The price of one countrys currency in terms of another countrys currency is called the

10.3 Skills or (bad) luck?

Limited Partners may be exposed to currency risk even if they commit capital only to private equity funds in their home currency. As we have seen in Chapter 7, private equity funds invest a nontrivial part of their capital in foreign markets acquiring assets in currencies different from the fund currency. Some funds have become truly global, chasing deals across different geographies and holding an international portfolio of companies. To the extent that private equity funds acquire foreign portfolio companies, their performance may be affected by currency movements.

Exchange rate changes work both ways, not just for LPs but also for GPs. Adverse movements may reduce returns on an investment a fund makes and may even turn a gain into a loss. But exchange rate changes may also enhance returns. This raises the question to what extent a fund’s performance is strictly based on the GP’s operational and financial qualities as opposed to factors that are arguably beyond his control. Whether (adverse) exchange rate movements are just (bad) luck is of course debatable—a GP who decides to invest abroad deliberately accepts currency risk, which should be an integral part of his investment (and divestment) decision process. In fact, GPs interviewed for this book (Chapter 12) confirm that the timing of their foreign investments and exits do reflect their exchange rate views. Furthermore, foreign acquisitions by private equity funds tend to be biased toward export-oriented companies, which, other things being equal, helps mitigate exchange rate risk.2 Skills or bad luck—inextricably intertwined with this question is, of course, the issue of compensation. Should profits due to exchange rate movements be excluded from the calculation of carried interest? While LPAs are generally silent on the exchange rate question, Meyer and Mathonet (2005, p. 127) argue that in the future “…investors could ask for a carried interest calculation on the underlying investments’ currencies to strip off the effect of exchange rates.”

The academic literature has little to say on this issue due to the lack of sufficiently detailed deal-level data and the fact that cross-border investments are a relatively recent phenomenon. To better understand the significance of exchange rate movements on investment returns, we look at individual transactions of private equity funds in AlpInvest Partners’ database. More specifically, we concentrate on cross-border deals by buyout funds that have already been exited. For each deal, we convert the cash flows of foreign-currency transactions into the funds’ currencies. As far as European funds are concerned, we identify 18 fully exited (and nonwrite off) deals in US dollars (Table 10.7); for buyout funds raised in USD, we have 24 deals undertaken in euros. The exchange-rate impact on the returns of the transactions is shown as the absolute difference between the money multiple calculated in the fund’s and the deal’s currency and as the deviation of the IRR in the deal’s currency in percentage points of the IRR in the fund’s currency.

Table 10.7. Impact of exchange rate changes on deal performance

Source: AlpInvest Research

Most USD-denominated deals by European funds were negatively impacted by the appreciation of the euro. The impact was sizable, with adverse exchange rate movements shaving around 4–5 percentage points off the IRR calculated in the funds’ currency. In some cases, the currency effect was even larger, depending on the exact entry and exit dates of the deals. For instance, over the holding period from 2003 to 2008, a European fund saw the IRR of one of its US buyouts reduced by as much as nine percentage points when calculated in EUR, the fund’s currency.

Conversely, in our sample, the overwhelming majority of transactions undertaken by USD-based funds in Europe benefited from the EUR appreciation. In some cases, the exchange rate effect added 10 percentage points or more to the IRR of individual European deals when converted into USD, the funds’ currency. In other words, the performance of these transactions, and hence the performance of the buyout funds that have sponsored them, would have been considerably worse in the absence of—from their perspective—favorable exchange rate movements.

Fundamental Versus Technical Trading Models

Exchange rate forecasters typically use two types of models: technical or fundamental. A fundamental model forecasts exchange rates based on variables that are believed to be important determinants of exchange rates. As we shall learn later in the text, fundamentals-based models of exchange rates view as important things like government monetary and fiscal policy, international trade flows, and political uncertainty. An expected change in some fundamental variable leads to a current change in the forecast. A technical trading model uses the past history of exchange rates to predict future movements. Technical traders are sometimes called chartists because they use charts or diagrams depicting the time path of an exchange rate to infer changing trends. Finance scholars typically have taken a dim view of technical analysis, since the ability to predict future price movements by looking only at the past would bring the concept of efficient markets into question. However, recent research has led to a more supportive view of technical analysis by some scholars and the method is widely popular among foreign exchange market participants. Surveys indicate that nearly 90% of foreign exchange dealers use some sort of technical analysis to form their expectations of exchange rates. However, the same surveys suggest that technical models are seen as particularly useful for short-term forecasting, while fundamentals are seen as more important for predicting long-run changes.

