Virtue or Mirage? Complexity in Exchange Rate Prediction

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Virtue or Mirage? Complexity in Exchange Rate Prediction Rehim Kilic 2025-089 Please cite this paper as: Kilic,Rehim(2025). “VirtueorMirage? ComplexityinExchangeRatePrediction,”Finance and Economics Discussion Series 2025-089. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.089. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Virtue or Mirage? Complexity in Exchange Rate Prediction Rehim Kılıç∗ September 16, 2025 Abstract This paper investigates whether the “virtue of complexity” (VoC), documented in equity return prediction, extends to exchange rate forecasting. Using nonlinear Ridge regressions with Random Fourier Features (Ridge–RFF), we compare the predictive performance of complex models against linear regression and the robust random walk benchmark. Forecasts are constructed across three sets of economic fundamentals—traditional monetary, expanded monetary and non-monetary, and Taylor-rule predictors—with nominal complexity varied through rolling training windows of 12, 60, and 120 months. Our results offer a cautionary perspective. Complexity delivers only modest, localized gains: in very small samples with rich predictor sets, Ridge–RFF can outperform linear regression. Yet these improvements never translate into systematic gains over the random walk. As training windows expand, Ridge–RFF quickly loses ground, while linear regression increasingly dominates, at times even surpassing the random walk under expanded fundamentals. Market-timing analyses reinforce these findings: complexity-based strategies yield occasional short-sample gains but are unstable and prone to sharp drawdowns, whereas simpler linear and random walk strategies provide more robust and consistent economic value. By incorporating formal forecast evaluation tests—including Clark–West and Diebold–Mariano—we show that apparent gainsfromcomplexityarefragileandrarelystatisticallysignificant. Overall,ourevidence points to a limited virtue of complexity in FX forecasting: complexity may help under narrowly defined conditions, but parsimony and the random walk benchmark remain more reliable across samples, predictor sets, and economic evaluations. JEL Classification: F41, C50, G11, G15. Keywords: Foreign exchange rate, Exchange rate disconnect puzzle, predictability, complexity, machine learning, Ridge, RFF. ∗Federal Reserve Board, Washington, DC E-mail: rehim.kilic@frb.gov. The views presented in this paper are solely those of the author and do not represent those of the Board of Governors or any entities connected to the Federal Reserve System. 1

1 Introduction Accurately forecasting exchange rates remains one of the most challenging and enduring puzzles in international finance, dating back to the seminal study by Meese and Rogoff (1983). Their influential finding—that structural models based on economic fundamentals consistently underperform a naive random walk in out-of-sample predictions—continues to be corroborated by subsequent empirical investigations; see Rossi (2013) for a comprehensive review. Despite considerable theoretical advances and methodological innovations, the so-called Meese–Rogoff puzzle persists, underscoring the robustness of the random walk benchmark and casting doubt on the predictive power of economic fundamentals. Even so, recent work has identified conditions under which exchange rate predictability can emerge. Empirical research highlights the role of richer predictor sets, attention to structural policy regime changes, and methodological refinements such as panel data methods, adaptive modeling frameworks and machine learning. In particular, the integration of monetary and non-monetary fundamentals, global risk measures, and Taylor-rule fundamentals has shown promise in specific contexts and horizons (see, among others, Molodtsova and Papell, 2009; Zorzi et al., 2015; Pfahler, 2022; Engel and Wu, 2024; Filippou et al., 2025). Parallel advances in econometrics—especially in high-dimensional and machine-learning settings—have renewed interest in exploiting nonlinear structure in forecasting. Kelly et al. (2024) reinvigorate the discussion through the virtue of complexity (VoC), arguing that high-dimensional models with nonlinear transformations, such as Ridge regression with Random Fourier Features (RFF), can outperform simpler linear models by harnessing “benign overfitting” under appropriate regularization. These claims have spurred a nuanced debate: Nagel (2025) and Buncic (2025) caution that apparent gains may reflect mechanical volatilitytiming artifacts or restrictive implementation choices rather than genuine economic structure. In response, Kelly and Malamud (2025) clarify the distinction between nominal and effective complexity and show that the slope of the VoC curve depends critically on the parameterto-sample ratio, implying that benefits attenuate as effective sample size grows; they also discuss ensemble complexity as a more robust way to harness high-capacity models. Motivated by these debates and the persistent exchange-rate puzzle, this paper asks whether the VoC documented primarily in equities extends to exchange rate predictability. We address three questions: (i) does complexity—implemented via Ridge regressions with RFF—deliver meaningful out-of-sample gains over linear regression and the robust random walk benchmark in FX? (ii) how sensitive are any gains to the choice of predictors? and (iii) do complex models translate predictive gains into economic value in market-timing strategies? 2

We study three sets of widely used fundamentals: (i) traditional monetary variables (money growth, interest rate differentials, output growth, and inflation differentials); (ii) an expanded set combining monetary and non-monetary fundamentals, including global risk indicators as in Engel and Wu (2024); and (iii) Taylor-rule fundamentals incorporating interest rate differentials and output gaps following Molodtsova and Papell (2009). To ensure a comprehensive evaluation, we consider rolling training windows of 12, 60, and 120 months. Beyond standard out-of-sample R2 and Mean Squared Prediction Error (MSPE), we employ Clark–West (CW) tests to evaluate predictive accuracy relative to the random walk and Diebold–Mariano (DM) tests to compare high-complexity Ridge–RFF against linear regression, sharpening inference on statistical significance and robustness. We then assess economic relevance through market-timing strategies for both single-currency and equal-weighted currency portfolios. This paper makes three contributions. First, it delivers one of the first rigorous tests of the VoC hypothesis in exchange rates, a domain where the random walk has long been the dominant benchmark. Unlike prior VoC studies in equities, which focus almost exclusively on comparisons between complex and linear regressions, we explicitly evaluate Ridge–RFF models against the random walk, providing a more demanding and relevant benchmark. Second, our results show that while Ridge–RFF can yield localized gains in very small samples with rich fundamentals, these improvements are fragile: as training windows expand, linear regression often matches or exceeds RFF performance, and the random walk remains remarkably robust. Third, by linking forecast statistics to portfolio outcomes, we demonstrate that complexity rarely converts into durable economic value. Methodologically, we extend the equity-focused VoC literature by incorporating CW and DM tests—tools largely absent in that debate—to provide sharper evidence on when apparent gains are statistically meaningful. Our findings also speak directly to the evolving VoC discussion: in FX, Ridge–RFF delivers localized improvements when nominal complexity is high relative to sample size, but once windows expand and the complexity ratio falls, parsimony prevails—linear regression and, often, the random walk dominate both statistically and economically. The remainder of the paper proceeds as follows. Section 2 reviews related work and positions our contribution. Section 3 describes the empirical methodology, data, and construction of exchange-rate fundamentals. Section 4 presents out-of-sample forecasting results and statistical tests. Section 5 evaluates market-timing performance for single-currency and equal-weighted portfolios. Section 6 concludes. Additional data details appear in Appendix A. 3

2 Literature Review Empirical exchange rate forecasting has long been challenged by the seminal finding of Meese and Rogoff (1983) that no structural model could consistently beat a naive random walk. This “random walk benchmark” — typically a no-change forecast — remains notoriously difficult to outperform in out-of-sample tests. Early and recent studies alike confirm that a random walk (especially without drift) often produces lower forecast errors than economic models. For example, Cheung et al. (2005) examined an expanded set of traditional models (including monetary and productivity-based specifications) and found that no model consistently outperformed a random walk in terms of mean squared error. An updated analysis by Cheung et al. (2017) reached a similar conclusion: even with new variants (e.g., real interest rate parity with shadow rates, Taylor-rule-based models), “the more recent models do not consistently outperform older ones” or the random walk, especially for major pairs like EUR/USD. They did note, however, a few instances of predictive success at longer horizons — for instance, models beating the random walk at the 5-year horizon occurred more frequently than at short horizons. This aligns with earlier hints in the literature that any predictability might emerge only at long horizons or under specific conditions, though such gains are modest and sample-dependent. Overall, the random walk without drift remains the toughest benchmark to beat in exchange rate forecasting, underscoring the persistence of the Meese–Rogoff puzzle. Nevertheless, numerous studies in the last decade have explored when and how economic fundamentals can help forecast exchange rates. Rossi (2013) provides a comprehensive survey of post-2000 findings, concluding that the answer to “Are exchange rates predictable?” is “It depends.” Predictability appears strongest under specific choices of predictors, models, and horizons. Notably, Rossi finds that using certain economic fundamentals like Taylor rule differentials (which proxy relative monetary policy stances) or external imbalances (e.g., net foreign asset positions) can yield improved forecasts under the right conditions. In particular, these fundamentals showed promise at shorter horizons when used in simple linear models with limited parameter estimation. This result echoes earlier work suggesting that imposing theoretical long-run relationships can aid forecasting: for example, monetary models that enforce long-run equilibrium (via error-correction terms) had some success at multi-year horizons in the 2000s. A recent study by Engel and Wu (2024) further supports the perspective of circumstantial feature of predictability by showing significant improvements in the performance of standard exchange rate models since the early 2000s. Engel and Wu argue that these models, incorporating both monetary and non-monetary fundamentals alongside global risk and liquidity measures, perform substantially better in recent decades compared to the earlier periods 4

