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Skewness Risk Premia and the Cross Section of Currency Returns

Published online by Cambridge University Press:  02 September 2025

Junye Li
Affiliation:
Fudan University li_junye@fudan.edu.cn
Lucio Sarno*
Affiliation:
Cambridge Judge Business School and Girton College, University of Cambridge , and Centre for Economic Policy Research (CEPR)
Gabriele Zinna
Affiliation:
Bank of Italy gabriele.zinna@bancaditalia.it
*
l.sarno@jbs.cam.ac.uk (corresponding author)
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Abstract

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Using model-free skewness measures that exploit the asymmetry in semivariances and option data from the over-the-counter currency market, we find that buying currencies with a high skewness risk premium (SRP) and selling currencies with a low SRP generates high returns and a Sharpe ratio. Asset pricing tests—which control for omitted variables and measurement errors—show that a SRP factor enters the currency pricing kernel and is central to the pricing of risks inherent in a broad currency cross section of 60 portfolio excess returns. These results imply that skewness risk is a strong and priced source of currency risk.

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Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of the Michael G. Foster School of Business, University of Washington

Footnotes

We are indebted for constructive comments and suggestions to George G. Pennacchi (the editor), an anonymous referee, Tim Bollerslev, Stefanos Delikouras, Pasquale Della Corte, Wenxin Du, Massimo Guidolin, Alex Kostakis, Roman Kozhan, Anthony Neuberger, Chris Povey, Paul Schneider, Xiao Xiao, Irina Zviadadze, and participants at presentations held at the University of Liverpool, the 10th Italian Congress of Econometrics and Empirical Economics (2023), the 2023 SoFiE Annual Conference, and the 10th Asset Pricing Workshop at the University of York. J. Li acknowledges financial support from National Science Foundation of China [Grant 72473026]. All errors are our responsibility. This research was partly carried out l.sarno@jbs.cam.ac.uk (corresponding awhen Gabriele Zinna was Visiting Scholar at Amsterdam Business School and Tilburg University. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of Italy. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.

References

Andrews, S.; Colacito, R.; Croce, M. M.; and Gavazzoni, F.. “Concealed Carry.” Journal of Financial Economics, 159 (2024), 103874.Google Scholar
Arditti, F. D.Risk and Required Return on Equity.” Journal of Finance, 22 (1967), 936.Google Scholar
Arditti, F. D.Another Look at Mutual Fund Performance.” Journal of Financial and Quantitative Analysis, 6 (1971), 909912.Google Scholar
Asness, C.; Moskowitz, T.; and Pedersen, L.. “Value and Momentum Everywhere.” Journal of Finance, 68 (2013), 929985.Google Scholar
Bakshi, G.; Carr, P.; and Wu, L.. “Stochastic Risk Premiums, Stochastic Skewness in Currency Options, and Stochastic Discount Factors in International Economics.” Journal of Financial Economics, 87 (2008), 132156.Google Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101143.Google Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative Security Valuation.” Journal of Financial Economics, 55 (2000), 205238.Google Scholar
Barberis, N., and Huang, M.. “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices.” American Economic Review, 98 (2008), 20662100.Google Scholar
