging ratios.)  The consequent risk reduction through a passive hedging policy may be translated to equivalent return enhancement units by taking into account the investor’s implied risk tolerance.


One might rationally set different hedging ratios for stocks in different countries.  However, the further potential value-added is sometimes small and the risk of a poor decision based on inadequate data is very large.


Beyond passive benefits, a partially hedged benchmark adds significantly to opportunities for active management results, as will be described shortly.


Over-attention to short-term downside protection:


Given a concern with currency risk, isn’t downside protection what we should be interested in?  If by that one means protection over periods such as a few months, the answer is “probably not.”  Since the pursuit of short-term downside protection has been a large part of currency overlay management practice in the last few years, we now take an extended look at the phenomenon of disappearing downside protection with longer time horizons.


A popular approach to currency risk protection involves the purchase of puts against currency futures, or the replication of option results through dynamic hedging or equivalents.  Such methods attempt to alter the statistical distribution of returns so as to prevent large losses in a single period.  While this can be a valuable short-term exercise, it is not generally understood that the resulting skewness does not carry over to the distribution of returns over multiple periods.


The most famous theorem of statistics is the Central Limit Theorem.  It states that the sum of independent random variables tends with increasing numbers of variables to be distributed as a normal distribution.  This is true no matter what the probability distributions of the variables being added, so long as they have finite variances.  The normal distribution is bell-shaped and symmetrical.


To construct an example, since we are concerned with compound returns, we put returns into log form.  (If we wanted to analyze percentage returns, there would automatically be downside protection for losses greater than 100%, but this would provide no comfort to the investor.)   Each period’s log return has a probability distribution which with downside protection will be skewed so that large losses are prevented.


The returns in successive periods are close to being independent.  What is the average log return over multiple periods?  It is the sum of these log returns, divided by the number of periods.  As the number of periods increases, the mean log return becomes distributed more similarly to a normal distribution, with less and less downside protection.


Exhibit 3 shows a beginning distribution of monthly returns representing a simulated program of monthly downside risk protection applied to currency returns.  (It is the result of 12000 drawings from a non-central chi-square distribution.)   The exhibit is a histogram showing what fraction of the outcomes falls within equally-spaced bins.  The mean of the sample distribution is adjusted to be zero, and the standard deviation adjusted to within a plausible range of currency volatility.  With downside protection, losses are limited to less than 2%, the median is a small loss of 0.2%, and there are some large gains of up to about 8%.


Monte Carlo Simulation

Exhibit 3 might appeal to many institutional investors.  However, this short-term picture is quite deceptive as to what will be received over longer periods.  Exhibit 4 shows the distribution of the cumulative log for this example over non-overlapping 12 month periods.  Because it contains only 1000 observations, the sample distribution is not as smooth as in Exhibit 3.  However, it is obviously much more symmetric.  It shows almost as much “protection” against upside results as downside results.  And whereas there was only a 1% chance of a one-month result worse than -.016, there is a 10% chance of a twelve-month result worse than -.046.  Short-term downside protection does not defend against the accumulation of small losses into substantial ones over longer periods.



One-Year Monte Carlo Simulation

At normal risk levels, there is little long-term impact from short-term downside risk protection.  This is not to say that short-term benefits should be entirely disregarded, especially if they come for free as part of return enhancement efforts.  But they do not provide downside currency risk protection over normal institutional investment horizons.


Separating Active Risk Reduction from Return Enhancement:


Some currency overlay managers have argued that forecasting currency returns is essentially impossible.  However, they advocate active hedging through a program that involves forecasting risk.  At times of higher risk, simply hedge more.


Although forecasting currency hedging returns is highly uncertain, in our experience it is no more so than is forecasting stock returns.  As for the distinction between active bets based on return forecasts and on risk forecasts, there is less here than meets the eye.  Once you actively depart from a benchmark there will be parallel consequences for both risk and return.  Active managers of any stripe should always be judged on both active return enhancement and active risk impact.  The question of how much value can be added by one or another active investment approach is strictly empirical.  Forecasting both risk and return seems to have more potential than either alone.