(1970s–1990s). They attribute this enhanced predictability largely to improved and more credible monetary policy regimes, such as inflation targeting, which reduce the scope for self-fulfilling expectations and excessive volatility. Similarly, studies have re-examined purchasing power parity (PPP) as a predictor. While PPP was historically critiqued for poor short-run performance, recent evidence suggests it can be useful over longer periods. Zorzi et al. (2015) show that a calibrated half-life PPP model (assuming the real exchange rate slowly mean-reverts to its equilibrium) forecasts real and nominal exchange rates better than a random walk at both short and long horizons. In fact, a series of papers find that a simple PPP-based forecast often significantly outperforms the random walk, provided one assumes realistic slow adjustment of exchange rates toward their PPP value. The intuition is that even if fundamental/value relationships are weak in the short run, the gradual pull of exchange rates toward relative price parity can provide exploitable forecasting power at medium to long horizons. By contrast, other traditional fundamentals have a more mixed record. Standard monetary models (which include money supplies, outputs, and interest rates) and uncovered interest parity (UIP, using interest differentials) generally fail to beat the random walk at short horizons. There is some evidence of monetary models improving forecast accuracy at longer horizons or in panel estimations, but results are not consistent across samples. For instance, Molodtsova and Papell (2009) found that incorporating Taylor rule fundamentals yields better-than-random-walk forecasts for certain currency pairs during the early 2000s, though such gains dissipate in other periods. Likewise, interest rate parity deviations alone have limited predictive power due to time-varying risk premia (the forward premium puzzle). Researchers have tried augmenting models with proxies for risk or liquidity conditions — e.g., global volatility indices or financial stress measures — to capture these time-varying premiums. Cheung et al. (2017) report that adding risk and liquidity factors can improve the in-sample fit of a sticky-price monetary model, but the out-of-sample predictive improvement remains still unimpressive. In summary, traditional macro fundamentals by themselves have struggled to consistently forecast exchange rates better than a random walk, except in specific circumstances such as enforcing long-run PPP or when particular fundamental imbalances become extreme. One reason for the inconsistent performance of fundamentals is structural instability — the idea that the relationship between exchange rates and fundamentals may change over time. Recent research has tackled this challenge through model uncertainty and regime-switching approaches. For example, Kouwenberg et al. (2017) develop a model selection framework that allows the set of relevant fundamentals to shift over time, aligning with theories that investors pay selective attention to different variables in different periods. They design an adaptive forecasting rule that at any given time picks the best-performing fundamentals-based 5

model out of a broad menu of economic variables. This approach yields notable forecasting gains: out-of-sample tests show it significantly beats the random walk for 5 out of 10 major currencies. The selected fundamentals — and their weights — vary over time, suggesting that part of the exchange rate disconnect may be due to markets periodically rotating their focus (e.g., from interest differentials at one time to terms-of-trade or external deficits at another). Such findings are consistent with the “scapegoat” models of Bacchetta and van Wincoop (2004), which posit that agents might rationally latch onto different fundamentals in explaining currency movements when true underlying drivers are unobservable. By accounting for model uncertainty and allowing for time-varying parameter emphasis, the literature shows improved forecast accuracy and even economic value (e.g., the adaptive forecasts can inform profitable currency trading strategies). Other studies exploit panel data and factor models to pool information from multiple currencies. Engel and West (2012) extract common factors from a panel of bilateral dollar exchange rates and combine them with fundamentals; at long horizons (8 to 12 quarters) in more recent samples, these factor-based forecasts modestly outperform the random walk. Similarly, panel econometric techniques can increase predictive power by sharing information across countries: Ince and Kubler (2014) finds that using panel estimation with real-time data helps uncover predictability that is missed in single-currency, revised-data regressions. The general message is that incorporating more data (cross-sectional or temporal) and allowing for structural change can enhance the forecastability of exchange rates, albeit incrementally. In the past several years, a wave of novel methodological developments — particularly those drawn from machine learning (ML) and big data — have been applied to exchange rate prediction. The motivation is that flexible, data-driven algorithms might detect complex nonlinear relationships or interactions in the data that elude traditional linear models. One strand of this research applies relatively simple ML tools to fundamentals-based forecasting. Forexample,Amat(2018)useregularizationtechniques(ridgeregressionsandanexponentially weighted averaging of predictors) to forecast exchange rates with a range of economic fundamentals. They report slight improvements over OLS: while no large reduction in RMSE was found, their models were able to predict the correct direction of quarterly exchange rate changes a bit above 50% of the time for most major currency pairs — a small but non-trivial gain given that a random guess would be 50%. Building on that work, Pfahler (2022) explore more complex ML models like artificial neural networks (ANNs) and gradientboosted trees (XGBoost) in a panel of 10 OECD currencies. Their findings indicate that nonlinear ML methods can indeed outperform the random walk under certain setups. In particular, when predicting the direction of change rather than exact amounts, the ML models showed significant predictive power. The XGBoost models beat the random walk’s directional 6

accuracy by a small margin (sometimes significantly so), and the ANN models by an even larger margin — often statistically significant at the 1% level. However, an interesting nuance emerged: these strong results depended on including “time dummy” variables in the model, suggesting that the algorithms were capturing some time-specific effects or regimes. In fact, an ANN using only time fixed effects (with no fundamentals) could predict well out-of-sample in many cases, raising the concern that ML might be picking up patterns such as trends or momentum rather than genuine economic relationships. Nonetheless, when the ANN was fed both time dummies and fundamental variables (especially those from a monetary model), its performance improved beyond using time dummies alone. This implies that the ML model was able to exploit interactions between economic fundamentals and time-specific factors — possibly capturing how the impact of fundamentals changes over different periods. In sum, machine learning methods have shown promise in extracting predictive signals from data that traditional approaches deemed unforecastable, but they also highlight the importance of handling structural change and of carefully interpreting what drives the forecast gains. More advanced data-driven approaches have likewise been tested. Deep learning architectures — such as recurrent neural networks (LSTM), convolutional neural networks, and transformers — have been applied to exchange rate series with large sets of input features. Meng et al. (2024), for example, forecast the Chinese RMB/USD rate using 40 input features spanning macroeconomic indicators and market data. They find that a sophisticated transformer-based model achieved the best accuracy, outperforming simpler models on this task. Notably, their study emphasizes the role of economic fundamentals even in a data-rich, machine-learning context: using explainability techniques, they show that variables such as China–U.S. trade volumes and the exchange rates of major related currencies were among the most influential features for the model’s predictions. In other words, the deep learning model’s success still hinged on fundamental economic information, but the flexible ML framework was better able to capture the nonlinear and interactive effects of those fundamentals on the exchange rate. Similarly, in a recent study by Filippou et al. (2025) demonstrates that short-horizon exchange rates can be predicted by combining economic fundamentals with machine learning methods. Using an ensemble of elastic net and deep neural networks applied to country-level and global variables, they show consistent outperformance over the random walk benchmark—especially during periods of financial stress. Their findings highlight the importance of modeling nonlinearities and state-dependent dynamics, offering both statistical and economic value in forecasting. These results generally align with a broader insight in the forecasting literature that more complex models can utilize large information sets more effectively. 7

This paper is closely related to the recent literature on return predictability and the so-called virtue of complexity (VoC). While most existing studies, including Kelly et al. (2024), focus on equity return forecasting, our analysis provides an external test of these ideas in the distinct setting of exchange rate predictability. Kelly et al. (2024) argue that high-dimensional predictive models—implemented with random Fourier features and ridge regularization—can outperform simpler alternatives, especially in short-horizon equity return forecasts. They attribute these gains to “benign overfitting,” whereby large models, when appropriately regularized, exploit weak but pervasive predictive signals. Consistent with this view, our results across eight USD exchange rates show that Ridge–RFF can yield localized improvements in small samples with rich predictor sets. Subsequent research has both refined and challenged this perspective. Nagel (2025) argues that RFF forecasts in small samples mimic volatility-timed momentum strategies rather than capturing genuine nonlinear structure, which aligns with our finding that RFF advantages vanish once sample size expands. Likewise, Buncic (2025) demonstrates that methodological choices—such as excluding intercepts or aggregating features rigidly—can overstate the apparent benefits of complexity. Our results resonate with these critiques: as sample sizes grow and nominal complexity falls in relative terms, the edge of complex models dissipates. In FX, linear regression and, in many cases, the random walk not only regain ground but consistently dominate both statistically and economically. Responding to such critiques, Kelly and Malamud (2025) clarify the distinction between nominal complexity (c = P/T, the parameter-to-sample ratio) and effective complexity, which reflects shrinkage and implicit regularization. They show that nominal complexity is central for understanding out-of-sample performance in equities. Our evidence suggests that, in FX, high nominal complexity does not translate into lasting effective gains—particularly relative to the random walk—underscoring domain-specific limits of the VoC framework. Moreover, the attenuation of complexity’s benefits as training samples expand is consistent with their theoretical perspective: as T rises relative to P, the slope of the VoC curve flattens, and the marginal payoff to nominal complexity diminishes. Overall, our results confirm the conditional nature of complexity’s value. Ridge–RFF delivers localized gains in very small samples with rich predictors, reflecting benign overfitting, but these advantages do not scale. As training windows lengthen, complexity’s edge disappears or reverses, and simpler models—linear regression or even the random walk—become systematically more reliable. This pattern echoes critiques by Nagel (2025) and Buncic (2025), and also complements Cartea et al. (2025), who show that in high-dimensional settings the benefits of complexity erode once feature noise is accounted for. Our FX evidence reinforces 8