Barillas, F.; Kan, R.; Robotti, C.; and Shanken, J.. “Model Comparison with Sharpe Ratios.” Journal of Financial and Quantitative Analysis, 55 (2020), 18401874.Google Scholar
Barillas, F., and Shanken, J.. “Which Alpha?Review of Financial Studies, 30 (2017), 13161338.Google Scholar
Barndorff-Nielsen, O.; Kinnebrock, S.; and Shephard, N.. “Measuring Downside Risk–Realized Semivariance.” In Volatility and Time Series Econometrics: Essays in Honor of Robert Engle, Bollerslev, T., Russell, J., and Watson, M., eds. Oxford: Oxford University Press (2010), 117136.Google Scholar
Baron, M.; Xiong, W.; and Ye, Z.. “Measuring Time-Varying Disaster Risk: An Empirical Analysis of “Dark Matter” in Asset Prices.” (2024).Google Scholar
Barro, R. J.Rare Disasters and Asset Markets in the Twentieth Century.” Quarterly Journal of Economics, 121 (2006), 823866.Google Scholar
Barro, R. J.Rare Disasters, Asset Prices, and Welfare Costs.” American Economic Review, 99 (2009), 243264.Google Scholar
Bekaert, G., and Panayotov, G.. “Good Carry, Bad Carry.” Journal of Financial and Quantitative Analysis, 55 (2020), 10631094.Google Scholar
Bianchi, F.The Great Depression and the Great Recession: A View from Financial Markets.” Journal of Monetary Economics, 114 (2020), 240261.Google Scholar
Bollerslev, T.Realized Semi(co)variation: Signs that All Volatilities Are Not Created Equal.” Journal of Financial Econometrics, 20 (2021), 219252.Google Scholar
Bollerslev, T.; Li, J.; Patton, A. J.; and Quaedvlieg, R.. “Realized Semicovariances.” Econometrica, 88 (2020a), 15151551.Google Scholar
Bollerslev, T.; Li, S. Z.; and Zhao, B.. “Good Volatility, Bad Volatility, and the Cross Section of Stock Returns.” Journal of Financial and Quantitative Analysis, 55 (2020b), 751781.Google Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 44634492.Google Scholar
Bollerslev, T., and Todorov, V.. “Tails, Fears, and Risk Premia.” Journal of Finance, 66 (2011), 21652211.Google Scholar
Bollerslev, T.; Todorov, V.; and Xu, L.. “Tail Risk Premia and Return Predictability.” Journal of Financial Economics, 118 (2015), 113134.Google Scholar
Boothe, P., and Glassman, D.. “The Statistical Distribution of Exchange Rates: Empirical Evidence and Economic Implications.” Journal of International Economics, 22 (1987), 297319.Google Scholar
Boyer, B.; Mitton, T.; and Vorkink, K.. “Expected Idiosyncratic Skewness.” Review of Financial Studies, 23 (2010), 169202.Google Scholar
Brunnermeier, M. K.; Gollier, C.; and Parker, J. A.. “Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns.” American Economic Review, 97 (2007), 159165.Google Scholar
Brunnermeier, M. K.; Nagel, S.; and Pedersen, L. H.. “Carry Trades and Currency Crashes.” NBER Working Paper No. 14473 (2008).Google Scholar
Burnside, C.The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk: a Comment.” American Economic Review, 101 (2011), 34563476.Google Scholar
Burnside, C.; Eichenbaum, M.; Kleshchelski, I.; and Rebelo, S.. “Do Peso Problems Explain the Returns to the Carry Trade?Review of Financial Studies, 24 (2011a), 853891.Google Scholar
Burnside, C.; Eichenbaum, M.; and Rebelo, S.. “Carry Trade and Momentum in Currency Markets.” Annual Review of Financial Economics, 3 (2011b), 511535.Google Scholar
Carr, P., and Wu, L.. “Stochastic Skew in Currency Options.” Journal of Financial Economics, 86 (2007), 213247.Google Scholar
Chernov, M.; Dahlquist, M.; and Lochstoer, L. A.. “Pricing Currency Risks.” Journal of Finance, 78 (2023), 693730.Google Scholar