Although the returns to a superior forecaster would be considerable, there is no evidence to suggest that abnormally large profits have been produced by following the advice of professional advisory services. But then if you ever developed a method that consistently outperformed other speculators, would you tell anyone else?

Abstract

The exchange rate and terms of trade are two variables that are intertwined and quite often are used as a proxy for one another. While under some circumstances the interchangeability may be appropriate, that is not always the case. An exchange rate measures the price of one currency in terms of another. In turn, the terms of trade measure how many units of the foreign goods can one unit of the domestic good acquire. If the ratio of the Consumer Price Index (CPIs) in local currencies remains unchanged, the terms of trade and exchange rates will move in the same proportion, that is, the precise conditions under which the nominal exchange rate and the terms of trade are equivalent and thus interchangeable. But there is no reason to expect the ratio of the CPI’s to be constant, in which case the nominal exchange rate and real exchange rates will no longer be interchangeable or equivalent. If as we believe inflation is a monetary phenomenon, we need to introduce money into the framework that we have been developing. The determinants of the underlying inflation rate will drive the nominal exchange rate, the price of one currency in terms of another, while the real variables will determine the terms of trade.

4.1 Recent Empirical Evidence

Exchange-rate models that incorporate uncovered interest parity have difficulty accounting for the high volatility of exchange rates across high-income countries. For example, the calibrated variance of the nominal exchange rates in some sticky-price dynamic stochastic general equilibrium models is too low if the model assumes interest parity. Many models simply assume an exogenous stochastic process for λt in equation (1) in order to account for the high volatility.33 Duarte and Stockman (2005), develop a model in which news drives exchange rates. As in the example given in equation (27), the news leads to a disconnect between the exchange rate and the economic fundamentals. But in their model, the news concerns the foreign exchange risk premium. Their model allows for disconnect to occur because the econometrician does not observe the risk premium, which in turn is time varying because it is driven by news.

One reason the literature has focused on the foreign exchange risk premium is to explain exchange-rate volatility and exchange-rate disconnect.34 A second reason is the uncovered interest parity puzzle. Equation (6), repeated here for convenience, is the regression estimated by Bilson (1981) and Fama (1984) that tests uncovered interest parity

(54)st+1-st=a+b(it-it ∗)+ut+1.

Under the null, the regression coefficients should be a=0 and b=1. However, a long history of empirical work has found the estimated value of b to be less than one, and usually less than zero. Hodrick (1987), Froot and Thaler (2001), and Engel (1996) are older surveys of the empirical work, but the puzzle is still present in more recent studies. For example, Burnside et al. (2006) estimate equation (54) for nine currencies against the U.K. pound using monthly data from January 1976 to December 2005. In all cases, the estimated slope coefficient is negative. It is always found to be significantly less than one (at the 5% level of significance), and usually significantly less than zero.35

Several recent studies have measured the economic return to taking positions based on the deviation from uncovered interest parity implied by the empirical findings of regression (54). One investment rule is the “carry trade,” under which the investor simply takes a long position in the currency with the higher interest rate. Suppose that interest parity does not hold, but that the only time t information that is useful in forecasting the exchange rate is the interest differential, it-it∗. Suppose further that the intercept term in (54) is zero: a=0. Then

(55)λt =it∗+Etst+1- st-it=(1-b)(it∗-it).

As long as b<1, the ex ante excess return on the Foreign bond, λt, is positive precisely when it∗>it . If the Foreign interest rate is higher than the Home interest rate, the Foreign deposit has a higher expected return than the Home deposit, and vice versa.

