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Journal of Financial Economics Carry Journal of Financial Economics 127 (2018) 197–225 Contents lists available at ScienceDirect Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec R Carry ∗ Ralph S.J. Koijen a,e,f, , Tobias J. Moskowitz b,e,g, Lasse Heje Pedersen a,c,f,g, Evert B. Vrugt d a Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, United States b Yale School of Management, 165 Whitney Ave, New Haven, CT 06511, United States c Copenhagen Business School, Solbjerg Plads 3, Frederiksberg 20 0 0, Denmark d School of Business and Economics, Vrije Universiteit Amsterdam, De Boelelaan 1105, Amsterdam HV 1081, Netherlands e National Bureau of Economic Research, 1050 Massachusetts Avenue, Cambridge, Massachusetts 02138-5398, United States f Centre for Economic Policy Research (CEPR), 33 Great Sutton Street, London EC1V 0DX, United Kingdom g AQR Capital Management, LLC, Two Greenwich Plaza, Greenwich, CT 06830, United States a r t i c l e i n f o a b s t r a c t Article history: We apply the concept of carry, which has been studied almost exclusively in currency mar- Received 8 March 2016 kets, to any asset. A security’s expected return is decomposed into its “carry,” an ex-ante Revised 1 November 2016 and model-free characteristic, and its expected price appreciation. Carry predicts returns Accepted 22 November 2016 cross-sectionally and in time series for a host of different asset classes, including global Available online 21 November 2017 equities, global bonds, commodities, US Treasuries, credit, and options. Carry is not ex- JEL classification: plained by known predictors of returns from these asset classes, and it captures many G10 of these predictors, providing a unifying framework for return predictability. We reject a generalized version of Uncovered Interest Parity and the Expectations Hypothesis in favor Keywords: of models with varying risk premia, in which carry strategies are commonly exposed to Carry trade global recession, liquidity, and volatility risks, though none fully explains carry’s premium. Predictability Stocks ©2017 Elsevier B.V. All rights reserved. Bonds Currencies Commodities Corporate Bonds Options Liquidity risk Volatility risk R We are grateful for helpful comments from John Y. Campbell (referee), annual Paul Woolley Centre conference. Further, we thank Tarek Hassan, Cliff Asness, Ari Levine, Lars Nielsen, and Ashwin Thapar, Jules van Bins- Rui Mano, and Adrien Verdelhan for their help with the currency data bergen, Peter Christoffersen, John Cochrane, Pierre Collin-Dufresne (dis- and Rui Cui, Laszlo Jakab, and Minsoo Kim for excellent research assis- cussant), Kent Daniel (discussant), Lars Hansen, John Heaton, Antti Ilma- tance. Ralph Koijen gratefully acknowledges support from the European nen, Ronen Israel, Andrea Frazzini, Owen Lamont (discussant), John Liew, Research Council (ERC grant no. 338082). Lasse Heje Pedersen gratefully Francis Longstaff, Hanno Lustig (discussant), Yao Hua Ooi, Lubos Pastor, acknowledges support from the European Research Council (ERC grant no. Anna Pavlova, Maik Schmeling (discussant), Stijn Van Nieuwerburgh, An- 312417) and the Center for Financial Frictions (FRIC, grant no. DNRF102). drei Shleifer, Dimitri Vayanos, Moto Yogo, as well as from seminar par- AQR Capital Management is a global investment management firm, which ticipants at AQR Capital Management, the 2012 American Finance As- may or may not apply similar investment techniques or methods of analy- sociation Conference meetings (Chicago, Illinois), University of Chicago, sis as described herein. The views expressed here are those of the authors Booth School of Business, the Chicago Mercantile Exchange, the Univer- and not necessarily those of AQR. ∗ sity of Exeter, NOVA University of Lisbon (Portugal), State Street Global Corresponding author at: Stern School of Business, New York Univer- Markets, the 2012 National Bureau of Economic Research (NBER) Asset sity, 44 West 4th Street, 10012 New York, NY, United States. Pricing Summer Institute, the First Foreign Exchange Markets Conference E-mail addresses: [email protected] (R.S.J. Koijen), tobias. at Imperial College, the 2012 Red Rock Finance Conference, and the fifth [email protected] (T.J. Moskowitz), lhp.fi@cbs.dk (L.H. Pedersen), [email protected] (E.B. Vrugt). https://doi.org/10.1016/j.jfineco.2017.11.002 0304-405X/© 2017 Elsevier B.V. All rights reserved. 