Chernov, M.; Graveline, J.; and Zviadadze, I.. “Crash Risk in Currency Returns.” Journal of Financial and Quantitative Analysis, 53 (2018), 134.Google Scholar
Cochrane, J. Asset Pricing, Revised Edition. Princeton: The Princeton University Press (2005).Google Scholar
Colacito, R.; Riddiough, S.; and Sarno, L.. “Business Cycles and Currency Returns.” Journal of Financial Economics, 137 (2020), 659678.Google Scholar
Conine, T. E., and Tamarkin, M. J.. “On Diversification Given Asymmetry in Returns.” Journal of Finance, 36 (1981), 11431155.Google Scholar
Dahlquist, M., and Hasseltoft, H.. “Economic Momentum and Currency Returns.” Journal of Financial Economics, 136 (2020), 152167.Google Scholar
Daniel, K.; Hodrick, R.; and Lu, Z.. “The Carry Trade: Risks and Drawdowns.” Critical Finance Review, 6 (2017), 211262.Google Scholar
Daniel, K.; Mota, L.; Rottke, S.; and Santos, T.. “The Cross-Section of Risk and Returns.” Review of Financial Studies, 33 (2020), 19271979.Google Scholar
Della Corte, P.; Ramadorai, T.; and Sarno, L.. “Volatility Risk Premia and Exchange Rate Predictability.” Journal of Financial Economics, 120 (2016), 2140.Google Scholar
Della Corte, P.; Riddiough, S. J.; and Sarno, L.. “Currency Premia and Global Imbalances.” Review of Financial Studies, 29 (2016), 21612193.Google Scholar
Della Corte, P.; Sarno, L.; Schmeling, M.; and Wagner, C.. “Exchange Rates and Sovereign Risk.” Management Science, 68 (2022), 55915617.Google Scholar
Dew-Becker, I.; Giglio, S.; and Kelly, B.. “Hedging Macroeconomic and Financial Uncertainty and Volatility.” Journal of Financial Economics, 142 (2021), 2345.Google Scholar
Dew-Becker, I.; Tahbaz-Salehi, A.; and Vedolin, A.. “Skewness and Time-Varying Second Moments in a Nonlinear Production Network: Theory and Evidence.” NBER Working Paper No. 29499 (2021).Google Scholar
Dobrynskaya, V.Downside Market Risk of Carry Trades.” Review of Finance, 18 (2014), 18851913.Google Scholar
Du, D.General Equilibrium Pricing of Currency and Currency Options.” Journal of Financial Economics, 110 (2013), 730751.Google Scholar
Fan, Z.; Londono, J. M.; and Xiao, X.. “Equity Tail Risk and Currency Risk Premiums.” Journal of Financial Economics, 143 (2022a), 484503.Google Scholar
Fan, Z.; Xiao, X.; and Zhou, H.. “Moment Risk Premia and Stock Return Predictability.” Journal of Financial and Quantitative Analysis, 57 (2022b), 6793.Google Scholar
Farhi, E., and Gabaix, X.. “Rare Disasters and Exchange Rates.” Quarterly Journal of Economics, 131 (2016), 152.Google Scholar
Feunou, B.; Jahan-Parvar, M. R.; and Okou, C.. “Downside Variance Risk Premium.” Journal of Financial Econometrics, 16 (2018), 341383.Google Scholar
Gabaix, X.Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance.” Quarterly Journal of Economics, 127 (2012), 645700.Google Scholar
Garman, M., and Kohlhagen, S.. “Foreign Currency Option Values.” Journal of International Money and Finance, 2 (1983), 231237.Google Scholar
Ghysels, E.; Plazzi, A.; and Valkanov, R.. “Why Invest in Emerging Markets? The Role of Conditional Return Asymmetry.” Journal of Finance, 71 (2016), 21452192.Google Scholar
Giglio, S., and Xiu, D.. “Asset Pricing with Omitted Factors.” Journal of Political Economy, 129 (2021), 19471990.Google Scholar
Giglio, S.; Xiu, D.; and Zhang, D.. “Test Assets and Weak Factors.” Journal of Finance, 80 (2025), 259319.Google Scholar
