The Hedging Channel of Exchange Rate Determination

Abstract

We propose the currency hedging channel that connects countries’ external imbalances to their exchange rate behavior. We present a model in which investors increase their currency hedging during periods of financial distress in proportion to their net foreign asset exposure. This behavior coupled with constrained financial intermediation explains observed relationships between gradually adjusting external imbalances and volatile spot and forward exchange rates. We find empirical support for the hedging channel in both the conditional and unconditional moments of exchange rates, option prices, and countries’ uses of Federal Reserve swap lines.

The disconnect between exchange rates and macroeconomic variables remains one of the most persistent puzzles in international economics. Conventional macroeconomic models that match international business cycle moments often generate counterfactual exchange rate dynamics with insufficient volatility. In recent years, a growing body of evidence suggests financial intermediary constraints and global imbalances are potential drivers of exchange rate dynamics.¹ However, the precise investor actions that connect imbalances with exchange rates remain unclear. This paper shows how variation in investors’ (and borrowers’) desires to hedge exchange rate risks in their net foreign asset positions, coupled with intermediary frictions, can explain a number of stylized facts in international financial markets. By centering our channel on a quickly adjusting, countercyclical financial variable— the currency hedge ratio–we link exchange rate movements with country-level external imbalances that adjust gradually.

Our proposed channel centers on foreign exchange rate (FX) hedging activities. Figure 1 shows the hedge ratio of nine large Japanese life insurers on their foreign asset holdings and the Currency Volatility Index (CVIX) — a measure of implied exchange rate volatility analogous to the VIX Index for equities. This figure highlights several common trends in the data. Foreign institutional investors have in recent years hedged a large fraction of the currency exposure on their foreign asset holdings through forwards and swaps. Their hedging behavior is time-varying, and, moreover, their hedge ratio typically increases with currency volatility.

Fig. 1

Japanese life insurer hedge ratio

The hedge ratio is calculated by dividing the net notional amount of foreign currency forward and swap contracts (sold minus bought) and put options by the foreign currency-denominated asset holdings reported in public disclosures of nine large Japanese insurers. See Internet Appendix Section 5 for details.

In this paper, we start by highlighting several facts that are consistent with the hedging channel of exchange rate determination. First, a large set of institutional investors and borrowers hedge a sizable portion of their currency mismatches. This set of market participants has a particularly strong presence in the bond market, and therefore hedging in global fixed-income investments is more salient than in equities.

Second, in periods of increased market volatility, countries with large positive net U.S. dollar debt asset holdings, which we term “dollar imbalances,” experience domestic currency appreciation in both spot and forward exchange rate markets whereas countries with negative dollar imbalances experience currency depreciation. Our primary analysis focuses on net external U.S. dollar debt asset holdings, because exchange rate hedging is more prevalent for fixed income assets than for equities. The changes in forward exchange rates in periods of increased market volatility are larger than those of the spot exchange rates after adjusting for interest rate differentials, which produces an increase in the dispersion of cross-currency bases in line with the direction and magnitude of countries’ dollar imbalances.² We find an analogous pattern in the cross-section of currency options prices that aligns with the hedging channel.

We build a stylized model to show how variation in the demand to hedge currency mismatches coupled with constrained financial intermediation can explain the observed relationships between dollar imbalances, cross-currency bases, and other exchange rate phenomenon. We consider a foreign country and an associated representative investor who owns a portfolio of U.S. dollar-denominated securities (or owes dollar-denominated debt if the country is on net a borrower). This risk-averse investor chooses to optimally hedge a fraction of her net dollar imbalance with forward contracts. If the investor is a net purchaser of dollar securities, then she hedges her exchange rate risk by selling dollars in the forward market. On the other hand, a net borrower hedges exchange rate risk by buying dollars forward. Hence, the quantity of dollar forwards demanded depends on the product of the fraction of her dollar imbalance she wants to hedge (ie, her hedge ratio) and her net foreign asset position.³

To satisfy investors’ hedging demands, financial intermediaries produce forwards by trading the spot exchange rate along with the two countries’ interest rates. Because the financial intermediary has competing outside investment opportunities, it charges a spread for providing liquidity in forward exchange rate markets, which shows up as a cross-currency basis.

As a concrete example, take Japan, which has substantial holdings of dollar assets and a positive foreign asset position. The representative Japanese investor would like to hedge against the risk of yen appreciation, which would make her dollar position worth less in domestic currency. She hedges her exchange rate exposure by selling dollars and buying yen in the forward market with a financial intermediary. The financial intermediary must supply yen in the forward market to the Japanese investor. She does so by borrowing in dollars, converting dollars to yen in the spot market, and holding yen deposits until the forward contract’s delivery. In equilibrium, the price of the yen in forward markets has to be elevated relative to spot markets after adjusting for interest rate differentials, because the financial intermediary must be compensated for the intermediation activity.

Investor hedging demand combined with constrained financial intermediation generates predictable movements in forward and spot exchange rates. When exchange rate volatility is expected to increase, the risk-averse investor chooses to hedge a larger fraction of her dollar imbalance. This rise in a country’s hedge ratio increases the magnitude of the investor’s demand for forwards in proportion to the country’s dollar imbalance. Countries that are net savers should observe a cross-currency basis and spot exchange rate movement in the opposite direction of countries that are net borrowers.

After showing the relationships between exchange rate volatility, hedging demand and exchange rates in theory, we present evidence for our hedging channel in the data. Unfortunately, the hedge ratios of institutional investors are not widely available at the country level, and we do not directly observe hedge ratios across countries.⁴ We therefore cannot provide direct causal evidence linking hedging behavior to exchange rate phenomena. Instead, we present a number of empirical results showing a systematic relationship between exchange rates, exchange rate derivatives, dollar imbalances and exchange rate volatility that is consistent with currency hedging channel. Ultimately, we find this totality of the empirical evidence supportive of the hedging channel.

We begin by showing how hedging demand explains the cross-section of cross-currency bases and currency options prices, which are perhaps the most natural financial indicators of exchange rate hedging. We show the unconditional magnitude of cross-currency bases and currency option risk reversals align with countries’ dollar imbalances. We then regress changes in cross-currency bases and options risk-reversals on changes in expected exchange rate volatility interacted with countries’ dollar imbalances. Consistent with our theory, we find that the cost of hedging against domestic currency appreciation increases for countries with positive dollar imbalances during periods of higher volatility. By contrast, the cost of hedging against domestic currency depreciation increases for countries with negative dollar imbalances.

Next, we show that the hedging channel can explain movements in spot exchange rates in response to changes in expected exchange rate volatility. Consistent with our model, spot exchange rates of countries with more positive dollar imbalances appreciate more when expected exchange rate volatility increases. Moreover, because expected exchange rate volatility tends to mean-revert,⁵ we show our proxy for hedging demand predicts future movements in spot exchange rates.

Our results showing the relationship between spot exchange rate returns, external imbalances and exchange rate volatility are closely related to earlier findings Lustig, Roussanov, and Verdelhan (2011), Menkhoff et al. (2012), and Della Corte, Riddiough, and Sarno (2016). These papers provide risk-based explanations for currency returns in which currencies that depreciate in bad states of the world are deemed riskier and therefore must pay higher excess returns in equilibrium.⁶  Menkhoff et al. (2012) characterize risky currencies as those that were more exposed to innovations global exchange rate volatility, and Della Corte, Riddiough, and Sarno (2016) characterize risky currencies as currencies of net debtor countries. Importantly, Della Corte, Riddiough, and Sarno (2016) show that currencies of net debtor countries depreciate when global exchange rate volatility increased.

Relative to this literature, our paper makes two key contributions. First, we highlight a specific investor motive that connects countries external imbalances to its exchange rate behavior during periods of high volatility. Second, we show that within our sample of G-10 currencies, the dollar debt imbalance is more relevant for explaining exchange rate returns than the aggregate net foreign asset position studied in these earlier papers. Our result suggests that even though the broad intuition that net debtor countries are riskier is correct, there are potentially different mechanisms that link countries’ external imbalances to their exchange rates. We believe more research is needed to understand what these mechanisms are, and when these mechanisms are most salient.

Finally, to quantify the significance of the hedging channel, we analyze the behavior of cross-currency bases during the introduction of the Solvency II directive. Solvency II standardized the penalty on currency mismatches for insurance companies in the European Union and the United Kingdom, which likely acted as a positive shock to currency hedging demand. Consistent with an increase in hedging demand, we show the magnitude of cross-currency bases for currencies affected by Solvency II increased relative to other G-10 currencies. The magnitude of cross-currency bases in the United Kingdom and the euro area jumped by around 1 standard deviation after the regulation change and remained elevated for at least 2 years.

Our paper is broadly inspired by the exchange rate disconnect literature. Since the influential work of Meese and Rogoff (1983), a large literature has tried to connect economic variables with exchange rates. Recent empirical work has found some predictive power using the cyclical component of net external balances (Gourinchas and Rey 2007), investor capital flows (Evans and Lyons 2002; Froot and Ramadorai 2005; Camanho, Hau, and Rey 2022), quanto risk premiums (Kremens and Martin 2019), and shocks to intermediary constraints (Barbiero et al. 2024). Lilley et al. (2020) show that proxies for global risk appetite and risk premiums explain a significant share of currency returns after the Global Financial Crisis. With respect to currency hedging, Hau and Rey (2006) and Camanho, Hau, and Rey (2022) show how incomplete hedging of currency risks can drive cross-border equity flows and exchange rates. We contribute to this literature by linking the hedged part of investor portfolios to exchange rate derivatives transactions and exchange rate dynamics.

