The forward premium puzzle — the finding that the slope of the Fama regression of the future spot-rate change on the forward premium is far below the value of one implied by uncovered interest parity — remains a central anomaly of international finance. Liu and Sercu (2009) conjectured that a career-risk ('fallen-angel') mechanism contributes to it: professional portfolio managers, whose career prospects suffer disproportionately from cash losses taken against publicly visible danger signals, shun currencies exhibiting such signals and therefore require a premium to hold them. In Exchange Rate Mechanism data they find an inverse-U-shaped Fama beta, consistent with the conjecture, but the observed nonlinearity does not uniquely identify career risk, and the paper provides no structural model or discriminating test. The source leaves open the problem of identifying the mechanism behind the nonlinear Fama beta — separating career-risk premia from alternative nonlinear risk-premium and behavioral explanations, and identifying what the long-memory component of the forward premium that appears to carry the risk premium economically represents, an identity the source leaves conjectural.

Background

Under uncovered interest parity (UIP), the forward exchange rate should be an unbiased predictor of the future spot rate, so a regression of the future change in the log spot rate on the forward premium (the forward rate minus the spot rate, in percent) should have a slope of one. This 'Fama regression' was studied by Fama (1984), who showed that empirically the slope is typically far below one, often near zero or negative: currencies with high interest rates (a large forward premium) tend to depreciate by less than the premium, so that forward rates systematically mispredict spot rates. This is the forward premium puzzle (also called forward bias or the UIP puzzle). Fama's own decomposition attributes a slope below one to a negative covariance between the foreign-exchange risk premium and the forward premium, and the subsequent literature has been dominated by risk-premium interpretations. Standard consumption-based equilibrium models largely failed to account for the magnitude of the premium, but Bansal (1997) showed that an orthodox consumption-based asset-pricing model implies a currency risk premium approximately quadratic in the forward premium, so that the Fama beta should fall as the forward premium rises. A second family of explanations relies on frictions: transaction costs and limits to arbitrage, in which traders ignore profit opportunities too small relative to costs. Huisman et al. (1998) found that UIP holds better at large absolute premia ('extreme support for UIP'), and smooth-transition nonlinear versions of this idea, in which the regression switches regime as a function of the premium, were developed by the limits-to-arbitrage literature, including the asymmetric nonlinear adjustment model of Baillie and Kiliç (2006). These stories predict U-shaped or inverse-bell-shaped beta patterns. Liu and Sercu (2009) proposed a different mechanism. They start from the observation that foreign-exchange markets are dominated by professional investors — traders and portfolio managers managing other people's money — whose ultimate decision criterion is career and remuneration prospects rather than the portfolio's return alone. A cash loss incurred by taking a position against a publicly visible 'danger signal' damages a career far more than an equivalent opportunity loss from following the consensus, so professionals head for the exit when bad news hits even if an expected gain from the subsequent recovery remains. This is the foreign-exchange analogue of the 'fallen angel' effect in equity markets, where stocks that have fallen are shunned by portfolio managers and subsequently earn high returns (Ikenberry, Lakonishok and Vermaelen 1995). The predicted career-risk premium is large when the forward premium is markedly negative (a deep forward discount is one danger signal among others) and small near zero — a premium shaped roughly like a cotangent curve, high at deep forward discounts and falling toward zero as the premium rises toward zero, and not necessarily symmetric in positive versus negative premia — which implies an inverse-U-shaped Fama beta. Because the mechanism works through any publicly visible danger signal, not only the forward premium, the authors first verify that excess returns load positively on principal components (principal component analysis being a dimension-reduction technique summarizing several correlated signals in a few factors) of seven ERM danger signals: the position in the European Exchange Rate Mechanism band (the ERM was the 1979–1998 system of bilateral fluctuation bands around central parities among European currencies), the ECU divergence indicator (a measure of how far a currency strayed from its central parity in the European Currency Unit basket), and recent spot-rate trends. Using weekly one-month forward rates of ERM currencies against the German mark (DEM) from 1976 to 1998, they then estimate Fama regressions in which the beta is a quadratic, cubic, or quadratic-spline function of the forward premium, with significance evaluated by Monte Carlo simulation (confidence intervals obtained by simulating the regression under a data-generating process that mimics the strong persistence of the premium and the overlapping one-month observation windows). Wald tests (joint significance tests of the nonlinearity coefficients) reject constant betas, and the cubic model produces an inverse-U-shaped beta peaking at small positive premia — a pattern that contradicts the monotonically falling Bansal beta and the U-shaped friction stories, and is consistent with the fallen-angel prediction, though the spline adds little beyond the cubic and performs worse under the Schwarz information criterion (a model-selection criterion penalizing parameter count). To handle the near-unit-root persistence of the forward premium (its autocorrelation is so high that the series is statistically hard to distinguish from a random walk), they also decompose it into a slow-moving long-memory trend and a stationary filtered component (using the Hodrick–Prescott filter, a smoothing procedure that splits a series into a smooth trend and a transitory deviation). Regressions on the long-memory component produce much lower betas — it appears to load on the 'missing variable', the risk premium — while the filtered component produces higher, positive betas that appear to load on exchange-rate expectations. Crucially, the authors frame the whole mechanism as a conjecture, and their evidence is deliberately indirect: the estimated nonlinearity matches the predicted shape, but nothing in the design separates career risk from other mechanisms that could produce similar nonlinearities.