Linking Currency Decisions Too Closely To Asset Exposures:


Institutional investors come to currency from the viewpoint of hedging the risk of currency fluctuations as they affect investments in international stocks and bonds.  The currency position is seen as an adjunct to the underlying foreign security rather than as a portfolio in its own right.  Unfortunately, the tighter this linkage, the narrower the perspective within which the currency portfolio can be managed.  As compared to the Markowitz optimal portfolio, the problem is overconstrained.


In the evolution toward more sophisticated active currency management, most institutional investors retain single currency position constraints based on whatever they happened to have invested in particular country’s stocks and bonds.  They do not take a portfolio viewpoint.  Keep in mind that active currency returns reflect two main components that may be differentially constrained.  The first is position in the home currency versus a basket of foreign currencies.  The second is the position of each foreign currency exposure relative to that basket.  Three realistic examples follow.


1.  The benchmark is 100% hedged.  (This sometimes comes about because an institutional investor is attempting to reduce management fees by putting only a fraction of their international assets into a hedging program, rather than truly choosing 100% hedged as their passive strategy allocation.)  Within this mandate, the currency overlay manager may only choose not to hedge, creating a currency position in each country of between 0% and 100%.  Any manager skill in forecasting degrees of above-average home-currency strength will be lost, and since there is no cross-hedging, much of the ability to forecast relative strength among different foreign currencies will also be lost.  (Cross hedging is selling one foreign currency and buying another.)


2.  The benchmark is 50% hedged, but cross-hedging is still not allowed. This is better than 100% hedged because the manager can exploit skill in forecasting the home currency in either direction.  There is also less stress likely to result from incurring tracking error.  On the other hand, since there is no cross-hedging, exploitation of skillful forecasts of the relative strength of foreign currencies will still be inhibited.

3.  The benchmark is 0% hedged, but unlike the first case, cross-hedging is allowed.  However, the total of active positions must be such that the portfolio is never short in the home currency.  This alternative permits a reasonable degree of exploitation of skill in forecasting relative strength among a larger number of currencies.  However, it is like the 100% benchmark in that skill in forecasting the home currency will be used over only half its range because of the restriction against a net short position in the home currency.

Note that for all three cases, the ability to exploit information regarding weak foreign currencies is especially restricted in the case of small countries.  Suppose Singapore is 1% of the equity portfolio.  Then conventionally one can only short Singapore dollars by 1%.  However, a larger amount might be optimal in the sense of efficiency in achieving the least portfolio risk for a given level of expected portfolio return.


One must respect the organizational realities that bring about such mandated constraints, this is the usual case confronting the currency manager.  Paradoxically, however, constraints on individual currencies tied to underlying assets, imposed to reduce currency risk, may actually hamper currency risk diversification at a given level of expected return.  The fewer such constraints, while maintaining overall risk control, the better the job that can be done through currency management.


Currency Return Statistical Characteristics


The first statistical property we illustrate is that of dispersion of currency returns, examining them for non-normality.  We will examine, not spot returns, but hedging returns.  Exhibit 5 compares to a normal distribution the distribution of weekly log hedging returns into the US dollar for each of the 21 currencies represented in the EAFE Index plus Canada over the period 1981-1997. Over 20,000 observations are summarized.

Histogram of Weekly Hedging Returns

The exhibit shows two major departures from a normal statistical distribution.  The first is an excessive fraction of returns near zero.  It is as though exchange rates were sticky with respect to small changes.  This is not the result of artificial restriction in prices, such as we find in stocks that are quoted in eighths – exchange rates are quoted with far greater precision.  The second departure is the existence of a fair number of returns that are from five to eight standard deviations from the mean.  These would be almost impossible to observe if the distribution were truly normal.


Exhibit 6 explores these events in the tails of the distribution in more detail.  Each small circle represents the weekly hedging return for a particular currency in a particular week.  Since over 20,000 observations are represented on the chart, only the widely separated extreme cases show up as separate events on the exhibit.  For each circle, the vertical scale shows the actual hedging return, while the horizontal scale shows the return that would have occurred if the return fractile (quantile) were drawn from a normal distribution with the same mean and standard deviation as the actual distribution.  The straight line represents that set of values mapped to the vertical axis.

Hedging Returns vs. Normal Distribution


The peak near zero seen in Exhibit 5 shows up as a small flat area in the center of the curve of the distribution in Exhibit 6.  What is better revealed are the points in the tails –those with more than a 4% weekly currency movement that would come as a surprise to any investor projecting normality on future currency returns.