From a theory perspective, our paper is most closely related to the literature studying inelastic demand in currency and fixed income markets (Gabaix and Maggiori 2015; Greenwood et al. 2023; Gourinchas, Ray, and Vayanos 2020). These papers argue for a quantity driven, supply-and-demand approach towards explaining asset prices, and has been successful in explaining patterns in bonds (Vayanos and Vila 2021; Greenwood and Vayanos 2010; Krishnamurthy and Vissing-Jorgensen 2011), swap spreads (Klingler and Sundaresan 2019), mortgage-backed securities (Hanson 2014), equities (Shleifer 1986; Koijen, Richmond, and Yogo 2023), and in international portfolio positions Koijen and Yogo 2020; Jiang, Richmond, and Zhang 2024. Most relevant to our paper is Gabaix and Maggiori (2015), which highlights the role of constrained financial intermediaries in determining spot exchange rate dynamics. Our paper builds on Gabaix and Maggiori (2015) in at least two ways. First, our paper describes a quick adjusting financial channel that can explain how slow-moving external imbalances are connected with fast-moving exchange rates. Second, we focus on a specific channel for currency demand rather than describe the broad financial intermediary sector in the aggregate.⁷

Finally, our paper relates to the growing body of literature studying persistent violations of covered interest rate parity. Much of this literature shows how regulation and shocks to dollar funding supply amplify cross-currency bases (Du, Tepper, and Verdelhan 2018; Cenedese, Della Corte, and Wang 2020), whereas we show demand-side factors are necessary for explaining the full cross-section of exchange rate behavior.⁸ Others have shown that the magnitude of CIP violations covaries systematically with the broad dollar exchange rate (Avdjiev et al. 2019; Jiang, Krishnamurthy, and Lustig 2019; Engel and Wu 2023). Wallen (2022) shows that intermediaries can exercise market power in producing FX forwards and thus earning arbitrage spread in the form of CIP deviations. Most related to our paper are two recent contributions that also emphasize demand-side factors in driving cross-currency bases. Borio et al. (2018) provides evidence that exchange rate hedging behavior can drive the cross-currency bases for the euro, yen, and Australian dollar. Hazelkorn, Moskowitz, and Vasudevan (2022) study deviations from the law of one price between futures and spot prices in equities and FX with a focus on leverage demand. Relative to these two studies, we show how hedging demand connects macroeconomic fundamentals to a broader set of exchange rate phenomena and across a broader set of currencies.

1 Currency Hedging and Institutional Details

This section provides additional motivating evidence and institutional details indicating the widespread use of currency hedges in financial markets today.⁹  Figure 1 shows large Japanese insurers substantially hedge their foreign asset portfolios against currency risk. This high currency hedge ratio is not unique to Japanese insurers, but rather is the norm among large non-U.S. institutional investors, such as pensions and insurers. Many countries have regulations that restrict currency mismatch and encourages currency hedging for foreign assets.¹⁰ Furthermore, the use of currency hedges is not limited to investors. Borrowers such as large global corporate debt issuers also frequently engage in currency-hedged foreign debt issuance in order to obtain cheaper borrowing costs (Liao 2020; Caramichael, Gopinath, and Liao 2021).¹¹ Additionally, the importance of FX hedging on financial intermediation and the real economy can be seen through policy measures that curbed the use of FX derivatives and resulted in unintended consequences on nonfinancial borrowers (Keller 2019; Jung 2020).

Internet Appendix Table A1 summarizes regulatory requirements on pension and insurance sectors and estimate the lower bound on FX hedging ratios for the countries associated with our sample of G-10 currencies. The regulations and currency match requirements are mainly applicable to large institutional investors, such as pensions and insurers. These two sectors hold relatively large amounts of debt investments and have been documented to have a large impact on the yield curve (Greenwood and Vissing-Jorgensen 2018) and swap spreads (Klingler and Sundaresan 2019). Australia additionally provides country-level surveys of foreign currency exposure and hedging, which shows a much higher level of hedging for debt relative to equities. Even absent of regulations, the high hedging ratio for debt is unsurprising because exchange rate risk is large relative to fixed income returns but small relative to equity returns, and the risk-minimizing currency strategy for a global bond investor is close to a full currency hedge (Campbell, Serfaty-De Medeiros, and Viceira 2010). Sialm and Zhu (2024), for instance, find that 90% of U.S. international fixed income funds use currency forwards to manage their foreign exchange exposure. Motivated by this evidence, we employ measures of dollar imbalances that exclude equity portfolio holdings to proxy for hedging demand.

Table 1

Summary statistics

	Mean	SD	Min	Max
Cross-currency basis (bps)	–8.39	17.93	–92.15	42.11
Abs. cross-currency basis (bps)	14.02	13.98	0.01	92.15
Currency excess returns (pct)	0.99	10.67	–37.25	35.1
5-yr minus 1-yr basis spread (bps)	2.68	11.28	–48.95	60.75
Risk-reversal (pct)	–0.66	1.55	–7.28	9.85
FX volatility (pct)	10.52	2.84	4.78	22.98
Δ FX volatility (pct)	0	0.06	–0.18	0.56
USD NFA / GDP	0.37	0.38	–0.25	1.71
USD net debt holdings / GDP	0.05	0.27	–0.32	0.99
USD net equity holdings / GDP	0.32	0.21	0.04	0.99

The sample comprises monthly data for all G-10 currencies (excluding the USD) between January 2000 and December 2021. A currencies’ cross-currency bases is the spread between the exchange rate implied currency risk-free rate and the actual risk-free rate. The annualized currency excess return is the difference between the log 12-month forward rate and the log spot exchange rate in 12 months. NIIP, Debt, FDI, Equity, and GDP are measured quarterly and provided by the International Financial Statistics (IFS) from the IMF.

2 Theory

To fix ideas, we start by presenting a stylized model of exchange rate determination that links exchange rate volatility with hedging demand, external imbalances, and asset prices. Two time periods exist, t = 1, 2. The model consists of N countries, where each country contains a representative investor. A currency trader manufactures forwards by trading the spot exchange rate while borrowing and lending in the associated currencies. The asset space consists of risk-free assets in each of the N countries as well as in the United States. The risk-free rate in country n is denoted by Rⁿ, and the U.S. risk-free rate is denoted R^D. We let |$S^n_t$| denote the spot exchange rate in period t, and we let Fⁿ denote the price of currency forward contract at t = 1 that settles at t = 2. Both |$S^n_t$| and Fⁿ are quoted in terms of foreign currency per dollar.

2.1 Hedging demand

In period 1, we assume the representative investor in country n has a preexisting net external position of Xⁿ in U.S. dollar-denominated debt that matures in period 2 and earns the return R^D.¹² In period 2, the country-n investor converts her dollar position into domestic currency for consumption. We assume investors exhibit mean-variance utility over their second-period wealth:

$$U^n =\mathbb{E}\left[W^n_2\right] -\frac{\gamma}{2}\text{Var}\left[W^n_2\right],$$

where |$W^n_2$| is the investor n wealth in domestic currency, and γ is a coefficient of risk aversion. This welfare function is meant to capture the objective of institutional investors who may hold dollar-denominated assets but pay their clients in domestic currency.

The country-n investor can hedge her exchange rate exposure by trading dollars in the forward market.¹³ She takes the forward exchange rate and interest rates as given, and she chooses her optimal hedge ratio hⁿ. Her second-period wealth given a hedge ratio hⁿ is

$$W^n_2 =\underbrace{h^n X^n R^D F^n}_{\text{hedged}} +\underbrace{(1 - h^n) X^n R^D S^n_2}_{\text{unhedged}}.$$

Solving the investor’s problem shows her optimal hedge ratio is given by

$$h^n = 1 -\frac{\mathbb{E}\left[S^n_2/S^n_1\right] - (F^n/S^n_1)} {\gamma\text{Var}[S^n_2/S^n_1] X^n S^n_1 R^D}.$$

(1)

Given the dynamics of the hedge ratios shown in Figure 1, we restrict the parameter space such that the hedge ratio hⁿ is bounded in |$[0, 1]$|⁠.

 

Assumption 1.

We assume the following two conditions hold:

1. |$\frac{\mathbb{E}\left[S^n_2/S^n_1\right] - (F^n/S^n_1)}{X^n} \gt 0$|

2. |$\gamma S^n_1 R^D\text{Var}[S^n_2/S^n_1] \gt =\frac{\mathbb{E}\left[S^n_2/S^n_1\right] - (F^n/S^n_1)}{X^n}$|

The first part of Assumption 1 requires that the expected currency return is positive for countries with positive external imbalances, and negative for countries with negative external imbalances. These relationships between currency returns and countries’ external imbalances are supported by both theories (Gabaix and Maggiori 2015) and empirics (Della Corte, Riddiough, and Sarno 2016). The second part of Assumption 1 ensures that investors are risk-averse enough and their imbalances large enough such that the optimal hedge ratio never drops below zero. As we discussed in the previous section, regulatory restrictions also impose a lower bound on institutional investors’ hedge ratios.

Under Assumption 1, the investor increases her hedge ratio as the variance of the exchange rate return, |$\text{Var}[S^n_2/S^n_1]$|⁠, increases. Thus, the investor’s optimal hedging behavior mimics the hedge ratio shown in Figure 1. Her optimal hedge ratio is positively correlated with her coefficient of risk aversion and the magnitude of her imbalance.¹⁴

2.2 Supply of forwards

A currency forward trader (or equivalently an FX swap trader) exists who devotes capital to provide liquidity in forward currency markets and an alternative investment opportunity that provides the profit G(I) for an investment of I.

 

Assumption 2.

For a given positive investment I > 0, we assume |$G\left(I\right) \gt 0,\G\prime\left(I\right) \gt 0$|⁠, and |$G\prime\prime\left(I\right) \lt 0$|⁠.

Formally, we assume investments in alternative opportunities lead to positive profits, that these profits are increasing in the size of the investment, and that the investment process exhibits decreasing returns to scale.¹⁵

Letting qⁿ denote the trader’s position in dollars take in period 1 to provide liquidity for the country-n investor, we can show the forward trader ultimately earns a profit of

$$q^n b^n = q^n\left((1 + r^D)-\frac{S^n}{F^n} (1 + r^n)\right)$$

(2)

from liquidity provision.¹⁶ The term in the parenthesis, bⁿ, is commonly known as the cross-currency basis for country-n and reflects the difference between the actual dollar risk-free rate and FX-implied dollar risk-free rate. A profit maximizing forward trader should only provide liquidity in forward markets when doing so is profitable: |$q^n b^n\ge 0$|⁠. Therefore, an immediate result is that bⁿ must be negative when Xⁿ is positive, and vice versa, to incentivize the trader to supply liquidity.

