NBER WORKING PAPER SERIES THE GLOBAL FACTOR STRUCTURE OF EXCHANGE RATES

We provide a model-free framework to study the global factor structure of exchange rates. To this end, we propose a new methodology to estimate international stochastic discount factors (SDFs) that jointly price cross-sections of international assets, such as stocks, bonds, and currencies, in the presence of frictions. We theoretically establish a two-factor representation for the crosssection of international SDFs, consisting of one global and one local factor, which is independent of the currency denomination. We show that our two-factor specification prices a large crosssection of international asset returns, not just inbut also out-of-sample with R2s of up to 80%. Sofonias Korsaye University of Geneva 24 rue du Général-Dufour Geneva 1211 Switzerland sofonias.korsaye@unige.ch Fabio Trojani University of Geneva Swiss Finance Institute fabio.trojani@alphacruncher.com Andrea Vedolin Questrom School of Business Boston University 595 Commonwealth Avenue Boston, MA 02215 and NBER avedolin@bu.edu One central finding of the large literature that studies the factor structure of exchange rates is that the co-movement of exchange rates can be described by a few factors. As a result, workhorse models in international finance posit international stochastic discount factors (SDFs) that are driven by a handful of global and local factors. These models are shown to fit many stylized facts in international macro-finance well. These results, however, rest on two pillars. On the theoretical side, it is assumed that agents can trade in global international markets that are integrated, frictionless, and complete. While a natural starting point, such an assumption has non-trivial consequences for the factor structure of exchange rates. First, the degree of market segmentation (or the lack thereof) affects the factor structure of SDFs. For example, as we increase the degree of segmentation across countries, SDFs become less correlated and hence the factor structure weaker. In such cases, the importance of global factors may decrease while local factors become more important. Second, the assumption that markets are complete and frictionless also implies that the rate of appreciation of the exchange rate (X) is uniquely recovered from the ratio of the foreign and the domestic SDFs: X = Mf/Md. This identity—which is known as the asset market view of exchange rates (AMV)—implies that shocks to foreign and domestic SDFs pin down the factor structure of exchange rates. However, it is well known that departures from the integrated and frictionless benchmark may cause AMV to be violated. As a result, the ensuing global factor structure would depend not only on the factor structure of SDFs but also on the ex ante assumptions about the degree of financial market integration and the presence of barriers to trade. On the empirical side, the literature extracts global factors from the cross-section of exchange rates alone. However, assumptions about the menu of tradable assets can have first-order implications for the nature of extracted factors. For example, it is well known that FX and fixed income markets are intimately linked, as many intermediaries hedge their FX exposure in bond markets. Moreover, recent empirical evidence in Koijen and Yogo (2020) suggests significant substitution effects across international stocks, bonds, and currencies. It is hence natural to study global factors by focusing not just on exchange rates but also on a broader cross-section of international assets. In this paper, we study the global factor structure of exchange rates in the presence of trade frictions and when global investors can trade a broad cross-section of international assets. We first develop a theoretical framework to study international SDFs while accommodating a wide class of trade frictions. Such barriers to trade generate market segmentation along assets and countries as an endogenous outcome rather than an assumption. As our main theoretical result, we show that, under fairly mild conditions and irrespective of the nature and extent of trade frictions, international SDFs exhibit a two-factor structure and the AMV continues to hold. As a result, two factors exactly span the cross-section of exchange rates. Empirically, we take the viewpoint of global investors who can trade stocks, bonds, and currencies across different numéraires and study their optimal portfolios. Extracting two factors from the cross-section of international SDFs of these global investors, we show that they price the cross-section of international assets not just inbut also out-of-sample. Moreover, we document a tight link between our two factors and those of Verdelhan (2018), who argues that two global factors, dollar and carry, account for a significant fraction of the variation in exchange rates. Our paper contributes to the literature along at least three dimensions. First, we provide a novel