Burnside et al. (2008, 2011c) consider the payoffs to holding portfolios of short-term bonds based on the carry trade. They assess the return to holding an equal-weighted portfolio of 23 currencies. The strategy is to borrow in the foreign country and invest in the U.S. when the U.S. interest rate is above the interest rate in each of these countries. When the U.S. interest rate is below the interest rate of the other country, the position is reversed. Burnside et al. (2008) consider monthly returns from January 1976 to June 2007, as well as sub-samples. The mean annualized return on this portfolio is 5.4%, with a Sharpe ratio (the ratio of the average return to the standard deviation of the return) of 0.83. Burnside et al. (2011c) extend the sample period through 2010, and find an average payoff of 4.6%, with a Sharpe ratio of 0.89. Both studies find that the volatility of the return on the carry trade is substantially reduced by holding the portfolio (compared to the average Sharpe ratio for the carry trade for individual currencies).

Lustig and Verdelhan (2007), Brunnermeier et al. (2009), and Lustig et al. (2011) all consider returns to a carry-trade portfolio in which assets are grouped. For example, Lustig and Verdelhan (2007) use exchange rate data and interest rate data for 81 countries to construct portfolios, and measure returns in the 1953–2002 period and the subperiod of 1971–2002. At the beginning of each month, they group the countries into eight equal-sized portfolios, ranked by their interest rate in the previous month relative to the U.S. interest rate, and rebalance the portfolio each month. Then they measure the average ex post annualized returns on a long position in each portfolio. The portfolio with the lowest interest rate (portfolio 1) has an average return of −2.99% in the 1971–2002 period, while the portfolios with the highest (portfolio 8) and next-highest interest rates (portfolio 7) have average returns of 1.48 and 3.94%, respectively. The Sharpe ratios for these three portfolios are −0.38, 0.10, and 0.39. Because the highest interest rate portfolio generally contains some very high-inflation countries, the most interesting comparison might be between the returns on portfolio 7 and portfolio 1. Clearly there is a high return and low standard deviation to the strategy of going long in high-interest rate countries and short in low-interest rate countries.

Jordà and Taylor (2012) suggest augmenting the carry-trade strategy by including economic fundamentals. They argue that the profits from the standard carry-trade strategy (using an equal-weighted portfolio of nine currencies relative to the U.S. dollar) disappeared for many currencies, and were even reversed, in the 2007–2008 period as low-interest rate currencies appreciated strongly. However, a strategy that takes into account not only the interest rate differential but also the deviation of the exchange rate from its “fundamental” level remained profitable over that time span. The fundamental value of the currency is measured as the long-run mean real exchange rate. The trading strategy that appears to be most robust across periods is a threshold one in which trades are only made when the absolute values of the interest differential and the deviation of the real exchange rate exceed certain amounts.

An alternative trading strategy that has been examined is a momentum strategy. Under this strategy, if returns on, say, the Foreign bond were positive in the previous period: it-1∗+st-st-1 -it-1>0, then the investor should go long in the Foreign asset and short the Home bond. Menkhoff et al. (2012b) and Burnside et al. (2011c) calculate the profits from following this rule. The former paper considers one-month returns for 48 countries relative to the U.S. dollar from January 1976 to January 2010. They report a return on the portfolio of around 10%, and a Sharpe ratio of around 0.95. The latter paper reports somewhat lower expected returns and Sharpe ratios, but ones that are still impressively high.

Burnside et al. (2006, 2011c), and Menkhoff et al. (2012b) investigate whether the excess returns on carry trade or momentum strategies can be explained by traditional risk factors such as the growth rate of real consumption, the market return, the term structure spread, the spread between LIBOR and Treasury rates, etc. None of these factors are correlated with the excess returns from either strategy in foreign exchange markets. On the other hand, Menkhoff et al. (2012a) do find that the returns to the carry trade are correlated with volatility of exchange rates. Sorting currencies into five portfolios as in Lustig and Verdelhan (2007), they find a high average return to the carry trade. They further find that ex post returns for high-interest rate currencies are low during times of high volatility. They interpret this to mean that high-interest rate currencies are risky because they have poor payoffs when a measure of global volatility is high.