Following Gârleanu and Pedersen (2011) and Ivashina, Scharfstein, and Stein (2015), we assume the forward trader must set aside a haircut |$\kappa H(q^n)$| when she devotes qⁿ dollars to providing liquidity for the country-n investor, and κ is a positive constant. Moreover, we assume the trader’s total haircut is the sum of the haircuts she sets aside for each position, |$\kappa\sum_n H(q^n)$|⁠.

 

Assumption 3.

For a nonzero position q, we assume (1)  |$H\left(q\right) \gt 0$|⁠, (2)  |$H\prime\left(q\right) \gt 0$| for q > 0, |$H\prime\left(q\right) \lt 0$| for q < 0, and (3)  |$H\prime\prime\left(q\right) \gt 0$|⁠. We also assume |$H(0) = H\prime(0) = H\prime\prime(0) = 0$|⁠.

Assumption 3 implies the cost of intermediation is increasing and convex in the magnitude of the position. The convex cost function might reflect the cost of holding concentrated position in a single currency.¹⁷

Finally, we assume the trader has an initial wealth of W dollars. After providing liquidity to forward markets, the trader is left with |$I = W -\kappa\sum_n H\left(q^n\right)$| dollars to devote to alternative investments. The trader chooses how much capital to devote to providing liquidity for each currency:

$$\max\limits_{q^n}\sum_n b^n q^n + G\left(W -\kappa\sum_n H\left(q^n\right)\right).$$

The trader’s first order condition shows the gain from devoting an additional unit of capital to providing liquidity in the forward dollar market is equal to the marginal profitability of the alternative investment:

$$b^n =\kappa G\prime\left(W -\kappa\sum_k H\left(q^k\right)\right) H\prime\left(q^n\right).$$

The country-n cross-currency basis bⁿ is a result of two forces: the country-n investor’s hedging demand and the average cost of financial intermediation. If the country-n investor does not demand dollars in the forward market, |$q^n = 0$| and the basis reduces to zero. Similarly, if providing liquidity in the forward market is costless, κ = 0, then the basis reduces to zero as well.¹⁸

2.3 Spot exchange rates

We assume bilateral spot exchange rates in each period clear the market for each currency:

$$\frac{\xi^n}{S^n} -\iota^D -\Gamma^D - q^n = 0.$$

(3)

where ξⁿ represents additional demand for dollars from country-n households denominated in the domestic currency due to trade. ι^D represents the demand for country-n currency from U.S. households due to trade, and |$\Gamma^D$| represents excess demand for dollars due to other financial flows. ξⁿ, ι^D and |$\Gamma^D$| represent demand for currencies from sectors of the economy that are not explicitly modeled.

As an example, Gabaix and Maggiori (2015) provide a model of exchange rate determination in which excess demand for dollars is determined by imbalances in goods trade. In their model, |$\left(\xi^n/S^n\right) -\iota^D$| corresponds to the net exports from the United States to the rest of the world and |$\Gamma^D$| represents the demand for dollars from some global financial intermediary, which is needed to absorb the excess demand. Within their model, the excess supply of dollar in the world responds slowly, because it depends on changes in net exports. By contrast, adding qⁿ to Equation (3) explicitly shows how demand from another financial channel can drive more rapid movements in exchange rates.

Equation (3) also clarifies the potential drivers of exchange rate volatility. The variance of exchange rate returns |$(\text{Var}[S^n_2/S^n_1])$| can increase if the demand for dollars from trade or other financial activities becomes more volatile.

2.4 Equilibrium

In equilibrium, the forward trader takes the country-n hedging demand as given, and enters into transactions to supply dollars in the forward market:

$$q^n = -h^n X^n.$$

(4)

Market clearing conditions in the forward and spot exchange rate markets determine the cross-currency basis bⁿ, the forward rate Fⁿ, and the spot exchange rate Sⁿ as a function of the hedge ratios hⁿ, each country’s external imbalance Xⁿ, and the demand for foreign exchange from other sectors of the economy, ι^D, ξⁿ, and |$\Gamma^D$|⁠.

The equilibrium is described by the following four equations:

$$h^n = 1 -\frac{\mathbb{E}\left[S^n_2/S^n_1\right] - (F^n/S^n_1)} {\gamma\text{Var}[S^n_2/S^n_1] X^n S^n_1 R^D}.\notag\\b^n =\kappa G\prime\left(W -\kappa\sum_m H\left(- h^m X^m\right)\right) H\prime\left(- h^n X^n\right),$$

(5)

 

$$S^n =\frac{\xi^n}{\iota^D +\Gamma^D - h^n X^n},$$

(6)

 

$$F^n =\frac {S^n\left(1 + r^n\right)}{\left(1 + r^D -\kappa G\prime\left(W -\kappa\sum_m H\left(- h^m X^m\right)\right) H\prime\left(- h^n X^n\right)\right)},$$

(7)

where the first equation reiterates the hedging demand Equation (1).

2.5 Model predictions

We now characterize the behavior of cross-currency bases and spot exchange rates with respect to external imbalances and exchange rate volatility. We show the exchange rates of various countries should load differently on domestic and global exchange rate volatility, and these are in line with countries’ external imbalances. All proofs are in the Internet Appendix.

2.5.1 Forward exchange rates

Our first proposition characterizes the unconditional moments of the cross-currency basis.¹⁹

 

Proposition 1.

Unconditional currency basis

A country with a positive external imbalance (X > 0) has a negative basis (b < 0), indicating an overvaluation of its currency forward. A country with a negative external imbalance (X < 0) has a positive basis (b > 0), indicating an undervaluation of its currency forward. Countries with larger imbalances are subject to larger cross-currency bases in absolute magnitude.

A country’s unconditional currency basis is a direct measure of the country’s external financial imbalance and its investors’ desires to hedge this imbalance. Intuitively, investors in countries with positive external imbalances demand domestic currency in forward markets for hedging purposes, and therefore pay a premium to purchase domestic currency in the forward market because producing currency forward is costly. This premium shows up as a negative currency basis. Conversely, countries with negative external imbalances have forward exchange rates that are unconditionally depressed relative to their spot. Investors in countries with negative external imbalances demand dollars in forward markets, and must pay a premium to exchange domestic currency for forward dollars.

 

Proposition 2.

Conditional currency basis

The magnitude of the country-n currency basis, |$|b^n|$|⁠, increases with respect to both its own exchange rate volatility, |$\text{Var}\left[S^n_2\right]$|⁠, as well as the exchange rate volatility of foreign countries, |$\text{Var}\left[S^m_2\right]$| for |$m\neq n$|⁠. Moreover, countries with larger external imbalances experience larger increases in the magnitudes of their currency bases.

Domestic and global exchange rate volatility raises the magnitude of currency bases through two channels. First, increases in the exchange rate volatility of a country n incentivizes the country n investor to hedge a greater fraction of her external imbalance. The country n basis therefore increases because the forward trader provides more liquidity to the currency n forward market, which is captured by an increase in the forward trader’s country n haircut. In addition, the forward trader faces greater balance sheet constraints overall, because of her limited intermediation capacity. As a result, the currency basis of any single country should also depend on global exchange rate volatility as a result of the exchange rate hedging.²⁰

Proposition 2 shows a country’s external imbalance identifies cross-sectional differences in the loading of currency bases on exchange rate volatility. For countries with positive imbalances, the country’s forward exchange rate becomes even more elevated relative to the spot exchange rate (bⁿ becomes more negative). By contrast, increases in exchange rate volatility further depress the forward rates of countries with negative external imbalances (bⁿ becomes more positive). Countries with larger external imbalances observe larger movements in their forward exchange rates as the costs of providing additional liquidity in the forward markets grow in proportion to the imbalance. Ultimately, Proposition 2 explains the widening of currency basis spreads during times of financial distress as the currency bases of countries with positive and negative external imbalances diverge.

2.5.2 Spot exchange rates

Next, we turn to the spot exchange rate market. Hedging demand in the forward market affects the spot market because forward traders transact in spot exchange rate markets to produce forwards.

 

Proposition 3.

Spot exchange rate

Countries’ spot exchange rates covary with domestic exchange rate volatility in proportion to their external imbalances. Countries with positive imbalances appreciate when volatility increases, and countries with negative imbalances depreciate when volatility increases.

As investors increase their hedge ratio in response to increased domestic exchange rate volatility, forward traders transact in spot exchange rate markets to satisfy the additional demand in forward markets. For a country n with a positive imbalance, forward traders use dollars to purchase additional units of country n currency, which leads to currency n appreciation. By similar logic, countries with large negative external imbalances experience domestic currency depreciation. Proposition 3 shows the magnitude of the hedging effect on spot exchange rate markets is directly proportional to the relative magnitude between the demand for dollars originating from hedging demand, and the demand for dollars from other sectors of the economy. Naturally, as the quantity of dollars required for hedging services increases, increases in the hedge ratio and forward production have a larger impact on the spot exchange rate.

Proposition 3 also shows that exchange rate hedging behavior is a source of quickly adjusting financial flows that can provide a link between slower-moving macroeconomic variables and volatile exchange rates. Equation (3) showed exchange rates are determined by the supply and demand for currencies. However, the macroeconomic sources of currency demand discussed in the literature, such as net exports, are typically slow-moving and therefore are unlikely to generate the financial flows necessary to explain volatile exchange rates. Our proposition highlights currency hedging behavior as a potential explanation for linking the slower-moving external imbalances with exchange rate movements. By contrast, currency hedge ratios respond to changes in the expected volatility of exchange rates and to changes in investor risk sentiment, which tend to be faster adjusting.

2.6 Term structure of currency basis

Recent work by Du, Hebert, and Huber (2023) shows the term structure of cross-currency bases also varies systematically over the business cycle. We extend the benchmark model by an additional period and show how hedging demand explains the systematic variation in the term structure of currency bases. We provide the general setup below but leave the model details for interested readers in Internet Appendix Section 2.5. Three time periods exist, t = 1, 2, 3. In period 1, the country-n investor still has a net external imbalance of Xⁿ, but she now hedges her period 3 payoff. The country-n investor can either trade dollars two periods forward, or trade dollars one period forward and then roll over her hedge position in period 2. For simplicity, we also take the hedging ratio as exogenous for this subsection.

