Coudert and Mignon (2013) showed that sovereign default risk, proxied by sovereign credit default swap (CDS) premia, partially accounts for the forward premium puzzle: default risk raises carry-trade gains in buoyant markets, deepens losses when volatility is high, and moves the Fama-regression coefficient toward unity for a sample of 18 emerging currencies. They acknowledge that this factor only partially explains the forward bias: the Fama coefficient gets closer to unity but still stays smaller than one once default risk is taken into account, leaving room for an unexplained part in the forward bias; and many carry trades are invested in advanced-country currencies such as the Australian and New Zealand dollars, with practically no sovereign default risk, so the results only show that default risk contributes to increase the forward bias in the case of risky emerging countries. The open problem is to complete this default-risk explanation of the forward premium puzzle: quantify the share of the forward bias and of carry-trade excess returns that default-related credit risk explains, and identify and quantify the determinants of the residual unexplained part, including for advanced-economy high-yield currencies where the sovereign-credit explanation cannot operate. Whether the share of the forward bias and of carry-trade excess returns explained by default-related credit risk can be quantified, and the determinants of the residual unexplained part identified and quantified, remains unresolved.

Background

Uncovered interest parity (UIP) — the proposition that the interest-rate differential between two currencies equals the expected depreciation of the high-interest currency — together with covered interest parity (the no-arbitrage condition that the forward premium equals the interest-rate differential) implies that the forward exchange rate should be an unbiased predictor of the future spot rate. Fama (1984) showed that this prediction fails systematically: in regressions of realized currency depreciation on the forward premium (the "Fama regression," st+1−st=α+β(ft−st)+εt+1s_{t+1}-s_t=\alpha+\beta(f_t-s_t)+\varepsilon_{t+1}, where sts_t is the log spot rate and ftf_t the log forward rate), the slope β\beta is typically well below its theoretical value of 1 and often negative. A slope below unity — the "forward bias" — means that high-interest-rate currencies do not depreciate enough to offset the interest advantage, so a "carry trade" that borrows in low-interest (funding) currencies and invests in high-interest (investment) currencies earns positive average excess returns that can reverse sharply in crises. Explaining these excess returns, the "forward premium puzzle," has been a central open question in international finance since the 1980s.

Several risk-based accounts compete. Brunnermeier, Nagel and Pedersen (2009) documented that carry traders bear crash risk tied to funding liquidity: exchange-rate movements between high- and low-interest currencies are negatively skewed, positions unwind when risk appetite and funding liquidity dry up, and controlling for liquidity helps explain the UIP violation. Lustig, Roussanov and Verdelhan (2011) identified a global "slope" risk factor on which high-interest currencies load more, accounting for most of the cross-sectional variation in currency excess returns. Farhi and Gabaix (2016) proposed a rare-disaster theory — time-varying country exposure to rare global disasters — that in calibration accounts for the forward premium puzzle and carry-trade excess returns, including for advanced-economy currencies. Coulibaly and Kempf (2019) showed that inflation-targeting regimes, by weakening the Fisherian link between expected depreciation and the interest differential, are conducive to the forward-bias puzzle in emerging countries.

Coudert and Mignon (2013) added a default-risk channel. Because a sovereign default is likely to trigger default of the country's banking system, an investor holding high-yield emerging-currency assets may never recover the invested funds even if the exchange rate behaves as UIP predicts; default risk should therefore command a risk premium in carry-trade returns. They proxied default risk by the sovereign credit default swap (CDS) premium — the price of insurance against a sovereign credit event, roughly the product of default probability and loss given default — and studied 18 emerging currencies funded in US dollars from June 2005 to September 2010, classifying market mood with the VIX (the CBOE index of implied US equity-option volatility, a standard gauge of global risk appetite). They found that (i) in buoyant markets, carry-trade gains are larger for high default-risk currencies; (ii) above a volatility threshold, losses deepen with default risk; and (iii) in a Fama regression augmented with the CDS premium, the coefficient on the interest-rate differential moves toward unity — default risk mitigates but does not remove the forward bias.