these points: complexity produces fragile, short-lived improvements, while parsimony proves robust across horizons and predictor sets. Wefurthershowthatundertheexpandedsetofmonetaryandnon-monetaryfundamentals, linear regression consistently outperforms the random walk benchmark in medium and especially long samples (notably at the 120-month window). This finding aligns with Engel and Wu (2024), underscoring the importance of richer predictor information and longer histories in recovering exchange rate predictability. Strikingly, however, Ridge–RFF fails even in this potentially data-rich environment—underperforming both linear regression and the random walk—suggesting that added complexity does not yield incremental gains when fundamentals are informative and sample size is sufficient. Taken together, our results, alongside recent contributions to the VoC debate, highlight the sharply conditional appeal of complexity. While complexity can generate localized benefits in equities and in very small-sample FX settings, its scope is limited, fragile, and benchmarkdependent. Parsimoniousmodels—particularlylinearregressionandtherandomwalk—remain more robust in FX, revealing that the “virtue of complexity” is tightly constrained by data availability and the economic structure of exchange rate dynamics. 3 Empirical Methodology and Data This section describes the random Fourier features (RFF) non-linear machine learning framework of (Rahimi and Recht, 2007, 2008) that Kelly et al. (2024) utilize to build increasingly more complex machine learning models, together with the linear models that has been used in the empirical exchange rate literature based on economic fundamentals. Our empirical analysis assesses the predictive performance of complex machine learning models, simpler linear forecasting models and the naive random walk for exchange rate returns. We apply these models across different sets of exchange rate fundamentals and sample sizes to provide a robust assessment of the so-called “virtue of complexity” in the context of exchange rate forecasting. Following the exchange rate forecasting literature, we define the target variable as the log return of the bilateral exchange rate between the U.S. dollar and a foreign currency: ∆s = log(S )−log(S ), t t t−1 where S denotes the spot exchange rate (defined as the domestic currency price of a foreign t currency) observed at time t, with ∆s is the log exchange rate return. Exchange rates used t are the U.S. Dollar against the major currencies including Australian dollar (AUD), Canadian 9

dollar (CAD), Swiss franc (CHF), the euro (EUR), U.K. pound sterling (GBP), Japanese yen (JPY), Norwegian krone (NOK), and Swedish krona (SEK). Details of the data and sources used in in the analysis are provided in Appendix A. The predictor information set consists of the time t measurable k×1 vector G containing t threedifferentsetsoffundamentalsmotivatedbythelargeliteratureonthesocalled“exchange rate disconnect” (Meese and Rogoff, 1983; Rossi, 2013; Molodtsova and Papell, 2009; Engel and Wu, 2024). 1. Traditional monetary fundamentals include money supply growth, inflation, interest rate, and output growth differentials between the home (US) and foreign countries which gives 4×1 vector, G = [∆(m −m∗), ∆(i −i∗), ∆(π −π∗), ∆(y −y∗)]′ with t t t t t t t t t ‘∗′ denoting the foreign variable and ∆ is the first difference operator and represents a one-month difference. The inflation over previous 12 months in the U.S. and foreign country defined as π = p −p and π∗ = p∗ −p∗ where p and p∗ are the log U.S. t t−12 t t t−12 t t and foreign consumer price indexes. Money supply in the U.S. and foreign country are measured by M , andM∗ and monthly logarithms are denoted by m andm∗. Therefore, t t t t ∆(m −m∗) gives the money supply growth differential between the U.S. and foreign t t country. The U.S. and foreign nominal interest rates are denoted by i andi∗ and t t measured by 3-month U.S. and foreign government bond rates.The log output in the U.S. and foreign countries are denoted by y andy∗ with output is captured by monthly t t industrial production index. The output growth differential between the U.S. and foreign country is then defined by ∆(y −y∗). The traditional fundamentals is motivated t t by the monetary model of exchange rate determination with sticky prices and the predictor set is more consistent with classical monetary models such as those tested by Meese and Rogoff (1983) and revisited in subsequent studies (Rossi, 2013). 2. Expanded monetary and non-monetary fundamentals includes variables introduced by Engel and Wu (2024). These fundamentals are home and foreign real interest rate changes (∆r , and∆r∗), home and foreign inflation rates, π , andπ∗, one-month lagged t t t t real exchange rate, q , the U.S. trade balance on goods and services divided by U.S. t−1 GDP, TB , and a measure of monthly change in global risk aversion, (∆Risk ). This GDP t (cid:104) (cid:105)′ gives us a 7×1 vector, G = ∆r , ∆r∗,π , π∗, ∆Risk , q , TBt . The real interest t t t t t t t−1 GDPt rates are defined as r = i − π and r∗ = i∗ − π∗ and the log real exchange rate as t t t t t t q = s +p∗ −p . t t t t 3. Taylor-rule-based fundamentals include the U.S. and foreign nominal interest rates, i t and i∗, inflation rates, π and π∗, output gaps, ygap and ygap∗, and the real exchange t t t t t 10

rate, q . Taylor-rule fundamentals give a 7×1 vector, G = [i , i∗,π , π∗, ygap, ygap∗, q ] ′ t t t t t t t t t (see, Molodtsova and Papell, 2009). We begin with a standard linear regression framework, estimated using ordinary least squares (OLS), where exchange rate returns between t and t+1 are regressed on a set of macroeconomic fundamentals at date t: ∆s = G′β +ε . (1) t+1 t t+1 This direct forecasting specification is also called ’‘single-equation, lagged fundamental model” and has been used extensively in the empirical exchange rate prediction literature (Rossi, 2013).1 If the relationship between exchange rate returns and predictors are not linear, following Kelly et al. (2024), one can assume that the true predictive model for exchange rate returns, ∆s , follows the process: t+1 ∆s = f(G )+ε , (2) t+1 t t+1 where G is “fixed set of predictive signals, and f(.) a smooth function ” (p. 460 Kelly et al., t 2024). Although the set of predictors G may be known to the researcher, the prediction t function f(.) is unknown and “can be approximated with a sufficiently wide neural network (Kelly et al., 2024): P (cid:88) f(G ) ≈ Z β (3) t i,t i i=1 where Z = g(ω′G ), P is the number of terms used in the approximation to f(G ), g() is i,t i t t a predefined non-linear activation function with weight vector ω , and G is the vector of i t predictor variables under a given set of fundamentals. The approximating model for the true predictive model in (2) then takes the form: P (cid:88) ∆s = Z β +ε˜. (4) t i,t i t i=1 The approximation accuracy of (cid:80)P Z β in (4) to the unknown (true) function f(.) i=1 i,t i in (3) depends on the number of predictor terms (or features) P. With a fixed number of data points T used to train the model, one has to decide how large a P to use. A model is said to be simple, when P << T (number of features is much less than the training sample size), and will have low variance due to a parsimonious parametrization, but it will only 1One advantage of this direct forecasting equation is that is less prone to endogeneity of fundamentals and hence, OLS can be used to estimate parameters. 11

provide a crude approximation to the true function f(.). A high-complexity model where P >> T will have better approximating properties to f(), but may be poorly behaved and require regularization (or shrinkage estimation), which can increase bias. As in Kelly et al. (2024), complexity c is defined as the ratio of the number of features P to the number of training observations T, c = P/T. In a recent paper, Kelly and Malamud (2025) labels this as ’nominal complexity’ in order to distinguish it from the notion of ’effective complexity’ that is introduced by Nagel (2025) and formally described as the ratio of effective number of parameters to sample size where effective number of parameters accounts for shrinkage, bias, or implicit regularization. Kelly et al. (2024) show theoretically that expected out-of-sample forecast accuracy and portfolio performance are strictly increasing in model complexity when appropriate shrinkage is applied. To verify their theoretical results, they utilize the RFF framework to be able to smoothly transition from a low-complexity model to a high complexity one. Specifically, the RFF methodology takes as input the k ×1 vector G of predictor variables under a given set t of fundamentals and converts the information contained in G into (a pair of) new signals t S defined as: i,t Z = [sin(γω′G ) cos(γω′G )]′, (5) i,t i t i t whereω ∼ i.i.d.N(0,I)isak×1randomweightvector, I istheidentifymatrixofconformable i size, and γ is a standard deviation parameter set to 2 in Kelly et al. (2024) that controls the variability in the Gaussian draws of ω . To generate P RFFs, one needs to generate P/2 i weights ω and then evaluate the transformation in (5). This approach allows generating i larger predictor sets based on a limited number of k predictors and thereby more ’complex’ models from the same underlying fundamentals and the associated information set by simply creating new random weight vectors ω and RFF pairs Z from (5). i i,t When P >> T, estimation of β is obtained by minimizing the Ridge objective function: i   (cid:32) (cid:33)2 T P P (cid:88) (cid:88) (cid:88) β(cid:98) i (λ) = argmin ∆s t − Z i,t β i +λ β i 2 , (6) β t=1 i=1 i=1 where λ is the regularization parameter and β(cid:98)(λ) is the vector of regularized least squares estimates of P ×1 vectors of stacked {β }P . The regularization term λ penalizes the size of i i=1 the coefficients, thereby mitigating overfitting when the number of predictors is large relative to the sample size. 12