In period 2, the forward trader faces uncertainty in investors’ hedging demands. With probability π, the hedging demand in period 2 equals |$h^n_L$|⁠, and with probability |$1 -\pi$|⁠, the hedging demand in period 2 equals |$h^n_H$|⁠. |$b^{n, <xref ref-type="disp-formula" rid="E4">(2)</xref>}_1$| denotes the cross-currency basis in period 1 on the forward exchange rate two periods ahead (in period 3); |$b^n_1$| denotes the one-period currency basis in period 1; |$b^n_{2, k}$| denotes the one-period basis in period 2 when the hedging demand equals |$h^n_k$| for |$k = L, H$|⁠; and |$1 + r^n_2$| denotes the one-period risk-free rate in period 2.

Solving the trader’s profit maximization problem shows the currency basis on the two-period forward is a weighted average of the one-period bases in periods 1 and 2.

 

Proposition 4.

Term structure of cross-currency bases

The term structure is upward sloping in magnitude when the short-term basis is narrow and downward sloping in magnitude when the short-term basis is wide. The long-term (two-period) cross-currency basis is the weighted average of expected basis in the two periods:

$$b^{n, <xref ref-type="disp-formula" rid="E4">(2)</xref>}_1 =\frac{b^n_1 (1 + r^n_2)}{2} +\frac{\pi b^n_{2, L} + (1 -\pi) b^n_{2, H}}{2}.$$

(8)

Equation (8) has a very natural interpretation: the two-period cross-currency basis is a weighted average of the expected period 2 basis and the period 1 basis. If, in expectation, the currency basis is expected to increase in magnitude from period 1 to period 2, the two-period basis |$b^{n, <xref ref-type="disp-formula" rid="E4">(2)</xref>}_1$| should be larger in magnitude than the period 1 basis |$b^n_1$|⁠. Proposition 2 showed currency bases increase in magnitude in response to increases in hedging demand or increases in the costs of financial intermediation. Hence, we should expect currency bases to increase in magnitude with maturity whenever the current magnitude of currency bases is relatively low (and is therefore likely to increase in the future). Conversely, we should expect currency bases to decrease in magnitude with maturity whenever the current magnitude of currency bases is relatively high.

3 Data

We assess the model predictions for the effects of currency hedging on forward and spot exchange rates, focusing on the G-10 currency regions: Australia (AUD), Canada (CAD), Switzerland (CHF), the Euro area (EUR), the United Kingdom (GBP), Japan (JPY), Norway (NOK), New Zealand (NZD), Sweden (SEK), and the United States (USD). These currencies are the most liquid and commonly traded free-floating currencies without significant capital control impediments.²¹

We measure the quantity of dollar imbalances at the country level using data on net U.S. dollar foreign debt holdings obtained from the International Monetary Fund. These measures are provided by Benetrix et al. (2019), and capture the currency composition of countries’ international investment positions from 1990 to 2017. Because these positions are relatively stable over time, we forward-fill the data to the end of our sample period.

We focus our main analysis on measures of dollar debt holdings for two main reasons. First, we focus on dollar asset position to match our pricing measures of bilateral exchange rates versus the U.S. dollar. Second, we focus on debt holdings, rather than debt and equity holdings, because the use of currency hedges is more prevalent for debt instruments. Cross-boarder debt investments are dominated by institutional investors that hedge a greater fraction of their currency exposure due to either regulatory mandates or risk constraints, likely because exchange rate risks are larger for debt investments than for equity investments. For instance, Campbell, Serfaty-De Medeiros, and Viceira (2010) shows that the risk-minimizing currency strategy for a global bond investor is close to a full currency hedge, whereas the currency risk is attractive for global equity investors.²²

We obtain measures of forward-looking currency volatility with at-the-money options implied volatilities of 1-year maturity. Alternative maturity choices (e.g., 1 month and 3 months) also yield similar results. The data are from Bloomberg.

To measure the price impact of hedging dollar imbalances, we use Libor-based currency basis defined as the difference between the forward premium and interest rate differential:

$$b^n_{t}\approx (f^n_{t, t + 1} - s^n_t) + (r^D_t - r^n_t),$$

(9)

where |$r^D_t$| and |$r^n_t$| are the Libor interest rates in the United States and foreign country n, respectively.²³ The use of alternative benchmarks (e.g., Overnight Index Swap rates or constant maturity Treasury rates), does not materially affect our findings. As defined here and equivalently in Equation (2) in levels, foreign currency appreciation in the forward market is represented by a more negative cross-currency basis |$b^n_t$|⁠. We focus on Libor rates and forward rates at the 1-year maturity. Forwards with maturities of less than 1 year are often affected by temporary spikes near quarter-ends and year-ends, because of banks’ regulatory window dressing (Du, Tepper, and Verdelhan 2018; Correa, Du, and Liao 2020).²⁴ We additionally analyze the relative pricing of call and put options as captured by currency risk reversals to provide evidence corroborating our hedging channel. Table 1 provides summary statistics for each of the variables used in our analysis.

4 Empirical Results

In this section, we present evidence for each of our propositions and characterize the systematic relationship between exchange rate returns, cross-currency bases, currency options, and exchange rate volatility. As we discussed in the introduction, the hedge ratios of institutional investors are not readily accessible at a country level, and therefore we do not directly observe the behavior of hedge ratios for a large sample of countries. Therefore, instead of providing direct evidence linking exchange rate behavior to hedging demand, we present a number of empirical results showing a systematic relationship between forward and spot exchange rates and exchange rate volatility that is consistent with currency hedging behavior as predicted by our model. In the final subsections, we analyze the behavior of cross-currency bases around the implementation of Solvency II, a regulatory change that likely increased currency hedging among U.K. and euro-area insurance companies.

4.1 Forward exchange rates

Consistent with Proposition 1, panel A of Figure 2 shows a strong inverse relationship between countries’ unconditional cross-currency bases and their dollar imbalances. To reiterate, a negative basis indicates the currency’s forward price is overvalued relative to its spot price after adjusting for the interest rate differentials, while a positive basis indicates an undervaluation of the currency in forward markets. Panel A of Figure 2 shows that investors in countries with more positive dollar debt imbalances pay a higher cross-currency basis in order to hedge their exchange rate exposure.²⁵

Fig. 2

Dollar imbalances, cross-currency bases, and options risk-reversals

This figure presents unconditional relationships between average cross-currency bases, currency risk reversals and dollar imbalances. Panel A shows the relationship between average cross-currency bases and average dollar imbalances. The slope of the regression line is –32.77 (s.e. = 13.68). Panel B shows the relationship between average risk reversals and average dollar imbalances. A risk reversal captures the relative pricing of calls and puts on currencies as measured by the difference in implied volatility between the 25-delta call minus put. The slope of the regression line is 3.34 (s.e. = 1.04). Our sample ranges from January 2000 to December 2021.

Table 2 formally tests for the negative unconditional relationship between countries’ dollar imbalances and their cross-currency basis. We run a panel regression of the level of cross-currency bases on various measure of dollar imbalances. Columns 1 and 2 focus on the relationship between currency basis and a general measure of imbalance–the country’s dollar net international investment positions (NIIP). The relationship between the overall dollar NIIP and cross-currency bases is statistically significant. Crucially, columns 3 and 4 show the inverse relationship between external imbalances and unconditional currency bases is primarily driven by dollar debt imbalances. The point estimate of –25.6 in column 3 indicates that a 10% increase in a country’s dollar imbalance coincides with an additional 2.56 bp increase in the country’s cross-currency basis. By contrast, the coefficients on equity imbalances in columns 5 and 6 are statistically insignificant. Thus, equity imbalances provide much less explanatory power, which aligns with the theoretical prediction of greater currency hedging in debt instruments (Campbell, Serfaty-De Medeiros, and Viceira 2010).²⁶

Table 2

External imbalances and cross-currency bases

	Cross-currency basis (basis points)
	(1)	(2)	(3)	(4)	(5)	(6)
USD NIIP	–17.50**	–17.43*
	(7.76)	(9.70)
USD debt			–25.56**	–24.43*
			(11.70)	(12.57)
USD equity					–17.64	–14.48
					(12.08)	(21.70)
Fixed effects		Month		Month		Month
Num. obs.	2, 363	2, 363	2, 363	2, 363	2, 363	2, 363
R-sq. (full)	.14	.37	.14	.38	.04	.28
R-sq. (proj)	.14	.15	.14	.17	.04	.03

This table presents panel regressions of monthly cross-currency bases on various measures of external imbalances. USD NIIP captures a region’s dollar denominated debt plus equity imbalance. USD debt captures the region’s dollar denominated debt imbalance, and USD equity captures a region’s dollar denominated equity imbalance. All measures are nomalized by GDP. The external imbalance measures are updated at an annual frequency. The sample period is from 2000 to 2021. Standard errors are clustered by currency.

*

p <.1;

**

p <.05;

***

p <.01

4.2 Currency options

We now turn our analysis to another asset class that is directly affected by currency hedging behavior–currency options. The relationship between currency options prices and exchange rate hedging is natural because currency options are also used to hedge against exchange rate risk. A Japanese investor who is holding onto dollars and wants to ensure her ability to convert those dollars into yen at a lower fixed price can hedge by buying call options on Japanese yen. Prior studies have used out-of-the-money options to gauge rare disaster risks Farhi and Gabaix 2016; Barro and Liao 2020 and currency crash risks Farhi et al. 2015; Chernov, Graveline, and Zviadadze 2018; Jurek 2014.

Our hedging demand channel explains the cross-sectional heterogeneity in the pricing of out-of-the-money calls and puts for different currencies. Intuitively, investors in countries with net positive foreign investments can alternatively hedge against the appreciation of home currency (or, equivalently, the devaluation of their foreign currency position) by purchasing calls on their domestic currency instead of buying forwards. Therefore, we would expect hedging demand to elevate both the price of forwards relative to spot and the price of calls relative to puts on the domestic currency when the dollar imbalance is positive. When a country’s dollar imbalance is negative, we would expect hedging demand to decrease the price of calls relative to puts.