Problem Statement

Liu and Sercu (2009) establish, for ERM-era forward rates against the German mark, that the Fama beta is an inverse-U-shaped function of the forward premium — a pattern consistent with their career-risk (fallen-angel) conjecture but, as they state, not proof of it: finding the pattern 'does not necessarily mean that it reflects a fallen-angel effect.' The open problem is to settle the identification question their work raises: establishing which economic mechanism generates the nonlinear Fama-regression beta, separating the career-risk premium of professional portfolio managers from the alternative mechanisms capable of generating similar nonlinear beta patterns, including Bansal-type nonlinear equilibrium risk premia, transaction-cost/limits-to-arbitrage frictions, behavioral overreaction or fads, and other nonlinear risk-premium stories (such as state-dependent default risk). Part of the same identification question is the economic identity of the long-memory component of the forward premium, which appears to carry the risk premium and whose shape the source reads as a clue consistent with a fallen-angel premium, but which the source leaves as a conjecture ('we do not even know what the missing variable is'): resolving the career-risk channel — confirming it, ruling it out in favour of a named alternative mechanism, or establishing observational equivalence — settles the identification question even if this component's identity is left open. The identification question is settled by identifying the mechanism — the career-risk channel confirmed, or eliminated in favour of a named surviving alternative from the mechanisms enumerated above — or by demonstrating formally that the enumerated candidate mechanisms are observationally equivalent in the ERM/DEM sample; refined functional forms or alternative decompositions alone, without identification, do not settle it.

References

  1. Fama, Eugene F. (1984). Forward and spot exchange rates. Journal of Monetary Economics 14, 319–338. DOI 10.1016/0304-3932(84)90046-1. https://doi.org/10.1016/0304-3932(84)90046-1
  2. Bansal, Ravi (1997). An Exploration of the Forward Premium Puzzle in Currency Markets. Review of Financial Studies 10, 369–403. DOI 10.1093/rfs/10.2.369. https://doi.org/10.1093/rfs/10.2.369
  3. Huisman, Ronald; Koedijk, Kees; Kool, Clemens; Nissen, François (1998). Extreme support for uncovered interest parity. Journal of International Money and Finance 17, 211–228. DOI 10.1016/S0261-5606(97)98057-8. https://doi.org/10.1016/S0261-5606(97)98057-8
  4. Baillie, Richard T.; Kiliç, Rehim (2006). Do asymmetric and nonlinear adjustments explain the forward premium anomaly? Journal of International Money and Finance 25, 22–47. DOI 10.1016/j.jimonfin.2005.10.002. https://doi.org/10.1016/j.jimonfin.2005.10.002
  5. Ikenberry, David; Lakonishok, Josef; Vermaelen, Theo (1995). Market underreaction to open market share repurchases. Journal of Financial Economics 39, 181–208. DOI 10.1016/0304-405X(95)00826-Z. https://doi.org/10.1016/0304-405X(95)00826-Z
  6. Liu, Fang; Sercu, Piet (2009). The Forex Forward Puzzle: The Career Risk Hypothesis. The Financial Review 44, 371–404. DOI 10.1111/j.1540-6288.2009.00222.x. https://doi.org/10.1111/j.1540-6288.2009.00222.x
  7. Liu, Fang; Sercu, Piet (2009). The Forward Puzzle: The Roles of Exchange Rate Regime and Base Currency Strength. The World Economy 32, 1055–1074. DOI 10.1111/j.1467-9701.2009.01196.x. https://doi.org/10.1111/j.1467-9701.2009.01196.x
  8. Liu, Fang; Sercu, Piet M. F. A. (2012). The Safe-Haven Effect in Forward Premia: What Makes a Currency Trustworthy? SSRN working paper. DOI 10.2139/ssrn.2136698. https://doi.org/10.2139/ssrn.2136698
  9. Coudert, Virginie; Mignon, Valérie (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
  10. Žigraiová, Diana; Havránek, Tomáš; Iršová, Zuzana; Novák, Jiří (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
  11. Verdelhan, Adrien (2010). A Habit-Based Explanation of the Exchange Rate Risk Premium. Journal of Finance 65, 123–146. DOI 10.1111/j.1540-6261.2009.01525.x. https://doi.org/10.1111/j.1540-6261.2009.01525.x
  12. Farhi, Emmanuel; Gabaix, Xavier (2016). Rare Disasters and Exchange Rates. Quarterly Journal of Economics 131, 1–52. DOI 10.1093/qje/qjv040. https://doi.org/10.1093/qje/qjv040
  13. Brunnermeier, Markus K.; Nagel, Stefan; Pedersen, Lasse H. (2008). Carry Trades and Currency Crashes. NBER Macroeconomics Annual 23, 313–348. DOI 10.1086/593088. https://doi.org/10.1086/593088
  14. Nagayasu, Jun (2011). The Common Component in Forward Premiums: Evidence from the Asia–Pacific Region. Review of International Economics 19, 750–762. DOI 10.1111/j.1467-9396.2011.00979.x. https://doi.org/10.1111/j.1467-9396.2011.00979.x
  15. Chen, Zilin; Gang, Jianhua; Qian, Zongxin (2021). Stock returns and carry trades. The North American Journal of Economics and Finance 58, 101507. DOI 10.1016/j.najef.2021.101507. https://doi.org/10.1016/j.najef.2021.101507