Clarida et al. (2009) find regularities similar to those in Menkhoff et al. (2012a). They examine weekly returns of G10 currencies relative to the dollar. They construct carry-trade portfolios that put the investor long in the n currencies with the highest interest rate relative to the U.S. and short in the n lowest return currencies, n=1,2,3,4,5. They divide their sample into periods of high, medium, and low return volatility for each portfolio using both measures of ex post volatility and volatility implied in options. They find that in the periods of lowest volatility, the slope coefficient in regression (54) is negative, but in the periods of highest volatility, the slope coefficient is positive. High-interest rate currencies pay a low return in volatile times, but a high return during less volatile times. These results also coincide with the conclusions of Brunnermeier et al. (2009) that the gains from the carry-trade unwind during times of “currency crashes,” when there are dramatic depreciations of the high-interest rate currencies.

There are some circumstances under which regression (54) does not provide much evidence of deviations from uncovered interest parity. Bansal and Dahlquist (2000) and Frankel and Poonawala (2010) find that the slope coefficient in that regression is much closer to 1 for emerging market currencies relative to the U.S. dollar. Another circumstance in which there is some evidence that uncovered interest parity holds is at longer horizons. Alexius (2001), Chinn and Meredith (2004), and Chinn (2006) all report a regression of long-term changes in exchange rates on long-term interest rate differentials. For example, Chinn (2006) considers a regression of the 10-year change in the log of the exchange rate on the difference in 10-year yields to maturity on quarterly data for Japan, Germany, the U.K., and Canada relative to the U.S. from 1983:I to 2004:IV. The equation is estimated as a panel, imposing the same slope coefficient across currencies. Chinn finds an estimated slope coefficient of 0.708, and cannot reject the null that the slope coefficient equals one. Similar results are found in currency-by-currency regressions, and regressions using 5-year yields.36

At the other end of the time spectrum, Chaboud and Wright (2005) find that uncovered interest parity holds well over very short horizons. Specifically, they take into account the fact that a position held during the day does not pay interest, but overnight balances do. A position is deemed to be overnight if it is held past 5 p.m. New York time. So any interest received on a deposit held at 5 p.m. is the same whether the position was held all day or just for a few minutes. The change in the exchange rate from right before until right after 5 p.m. is expected (before 5 p.m.) to equal the interest differential if uncovered interest parity holds. Using data on the Swiss franc, euro, U.K. pound, and yen relative to the dollar, Chaboud and Wright estimate regression (54) for very short time periods that span 5 p.m. New York time. They find that the slope coefficient is nearly one when the time interval is only an hour or two, but as the time interval increases toward six hours and more, the estimated slope coefficient turns negative.

1 Introduction

Exchange rate forecasting consumes a vast amount of space in the scholarly literature of international finance. Summaries of this large literature have been provided from time to time by several authors,1 but the focus has generally been on finding models that can forecast the future spot exchange rate better than a random walk. The well-cited paper by Meese and Rogoff (1983) spawned a leap in research attention as scholars attempted to take up the challenge of developing new models to beat a random walk for exchange rates. It is not clear that we have learned much since the 1980s other than it is still quite challenging to construct a model that is capable of systematically outperforming a random walk in predicting future spot exchange rates. This academic focus on predicting bilateral exchange rates is understandable and certainly a subject worthy of scholarly attention; however, the exercise undertaken by scholars is pursuing answers to questions that are not necessary for successful investing in currency markets. This chapter aims to lay out key issues of exchange rate forecasting from a quantitative practitioner’s perspective. By the end of the chapter, the reader should have answers to the following questions:

Why don’t we need accurate forecasts of future spot exchange rates to construct currency portfolios that yield attractive returns?

Section 2 addresses the irrelevance of the Meese–Rogoff exchange rate disconnect puzzle for currency investors. Of course, Meese and Rogoff were focused on testing popular exchange rate models from an academic perspective and not creating investment portfolios. One way of viewing the difference is in terms of different loss functions. The academic exercise uses a measure like mean square forecasting error, while the active currency investor focuses on a measure like a Sharpe ratio or risk-adjusted returns. We will give a clear example of the difference that results from the two perspectives.2

How does one go about constructing an actively managed currency portfolio?