Given the Ridge regression estimates of β(cid:98)(λ), 1−month ahead forecasts of ∆s , given t+1 information up to time t, are computed as P (cid:88) ∆(cid:100)s = Z β(cid:98)(λ). (7) t+1|t i,t i i=1 To evaluate out-of-sample predictive performance, we use rolling window regressions with window lengths of 12, 60, and 120 months. At each step, the model is re-estimated using only the training window, and forecasts are generated for the subsequent 1-month ahead exchange rate return. Similar to Kelly et al. (2024), we consider training window sizes as small as T = 12 and since in our case, G is of dimensions k = 4and7 depending on the t set of fundamentals used, we do not have Ridgeless regression as in Kelly et al. (2024), but note that in our case, linear regression corresponds to λ = 0 without the need for using ˆ Moore-Penrose pseudo-inverse to solve β. We follow Kelly et al. (2024) and set P = 12000 and λ = 1000 in our assessment of the complexity. We evaluate the forecasting performance of linear and high-complexity (nonlinear or Ridge-RFF) models against each other as well as random walk. Following Kelly et al. (2024), we do not include an intercept term in linear and Ridge-RFF models and compare them against a driftless random walk.2 We use out-of-sample R2, Mean Squared Prediction Error (MSPE) ratios, Clark-West (CW) and Diebold-Mariano (DM) forecast comparison tests. We use CW test in comparing the high-complexity and linear regressions relative to the random walk benchmark as random walk is nested while use DM test in comparing Ridge-RFF against the linear benchmark as linear benchamrk not necessarily nested within the Ridge-RFF. Similar to Kelly et al. (2024), we further evaluate the economic relevance of forecasts by implementing market-timing strategies that take positions in currency portfolios based on 1−month ahead predicted returns. At time t, the model-based strategy takes a long (short) position that is determined by the exchange rate return forecast under a model, yielding a portfolio return of ∆(cid:100)s ·∆s , where ∆(cid:100)s ) denotes the forecast of the excess exchange t+1|t t+1 t+1|t rate return under a model (Ridge-RFF and linear) and ∆s is the realized exchange rate t+1 return on date t+1. We construct market timing strategy under random walk in a similar fashion where positions are based on the the previous period’s exchange rate return, i.e., ∆s ·∆s . Portfolio returns under Ridge-RFF are averaged across 1000 simulations as in t t+1 Kelly et al. (2024). We use both single-currency market-timing portfolios for each currency as well as equal-weighted eight-currency portfolios by aggregating across currencies at each 2Note that the terms ‘linear’ and ‘OLS’ are used interchangeably, as are ‘nonlinear’ and ‘Ridge-RFF’, throughout the paper. 13

point in time and evaluate performance using a range of out-of-sample metrics, including Sharpe ratios (SR), Information ratios (IR), skew, maximum loss and t-tests. 4 Out-of-sample Performance Statistics In this section, we present and discuss out-of-sample performance of linear and nonlinear models relative to the random walk benchmark and to each other, using out-of-sample (OOS) R2, MeanSquaredPredictionError(MSPE),andtheClark–West(CW)andDiebold–Mariano (DM)predictiveaccuracytestsacrossthreepredictorsets—traditionalmonetaryfundamentals, the expanded monetary and nonmonetary set of Engel and Wu (2024) (we label this set by monetary+), and Taylor-rule fundamentals of Molodtsova and Papell (2009). Because the latter two sets include more predictors, they provide a natural setting to test whether greater nominal complexity improves performance through Ridge–RFF. Each table in this section corresponds to a single training-window length (T) and contains three panels—A: Traditional, B: Monetary+, and C: Taylor rule—so that all predictor sets are compared side-by-side for the same T. Within each panel, columns are grouped into three comparisons: Linear vs. Random Walk (reporting R2 and CW against RW), Ridge-RFF vs. Lin Random Walk (reporting R2 and CW against RW), and Ridge-RFF vs. Linear (reporting RFF the MSPE ratio MSPE = MSPERFF and the DM test).3 Positive and statistically significant r MSPELin CW (DM) values favor the first model named in the column header; negative and significant values favor the second. We employ DM because OLS need not be nested within Ridge–RFF. Table 1 reports the 1-month ahead forecasting results under traditional, monetary+, and Taylor rule fundamentals in Panels A, B, and C, respectively for the 12-month rolling window. In Panel A with traditional fundamentals where the number of predictors k = 4, neither linear regression nor Ridge-RFF succeeds in improving upon the random walk. Out-of-sample R2—values are uniformly negative across currencies—especially so for the linear model—while Clark–West tests rarely reject the null of equal predictive accuracy (only CAD for the linear model, and CAD and JPY for Ridge-RFF). Across all currencies, high-complexity RFF based model achieves substantially lower MSPE ratios (0.551–0.747) and statistically significant Diebold–Mariano test rejections in its favor against the linear regression. Results in Panels B and C extend the analysis to the broader predictor sets—monetary and non-monetary fundamentals (k = 7) and Taylor-rule fundamentals (k = 7). The linear model performs very poorly in these settings, generating severely negative out-of-sample R2 values for all currencies as the number of parameters estimated increases in rolling 3Equivalently, MSPE r = 1 1 − − R R R 2 2 FF allows back-out of model MSPEs from the reported OOS R2. Lin 14

Table 1: Out-of-sample forecast comparisons statistics for 12-month rolling-window across traditional, monetary+, and Taylor rule fundamentals Linear vs. Random Walk Nonlinear vs. Random Walk Nonlinear vs. Linear R2 CW R2 CW MSPE DM Lin Nlin r Panel A: Traditional fundamentals AUD −1.274 0.491 −0.252 −0.003 0.551 3.270*** CAD −0.726 1.767** −0.104 2.027** 0.640 5.148*** CHE −1.007 0.678 −0.244 0.245 0.620 3.752*** EUR −1.156 −0.188 −0.208 −0.417 0.560 2.674*** GBP −0.754 −0.886 −0.251 0.522 0.713 4.585*** JPY −0.990 1.084 −0.153 2.670*** 0.579 3.442*** NOK −0.636 −0.506 −0.222 0.519 0.747 2.323** SEK −0.771 −0.428 −0.209 0.113 0.682 4.059*** Panel B: Monetary and non-monetary fundamentals AUD −4.579 0.133 −0.153 −0.942 0.207 5.187*** CAD −4.949 −1.400* −0.147 0.226 0.193 4.649*** CHE −4.395 −0.403 −0.128 −0.186 0.209 5.527*** EUR −3.809 0.430 −0.104 1.017 0.230 6.372*** GBP −3.487 −1.275 −0.099 −0.153 0.245 7.905*** JPY −17.755 −0.701 −0.163 −0.341 0.062 1.773** NOK −151.536 −1.309* −0.147 −0.053 0.008 1.180 SEK −6.629 −1.284* −0.123 0.041 0.147 4.823*** Panel C: Taylor Rule fundamentals AUD −10.167 0.590 −0.224 1.069 0.110 4.825*** CAD −6.256 −1.057 −0.392 −0.646 0.192 7.028*** CHE −5.445 −0.251 −0.300 1.326* 0.202 5.879*** EUR −4.604 −0.102 −0.356 0.651 0.242 6.472*** GBP −4.490 0.953 −0.266 0.131 0.231 6.909*** JPY −28.664 1.676** −0.313 1.787** 0.044 1.267 NOK −5.868 0.409 −0.366 −1.026 0.199 8.071*** SEK −6.412 0.900 −0.365 −0.035 0.184 5.913*** This table reports 1-month ahead out-of-sample forecast accuracy performance comparison statistics between the linear (Lin) and random walk (RW), Ridge-RFF (RFF) and random walk, and Ridge-RFF and linear (see, the main text for details). The forecast target is the 1−month ahead forecast of log USD exchange rate return relative to given currency. Linear vs. Random Walk and Ridge-RFF vs. Random walk panels report oos R2 values (i.e., R2 , andR2 , respectively), and Clark-West (CW) statistic for equal predictive Lin RFF accuracy against RW. The columns for Ridge-RFF vs. Linear report Mean Squared Prediction Error (MSPE) ratios between RFF and Lin, and Diebold-Mariano (DM) test for equal forecast accuracy between these models. *, **, and *** for CW and DM tests indicate rejection of the null of equal predictive accuracy in favor of the first model (i.e., Lin against the RW and RFF against the RW under CW test, and RFF against the Lin under DM test) if the reported test is positive and in favor of the second model if negative. 15