We use risk-reversals to measure the relative pricing of calls and puts, which are defined as the implied volatility of the out-of-the-money call minus put,²⁷ Risk-reversals are routinely used by traders to assess the relative valuation of calls and puts and have been used in prior studies on currency options, such as in Farhi and Gabaix (2016).

Consistent with our intuition above, we find countries with more positive dollar imbalances have relatively more expensive out-of-the-money call options compared with put options on their currency. Panel B of Figure 2 plots each currency’s unconditional risk reversal against the country’s dollar debt imbalance. The two are clearly positively correlated. Call options are on average relatively more expensive than put options on the currencies of countries with higher average dollar imbalances.

Table 3 formally tests for the relationship between currency options prices and dollar imbalances. Columns 1 and 2 show variation in U.S. dollar NIIP explains the unconditional variation in risk reversals across countries. However, columns 3 and 4 show that the explanatory power of a country’s NIIP is primarily driven by the debt component of the imbalance. Column 4 shows that countries with a 10 percentage point higher dollar debt imbalance suffer from a 0.275 percentage point increase in the relative price of their call options. Table 1 shows the standard deviation of risk reversals is 1.55 percentage points, showing that the impact of dollar imbalances on risk reversals is economically significant.

Table 3

External imbalances and options risk-reversals

	Risk reversals (percentage points)
	(1)	(2)	(3)	(4)	(5)	(6)
USD NIIP	1.11*	1.52***
	(0.59)	(0.48)
USD debt			2.56**	2.75**
			(1.00)	(1.07)
USD equity					–0.42	–0.05
					(1.59)	(2.05)
Fixed effects		Month		Month		Month
Obs.	2, 363	2, 363	2, 363	2, 363	2, 363	2, 363
R-sq. (full model)	.08	.44	.19	.53	.00	.32
R-sq. (proj model)	.08	.17	.19	.31	.00	.00

This table presents panel regressions of monthly risk-reversals on various measures of external imbalances. See the notes in Table 2 for variable descriptions. The external imbalance measures are updated at an annual frequency. The sample period is from 2000 to 2021. Standard errors are clustered by currency.

*

p <.1;

**

p <.05;

***

p <.01.

A key feature of the data is that the results in Tables 2 and 3 are driven by cross-sectional differences in dollar imbalances. Put simply, there is not enough variation in dollar imbalances over time to explain the variation in these financial variables. Internet Appendix Table A3 introduces currency fixed effects into our specifications for Tables 2 and 3 and show coefficients are almost all statistically insignificant or are of the wrong sign. For dollar imbalances to explain time-series variation in cross-currency bases and options prices, we need to introduce time-varying currency hedging.

4.3 Dynamics of forwards and currency options

In the following section, we show the dynamics of forward exchange rates and currency options vary systematically with fluctuations in exchange rate volatility and in accordance with their dollar debt imbalances. To evaluate the variation in exchange rates, we run panel regressions of the following form:

$$\Delta y^n_t =\alpha^n +\delta_t +\beta\left(\text{Imbalance}^n_t\right)\times\left(\Delta\text{FX Vol.}^n_t\right) +\Xi^n_t +\varepsilon^n_t,$$

(10)

where |$\Delta y^n_t$| captures changes in the variable of interest (ie, cross-currency basis or the option risk-reversal), and βⁿ is the coefficient of interest on the interaction term between the country’s U.S. dollar imbalance, and changes in expected exchange rate volatility. We include date and currency fixed effects in each of our regressions, and we also cluster our standard errors by date and currency.

Columns 1 and 2 of Table 4 provide evidence for Proposition 2. The coefficients on the interaction terms between a country’s U.S. dollar imbalance and exchange rate volatility are both negative and statistically significant. Thus, a country’s currency basis increases in proportion to its dollar imbalance when expected exchange rate volatility increases. For a country with an external USD imbalance equal to its GDP, a one-standard-deviation increase in its expected exchange rate volatility decreases its currency basis by 1.74 bps. Countries with positive imbalances observe their currency bases becomes more negative and their currency become more overvalued in forward markets. On the other hand, countries with negative imbalances observe their currency bases become more positive, and their currency becomes more undervalued in forward markets.

Table 4

Cross-currency bases and risk-reversal dynamics

	Currency basis (bps)		Risk reversals (pps)
	(1)	(2)	(3)	(4)
USD imbalance ×Δ FX vol.	–1.74**		0.38*
	(0.56)		(0.17)
USD imbalance ×Δ Global FX vol.		–1.67**		0.40**
		(0.67)		(0.17)
USD imbalance	0.73	0.72	0.00	0.01
	(0.63)	(0.66)	(0.02)	(0.04)
Δ FX vol.	–0.31		–0.12***
	(0.25)		(0.03)
Obs.	2, 362	2, 362	2, 363	2, 363
R-sq. (full model)	.46	.46	.45	.45
R-sq. (proj model)	.03	.02	.14	.15

The following table presents panel regressions of monthly changes in cross-currency bases and risk-reversals on dollar debt imbalances and measures of exchange rate volatility. Cross-currency bases are measures in basis points and risk-reversals are measured in percentage points. Δ FX vol. captures changes in country specific FX volatility, and Δ Global FX vol. captures changes in global FX volatility defined as the average change in FX volatility across all countries. All regressions include month and currency fixed effects. Standard errors are clustered by currency and date.

*

p <.1;

**

p <.05;

***

p <.01.

The results in columns 1 and 2 show that currency bases vary systematically with measures of both domestic exchange rate volatility, as well as global exchange rate volatility. While this result does align with Proposition 2, expected exchange rate volatility tends to be highly correlated across countries empirically. Thus, it is perhaps less surprising that currency bases respond to both domestic and global volatility.

Figure 3 shows the time series of risk reversals for the sample currencies. The graph highlights a few systematic features that resemble the time series of cross-currency bases.²⁸ First, options risk reversals increased in magnitude starting in 2008, a fact highlighted in Farhi et al. (2015). Second, the figure shows substantial cross-sectional heterogeneity between currencies. Currency regions that have large negative dollar imbalances, for example, Australia, typically have the most negative risk-reversal, indicating a premium for put options over call options. Currencies with a more positive dollar imbalances (e.g., Japan), have more expensive calls relative to puts, as indicated by positive risk reversals. This positive risk-reversal indicates a more expensive hedging cost for currency appreciation than a depreciation. Lastly, the risk-reversals widen in times of crisis in directions that are aligned with the hedging demand of dollar imbalances. This dispersion indicates that a single dollar factor is unlikely to explain the dynamics of option skew.

Fig. 3

Currency options risk-reversals

This figure presents the time series of relative pricing of calls and puts on G-10 currencies as measured by their risk-reversals. The sample runs from January 2005 to December 2021.

Columns 3 and 4 of Table 4 show the results of regressing changes in risk-reversals on the interaction between countries’ dollar imbalances and changes in exchange rate volatility. Analogous to our earlier analysis of cross-currency bases, we show that the magnitude of the costs of hedging exchange rate risk increases with expected exchange rate volatility. As expected exchange rate volatility increases, call options on domestic currency become relatively more expensive for countries with positive imbalances, and put options become relatively more expensive for countries with negative imbalances.

4.4 Spot exchange rates and forecasting

Up to this point, we have focused on the asset prices most directly related to currency hedging. Now, we show the systematic behavior in spot currency markets that is also consistent with our hedging channel. We begin by estimating Equation (10) to understand spot exchange rate behavior in response to changes in expected exchange rate volatility.

Table 5 provides evidence for Proposition 3. The coefficients on the interaction terms between U.S. dollar imbalances and expected exchange rate volatility are negative and statistically significant. Column 1 shows that for a country with an external USD imbalance equal to its GDP, a one-standard-deviation increase in its expected exchange rate volatility explains a currency appreciation of 1.15 percentage points. The currencies of countries with more positive U.S. dollar imbalances appreciate relative to countries with more negative imbalances in response to increases in expected exchange rate volatility.

Table 5

Spot exchange rate dynamics

	(1)	(2)	(3)	(4)
USD imbalance ×Δ FX vol.	–1.15*		–1.44*
	(0.55)		(0.64)
USD imbalance ×Δ Global FX vol.		–1.16*		–1.43*
		(0.56)		(0.67)
NFA×Δ FX vol.			0.16
			(0.31)
NFA×Δ Global FX vol.				0.15
				(0.29)
USD imbalance	–0.08	–0.10	–0.08	–0.09
	(0.26)	(0.27)	(0.29)	(0.29)
Δ FX vol.	0.64***		0.62***
	(0.17)		(0.18)
NFA			0.00	0.01
			(0.08)	(0.09)
Obs.	2, 363	2, 363	2, 354	2, 354
R-sq. (full model)	.62	.61	.61	.61
R-sq. (proj model)	.07	.04	.07	.05

This table presents panel regressions of monthly changes in spot exchange rate returns on dollar debt imbalances and measures of exchange rate volatility. See the notes of Table 4 for variable definitions. All regressions include month and currency fixed effects. Standard errors are clustered by currency and date.

*

p <.1;

**

p <.05;

***

p <.01.

As we discussed in our introduction, these results echo earlier work by Lustig, Roussanov, and Verdelhan (2011), Menkhoff et al. (2012), and Della Corte, Riddiough, and Sarno (2016). Specifically, Della Corte, Riddiough, and Sarno (2016) showed that currencies of net debtor countries (as measured by aggregate net foreign asset positions) tended to depreciate more in response increasing exchange rate volatility. The primary difference between our regressions and those of Della Corte, Riddiough, and Sarno (2016) is that we focus on the dollar debt imbalance, rather than the entire net foreign asset position.

To highlight how our result is distinct from earlier work, we introduce the interaction between each countries aggregate net foreign position (normalized by GDP) and exchange rate volatility into our regressions in columns 3 and 4 of Table 5. The coefficients in the first two rows on the interaction between dollar debt imbalances and exchange rate volatility remain statistically significant, whereas the coefficients on the interaction between the aggregate net foreign asset position and exchange rate volatility are small and statistically insignificant.