198 R.S.J. Koijen et al. / Journal of Financial Economics 127 (2018) 197–225 1. Introduction the cross section and the time series. A carry trade that goes long high-carry assets and shorts low-carry assets We define an asset’s “carry” as its futures return, as- earns significant returns in each asset class with an annu- suming that prices stay the same. Based on this uniform alized Sharpe ratio of 0.8 on average. Further, a diversified definition, any security’s return can be decomposed into portfolio of carry strategies across all asset classes earns a its carry and its expected and unexpected price appreci- Sharpe ratio of 1.2. ation: The returns to carry are related to, but not explained by, other known return predictors. Carry generates positive return = carry + E(price appreciation) and unexplained alpha within each asset class relative to expected return other known factors in each asset class. A long literature + unexpected price shock. (1) studies return predictability in different asset classes, usu- ally focusing on one asset class at a time. Taking the main Hence, an asset’s expected return is its carry plus its ex- predictors of returns for each asset class, we show that pected price appreciation. That carry is a model-free char- carry provides unique return predictability. However, in acteristic directly observable ex ante from futures (or syn- many cases, the reverse is not true. Carry often subsumes thetic futures) prices makes it special. Expected price ap- the return predictability of other known factors. This sug- preciation, by contrast, must be estimated using an asset gests not only that carry is a stronger predictor of returns, pricing model. Empirically, we consider a variety of asset but also that it could be a unifying concept that ties to- classes and, in every asset class, define carry consistently gether many return predictors disjointly scattered across as the return on a futures (or synthetic futures) position the literature from many asset classes. when the price does not change. Carry can be directly ob- The literature on return predictability has traditionally served without relying on any particular model, and we been somewhat segregated by asset class. 2 Most studies show how carry can be used to test a variety of asset pric- focus on a single asset class or market at a time, ignor- ing theories. ing how different asset classes behave simultaneously. As We explore how carry is related to expected returns a consequence, return predictability and theory have of- and expected price appreciation across a wide range of ten evolved separately by asset class. We show that seem- diverse assets that include global equities, global govern- ingly unrelated predictors of returns across different as- ment bonds, currencies, commodities, credit, and options. sets can be bonded together through the concept of carry. We examine both the common and the independent vari- For instance, the carry for bonds is closely related to the ation of returns across asset classes through the lens of slope of the yield curve studied in the bond literature, plus carry to help shed light on theory. what we call a “roll down” component that captures the The concept of carry has been studied in the literature price change that occurs as the bond moves along the yield almost exclusively for currencies. In this case, our general curve as time passes. The commodity carry is akin to the definition recovers the well-known currency carry given by basis or convenience yield, and equity carry is a forward- the interest rate differential between two countries. The looking measure of dividend yields. 3 currency literature focuses on testing uncovered interest While carry is related to these known predictors of re- 1 rate parity (UIP) and explaining its empirical deviations. turns, it is different from many of these measures and However, Eq. (1) is a general relation that can be applied provides unique return predictability. Carry can be applied to any asset. Hence, we test a generalized, across many as- more broadly to other asset markets such as the cross sec- set classes, version of UIP, which also tests the expectations tion of US Treasuries across maturities, US credit portfolios, hypothesis (EH) in fixed income markets. Under this the- and US equity index call and put options across money- ory, a high carry should not predict a high return as it is ness. We find equally strong return predictability for carry compensated by an offsetting low expected price appreci- in these other markets, providing an out-of-sample test ation. However, under models of time-varying risk premia, and a broader unifying framework. a high return premium naturally shows up as a high carry. To further quantify carry’s predictability, we run a set The concept of carry can therefore be used to empirically of panel regressions of future returns of each asset on address some of the central questions in asset pricing: Do its carry. While carry predicts future returns in every as- expected returns vary over time and across assets? If so, set class with a positive coefficient, the magnitude of the by how much? How can expected returns be estimated predictive coefficient differs across asset classes, indicat- ex ante? Which economic mechanism drives the variation ing whether carry is positively or negatively related to in expected returns? How much common variation in ex- future price appreciation [see Eq. (1) ]. In global equities, pected returns exists across asset classes? We find that carry is a strong positive predictor of re- turns in each of the major asset classes we study, in both 2 Studies focusing on international equity returns include Chan et al.
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