Visualisation of foreign exchange rates.

The pricing of foreign exchange and the unique role of US Dollar risk

17 February 2023

The article at a glance

Trading in over-the-counter foreign exchange (FX) markets reached $7.5 trillion per day in April 2022 across all FX instruments (BIS, 2022), making it the most actively traded asset class, globally.

by Brandon A. McBride, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance

Trading in over-the-counter foreign exchange (FX) markets reached $7.5 trillion per day in April 2022 across all FX instruments (BIS, 2022), making it the most actively traded asset class, globally. However, the determinants of exchange rates are still illusive to many in both academic and policy-making circles. Are interest rates the fundamental exchange rate drivers? What role do risk-averse agents play? Can understanding the unique role of the US in the international monetary system better inform our understanding of observed currency prices? These are the questions at the heart of the empirical international finance literature.

FX literature is governed by the central uncovered interest rate parity (UIP) condition, the efficient markets hypothesis of currency markets. UIP states that, given risk-neutrality and rational expectations of agents, expected exchange rate changes must be offset by interest rate differentials. However, Fama (1984) evidenced that, post Bretton-Woods (early 1970s), UIP failed to hold in the data. To reconcile such deviations, the consensus was naturally to relax the unrealistic assumption of risk-neutrality, allowing agents to incorporate risk-averse preferences into the pricing of FX. This, in turn, has led to an international finance research agenda intent on identifying risk factors for which agents demand compensation for bearing their underlying macroeconomic risks, in order to reconcile UIP.

The seminal work of Lustig and Verdelhan (2007) presented a turning point in the FX literature. Their paper was the first to bring the techniques of the asset pricing literature to FX markets, investigating a broad cross-section of currencies, as opposed to bi-lateral time-series studies. This portfolio–sort-based approach has now become the convention in the literature, allowing researchers to incorporate the methods long implemented to study pricing in equity markets; using multi-factor models to capture the variation in the stochastic discount factor (SDF), and provide a risk-based explanation of returns (eg, Fama and French, 1992).

The SDF is what asset pricing is all about. Throughout the literature, the SDF is a linear model which contains factors. Under some general assumptions, such as the law of one price and no-arbitrage, this SDF is positive, and it represents the observed risk premia in the pricing of FX.

This is captured by the covariation of currency returns with the selected factors, specified to capture shocks that, a priori, are thought to impact exchange rates. It is in the identification, measurement, and fundamental understanding of these factors that we gain insight into the drivers of FX prices. Therefore, our question boils down to: which factors are really important?

Lustig, Roussanov and Verdelhan (2011) identify a common two-factor structure, which has formed the baseline risk factors in the literature. The first factor is a level factor, representing the returns to a US investor going long in an equally-weighted portfolio of foreign currencies, which the authors term the ‘Dollar risk factor’. The second factor is a carry trade factor, capturing the excess returns investors make to borrowing in low interest rate and investing in high interest rate currencies – a conventional carry trade investment strategy. It is well understood that the carry trade strategy is capturing a premium for investors bearing the risk of FX volatility (Menkhoff et al., 2012). This means that such a strategy pays-off well in good times and poorly in bad times, intuitively causing a more volatile consumption stream that risk-averse agents wish to hedge their bets against. However, the literature is divided on the Dollar risk factor. There appears no consensus on its risk exposures, nor even acceptance of is statistical significance in capturing time-series or cross-sectional variation in FX prices. Could decomposing the underlying risk exposures of this factor allow us to better understand the UIP risk premium component?

The Dollar risk factor has a number of key characteristics. Firstly, in all investment strategies it is the first principal component, capturing most of the variation in portfolio-sorted returns. Secondly, the statistical significance of this factor wavers over varying time-periods, as well as by the magnitude of the sample cross-section. Nucera, Sarno and Zinna (2022) provide the most significant empirical evidence of the importance of the Dollar risk factor to date, highlighting, robust to omitted-variable and measurement-error biases, that the Dollar risk factor is statistically and economically significant in a broad cross-section of FX. Intuitively, this risk premium is compensating for the appreciation of the US Dollar (the short leg of our portfolio strategy) in bad times, which increases the volatility of our consumption. But what drives this risk for which investors demand to be compensated? What are the macroeconomic shocks to the SDF that this risk factor is capturing? What is unique about the US Dollar that it warrants its own risk factor?

The uniqueness of the US and the US Dollar in the international monetary system has been heavily documented throughout the international economics literature, dating back to the early days of Bretton-Woods. The role of the US manifests itself through various channels. The Dollar has a funding advantage, such that safe Dollar bonds have lower returns (Du et al., 2018). There is also a Dollar debt dominance, through which a large, outsized quantity of Dollar-denominated bonds exist relative to the total wealth share of the US (Ivashina, 2015). This reflects the characteristic exorbitant privilege of the US (a phrase first coined by Valéry Giscard d’Estaing, the French Minister of Finance in the 1960s, as France signalled its intent to exchange its US reserves for their gold-backed value, signalling the end of the Bretton-Woods era). As such, the demand for Dollar debt, and particularly the flight-to-safety feature during global downturns (Jiang et al., 2018), allows for the US external portfolio to leverage safe Dollar assets with long risky foreign asset positions (Gourinchas and Rey, 2007). To top it all off, in the face of recent spiralling inflation, we have also observed the impact of the Global Financial Cycle (GFC) phenomenon, through which US monetary policy has a disproportionately outsized role in the macroeconomic outcomes for countries around the world, causing an aggregate excess spillover effect (Miranda-Agrippino and Rey, 2022).

Jiang, Krishnamurthy and Lustig (2022) have developed a structural model to reconcile these unique US features in equilibrium. Their central assumption is that US Treasurys carry a premium, a convenience yield (as evidenced by Jiang et al., 2021), as they are particularly safe and therefore highly valued by foreign investors to hedge against bad times. This emphasises the importance of US-specific shocks, and the global impact of their spillover and contagion effects for foreign countries: the GFC that we observe today, this high degree of co-movement in risky asset prices around the world, is in fact a Dollar Financial Cycle! Furthermore, if this equilibrium is representative, it foreshadows a Triffin (1960) Dilemma of the same style as the Bretton-Woods downfall, with the floating exchange rate regime and free capital mobility mechanism operating under a de-facto Dollar standard with persistent, perpetual asymmetric financial spillovers.

Undoubtedly, there exists a strong theoretical and intuitive basis for the existence of the Dollar as a common risk factor driving FX fluctuations. It naturally explains the general role of the US as the hegemon that we observe in international financial markets. However, we need greater empirical evidence of the central macroeconomic shocks that result in and from this underlying mechanism. Only in better understanding the risks that play-out in the real economy can we determine the risk-return behaviour of agents in financial markets and provide a better real-world economic foundation on which to develop equilibrium models of FX pricing.


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