regressions. It consistently fails to outperform either the random walk or Ridge-RFF, and under monetary+ fundamentals the Clark–West test even turns significantly negative at the 10% level for CAD, NOK, and SEK, formally favoring the random walk over the linear regression. In contrast, Ridge-RFF continues to dominate the linear model across most currencies, producing near-zero MSPE ratios and large statistically significant (at 1% level) positive Diebold–Mariano statistics. Taken together, these findings confirm the pattern observed with traditional fundamentals: at high nominal complexity, Ridge-RFF reliably improves upon linear regression but does not deliver systematic gains against the random walk benchmark across all currencies. These gains reflect not just nominal complexity, but also the model’s ability to exploit “effective complexity,” as Ridge regularization (λ = 1000) selects only a subset of relevant RFFs at each estimation. In sum, when T is small and complexity is at its peak, Ridge-RFF shows advantages over linear regression, but these do not translate into systematic gains against the random walk benchmark. With the increase in the rolling window size to 60 months, reported in Panels A–C of Table 2, the linear model begins to show improved performance. Out-of-sample R2 values remain negative, but the magnitudes are substantially smaller, and in several cases the linear model outperforms the random walk, as indicated by positive and statistically significant CW test statistics. For instance, under the Taylor rule fundamentals the linear model outperforms the random walk for three of the eight currencies (GBP, JPY, and NOK) at the 10% or 5% levels. Similarly, the linear model beats the random walk for CAD under traditional fundamentals (Panel A) and for GBP, NOK, and SEK under the monetary+ fundamentals at 10% or 1% significance levels (Panel B). At the same time, Ridge-RFF performance weakens relative to both the linear model and the random walk. While OOS R2 values improve modestly, MSPE ratios often reach or exceed unity, indicating that Ridge-RFF offers no efficiency gains over linear regression. For example, MSPE ratios exceed one for all currencies except for AUD and EUR, with DM tests generally failing to reject equal predictive accuracy under the monetary fundamentals (Panel A). In several cases, the balance even tips in favor of the linear model: the DM test rejects in favor of OLS for CHE under traditional fundamentals and for EUR, GBP, NOK, and SEK under Taylor rule fundamentals, with negative and statistically significant DM values at the 10% or 5% levels. Moreover, Ridge-RFF begins to underperform the random walk, with CW tests not only negative but also statistically favoring the benchmark for CHE and NOK under traditional fundamentals and for AUD and EUR under monetary+ fundamentals. In the case of JPY under Taylor rule fundamentals, both linear regression and Ridge–RFF outperform the random walk, as confirmed by statistically significant CW test rejections, 16

Table 2: Out-of-sample forecast comparisons statistics for 60-month rolling-window across traditional, monetary+, and Taylor rule fundamentals Linear vs. Random Walk Nonlinear vs. Random Walk Nonlinear vs. Linear R2 CW R2 CW MSPE DM Lin Nlin r Panel A: Traditional fundamentals AUD −0.155 0.964 −0.116 −0.860 0.966 0.603 CAD −0.060 2.294** −0.065 −0.164 1.005 −0.124 CHE −0.097 0.718 −0.182 −2.488*** 1.078 −1.338* EUR −0.077 −0.276 −0.076 −0.886 0.999 0.018 GBP −0.056 0.101 −0.079 0.605 1.021 −0.578 JPY −0.109 0.312 −0.137 −0.393 1.025 −0.583 NOK −0.093 −0.332 −0.204 −1.290* 1.101 −1.129 SEK −0.097 −1.062 −0.100 −0.211 1.003 −0.086 Panel B: Monetary and non-monetary fundamentals AUD −0.353 0.854 −0.238 −1.635* 0.915 0.834 CAD −0.280 −0.620 −0.242 −0.277 0.970 0.412 CHE −0.266 −1.007 −0.210 −1.178 0.956 0.601 EUR −0.227 0.216 −0.338 −1.327* 1.091 −0.802 GBP −0.136 2.420*** −0.118 0.642 0.984 0.274 JPY −0.246 0.520 −0.208 −0.208 0.970 0.531 NOK −0.224 1.341* −0.206 −0.966 0.986 0.202 SEK −0.198 1.386* −0.205 −0.896 1.005 −0.095 Panel C: Taylor Rule fundamentals AUD −0.234 0.721 −0.224 1.134 0.992 0.152 CAD −0.292 0.429 −0.395 −0.754 1.080 −0.917 CHE −0.213 0.325 −0.301 1.263 1.073 −1.023 EUR −0.221 1.202 −0.362 −0.116 1.116 −1.294* GBP −0.218 1.849** −0.308 −0.448 1.074 −1.382* JPY −0.282 1.420* −0.287 1.874** 1.003 −0.053 NOK −0.221 1.783** −0.338 −0.552 1.096 −1.888** SEK −0.258 0.773 −0.353 0.068 1.075 −1.366* See, Table 1. while the DM test indicates no significant difference between the two models, underscoring that they remain broadly competitive with each other. With the increase in the training window to 120 months, reported in Panels A–C of Table 3, the relative performance of linear and Ridge-RFF models shifts decisively in favor of parsimony. First, the linear model shows clear signs of improvement. Out-of-sample R2 values, while often still slightly negative, are closer to zero and accompanied by several cases of statistically significant CW test rejections in favor of the linear model against the random walk. Under traditional fundamentals (Panel A), CAD and CHE exhibit positive CW test statistics at the 1% and 5% levels, respectively, while under Taylor rule fundamentals (Panel C), where the linear model achieves statistically significant gains for AUD and EUR at the 5% level. Similar to Engel and Wu (2024), the strongest results emerge under monetary+ 17

Table 3: Out-of-sample forecast comparisons statistics for 120-month rolling-window across traditional, monetary+, and Taylor rule fundamentals Linear vs. Random Walk Nonlinear vs. Random Walk Nonlinear vs. Linear R2 CW R2 CW MSPE DM Lin Nlin r Panel A: Traditional fundamentals AUD −0.067 0.257 −0.056 −0.792 0.989 0.484 CAD −0.010 2.471*** −0.019 0.845 1.009 −0.410 CHE −0.019 1.654** −0.104 −0.957 1.083 −1.130 EUR −0.017 0.539 −0.038 −0.396 1.020 −0.592 GBP −0.024 0.409 −0.021 0.746 0.997 0.157 JPY −0.060 −0.204 −0.059 −0.498 0.999 0.030 NOK 0.016 1.096 −0.157 −0.371 1.176 −1.388* SEK −0.057 −1.300* −0.087 −0.811 1.028 −0.795 Panel B: Monetary and non-monetary fundamentals AUD −0.081 1.754** −0.244 −1.189 1.151 −2.465*** CAD −0.073 0.853 −0.250 −0.470 1.165 −2.853*** CHE −0.095 0.193 −0.238 −0.390 1.131 −1.874** EUR 0.002 2.878*** −0.449 −1.007 1.451 −3.337*** GBP −0.024 2.682*** −0.140 0.884 1.113 −2.217** JPY −0.103 0.466 −0.233 0.220 1.118 −1.934** NOK −0.088 2.007** −0.187 0.210 1.091 −1.377* SEK −0.069 1.856** −0.212 −0.366 1.134 −2.540*** Panel C: Taylor Rule fundamentals AUD −0.046 2.043** −0.235 1.103 1.181 −3.301*** CAD −0.062 1.145 −0.414 −0.781 1.332 −3.193*** CHE −0.105 0.448 −0.314 1.446* 1.189 −3.128*** EUR −0.092 2.139** −0.488 −0.882 1.363 −3.147*** GBP −0.126 0.786 −0.335 −0.565 1.186 −3.407*** JPY −0.124 0.258 −0.305 1.779** 1.161 −2.033** NOK −0.098 0.972 −0.343 −0.558 1.223 −3.952*** SEK −0.126 −0.040 −0.368 0.068 1.215 −3.380*** See, Table 1. fundamentals (Panel B), the linear model outperforms the random walk for five out of eight currencies including AUD, EUR, GBP, NOK, and SEK, all at conventional significance levels. By contrast, Ridge-RFF performance deteriorates further. Out-of-sample R2 values are consistently more negative than those of the linear model, and CW tests rarely provide evidenceofpredictivegainsrelativetotherandomwalk. Moreover, MSPEratiosareuniformly above one, and DM tests overwhelmingly reject the null of equal predictive accuracy in favor of the linear model under Monetary+ and Taylor rule fundamentals. DM tests are not only negative but also highly significant (often at the 1% level) across virtually all predictor sets and currencies. Even in cases where Ridge-RFF attains positive CW values (e.g., JPY and CHE under Taylor rule fundamentals), the corresponding DM tests indicate that these modest gains are eclipsed by the stronger and more robust performance of the linear model. 18