Our interpretation of this result is that even though Della Corte, Riddiough, and Sarno (2016) showed a broad relationship between external imbalances, volatility and spot exchange rates, the specific mechanisms that tie these variable together can differ across countries. Within our sample of large, developed economies, the relationship between dollar debt imbalances and exchange rates may be more salient due to the increased presence of exchange rate hedging. Internet Appendix Table A7 shows the interaction between countries’ U.S. dollar equity imbalance and volatility does not explain exchange rate returns, and suggests that not all components of countries’ net foreign asset positions are relevant for explaining currency returns within our sample.²⁹ In more recent work, Brauer and Hau (2022) construct a proxy for hedging pressure using Continuous Linked Settlement (CLS) data, and they find that time-varying fluctuations in hedging demand can account for approximately 30% of all monthly variation in the seven most important dollar exchange rates from 2012 to 2022. In this sense, our research shows that more research is necessary to understand the mechanisms linking external imbalances and exchange rates, and when these mechanisms are most salient.

Currency hedging also forecasts future exchange rate returns. Expected exchange rate volatility and, therefore, the associated response in optimal hedging ratio tend to be mean reverting.³⁰ During periods of higher expected exchange rate volatility, investors optimally increase their hedge positions, and financial intermediaries produce forward currency to meet this demand. As expected exchange rate volatility declines, investors and financial intermediaries will naturally unwind their positions.

Thus, the hedging channel yields an additional prediction about exchange rate predictability. In a period of above-average exchange rate volatility, countries with positive dollar imbalances should depreciate in the future, whereas countries with negative dollar imbalances should appreciate. To test this prediction, we run the following panel regression:

$$\Delta s^n_{t, t +\tau} =\alpha^n +\gamma\left(\text{Imbalance}^n_t\right)\times\left(\text{FX Vol}^n_t\right) +\Xi^n_t +\eta^n_t,$$

(11)

where |$s^n_{t, t +\tau}$| is the log spot exchange rate return between period t and |$t +\tau$|⁠, αⁿ continues to capture a currency fixed effect, |$\Xi^n_t$| is a vector of controls. Notably, we interact the country n imbalance with the level of the currency n volatility, rather than the change in volatility, because a higher than average exchange rate volatility level will likely revert in the future. γ is the coefficient of interest, which should be positive.

Table 6 shows the results of estimating regression 11 for forecast horizons of 3, 6, and 12 months. The top row shows that across all forecast horizons, an above-average level of expected exchange rate volatility predicts currency depreciation for countries with positive imbalances, and currency appreciation for currencies with negative imbalances. For a country with a positive imbalance equal to its GDP, a one-standard-deviation above-average exchange rate volatility predicts exchange rate depreciation of 2.33% over the next 6 months and 4.00% over the next 12 months. These estimates are both quantitatively large and statistically significant. The magnitude and significance of the currency returns increase over time, which reflects a gradual decline in hedge ratios following a period of high exchange rate volatility.³¹

Table 6

Exchange rate forecasting regressions

	3 month	6 month	12 month
USD imbalance × FX vol	0.93	2.33*	4.00*
	(0.67)	(1.20)	(2.23)
FX vol	–0.49**	–1.07***	–1.62***
	(0.20)	(0.36)	(0.58)
USD imbalance	1.34	3.07	5.83
	(1.68)	(3.06)	(5.22)
Obs.	2, 336	2, 309	2, 255
R-sq.	.01	.02	.03

This table presents the results of exchange rate return forecasting regressions. At time horizons of 3, 6, and 12 months, we regress exchange rate returns on FX vol, USD imbalance, and the interaction term USD imbalance × FX vol at the start of the period. We include a currency fixed effect in all specifications. We compute Newey-West standard errors with lags equal to 1.5 times the return horizon.

*

p <.1;

**

p <.05;

***

p <.01.

Table 7

Cross-currency basis term structure and dynamics

	Level (pps)		Changes (pps)
	(1)	(2)	(3)	(4)
USD imbalance	–19.35***	–20.60**	0.00	0.00
	(7.32)	(7.30)	(0.12)	(0.12)
USD imbalance ×Δ FX Vol.			0.74*
			(0.34)
USD imbalance ×Δ Global FX vol				0.61
				(0.35)
Δ FX vol			0.12
			(0.16)
Date F.E.		Y	Y	Y
Currency F.E.			Y	Y
Num. obs.	2, 360	2, 360	2, 347	2, 347
R-sq. (full model)	.21	.37	.34	.34
R-sq. (proj model)	.21	.26	.01	.00

This table presents panel regressions of levels and changes in the 5-year minus 1-year currency basis spread on dollar debt imbalances and measures of exchange rate volatility. Columns 1 and 2 regress the level of the basis spread on dependent variables, while columns 3 and 4 regress changes in the basis spread. See Table 4 for additional variable definitions. Standard errors are clustered by currency and date.

*

p <.1;

**

p <.05;

***

p <.01.

The exchange rate returns predicted by the interaction of dollar imbalances and expected exchange rate volatility are distinct from the predictive power of each of these covariates alone. We include both dollar imbalances and volatility into the regressions as controls. The negative coefficient estimate on volatility suggests that when volatility is high, the dollar tends to depreciate against all currencies in the next 3 to 12 months. This predicted dollar depreciation corroborates the notion that our regression captures exchange rate behavior in which investors are likely to decrease exchange rate hedges in a period of declining risk and vice versa.

4.5 Discussion: Implications for currency risk premiums

The conditional spot exchange rate returns discussed in the previous section provide an additional explanation for the highly persistent differences in interest rates and currency returns across countries, which capture differences in risk premiums (Lustig and Verdelhan 2007; Lustig, Roussanov, and Verdelhan 2011).

We showed that time-varying currency hedging behavior leads to predictable currency returns in both the time series and in the cross-section of countries that are aligned with countries’ dollar imbalances. Currencies of countries with positive dollar debt imbalances appreciate during periods of financial distress as a result of increased hedging demand, and depreciate when risks diminish. These currencies are therefore safer and investing in currencies of countries with positive imbalances should yield lower returns. On the other hand, currencies of countries with negative imbalances behave in exactly the opposite manner, and thus must reward investors for taking more risk by paying higher returns.

Figure 4 shows the unconditional relationship inverse relationship between average currency excess returns and forward premiums against countries’ net dollar debt holdings.³² Currencies with large positive net dollar debt investments typically embed lower currency risk premiums and yield lower excess returns. Meanwhile, currencies associated with countries that have large negative net dollar debt yield higher returns. A version of these relationships have been highlighted previously by Della Corte, Riddiough, and Sarno (2016), who showed cross-sectional variation in currency excess returns is related to countries’ aggregate net foreign asset positions. As discussed in the last section, our results suggest different components of countries’ net foreign asset positions may be responsible for the patterns in unconditional currency returns depending on the economic mechanisms at work.

Fig. 4

Dollar imbalances, forward premiums, and currency excess returns

The left-hand-side panel of this figure plots the average 12-month forward premiums of each G-10 currency against the countries’ average dollar imbalances. The slope of the regression line is -4.52 (s.e. = 1.53). The right-hand-side panel plots the average 12-month currency excess returns of each G-10 currency against countries’ dollar debt imbalances. The slope of the regression line is -3.70 (s.e.=2.62).

4.6 The term structure of currency basis

The demand for hedging instruments can also explain the term premia on cross-currency basis.³³  Proposition 4 shows the magnitude of longer maturity forwards (and currency bases) should be larger in magnitude to compensate intermediaries for the possibility of financial crises. In other words, longer maturity forwards embed a term premium, and therefore, the term structure of currency basis is typically upward sloping in magnitude.

We test for this systematic variation in the term structure of forward exchange rates formally in Table 7. In the first two columns of Table 7, we regress the level of the 5-year minus 1-year currency basis spread on countries’ U.S. dollar imbalances. The estimated coefficient is negative and highly statistically significant, which indicates that countries with negative imbalances have, on average, an upwards-sloping basis term structure. By contrast, countries with positive imbalances have a downwards-sloping term structure. Thus, the results confirm our model predictions in 4. Figure 5 presents this finding graphically.

Fig. 5

Term structure of cross-currency basis

This figure plots the average spread between the 5-year and the 1-year cross-currency basis against average U.S. dollar imbalances for the G-10 currencies from January 2000 to December 2021.

Columns 3 and 4 show the results of regressing changes in the 5-year minus 1-year basis spread on the interaction between countries’ dollar imbalances and changes in exchange rate volatility. The positive and statistically significant coefficients show that during periods of financial distress, the term structures of cross-currency bases systematically invert: the slopes of the term structures of countries with negative dollar imbalances become more negative, and the slopes of the term structure of countries with positive dollar imbalances become more positive.

5 Case Study: Solvency II

To provide more evidence for the hedging channel’s impact on exchange rate markets, we study the implementation of Solvency II. The Solvency II directive was implemented on January 1, 2016, and it harmonized the insurance regulatory regime in Europe and the United Kingdom. Part of the Solvency II directive imposed a significant capital charge (usually 25%) on currency mismatches of European and U.K. insurers. While we do not have direct evidence of hedging practices prior to or after the implementation of Solvency II, industry analysis suggests that these new rules increased the regulatory burden on insurance companies for at least some jurisdictions (Rae et al. 2018). Thus, the implementation of Solvency II presents an opportunity to study the impact of an increase in hedging demand on the currency market. This increase in hedging demand should have increased the magnitude of currency basis for currency regions that were affected by Solvency II, because at least some insurance companies in these regions would have needed to trade in currency forward markets to hedge more of their exposures.³⁴

Figure 6 presents the average difference between the magnitude of currency bases in currencies affected by the Solvency II regulation relative to the countries not affected by Solvency II after controlling for differences in external imbalances. The left-hand-side figure shows data for currency bases at the 1-year tenor. Prior to 2016, the dots in the left-hand-side figure lie close to zero and indicate that the magnitude of the euro and U.K. pound cross-currency bases were similar to the magnitude of other currencies bases after controlling for differences in external imbalances. Starting around the end of 2015 and especially after 2016, the magnitude of the 1-year cross-currency bases rose notably in both the euro area and United Kingdom relative to other currency regions before leveling off. A similar pattern can be observed in the 5-year cross-currency bases, except that the rise in the 5-year cross-currency bases began earlier. Overall the increase in the cross-currency basis is roughly 10 basis points for the 1-year tenor and 20 bps for the 5-year tenor, with some of the increase occurring in 2015.