Goldstein, I.; Koijen, R. S. J.; and Mueller, H. M.. “COVID-19 and Its Impact on Financial Markets and the Real Economy.” Review of Financial Studies, 34 (2021), 51355148.Google Scholar
Gospodinov, N.; Kan, R.; and Robotti, C.. “Too Good to Be True? Fallacies in Evaluating Risk Factor Models.” Journal of Financial Economics, 132 (2019), 451471.Google Scholar
Gourio, F.Disaster Risk and Business Cycles.” American Economic Review, 102 (2012), 27342766.Google Scholar
Groeneveld, R., and Meeden, G.. “Measuring Skewness and Kurtosis.” Journal of the Royal Statistical Society: Series D, 33 (1984), 391399.Google Scholar
Harvey, C., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 53 (2000), 12631295.Google Scholar
Huang, T., and Li, J.. “Option-Implied Variance Asymmetry and the Cross-Section of Stock Returns.” Journal of Banking and Finance, 101 (2019), 2136.Google Scholar
Ilmanen, A.; Israel, R.; Lee, R.; Moskowitz, T. J.; and Thapar, A.. “How Do Factor Premia Vary Over Time? A Century of Evidence.” Journal of Investment Management, 19 (2021), 1557.Google Scholar
Jiang, Z.; Krishnamurthy, A.; and Lustig, H.. “Foreign Safe Asset Demand and the Dollar Exchange Rate.” Journal of Finance, 76 (2021), 10491089.Google Scholar
Jiang, G., and Tian, Y.. “The Model-Free Implied Volatility and Its Information Content.” Review of Financial Studies, 18 (2005), 13051342.Google Scholar
Jondeau, E.; Zhang, Q.; and Zhu, X.. “Average Skewness Matters.” Journal of Financial Economics, 134 (2019), 2947.Google Scholar
Jurek, J. W.Crash-Neutral Currency Carry Trades.” Journal of Financial Economics, 113 (2014), 325347.Google Scholar
Kane, A.Skewness Preference and Portfolio Choice.” Journal of Financial and Quantitative Analysis, 17 (1982), 1525.Google Scholar
Kelly, B., and Jiang, H.. “Tail Risk and Asset Prices.” Review of Financial Studies, 27 (2014), 28412871.Google Scholar
Kilic, M., and Shaliastovich, I.. “Good and Bad Variance Premia and Expected Returns.” Management Science, 65 (2019), 25222544.Google Scholar
Kim, T., and White, H.. “On More Robust Estimation of Skewness and Kurtosis.” Finance Research Letters, 1 (2004), 5673.Google Scholar
Koijen, R. S.; Moskowitz, T. J.; Pedersen, L. H.; and Vrugt, E. B.. “Carry.” Journal of Financial Economics, 127 (2018), 197225.Google Scholar
Kozhan, R.; Neuberger, A.; and Schneider, P.. “The Skew Risk Premium in the Equity Index Market.” Review of Financial Studies, 26 (2013), 21742203.Google Scholar
Kraus, A., and Litzenberger, R. H.. “Skewness Preference and the Valuation of Risk Assets.” Journal of Finance, 31 (1976), 10851100.Google Scholar
Kroencke, T.; Schindler, F.; and Schrimpf, A.. “International Diversification Benefits with Foreign Exchange Investment Styles.” Review of Finance, 18 (2014), 18471883.Google Scholar
Kumar, A.Who Gambles in the Stock Market?Journal of Finance, 64 (2009), 18891933.Google Scholar
Langlois, H.Measuring Skewness Premia.” Journal of Financial Economics, 135 (2020), 399424.Google Scholar
Lettau, M.; Maggiori, M.; and Weber, M.. “Conditional Risk Premia in Currency Markets and Other Asset Classes.” Journal of Financial Economics, 114 (2014), 197225.Google Scholar
Lettau, M., and Pelger, M.. “Factors that Fit the Time Series and Cross-section of Stock Returns.” Review of Financial Studies, 33 (2020), 22742325.Google Scholar
Lewellen, J. “How Many Factors?” Tuck School of Business at Dartmouth (2022).Google Scholar
Lewellen, J.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset Pricing Tests.” Journal of Financial Economics, 92 (2010), 175194.Google Scholar