Taken together, the 120-month results highlight a decisive reversal: Ridge-RFF loses the edge it displayed in very small samples, while the linear model steadily gains ground, occasionally outperforming the random walk benchmark and dominating Ridge-RFF in direct comparisons. The results across the three training windows (12, 60, and 120 months) reveal a coherent narrative about the role of complexity in FX predictability: At short horizons (T = 12), nominal complexity is at its peak (p = P/T very large), and Ridge-RFF demonstrates tentative advantages over linear regression. It produces lower MSPE ratios and statistically significant DM rejections in its favor across several currencies. The performance of Ridge-RFF in short training samples is consistent with the results in equity return prediction as reported by Kelly et al. (2024), highlighting the potential of virtue of complexity in very small windows against linear regression. Yet, these gains are relative: Ridge-RFF still fails to systematically outperform the random walk benchmark, which remains a formidable hurdle and a benchmark that has not been explored by the recent studies exploring the ‘virtue of complexity’ in equity return prediction. At intermediate horizons (T = 60), the picture becomes more balanced. The linear model begins to close the gap, with smaller negative R2 values and occasional statistically significant outperformance of the random walk. Ridge-RFF’s edge diminishes: MSPE ratios hover around one, DM tests often fail to reject, and in some cases significantly favor the linear model. Ridge-RFF also begins to underperform the random walk in selected currencies. This marks a turning point, where the “virtue of complexity” weakens and parsimony regains traction. At long horizons (T = 120), the balance tips decisively in favor of parsimony. The linear model consistently outperforms Ridge-RFF, both in terms of MSPE ratios and DM tests, with multiple cases of statistical significance, especially under Monetary+ and Taylor rule fundamentals. It also delivers meaningful gains against the random walk under several predictor sets. Ridge-RFF, by contrast, fails to match this performance, producing uniformly inferior outcomes relative to linear regression and often underperforming the random walk. Overall, the evidence suggests that the benefits of complexity in FX return prediction are highly sensitive to sample size. In very small samples, consistent with the notion of benign overfitting (Kelly et al., 2024), Ridge-RFF can exploit nominal complexity to improve upon linear regression, though never consistently against the random walk. As the training window expands, however, effective complexity declines, regularization reduces the marginal contribution of RFFs, and linear regression reasserts itself as the stronger predictor—at times even outperforming the random walk. 19

5 Market timing strategy performance In this section, we evaluate model performance through their ability to generate market-timing portfoliosatboththesingle-currencyandequal-weightedlevels,followingtheapproachofKelly et al. (2024). For the linear and Ridge–RFF models, positions are based on 1-month-ahead exchange rate return forecasts constructed under three sets of fundamentals—Traditional, Monetary+, and Taylor rule—using rolling training windows of 12, 60, and 120 months. Portfolio returns are generated by taking positions proportional to the model’s forecast: when the forecast is positive, the strategy takes a long position; when negative, it reduces or reverses exposure. The same trading logic applies uniformly across all models, including the random walk benchmark, where the one-month lagged return dictates position-taking (see Section 3). In addition to single-currency strategies, we also examine an equal-weighted markettiming portfolio, in which currency positions are aggregated into an equally weighted basket that is rebalanced monthly. Analyzing both types of strategies allows us to distinguish between model performance at the individual currency level and the aggregate portfolio level, thereby capturing differences between idiosyncratic predictability and systematic gains across currencies. In the following we first present and discuss results for the single currency strategies (5.1) and then the results under equal-weighted portfolio (5.2). 5.1 Single-currency portfolios Table 4 reports results under the random walk–based market timing strategy while Tables 5, 6, and 7 under Ridge-RFF and linear regression-based strategies across traditional, monetary+, and Taylor-Rule fundamentals in columns A-C for T = 12, 60,and120, respectively. Because random-walk-based strategy relies solely on lagged exchange rate returns, results in Table 4 remain broadly similar across training windows, with differences largely reflecting variationintheout-of-sampleevaluationperiods. Overall, theRWstrategygeneratesmodestly positive Sharpe ratios and information ratios relative to the market across most currencies, though statistical significance is generally weak. The standout case is the Japanese yen (JPY), which delivers consistently higher Sharpe ratios (ranging from 0.257 to 0.288) with t-statistics around 1.8, achieving statistical significance at the 10 percent level in all windows. Its information ratios relative to the market are also positive and significant, making JPY the clearest case where lagged return–based timing has predictive value. By contrast, CAD, EUR, and NOK tend to produce small or negative Sharpe ratios across all windows, indicating little or no timing ability. Other currencies (AUD, GBP, SEK, and CHF) display positive but statistically insignificant Sharpe ratios. Distributional properties are heterogeneous: GBP 20

Table 4: Market timing performance metrics: Random walk-based timing stratgey SR t IRv. t Skew Max Mkt Loss PanelA:TrainingwindowsizeT =12 AUD 0.064 0.450 0.040 0.281 0.327 10.552 CAD −0.174 −1.214 −0.167 −1.166 −1.458 9.770 CHE 0.115 0.763 0.101 0.666 −1.778 9.953 EUR 0.058 0.289 0.056 0.275 −2.607 9.430 GBP 0.183 1.278 0.172 1.197 4.129 4.412 JPY 0.257 1.791* 0.236 1.646* −0.259 8.201 NOK −0.034 −0.234 −0.040 −0.276 0.151 7.377 SEK 0.113 0.787 0.075 0.522 2.895 7.057 PanelB:TrainingwindowsizeT =60 AUD 0.145 0.970 0.128 0.855 3.035 5.351 CAD −0.173 −1.154 −0.168 −1.123 −1.396 9.461 CHE 0.053 0.335 0.030 0.189 −2.084 9.896 EUR −0.063 −0.288 −0.065 −0.293 −3.583 9.798 GBP 0.185 1.240 0.169 1.129 4.842 4.471 JPY 0.268 1.793* 0.257 1.716* 0.219 8.650 NOK 0.009 0.060 −0.008 −0.051 0.905 4.878 SEK 0.171 1.143 0.122 0.815 3.174 6.961 PanelC:TrainingwindowsizeT =120 AUD 0.119 0.748 0.112 0.702 2.936 5.076 CAD −0.167 −1.053 −0.166 −1.047 −1.334 8.988 CHE 0.047 0.278 0.036 0.215 −3.011 10.679 EUR −0.178 −0.706 −0.201 −0.792 −0.745 4.313 GBP 0.170 1.074 0.176 1.111 5.344 4.434 JPY 0.288 1.814* 0.271 1.704* −0.229 8.979 NOK −0.045 −0.282 −0.048 −0.302 0.938 4.659 SEK 0.153 0.965 0.148 0.932 3.161 6.675 This table reports one-month-ahead out-of-sample market-timing strategy performance metrics for singlecurrency portfolios under the random walk (RW) benchmark. Reported statistics include the Sharpe ratio (SR) of each strategy with associated t-statistics for mean returns, the Information Ratio relative to the market (IR v. Mkt) with corresponding t-statistics, as well as skewness of returns (Skew) and the maximum loss (Max Loss) in standard deviation units. Statistical significance of mean returns and information ratios is denoted by *, **, and *** at the 10%, 5%, and 1% levels, respectively. and SEK exhibit large positive skew, while CHF and EUR exhibit persistent negative skew. Drawdown risks remain material across all currencies, with maximum losses often between 7 and 10 standard deviations, underscoring the volatility inherent in return-based timing even for this simple benchmark. Notably, GBP combines reasonably strong Sharpe ratios with relatively low drawdowns (around 4.4), while CAD and CHF combine weak or negative Sharpe ratios with among the largest drawdowns, highlighting variation in risk-return trade-offs across currencies. Turning to fundamentals-based models, Table 5 reports market-timing performance for individual currencies under the traditional monetary fundamentals. At the shortest window (T = 12), Ridge–RFF shows clear pockets of strength but no broad dominance. In particular, CAD and JPY stand out for RFF with economically meaningful and statistically significant Sharpe ratios (CAD: SR = 0.306, t = 2.114; JPY: SR = 0.373, t = 2.580), supported by significant information ratios against both the market and the random walk. Crucially, “IR 21