Fig. 6

Solvency II and cross-currency bases

These figures present the average difference between the magnitude of cross-currency bases in the United Kingdom and the euro area against the other G-10 currencies after controlling for differences in dollar imbalances. We compute the residuals from a regression of the magnitude cross-currency bases on the magnitude of dollar imbalances. We then compute the difference between the residuals for the euro area and United Kingdom against the other G-10 currencies. The left-hand-side figure shows results for the 1-year tenor, and the right-hand-side figure shows results for the 5-year tenor.

Table 8 formally quantifies the change in the magnitude of currency basis in regions affected by the Solvency II directive through a differences-in-differences regression. We regress the magnitude of currency bases an indicator for post-2016 observations, a treatment indicator, the interaction of the two indicator variables and we control for the magnitude of external imbalances. The coefficient of interest is on the interaction of the treatment indicator with the post-2016 indicator. The first two columns show currency bases in the United Kingdom and euro area increased 9 bps for the 1-year and 10 bps for the 5-year tenor relative to currency basis for the other G-10 currencies after the implementation of Solvency II. This increase is statistically significant and also economically meaningful given that the average magnitude of currency basis at the 1-year tenor is only 14 bps. The last two columns collapses the time series into just a pre- and post-implementation period following Bertrand, Duflo, and Mullainathan (2004), and shows results are qualitatively similar under this alternative specification.

Table 8

Solvency II and cross-currency basis

	Monthly data		Collapsed data
	1 year	5 year	1 year	5 year
Solvency 2 × Post	8.96**	10.03**	8.87***	10.15**
	(3.47)	(4.72)	(2.22)	(3.67)
Solvency 2	5.54	1.63	5.67***	1.46
	(3.56)	(2.11)	(0.85)	(2.65)
Post	–3.17	1.39	–3.47	1.80
	(6.67)	(9.38)	(5.48)	(8.99)
|$\left| \text{USD imbalance} \right|$|	31.10***	60.12***	29.52***	62.22*
	(10.05)	(23.18)	(7.13)	(28.89)
Constant	11.67***	7.68	12.06***	7.16
	(2.57)	(5.73)	(2.18)	(6.86)
Num. obs.	441	441	18	18
R-sq. (full model)	.28	.27	.35	.30
R-sq. (proj model)	.28	.27	.35	.30

This table presents results of a differences-in-differences regression around the implementation of Solvency II. Specifically, we run the following regression:

$$|b^n| =\alpha_0 +\alpha_1\mathbb{1}_{\text{Solvency 2}} +\alpha_2\mathbb{1}_{\text{Post}} +\alpha_3\left(\mathbb{1}_{\text{Solvency 2}}\times\mathbb{1}_{\text{Post}}\right)+ |(\text{USD Imbalance})^n| +\eta^n_t$$

where |$|\cdot|$| represents the absolute value function, |$\mathbb{1}_{\text{Solvency 2}}$| is an indicator for whether the currency region was affected by the Solvency II regulation and |$\mathbb{1}_{\text{Post}}$| is an indicator equal to 1 for months including and after January 2016. We restrict the sample to observations in a two-year window around January 2016 (January 2014 to December 2017). In the first two columns, we run a the regression above using data at the monthly frequency. In the last two columns, we run the same specification, but we collapse the data into a pre- and post-implementation period. Standard errors are clustered by currency and date.

*

p <.1;

**

p <.05;

***

p <.01.

We provide two caveats to our analysis of the introduction of Solvency II and its potential effects on cross-currency bases. First, the implementation of the Solvency II directive was known years in advance. The EU Parliament vote agreeing to implement Solvency II occurred on March 14, 2014. Therefore, we observe increases in cross-currency bases before the actual implementation date. These pre-trends make it impossible to estimate the causal impact of Solvency II, and our measure of the increase in cross-currency bases due to the demand shock is likely understated because financial intermediaries could have increased their supply of currency forward in anticipation of the increase in hedging demand.

Second, during the same time as the implementation of Solvency II, interest rates declined in treated countries relative to untreated countries. Internet Appendix Table A7 shows the interest rate differential widened significantly more in countries affected by the implementation of Solvency II relative to countries that were not affected. The widening of interest rate differentials could potentially have led to behavior that increased cross-currency basis in treated countries. For example, one narrative during this period of time was that U.S. firms were issuing euro-denominated debt in the euro area to take advantage of lower European interest rates Borio et al. (2018). These U.S. firms would then buy euros forward to hedge their exchange rate risk, and this behavior would contribute to a widening the EUR-USD cross-currency basis. While this behavior does fall under the category of currency hedging, it is not the specific hedging behavior induced by the implementation of Solvency II.

Ultimately, we believe the analysis in this section adds to the collection of results that are explained by the currency hedging channel. Cross-currency bases widened in countries where institutional investors were required to hedge a larger share of their currency imbalance. Our results suggest that gathering micro-data on institutional investor hedging behavior during this period could be a useful avenue for future research.

6 Case Study: Central Bank Swap Lines

In this last section, we show our hedging channel identifies a unique mechanism through which central bank swap lines reduces currency bases and affect exchange rate behaviors. The Federal Reserve dollar swap lines lend dollars against foreign currency as collateral with foreign central banks as counterparties. These foreign central banks, in turn, lend dollars from the swap line to their domestic institutions on a collateralized basis. Previous studies have emphasized the use of dollar swap lines to satisfy short-term funding needs of the banking sector (Goldberg, Kennedy, and Miu 2011; Ivashina, Scharfstein, and Stein 2015) and the role of the Federal Reserve as a “lender of last resort” through the provision of loans to the rest of the world via swap lines (Bahaj and Reis 2022). Relative to other studies, we emphasize the role of the dollar swap line in fulfilling the hedging demand from nonbank sectors of the economy. Our model also predicts that the dollar swap line is most used by countries that have a surplus of dollar investments rather than dollar debt.

Within our framework, central bank swap lines influence exchange rates through two potential channels. In the first channel, the dollar swap line provides funding for intermediaries that produce hedging instruments for nonbanks. Thus, central bank swap lines are useful for intermediaries providing liquidity to countries with positive external imbalances, because these intermediaries need to borrow in dollars today to produce foreign currency forward.³⁵ On the other hand, intermediaries providing hedging services to countries with negative imbalances would demand foreign currency rather than U.S. dollars.³⁶ In the second channel, the announcement of swap lines may also affect exchange rate markets by instilling confidence in the financial sector. This channel could lower balance sheet costs and lower institutional hedging demand.

Thus, the actual use of central bank swap lines should differ according to countries’ external imbalances as a result of differential hedging demands. Countries with positive external imbalances, “dollar-rich” countries, would benefit more from the dollar swap line through the direct injection of dollar cash that lowers the cost of producing local currency forwards. By contrast, countries with negative external imbalances, “dollar-poor” countries, do not benefit from a direct dollar cash injection, and thus should exhibit little draws on their dollar swap lines. In fact, any draw on the dollar swap line would worsen negative external imbalances, which would widen their cross-currency basis.

We view the sudden financial shock from early periods of the COVID-19 pandemic in March of 2020 as a case study on the draws of Federal Reserve dollar swap line in relation to funding and hedging needs of intermediaries.³⁷ This period of extreme market volatility led to a draw of the dollar swap line of $449 billion at its peak.

Figure 7 provides evidence for the hypothesis on hedging use by demonstrating the positive relationship between the maximum swap draws outstanding during the weeks following the Fed’s swap line expansions, and the associated countries’ net dollar external debt holdings. Countries with low or negative net dollar debt positions made little or no use of the dollar swap line, while countries with higher net dollar debt investments had larger draws in the absolute amount of the dollar swap line.

Fig. 7

Dollar imbalances and swap lines during COVID-19

This figure plots the maximum swap line draw by each central bank between March 2020 and July 2020 against the country’s dollar imbalance. The regression line has a slope of 0.02 (s.e. = 0.01).

Even though debtor countries are generally more in need of dollars, the countries with positive dollar fixed-income holdings and overall positive net foreign investments drew on the swap line the most. This counterintuitive pattern can be explained through the hedging channel. Exploiting the heterogeneity across maturity in addition to that across currencies, we find the increased demand for longer maturity swap line operations (84 days) during the COVID-19 pandemic, as opposed to the 7-day operations, likely reflect hedging demand in addition to funding demand. Because short-term FX swaps are substitutable with domestic repo funding (Correa, Du, and Liao 2020), a lower fraction of short-term swap line draws relative to total swap line usage suggests swap lines were used less for funding and more for hedging purposes. At the time of the max swap line usage during the COVID-19 market distress period, the fraction of short-term (7-day) swap usage was less than 3% of the total, whereas it was more than 40% during the most distressed days of the GFC.³⁸

7 Conclusion

In this paper, we presented a novel hedging channel of exchange rate determination. Recent evidence shows the use of currency forwards and swaps to hedge exchange rate risk is a common phenomenon around the world. We argued this hedging behavior generates predictable movements in both spot and forward exchange rate markets that are intimately linked to countries’ dollar-denominated external imbalances. Using data from the G-10 currencies, we found evidence in support of the hedging channel of exchange rate determination in both conditional and unconditional moments of spot and forward exchange rate markets. Moreover, we showed our hedging channel explains the behavior of spot and forward exchange rates that result in observed systematic variation in currency excess returns, term premia, and out-of-the-money options on currencies. The behavior of exchange rates around the implementation of the Solvency II directive indicate that currency hedging is a quantitatively important channel in exchange rate markets. The currency hedging framework also explains the relative take-ups of central bank swap lines during periods of liquidity shortage.

Code Availability: The replication code is available in the Harvard Dataverse at: https://doi.org/10.7910/DVN/EFVLUL.

Acknowledgement

We thank seminar and conference participants at the Federal Reserve Board, University of Maryland, UNC Junior Round Conference, Federal Reserve Bank of San Francisco, Bank of International Settlements, Nanyang Business School, BdF-BoE International Macroeconomics Workshop, Vienna Symposium on Foreign Exchange Markets, and BFI IFM Conference. We thank Wenxin Du, Andrew Lilley, Matteo Maggiori, Simon Lloyd, Kaushik Vasudevan, and Andrea Vedolin for helpful suggestions. We thank John Caramichael for excellent research assistance. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. Supplementary data can be found on The Review of Financial Studies web site.