Section 3 provides a high-level overview of the elements of building actively-managed quantitative currency portfolios as a currency hedge fund manager might use. While currency return forecasts are key, one needs more than just return forecasts to put together a successful long-short model.

How should currency portfolio managers be evaluated?

A simple answer is whether they generate attractive risk-adjusted returns or not. But is there such a concept as “beta” in currency investing, as exists in equity investing? In other words, is there a passive investment style benchmark against which one can judge performance in currency investing? Section 4 looks into this question and finds that identifying useful benchmarks for active currency investing is problematic.

Lacking good benchmarks for assessing currency portfolio performance, are there other analytical tools that can be employed to help evaluate portfolio managers?

Section 5 describes how one can break down portfolio returns to evaluate a manager’s skill in timing return-generating factors. Portfolio returns are decomposed into tilt and timing components. The “tilt” in a portfolio refers to holding constant exposures to assets over time, and is a kind of passive investing. The “timing” component of portfolio returns is the difference between total returns and the tilt returns. We can see that different generic currency investing styles offer different tilt versus timing returns.

Can one enhance returns by the use of conditioning information to help time exposures to return-generating factors?

Following on from the timing discussion of Section 5, Section 6 creates a specific example of the use of conditioning information to enhance returns from the carry trade. A carry trade involves buying (or being long) high interest rate currencies, while selling (or being short) low interest rate currencies. By dialing down risk in times of financial market stress, one can realize substantially higher returns from investing in the carry trade.

The chapter concludes with a summary in Section 7.

ERR and Inflation: Anchors

Exchange rate pegs have typically been associated with what could be broadly referred to as a ‘deficit in monetary credibility,’ reflected in high inflation expectations, inflation inertia (backward indexation to past inflation), and a low impact of monetary policy announcements. Underlying this credibility deficit, there is a time inconsistency problem: inflation expectations increase nominal interest rates thereby raising the fiscal deficit of an indebted government and making it optimal for the government to dilute its debt burden through inflation – inducing equilibrium inflation and generating an inflation bias.12 In this case, the use of an exchange rate anchor may make dilution more costly, to the extent that abandoning the anchor entails some (political or economic) reputation cost. In other words, if a low inflation target is not credible, the peg works as a second-best commitment mechanism.13 ‘Hard’ pegs provide an extreme example of this reasoning, as they add to the exit cost in a number of ways, including by establishing the peg through a binding legal framework, fostering the use of the peg currency in everyday transactions, and even eliminating altogether the national currency in the case of unilateral dollarization.

An exchange rate anchor, much in the same way as an inflation target, has the additional advantage of coordinating expectations. In high-inflation economies, where agents tend to index prices partially to the exchange rate to minimize inflation risk, an exchange rate anchor provides a vehicle to transition from backward indexation to past inflation, to forward indexation to a preannounced exchange rate path. Canavan and Tommasi (1997) made this point to argue that, with incomplete information and imperfect monitoring, policy makers would prefer visible anchors like the peg even if the latter limits the ability to respond to external shocks.

From an empirical perspective, the literature has focused on the link between ERR – and, in particular, varieties of exchange rate anchors such as (crawling) bands and pegs – and the inflation rate. Overall, there seems to be agreement on the fact that pegs are associated with lower inflation, even after controlling for money creation.14 The result is robust to controlling for the presence of a peg in a standard monetary equation, which indicates that the benign effect of the peg may work through the anchoring of expectations rather than through the imposition of monetary discipline. However, the direction of causality and, more importantly, the duration of the effect are more controversial.