Both the stickiness of small movements and the occasional appearance of surprisingly large movements would be characteristic of a system in which governments resist and then capitulate to economic change.  The dam breaks and the accumulated economic problems flood out to be incorporated in a new price.

The second major property of currency hedging returns is the existence of more trends than could be accounted for if successive returns were precisely independent.  To demonstrate this property, we first do a sequence of 25 regressions, each based on the more than 20,000 weekly currency hedging return observations previously collected.  The first regression forecasts next week’s returns against last week’s returns.  The second forecasts next week’s returns based on the average weekly return over the past two weeks.  The twenty-fifth regression forecasts next week’s return based on the average weekly return over the past twenty-five weeks.


Exhibit 7 charts the successive regression coefficients of the 25 best fits over weekly lags from 1 to 25.  An additional point is placed at the origin to make clear the cumulative nature of the coefficient as we take more and more information into account.

Influence of Prior Hedging Returns

A smooth line is drawn through the points to show the overall tendency.  The function appears to rise rather steadily, although at a declining rate, through the first 10 weeks or so, and then to level  off.  Those with a good imagination may see somewhat more structure, possibly an overshoot near the 15th week, but that is not our point.  The key fact is that returns up to about 10 weeks old seem to positively affect the subsequent return.  The market, at least in an overall sense, seems to only gradually adjust to new information.


Showing in a rigorous way that this effect is statistically significant is more subtle than it looks, not only because of correlated residuals within the same time period, but because we extend the effect through successive regressions.  If we look at any single regression in the range between 3 and 16 weeks and also take the extraordinarily conservative assumption that we have only one degree of freedom at each time-period because of cross-sectionally correlated returns, the effect is significant at between the 2% and 10% levels.  For eight of the first ten lags, the coefficient on the average prior return increases as each lag’s effect is added.  This gives us evidence not on a single regression, but on the overall pattern.  The binomial probability of 8 out of 10 increases if there were no overall lag structure would be .05.


While it is possible that the tendencies toward currency trending arise from speculative dynamics, the relatively long delay and the lack of a greater overshoot suggest adaptive sluggishness caused by governments resisting economic change already signaled to the market.  Taken together, Exhibits 5,6, and 7 reinforce that picture.

The existence of fat-tails tells us that risk control should be conservative relative to the evidence of recent periods.  The existence of trends tells us that technical models are likely to be helpful.

Optimally Hedged Asset Allocation


One should determine an optimal passive hedge policy as part of an overall asset allocation study.  In doing so, it is important to consider the total portfolio including both domestic bonds and stocks.  This is because currency-hedged assets may have return correlations with these other assets that differ asset by asset from those of the unhedged foreign securities.


Let us go through a simple example, in which all foreign stocks will be aggregated as the MSCI EAFE Index.  For the purpose of estimating risk, we will approximate the risk of hedged EAFE as though it were EAFE in local currency terms.  This is a good estimate since short-term interest rate volatility is quite small compared to stock volatility.


The risk and correlation statistics shown in Exhibit 8 are for quarterly returns for the 55 calendar quarters beginning in 1982 and running through 1995.  The risk standard deviations have been doubled to annualize them on a familiar scale.  Cash and  US bonds have been added to the asset menu.

Optimal Allocation Input

We will use our own a priori estimates for expected return based loosely on long-term history.  The difference between expected hedged returns and unhedged returns reflects an estimated annual cost of 40 basis points for hedging in terms of frictional costs and fees.  These priors, though plausible, are given simply for illustration.


Exhibit 9 shows the resulting efficient frontier if no hedging is allowed.  The rows labeled CASH, SP500 and so on, show the percentage of total assets allocated to that asset at points of increasing risk and return on the frontier as one moves rightward.  Since we have used a historical correlation of only 0.53 between US and foreign stocks, diversification benefits cause large fractions of non-US stocks to be allocated at every risk level, upwards of 37%.  This effective risk diversification also allows large amounts of stock to be used for quite conservative portfolios.

Efficient Frontier Without Hedging


When in Exhibit 10 we add the opportunity to hedge the currency exposure, we see very little change in the overall efficient frontier for a US investor.  (The standard deviation in the middle of the frontier is reduced only from 11.2% to 11.1%.  Again, however, the improvement can be much larger in smaller countries.)  However, the optimal composition in terms of assets is noticeably altered.  This form of analysis allows us to see immediately the best hedging ratios as well as the additional foreign exposure that is optimum.