v. LIN” confirms incremental value for RFF in these two currencies (CAD: t = 1.753, JPY: t = 2.414). Elsewhere, performance is mixed: RFF’s SR is near zero for AUD and CHE, negative for EUR, and small for GBP/NOK/SEK; the linear model’s gains are limited to CAD (modestly significant) and JPY (positive but not significant). Drawdowns at T = 12 are nontrivial across both models—for example, AUD exhibits large maximum losses (about 11 standard deviations) for both LIN and RFF—whereas CAD shows comparatively mild losses (about 4.4–4.5 standard deviations), aligning with its stronger risk-adjusted performance. Skewness varies widely: LIN returns are strongly negatively skewed for GBP and EUR, while RFF skewness is more benign for JPY and mixed elsewhere. With the 60-month window (T = 60), in line with the out-of-sample performance statistics discussed in Section 4, the balance tilts toward parsimony. Linear timing improves—CAD is now solidly significant (LIN: SR = 0.345, t = 2.279)—while RFF deteriorates sharply across most currencies. RFF delivers negative and often statistically significant Sharpe ratios for CHE (SR = −0.426, t = −2.672) and NOK (SR = −0.391, t = −1.315, with “IR v. Mkt” t = −2.506), and remains weak or marginal elsewhere (e.g., AUD, EUR, JPY, SEK). The new “IR v. LIN” column makes the underperformance explicit: RFF is significantly worse than LIN for CHE (t = −2.587), and negative (though not always significant) for several others. Importantly, tail risk rises under complexity: RFF maximum losses are elevated—e.g., CAD (about 15 standard deviations), CHE (about 10.7 standard deviations), AUD (about 10.1 standard deviations)—and generally exceed those of LIN, underscoring fragility when the sample expands and nominal complexity (c = P/T) falls. LIN drawdowns are materially lower (typically 4–10 standard deviation) and more in line with its steadier SR profile. At the longest window (T = 120), the reversal is complete. Linear timing is most effective in CAD (LIN: SR = 0.401, t = 2.494), with additional positive though weaker SRs for CHE, EUR, and NOK; SEK and JPY are the notable laggards for LIN (negative or near zero). By contrast, RFF is broadly weak: SRs are negative for AUD, CHE, EUR, JPY, NOK, and SEK, and only small and insignificant for CAD and GBP. The “IR v. LIN” metric rarely favors RFF (mostly negative or near zero), indicating that any incremental value of complexity has evaporated in data-richer settings. Risk metrics reinforce this: RFF exhibits some of the largest drawdowns in the table—e.g., CHE (about 12.6 standard deviations)—and more negative skew (e.g., CHE, SEK), whereas LIN’s tail risk is comparatively contained for the few currencies where it performs best (e.g., CAD with Max Loss around 4.9 standard deviations). In sum, under traditional fundamentals, Ridge–RFF’s advantages are localized to very small samples and a couple of currencies (CAD, JPY) where “IR v. LIN” confirms incremental content. As the training window grows from 12 to 60 and 120 months, linear timing becomes relatively stronger, whereas RFF performance turns persistently negative with 22

Table 5: Market timing performance metrics for single currency portfolios under traditional fundamentals SR t IRv. t IRv. t IRv. t Skew Max Mkt RW LIN Loss PanelA:TrainingwindowsizeT =12 AUD 0.068 0.471 0.074 0.511 0.055 0.382 −3.193 11.082 CAD 0.260 1.797* 0.264 1.822* 0.271 1.867* 2.023 4.466 CHE 0.107 0.703 0.142 0.932 0.134 0.883 8.809 4.010 EUR −0.036 −0.175 −0.044 −0.215 −0.049 −0.239 −2.432 8.989 LIN GBP −0.128 −0.884 −0.139 −0.957 −0.156 −1.074 −2.460 11.233 JPY 0.155 1.071 0.144 0.991 0.120 0.827 2.870 7.004 NOK −0.129 −0.506 −0.163 −0.632 −0.200 −0.772 −1.448 6.268 SEK −0.081 −0.407 −0.091 −0.457 −0.082 −0.413 −0.746 5.535 AUD 0.000 −0.003 −0.031 −0.218 −0.011 −0.076 −0.011 −0.076 −2.090 11.078 CAD 0.306 2.114** 0.294 2.024** 0.338 2.328** 0.255 1.753* 2.297 4.383 CHE 0.036 0.234 0.008 0.054 0.001 0.007 0.046 0.299 −1.568 9.409 EUR −0.080 −0.397 −0.082 −0.405 −0.130 −0.637 −0.073 −0.357 −1.843 7.299 RFF GBP 0.075 0.519 0.060 0.415 0.049 0.339 0.131 0.902 1.319 5.688 JPY 0.373 2.580*** 0.354 2.442** 0.320 2.201** 0.350 2.414** 0.519 5.534 NOK 0.123 0.484 0.053 0.208 0.154 0.595 0.193 0.750 −0.797 4.821 SEK 0.022 0.110 0.017 0.086 0.022 0.108 0.090 0.452 −0.528 6.589 PanelB:TrainingwindowsizeT =60 AUD 0.135 0.896 0.152 1.008 0.156 1.033 0.508 10.527 CAD 0.345 2.279** 0.344 2.273** 0.346 2.279** 1.575 5.152 CHE 0.105 0.655 0.152 0.948 0.103 0.644 2.603 6.384 EUR −0.058 −0.260 −0.034 −0.151 −0.049 −0.221 −0.307 5.286 LIN GBP 0.015 0.102 −0.004 −0.026 −0.065 −0.431 3.644 5.603 JPY 0.048 0.321 0.056 0.369 0.027 0.178 1.848 5.815 NOK −0.107 −0.360 −0.199 −0.660 −0.134 −0.448 0.496 4.824 SEK −0.242 −1.118 −0.230 −1.059 −0.256 −1.180 −2.862 8.271 AUD −0.128 −0.850 −0.142 −0.943 −0.131 −0.868 −0.190 −1.261 −1.391 10.056 CAD −0.025 −0.163 −0.007 −0.049 −0.018 −0.116 −0.034 −0.221 −6.397 15.032 CHE −0.426 −2.672***−0.491 −3.063***−0.448 −2.802***−0.414 −2.587***−5.771 10.701 EUR −0.193 −0.871 −0.189 −0.850 −0.183 −0.823 −0.186 −0.834 −1.705 6.726 RFF GBP 0.096 0.635 0.062 0.408 −0.013 −0.089 0.106 0.700 7.461 6.552 JPY −0.060 −0.398 −0.073 −0.484 −0.093 −0.611 −0.068 −0.448 −1.569 7.802 NOK −0.391 −1.315 −0.757 −2.506** −0.379 −1.262 −0.386 −1.291 −1.856 6.736 SEK −0.047 −0.216 −0.040 −0.184 −0.055 −0.252 0.123 0.566 −4.107 8.928 PanelC:TrainingwindowsizeT =120 AUD 0.039 0.244 0.042 0.261 0.044 0.277 1.166 7.568 CAD 0.401 2.494** 0.401 2.490** 0.412 2.553** 1.417 4.938 CHE 0.269 1.574 0.318 1.859* 0.274 1.600 6.779 6.753 EUR 0.132 0.517 0.142 0.554 0.140 0.545 0.349 4.012 LIN GBP 0.064 0.399 0.068 0.422 −0.006 −0.037 2.307 5.923 JPY −0.033 −0.206 −0.017 −0.106 −0.049 −0.303 −3.012 11.045 NOK 0.480 1.209 0.427 1.053 0.458 1.132 0.539 3.848 SEK −0.352 −1.423 −0.266 −1.068 −0.394 −1.585 −3.696 8.594 AUD −0.119 −0.748 −0.119 −0.745 −0.125 −0.779 −0.180 −1.127 3.425 5.032 CAD 0.130 0.807 0.136 0.846 0.120 0.742 0.026 0.161 −0.941 9.796 CHE −0.183 −1.075 −0.223 −1.301 −0.213 −1.245 −0.069 −0.404 −6.962 12.551 EUR −0.104 −0.408 −0.084 −0.326 −0.146 −0.568 −0.140 −0.543 0.551 4.100 RFF GBP 0.122 0.762 0.129 0.803 0.050 0.311 0.106 0.658 6.390 5.040 JPY −0.081 −0.506 −0.136 −0.848 −0.123 −0.765 −0.078 −0.485 −0.208 6.581 NOK −0.152 −0.383 −0.486 −1.199 −0.155 −0.384 −0.220 −0.541 −1.317 5.501 SEK −0.199 −0.804 −0.191 −0.767 −0.200 −0.805 0.033 0.132 −3.181 7.583 Thistablereportsone-month-aheadout-of-samplemarket-timingstrategyperformancemetricsforsingle-currencyportfolios underthetraditionalmonetaryfundamentals. Resultsarepresentedforlinearregression(LIN)andRidge–RFF(RFF)models, evaluatedrelativetothemarket,therandomwalk(RW),andtoeachother. ReportedstatisticsincludetheSharperatio(SR) ofeachstrategywithassociatedt-statisticsformeanreturns;InformationRatios(IR)relativetothemarket,LINrelativeto RW,andRFFrelativetobothRWandLIN,eachwithcorrespondingt-statistics;aswellashigher-momentanddownsiderisk measures: skewnessofreturns(Skew)andthemaximumloss(MaxLoss)instandarddeviationunits. Statisticalsignificanceof meanreturnsandinformationratiosisdenotedby*,**,and***forthe10%,5%,and1%levels,respectively. 23