Footnotes

1

For instance, Gabaix and Maggiori (2015) and Malamud and Schrimpf (2020) model exchange rate determination under limited financial intermediation; Jiang, Krishnamurthy, and Lustig (2019) emphasize the role of safe asset demand.

2

A nonzero cross-currency basis (or currency basis) indicates a breakdown of the covered interest rate parity condition as previously studied by Du, Tepper, and Verdelhan (2018), among others.

3

Throughout the paper, we illustrate the demand for forward contracts and intermediaries that deal in forwards. In practice, however, forwards are often packaged and traded as swap contracts. A FX swap comprises a spot and a forward transaction. A swap of yen for dollars is equivalent to a purchase of dollars against yen in the spot market and simultaneous selling of dollars against yen in the forward market.

4

A growing number of researchers have begun constructing measures of institutional investors’ currency hedging practices and analyzed their impact on financial markets in various settings, including currency hedging by Israeli institutional investors (Ben Zeev and Nathan 2024a,b) and by fixed income mutual funds (Sialm and Zhu 2024). Notably, Du and Huber (2023) construct and analyzes a comprehensive database of global institutional investors’ hedging practices covering almost $2 trillion per annum.

5

Volatilities in financial markets are predictably mean-reverting and often studied with ARCH models (Engle 2004).

6

Beyond the three papers discussed in this paragraph, a much larger literature on currency risk premiums identifies various macroeconomic characteristics that could lead to differences in unconditional currency returns. Other characteristics include, but are not limited to, country size (Hassan 2013), financial development (Maggiori 2017), resilience to disaster risk (Farhi and Gabaix 2016), and location in the trade network (Richmond 2019). For a more comprehensive literature review, see Hassan and Zhang (2021).

7

Our framework also provides an explanation to the behavior of currency option risk-reversals previous studies have examined (Brunnermeier, Nagel, and Pedersen 2008; Farhi and Gabaix 2016). Relative to earlier studies, the hedging channel can explain both the level and the fluctuations in currency option skews, as well as connecting the observed asset pricing behaviors to macro-level asset holding imbalances.

8

Other contributions to this strand of literature include Du, Im, and Schreger (2018), Liao (2020), and Du, Hebert, and Huber (2023).

9

For institutional details discussing the increase in currency hedging over the last two decades, see Internet Appendix Section 1.

10

For instance, pension investment regulations in Germany, Switzerland, Denmark, and Italy each mandate at least 70% to 80% currency matching between assets and liabilities (OECD Survey of investment regulation of pension funds, 2019). Moreover, the Solvency II Directive imposes a capital charge (usually 25%) on currency mismatches of European and U.K. insurers.

11

Large firms that likely have superior access to currency hedging tend to have less FX exposure in their valuation relative to smaller firms (Dominguez and Tesar 2006).

12

We take the investor’s external imbalance as exogenous to keep the model tractable and focused on our contribution: the exchange rate hedging behavior. Although risk premiums and interest rates can affect net asset positions, we believe that exogenous imbalances is a good first approximation because hedging positions tend to change more rapidly than net foreign asset positions.

13

If the country-n investor has a positive external imbalance in U.S. dollars at the end of period 1 |$(X^n \gt 0)$|⁠, she receives dollars in period 2 and wants to exchange those dollars into domestic currency. She hedges her exchange rate exposure by selling dollars in the forward market. On the other hand, if the country-n investor has a negative external imbalance |$(X^n \lt 0)$|⁠, then she owes dollars in period 2 and hedges her exposure by buying dollars in the forward market.

14

One caveat to the mechanism described here is that currency excess returns are exogenous in our setup, but they could respond to changes in exchange rate volatility in the data. From a theory perspective, we would be concerned that an increase in exchange rate volatility drives a large enough increase in currency risk premiums such that the investor would want to decrease her hedge ratio. In Internet Appendix Section 2.1, we derive a condition necessary for the investor to want to decrease her hedge ratio when expected exchange rate volatility increases. We also evaluate this condition in the data and fail to find evidence that it holds.

15

Within our framework, the return on the outside investment opportunity only depends on the investment I following Ivashina, Scharfstein, and Stein (2015). One could allow the returns to the outside investment opportunity to also fluctuate over the business cycle such that returns to the outside option are particularly high during periods of financial distress. Adding the relationship between |$G(\cdot)$| and the business cycle and regulatory cycle could also capture the supply side determinants of cross-currency bases as emphasized in Du, Tepper, and Verdelhan (2018), which we have left out in order to streamline our model.

16

If |$X^n \gt 0$|⁠, the country-n investor sells dollars and buys currency n in the forward market against the forward trader. To provide liquidity (without incurring currency risk), the forward trader borrows in dollars (⁠|$q^n \lt 0$|⁠), and buys currency n in the spot market in period 1 with her borrowed dollars. Her converted cash in currency n then accrues an interest of rⁿ. In period 2, the trader delivers currency n to the country n investor and receives dollars at the forward price Fⁿ. Finally, the trader pays back her dollar loan: |$q^n (1+r^D)$|⁠. Ultimately, the trader earns a profit of dollars from this transaction. The case with |$X^n \lt 0$| is analogous.

17

Even though the forward trader faces no exchange rate risk in the model, arbitrage in basis trades has known limits (Shleifer and Vishny 1997).

18

For the purpose of simplicity, we assume liquidity provision in the forward markets as being competitive, however, it is possible that liquidity providers possess market power, which can result in nonzero basis spreads even when the cost of liquidity provision is low. Wallen (2022) investigates the presence of markups in the FX forward market that could contribute to CIP deviations.

19

These results have been shown previously in a no arbitrage model in Borio et al. (2018). However, the results (in Propositions 1 and 2) of Borio et al. (2018) stem from empirical relationships between cross-currency bases and external imbalances, rather than micro-foundations of investor and FX swap trader behavior.

20

Increases in κ can also increase the magnitude of currency bases globally and can be interpreted as directly capturing increases in balance sheet costs. Du, Tepper, and Verdelhan (2018) show currency bases are partially driven by bank balance sheet costs.

21

The Chinese yuan and Hong Kong dollar are also among the most frequently transacted, but they are actively managed against the U.S. dollar and affected by capital flow restrictions.

22

To supplement our primary measure of external imbalance based on dollar debt holding positions, we also show results based on the aggregate NIIP, and the net debt and foreign direct investment (FDI) components of NIIP. The net debt component of NIIP comprises both portfolio debt other debt investment. The net FDI component of NIIP comprises both debt and equity FDI. FDIs are investments in which the direct investor owns at least 10% of the voting power in the direct investment enterprise. These results are presented in the Internet Appendix, and they support the primary results using the measure of net dollar debt holding. The alternative measures indicate dollar net debt holdings are representative of the overall external imbalance. Furthermore, the disaggregated measures using data that separate debt and equity NIIP positions validate the theoretical insight that, indeed, greater levels of currency hedging occur in debt than in equities.

23

All market data are from Bloomberg.

24

Internet Appendix Figure A2 shows the updated time series of cross-currency bases for G-10 currencies since 2000.

25

Panel A of Figure A3 in the Internet Appendix shows the inverse relationship between cross-currency bases and dollar imbalances is not just a post-GFC phenomenon. Comparing the precrisis figure and the full-sample figure shows the magnitude of the inverse relationship between currency bases and dollar imbalance rose in the postcrisis period, which plausibly reflects a stronger hedging demand coupled with more intermediary constraints after the GFC.

26

Internet Appendix Table A4 shows our empirical results are qualitatively unchanged if we also control for time-series variation in exchange rate volatility.

27

Our primary measure is the 1-year 25-delta risk-reversal, defined as the implied volatility of the call options with 25-delta minus the implied volatility of the put option with 25-delta. The delta of the option is used in the currency market to indicate an option’s moneyness. The price of a 25-delta option changes by one-quarter of a unit for every one unit of change in the underlying currency price. The 25-delta risk reversal is the most frequent indicator of option skewness used in practice.

28

We present the times series of cross-currency basis in Internet Appendix Figure A2.

29

As a whole, the aggregate net foreign asset position and dollar debt imbalances are highly correlated. A regression of dollar debt imbalances on net foreign asset positions has an R-squared of 0.64 within our sample.

30

Previous studies such as Engle (2004) have shown that financial market volatilities are mean-reverting.

31

Table 6 presents estimates using our full sample with Newey-West standard errors. We also present these forecasting regression results using nonoverlapping observations in Internet Appendix Table A8. The results are quantitatively similar. A one-standard-deviation above-average exchange rate volatility predicts exchange rate depreciation of 1.83% over the next 6 months and 3.59% over the next 12 months.

32

We calculate the log currency excess returns as: |$rx_{t+1} = f_t - s_{t+1} = (f_t - s_t) - (s_{t+1} - s_t)$|⁠.

33

Recent papers have approached the term structure of currency basis from a perspective of intermediary-based asset pricing (Du, Hebert, and Huber 2023; Augustin et al. 2024). Relative to these papers, we highlight the demand drivers of the term structure.

34

In Internet Appendix Section 4, we provide an additional case study of the impact of hedging demand on exchange rates using the onset of the COVID-19 pandemic as a sharp and unexpected shock to expected exchange rate volatility. We discuss how the currency hedging mechanism explains exchange rate returns and the term structure of cross-currency bases during this period of time.

35

Intermediaries exchange borrowed dollars for foreign currency that is delivered at maturity to foreign investors that demand exchange rate hedges on their dollar investments.

36

To hedge dollar debt, debtor countries need to purchase dollar forwards. Borrowing dollars through the swap line exacerbates rather than reduces this need.

37

In Internet Appendix Section 4, we further discuss the impact of COVID-19 shock on the exchange rate markets.

38

Maximum swap line draws during the COVID-19 financial turmoil was $449 billion on May 27, 2020 ($436 billion for the 84-day operation and $13.3 billion for the 7-day operation). The max swap line draw during the GFC was $586 billion on December 4, 2008 ($345 billion for operations with maturities greater than 30 days and $241 billion for maturities less than 30 days).

Author notes

Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.