Among the many qualifications raised by these studies, perhaps the most troubling is the well-known fact that failed pegs tend to collapse to floats, which in imperfectly specified tests may result in a spurious association between floats and high inflation. Intuitively, in the long run, pegs may influence monetary policy, but they are also endogenous to it, as they cannot be sustained in the face of persistently high inflation. This may explain why empirical findings suggest that only long-lasting pegs are significantly linked to low inflation levels in the long run (Levy Yeyati and Sturzenegger, 2001). Ultimately, the effectiveness of a peg as an anti-inflation device remains debatable, as it depends on the policy maker's ability to reign in the fiscal deficit.15 If that is not fully achieved, his willingness and ability to refrain from monetary financing would inevitably be offset by fiscal needs, leaving the exchange rate anchor as a short-term patch. The declining effectiveness – and shortening life span – of successive (failed) exchange rate stabilization in Latin American countries in the 1980s and 1990s attest to the limits of exchange rate anchors in the presence of fiscal dominance.

Exchange Rates

Exchange rates denote the number of units of one currency that must be given up for one unit of a second currency. For example, the direct exchange rate of one dollar in terms of the South African rand might be SFR6, meaning that 6 rand are required to purchase one U.S. dollar. The indirect exchange rate is the inverse of the direct rate. Thus, if one U.S. dollar can be exchanged to purchase six South African rand, the direct exchange rate of rand for dollars is six. Correspondingly, the indirect exchange rate of dollars for rand is 0.1667; $0.1667 is the cost of one rand.

Foreign exchange rates are determined by supply and demand conditions. A variety of factors will affect these supply and demand conditions, including:

Government policies

Supply and demand conditions for commodities in the two countries

Income levels in the two countries

Interest rates in the two countries

The perceived risk of engaging in trade with the two countries

As of 2010, the most commonly traded currencies are the U.S. dollar (involved in 85% of all FX transactions), the EU euro (39%), the Japanese yen (19%), the UK pound (13%), and the Swiss franc (6%). The most common trading pair is the EUR/USD, representing approximately 28% of all FX transactions.

Exchange rate fluctuations

Exchange rate fluctuations can indirectly influence the extent of parallel trade, insofar as currency appreciations or depreciations affect relative prices of pharmaceutical products across countries. Ceteris paribus, currency depreciation could make exportation more attractive, or could even reverse the flow of trade, if price differences between the export and the import country are small. In the UK, moderate average price reductions in the context of the Pharmaceutical Price Regulation Scheme (PPRS), along with the depreciation of sterling vis-à-vis the Euro, reversed the flow of trade in 2007. Since then, the UK has been a net exporter of pharmaceutical products, compared with the opposite situation until that point; parallel imports accounted for approximately 20% of the UK prescription in-patent market in 2002.

The Global and Individual Countries’ Monetary Equilibrium Under a Floating Exchange Rate

The exchange rate is nothing more than the relative price of a currency. That is, the price of a currency in terms of another. Eq. (23.10) shows that the value of the exchange rate is easily calculated as the ratio of the two countries’ CPI. Eq. (23.11) then shows that the rate of exchange rate depreciation or appreciation is determined by the inflation rate differential. Eqs. (23.10) and (23.11) show that to determine the exchange rate levels and rate of appreciation all we need is information on each country’s CPI and nothing else.

But there is more to this story. The question is: what determines the price level and or the inflation rate of a country? Looking back at Eq. (23.6) we find that world monetary equilibrium for a particular currency requires that the world demand for that money equals the world supply of the currency in question. Once the demand for and supply of that money is specified, it is possible to solve for the price of the goods in consumer basket in terms of the currency in question, that is, the CPI. The equilibrium conditions allow us to determine the market-clearing price of money in terms of the goods and services produced in the economy.

Given the fact that there are two currencies, it follows that global equilibrium requires the equality of the world demand for and supply of each of the two currencies. Once the two equilibrium conditions are determined, one can solve for the two price levels and thus determine the price of one currency in terms of the other, that is, the exchange rate.

This is in theory a simple problem. However, in practice it is a bit more complicated. The complications arise from the possible alternative specifications for the demand and supply conditions. Different variations give rise to different equilibrium conditions, which in turn have profound policy and investment implications. That is why we are fond of saying that the organization of the monetary system determines the inflation potential of an economy.

The next few paragraphs explore how the different assumptions affect the equilibrium inflation rate in each of the countries as well as the rate of appreciation or depreciation of the exchange rate.