The authors are explicit that this account is partial, and the two limitations acknowledged in their conclusion define the open problem. First, after controlling for sovereign default risk the Fama coefficient still stays below one, leaving room for an unexplained part in the forward bias. Second, many carry trades are invested in advanced-country high-yield currencies such as the Australian and New Zealand dollars, with practically no sovereign default risk; hence the results only show that default risk contributes to increase the forward bias in the case of risky emerging countries. The estimation is additionally conditioned on methodological choices the authors state in the body of the paper: a one-year horizon, the smallest maturity for the CDS data, and sovereign CDS as a stand-in for the default exposure faced by foreign investors, justified by the high correlation between sovereign and banking credit events.

Problem Statement

The problem is to determine how much of the forward premium puzzle the default-risk channel can actually explain, and what remains, by resolving the limitations Coudert and Mignon (2013) acknowledged. The single overarching objective is a quantitative account of the forward bias and carry-trade excess returns in which the share explained by default-related credit risk is measured and the residual unexplained part and its determinants are identified and quantified, including for advanced-economy high-yield currencies (for example the Australian and New Zealand dollars) with negligible sovereign default risk, where the sovereign-credit explanation cannot apply.

The completion boundary is a quantitative account that reports the share of the forward bias and the share of carry-trade excess returns that default-related credit risk explains, and that identifies and quantifies the determinants of the residual unexplained part, for the 18 emerging currencies of Coudert and Mignon (2013), funded in US dollars over June 2005 to September 2010, and for the advanced-economy high-yield currencies with negligible sovereign default risk, namely the Australian and New Zealand dollars, where the source concedes the sovereign-default channel cannot operate. The share of the forward bias is the fraction of the raw Fama bias, 1−β1-\beta, that the sovereign-CDS term removes when it is added to the Fama regression; the share of carry-trade excess returns is the ratio of the mean fitted contribution of the sovereign-CDS term, in a regression of the carry-trade excess return on the forward premium and the sovereign-CDS term, to the mean carry-trade excess return. The residual unexplained part comprises two residuals, reported separately: the forward-bias residual is the part of the raw Fama bias, 1−β1-\beta, left once the sovereign-CDS term is added, and the excess-return residual is the part of the mean carry-trade excess return not accounted for by the sovereign-CDS term. For each, the account assesses which of the competing accounts named in the Background can account for that residual and by how much, using a decomposition it states and grounds in the source given for that account; because those accounts are rival, non-exclusive explanations rather than additive components of one residual, their explanatory shares are reported separately and ranked rather than apportioned. The estimation uses sovereign CDS premia, spot and one-year forward exchange rates, and the VIX, and the account states the data sources and sample period it uses.