Efficient Frontier With Hedging

In this case, the optimal foreign exposure is increased from 37% to 43% across most of the frontier.  The optimal hedging ratio varies depending on risk tolerance, but is in the range of 30% for all but the highest risk portfolios.


The apparent improvement in the efficient frontier possible through currency hedging may increase materially as one divides assets into more and more categories.  However, the problem is that the quality of the statistical estimation involved will decline in an offsetting way.


It is apparent that for the US investor the benefits of passive hedging are real but very modest.  Yes, optimally, you should hedge.  But the average benefit if you have no skill in forecasting will be small.


Ideas for Active Currency Management


Currency management efforts can usefully be split into better return enhancement and better risk control.  An effective process will do both.


Risk Control:


Currency risk is best controlled at the portfolio level – otherwise too many diversification benefits are left untapped.  The key challenge here is to prevent small errors in estimation from becoming big errors in allocation.  It is important to limit the size of apparently offsetting long and short positions.  It is also important to take into account inherent risk that may be apparent in the history of one currency pair that may not yet have appeared in the volatility of another, but is still latent.  The ability to forecast bursts of volatility can be useful if one does not become so enmeshed in statistical technique that the essential unreliability of the past to forecast the future is forgotten.  In the short-term, currency risks can also be converted into new forms through the passive use of options.  However, active option management is essentially an attempt at return enhancement through another means.


Return Enhancement:


In contrast to the literature on stocks, much less has been written about currency market efficiency and inefficiency.  It is our experience that the structured investor interested in currency management is in the enviable position of working in a field where the prevailing views are largely pre-scientific.  It appears that one can add value best through combining a large degree of fundamental analysis with a smaller portion of technical analysis.


As we have already seen, on average and over a long period of time, cumulative hedging returns have followed trends.  The problem for the currency manager is that these trends are highly clustered both by currency pair and by time period.  For example, in recent years the British pound and the US dollar have moved more or less together relative to continental Europe and to the Japanese yen.  To the extent that the British government makes an effort to maintain a stable dollar/pound relationship, one will observe more counter-trending, or reversion to the mean, than trending.  The challenge is to discriminate when trends are most likely.  This circumstance will reflect both any government intervention that may cause under-reaction to news, and the extent to which speculators have already built into the current price an expectation of trend continuance.


If the essence of hedging is a decision not to lend, then relative interest rates and relative creditworthiness are the factors of most interest.  (Trade-related indicators such as purchasing power parity, the ability to buy the same goods at the same real cost in different countries, are also important.  But these can be viewed as additional ingredients in the ability to repay.)


Relative interest rates are critical but tend to be impounded in prices very quickly indeed, especially for major currencies.  The better opportunity for most active investors is to become specialists in discerning changes in perceived creditworthiness, and, better, to forecast these changes.  In our experience, the key ingredients are of two kinds – economic expansion and recession on the one hand, and accumulated government mistakes or deliberate inflationary tactics on the other.  The classic currency deterioration comes when economic recession exposes an accumulation of economic problems.  The government comes under pressure to lower interest rates or otherwise devalue the currency in order to satisfy domestic political needs.


Conventional measures of accumulating problems include a poor current account balance, but better active returns are likely to come from unconventional measures.  For example, one might note the extent to which government or international agencies have subsidized the economy.  Another important source of information is the stock market, which can reveal information about coming recessions far ahead of actual events.




We have covered the basic mechanics and return characteristics of currency.  They are different from those involved in the more familiar world of stocks and bonds.  We discussed the strategic mistakes most investors make in consequence.  The antidote to poor strategy is to begin at the beginning, recognizing currency differences but including hedged assets as separate securities but including them in a general asset allocation.  When this is done, we conclude that although passive currency hedging of a portion of foreign assets is beneficial, the benefits are modest compared with the active return enhancement and risk reduction potential.  Finally, some ideas have been offered as to the appropriate investment approach for active currency management, focusing especially on forecasting changes in country creditworthiness, and having a broad view of the kinds of indicators that can be brought to bear on this fundamental issue.