Liao, G. Y., and Zhang, T.. “The Hedging Channel of Exchange Rate Determination.” Review of Financial Studies, 38 (2025), 138.Google Scholar
Liu, S.; Maurer, T. A.; Vedolin, A.; and Zhang, Y.. “Dollar and Carry Redux.” John M. Olin Business School (2024).Google Scholar
Londono, J. M., and Zhou, H.. “Variance Risk Premiums and the Forward Premium Puzzle.” Journal of Financial Economics, 124 (2017), 415440.Google Scholar
Lustig, H.; Roussanov, N.; and Verdelhan, A.. “Common Risk Factors in Currency Markets.” Review of Financial Studies, 11 (2011), 527553.Google Scholar
Lustig, H., and Verdelhan, A.. “The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk.” American Economic Review, 97 (2007), 89117.Google Scholar
Maggiori, M.Financial Intermediation, International Risk Sharing, and Reserve Currencies.” American Economic Review, 107 (2017), 30383071.Google Scholar
Menkhoff, L.; Sarno, L.; Schmeling, M.; and Schrimpf, A.. “Carry Trades and Global Foreign Exchange Volatility.” Journal of Finance, 67 (2012a), 681718.Google Scholar
Menkhoff, L.; Sarno, L.; Schmeling, M.; and Schrimpf, A.. “Currency Momentum Strategies.” Journal of Financial Economics, 106 (2012b), 620684.Google Scholar
Menkhoff, L.; Sarno, L.; Schmeling, M.; and Schrimpf, A.. “Currency Value.” Review of Financial Studies, 30 (2017), 416441.Google Scholar
Mitton, T., and Vorkink, K.. “Equilibrium Underdiversification and the Preference for Skewness.” Review of Financial Studies, 20 (2007), 12551288.Google Scholar
Morley, J., and Piger, J.. “The Asymmetric Business Cycle.” Review of Economics and Statistics, 94 (2012), 208221.Google Scholar
Muir, T.Financial Crises and Risk Premia.” Quarterly Journal of Economics, 132 (2017), 765809.Google Scholar
Nucera, F.; Sarno, L.; and Zinna, G.. “Currency Risk Premiums Redux.” Review of Financial Studies, 37 (2024), 356408.Google Scholar
OECD. “COVID-19 and Global Capital Flows.” (2020).Google Scholar
Patton, A. J., and Sheppard, K.. “Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility.” Review of Economics and Statistics, 97 (2015), 683697.Google Scholar
Rafferty, B.Currency Returns, Skewness and Crash Risk.” Working Paper, University of Melbourne (2012).Google Scholar
Ready, R.; Roussanov, N.; and Ward, C.. “After the Tide: Commodity Currencies and Global Trade.” Journal of Monetary Economics, 85 (2017), 6986.Google Scholar
Rietz, T.The Equity Risk Premium: A Solution.” Journal of Monetary Economics, 22 (1988), 117131.Google Scholar
Salgado, S.; Guvenen, F.; and Bloom, N.. “Skewed Business Cycles.” NBER Working Paper No. 26565 (2019).Google Scholar
Schneider, P., and Trojani, F.. “Divergence and the Price of Uncertainty.” Journal of Financial Econometrics, 17 (2018), 341396.Google Scholar
Schneider, P.; Wagner, C.; and Zechner, J.. “Low-Risk Anomalies?Journal of Finance, 75 (2020), 26732718.Google Scholar
Scott, R. C., and Horvath, P. A.. “On the Direction of Preference of Moments of Higher Order Than the Variance.” Journal of Finance, 35 (1980), 915919.Google Scholar
Simkowitz, M. A., and Beedles, W. L.. “Diversification in a Three-Moment World.” Journal of Financial and Quantitative Analysis, 13 (1978), 927941.Google Scholar
Wachter, J.Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?Journal of Finance, 68 (2013), 9871035.Google Scholar
Zeng, M.Currency Carry, Momentum, and Global Interest Rate Volatility.” Journal of Financial and Quantitative Analysis, 60 (2025), 839873.Google Scholar
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