References

  1. Virginie Coudert and Valérie Mignon (2013), 'The “forward premium puzzle” and the sovereign default risk', Journal of International Money and Finance 32, 491-511. DOI: 10.1016/j.jimonfin.2012.05.025. https://doi.org/10.1016/j.jimonfin.2012.05.025
  2. Virginie Coudert and Valérie Mignon (2011), 'The “Forward Premium Puzzle” and the Sovereign Default Risk', CEPII Working Paper No. 2011-17 (July 2011). https://www.cepii.fr/PDF_PUB/wp/2011/wp2011-17.pdf
  3. Eugene F. Fama (1984), 'Forward and spot exchange rates', Journal of Monetary Economics 14(3), 319-338. DOI: 10.1016/0304-3932(84)90046-1. https://doi.org/10.1016/0304-3932(84)90046-1
  4. Markus K. Brunnermeier, Stefan Nagel, and Lasse H. Pedersen (2009), 'Carry Trades and Currency Crashes', NBER Macroeconomics Annual 2008, vol. 23, University of Chicago Press, pp. 313-348. DOI: 10.1086/593088. https://doi.org/10.1086/593088
  5. Hanno Lustig, Nikolai Roussanov, and Adrien Verdelhan (2011), 'Common Risk Factors in Currency Markets', Review of Financial Studies 24, 3731-3777. DOI: 10.1093/rfs/hhr068. https://doi.org/10.1093/rfs/hhr068
  6. Emmanuel Farhi and Xavier Gabaix (2016), 'Rare Disasters and Exchange Rates', The Quarterly Journal of Economics 131(1), 1-52. DOI: 10.1093/qje/qjv040. https://doi.org/10.1093/qje/qjv040
  7. Dramane Coulibaly and Hubert Kempf (2019), 'Inflation targeting and the forward bias puzzle in emerging countries', Journal of International Money and Finance 90, 19-33. DOI: 10.1016/j.jimonfin.2018.09.003. https://doi.org/10.1016/j.jimonfin.2018.09.003
  8. Ibrahim Jamali, Ehab Yamani, and Aaron D. Smallwood (2023), 'An investment-based explanation of currency excess returns', Journal of International Money and Finance 133, 102830. DOI: 10.1016/j.jimonfin.2023.102830. https://doi.org/10.1016/j.jimonfin.2023.102830
  9. Vitaly Orlov (2019), 'Solvency risk premia and the carry trades', Journal of International Financial Markets, Institutions and Money 60, 50-67. DOI: 10.1016/j.intfin.2018.12.001. https://doi.org/10.1016/j.intfin.2018.12.001
  10. Huichou Huang and Ronald MacDonald (2013), 'Currency Carry Trades, Position-Unwinding Risk, and Sovereign Credit Premia', SSRN working paper. DOI: 10.2139/ssrn.2287287. https://doi.org/10.2139/ssrn.2287287
  11. Toby Im (2019), 'Interest Rate Parity with Credit Risk: Implications for Carry Trades', SSRN working paper. DOI: 10.2139/ssrn.3488456. https://doi.org/10.2139/ssrn.3488456
  12. Seunghoon Na, Stephanie Schmitt-Grohé, Martín Uribe, and Vivian Yue (2018), 'The Twin Ds: Optimal Default and Devaluation', American Economic Review 108(7), 1773-1819. DOI: 10.1257/aer.20141558. https://doi.org/10.1257/aer.20141558
  13. Ljubica Georgievska (2022), 'Currency Crashes and Sovereign Defaults: Two Markets and One Tail Risk', SSRN working paper. DOI: 10.2139/ssrn.4049079. https://doi.org/10.2139/ssrn.4049079
  14. Diana Zigraiova, Tomas Havranek, Zuzana Irsova, and Jiri Novak (2021), 'How puzzling is the forward premium puzzle? A meta-analysis', European Economic Review 134, 103714. DOI: 10.1016/j.euroecorev.2021.103714. https://doi.org/10.1016/j.euroecorev.2021.103714
  15. Giovanni Calice and Ming-Tsung Lin (2023), 'Sovereign Credit Default Swaps and the Currency Forward Bias', Journal of International Financial Markets, Institutions and Money 86, 101803. DOI: 10.1016/j.intfin.2023.101803. https://doi.org/10.1016/j.intfin.2023.101803
  16. Giovanni Calice and Ming-Tsung Lin (2024), 'Sovereign momentum currency returns', International Review of Financial Analysis 96, 103472. DOI: 10.1016/j.irfa.2024.103472. https://doi.org/10.1016/j.irfa.2024.103472
  17. Reinhold Heinlein, Gabriella D. Legrenzi, and Scott M. R. Mahadeo (2026), 'Exchange Rates and Sovereign Risk: A Nonlinear Approach Based on Local Gaussian Correlations', International Journal of Finance and Economics. DOI: 10.1002/ijfe.70236. https://doi.org/10.1002/ijfe.70236
  18. Nilanjana Chakraborty, Mohammed M. Elgammal, and David G. McMillan (2026), 'Forward premium anomaly explained', International Review of Economics and Finance 110, 105593. DOI: 10.1016/j.iref.2026.105593. https://doi.org/10.1016/j.iref.2026.105593
  19. Nilanjana Chakraborty, Mohammed M. Elgammal, and David G. McMillan (2026), 'Corrigendum to “Forward premium anomaly explained” [International Review of Economics & Finance 110 (2026) 105593]', International Review of Economics and Finance, article 105740. DOI: 10.1016/j.iref.2026.105740. https://doi.org/10.1016/j.iref.2026.105740