higher drawdowns. The evolution across T is consistent with a limited, short-sample “virtue of complexity” that does not scale once more data become available and parsimony can capitalize on signal more reliably. Table 6 evaluates timing strategies under the expanded set of monetary and non-monetary fundamentals. The results confirm that predictor richness does not translate into reliable benefits from added model complexity. At the shortest horizon (T = 12), both models perform weakly overall. Linear regression delivers mostly negative Sharpe ratios, with particularly poor results for CAD, GBP, NOK, and SEK, each with negative and often marginally significant t-statistics. Large maximum losses—for instance, NOK suffers a drawdown of over 23 standard deviations.—highlight instability in LIN despite its simplicity. Ridge–RFF offers only isolated and statistically weak improvements, most notably for EUR (SR = 0.216, t = 1.075), while for most currencies its performance remains flat or negative. Importantly, the “IR v. LIN” entries are uniformly weak, suggesting that RFF does not extract incremental value from the richer predictor set even in small samples. With medium-sized samples (T = 60), linear regression stabilizes. GBP is a clear standout: LIN achieves a Sharpe ratio of 0.404 (t = 2.703), significant at the 1% level, with supporting information ratios against the market and the random walk. Modest though less significant improvements are also observed for NOK and SEK. In contrast, Ridge–RFF systematically deteriorates. Across most currencies (e.g., AUD, CHE, EUR, NOK, SEK), RFF produces negative and often significant Sharpe ratios, coupled with elevated drawdowns. Notably, for EUR, RFF collapses to SR = −0.284 with “IR v. Mkt” t = −1.337, underscoring its fragility once longer training samples reduce nominal complexity. Tail risks remain consistently larger under RFF, while linear regression maintains more balanced drawdowns (typically between 5–10 standard deviations). At the longest horizon (T = 120), the advantage of parsimony is decisive. Linear regression strategies produce their strongest results across all predictor sets here: EUR (SR = 0.648, t = 2.571), GBP (SR = 0.464, t = 2.924), and AUD (SR = 0.314, t = 1.980) all record statistically significant Sharpe ratios, while NOK and SEK also deliver positive and marginally significant performance. By contrast, Ridge–RFF remains persistently weak, with negative or near-zero Sharpe ratios for most currencies and large drawdowns (e.g., JPY at 9.171 standard deviations, CHE at 8.364 standard deviations.). Even where RFF produces positive values (such as GBP or JPY), these gains are small and insignificant, and never competitive with linear regression. Overall, the Monetary+ results reinforce the fragility of complexity in FX timing. Ridge–RFF occasionally produces marginally positive outcomes in small samples (e.g., EUR 24

Table 6: Market timing performance metrics for single currency portfolios under Monetary and nonmonetary (monetary+) fundamentals SR t IRv. t IRv. t IRv. t Skew Max Mkt RW LIN Loss PanelA:TrainingwindowsizeT =12 AUD 0.019 0.132 0.032 0.225 0.007 0.046 −1.372 8.976 CAD −0.201 −1.402 −0.240 −1.673* −0.167 −1.159 −5.587 14.173 CHE −0.056 −0.368 −0.073 −0.479 −0.091 −0.601 −3.950 10.843 EUR 0.092 0.455 0.098 0.486 0.077 0.383 2.043 7.212 LIN GBP −0.187 −1.305 −0.197 −1.371 −0.259 −1.802* −2.496 10.083 JPY −0.093 −0.649 −0.120 −0.833 −0.144 −1.002 −0.721 7.280 NOK −0.187 −1.309 −0.184 −1.283 −0.188 −1.311 −21.551 23.198 SEK −0.184 −1.286 −0.172 −1.199 −0.177 −1.234 −3.750 12.836 AUD −0.139 −0.974 −0.145 −1.012 −0.141 −0.981 −0.138 −0.965 1.114 7.906 CAD 0.033 0.232 0.030 0.210 0.044 0.306 0.053 0.365 1.390 7.645 CHE −0.026 −0.173 −0.038 −0.250 −0.038 −0.248 −0.028 −0.187 0.171 9.832 EUR 0.216 1.075 0.219 1.087 0.209 1.036 0.212 1.049 1.400 5.051 RFF GBP −0.020 −0.140 −0.018 −0.124 −0.064 −0.443 −0.001 −0.005 0.257 6.006 JPY −0.051 −0.352 −0.079 −0.546 −0.172 −1.196 −0.043 −0.298 −0.746 11.293 NOK −0.009 −0.063 −0.010 −0.067 −0.004 −0.026 −0.006 −0.043 −0.428 7.206 SEK 0.004 0.028 0.014 0.099 −0.014 −0.101 0.011 0.074 0.458 6.978 PanelB:TrainingwindowsizeT =60 AUD 0.139 0.928 0.137 0.913 0.079 0.529 0.627 8.209 CAD −0.080 −0.532 −0.071 −0.472 −0.037 −0.249 −2.409 10.416 CHE −0.157 −0.989 −0.207 −1.300 −0.189 −1.191 −8.163 15.487 EUR 0.051 0.233 0.044 0.199 0.094 0.427 −2.693 7.807 LIN GBP 0.404 2.703*** 0.384 2.565** 0.360 2.399** 2.955 5.463 JPY 0.083 0.555 0.072 0.482 0.066 0.437 −0.827 8.077 NOK 0.192 1.285 0.178 1.189 0.193 1.288 −2.371 9.154 SEK 0.209 1.400 0.223 1.485 0.200 1.335 −3.436 10.064 AUD −0.247 −1.652* −0.251 −1.672* −0.257 −1.713* −0.237 −1.581 −1.496 7.203 CAD −0.042 −0.278 −0.042 −0.280 −0.030 −0.199 −0.044 −0.291 0.727 5.670 CHE −0.184 −1.158 −0.227 −1.426 −0.189 −1.191 −0.166 −1.043 −2.768 10.402 EUR −0.284 −1.294 −0.295 −1.337 −0.278 −1.262 −0.280 −1.271 −4.224 10.132 RFF GBP 0.098 0.658 0.098 0.652 0.069 0.462 0.050 0.331 1.916 4.719 JPY −0.032 −0.211 −0.035 −0.230 −0.109 −0.724 −0.042 −0.280 −1.126 9.685 NOK −0.150 −1.001 −0.149 −0.992 −0.152 −1.013 −0.163 −1.085 −1.018 7.296 SEK −0.145 −0.967 −0.132 −0.877 −0.166 −1.110 −0.158 −1.050 −0.901 6.841 PanelC:TrainingwindowsizeT =120 AUD 0.314 1.980** 0.311 1.958* 0.298 1.877* 2.470 4.331 CAD 0.106 0.668 0.112 0.706 0.162 1.020 1.069 9.341 CHE 0.027 0.160 −0.010 −0.061 0.011 0.062 −5.780 14.288 EUR 0.648 2.571** 0.667 2.632*** 0.658 2.595*** 1.126 4.795 LIN GBP 0.464 2.924*** 0.501 3.153*** 0.435 2.731*** 2.944 4.977 JPY 0.079 0.499 0.060 0.375 0.045 0.283 0.975 5.039 NOK 0.308 1.941* 0.306 1.927* 0.327 2.058** −2.442 11.616 SEK 0.302 1.904* 0.305 1.920* 0.305 1.915* 0.078 6.926 AUD −0.193 −1.218 −0.193 −1.215 −0.202 −1.271 −0.164 −1.028 −1.121 7.100 CAD −0.074 −0.469 −0.073 −0.461 −0.072 −0.456 −0.086 −0.541 −1.236 5.849 CHE −0.065 −0.384 −0.084 −0.496 −0.070 −0.413 −0.064 −0.375 −1.202 8.364 EUR −0.263 −1.045 −0.286 −1.127 −0.239 −0.942 −0.182 −0.705 −2.314 7.278 RFF GBP 0.143 0.903 0.144 0.903 0.118 0.741 0.103 0.645 1.976 3.658 JPY 0.035 0.222 0.032 0.200 −0.061 −0.381 0.027 0.171 −1.284 9.171 NOK 0.035 0.220 0.037 0.231 0.040 0.254 0.009 0.057 −0.563 7.446 SEK −0.062 −0.394 −0.059 −0.374 −0.085 −0.534 −0.081 −0.510 −0.986 5.501 This table reports one-month-ahead out-of-sample market-timing strategy performance metrics for singlecurrency portfolios under monetary+ fundamentals. See, notes for Table 5. 25

at T = 12), but these gains vanish quickly as training samples grow. Linear regression, by contrast, benefits systematically from the richer information set, delivering strong and statistically significant Sharpe ratios for multiple currencies at T = 120. Importantly, drawdown patterns show that RFF strategies entail higher downside risk across all horizons, further weakening the economic case for complexity. In this predictor environment, parsimony is not only more reliable but also economically safer, underscoring the limited virtue of complexity once richer fundamentals and longer histories are available. Table 7 presents timing strategy performance under Taylor rule fundamentals. Compared to traditional and Monetary+ predictors, the Taylor rule set provides the most consistent evidence of economic value for linear regression, particularly as the sample size grows, while Ridge–RFF offers selective short-sample advantages that erode quickly. In the short-window case (T = 12), linear regression produces a mixed profile. While CAD and CHE perform poorly (negative Sharpe ratios around –0.15 and –0.04), several currencies showencouragingresults. Notably,JPYachievesaSharperatioof0.249(t = 1.740),significant at the 10% level, while GBP, AUD, NOK, and SEK all record small but positive Sharpe ratios. Ridge–RFF delivers competitive, and in some cases stronger, results: JPY (SR=0.257, t = 1.796) and AUD (SR=0.159, t = 1.114) show robust short-horizon performance, and CHE and EUR also post positive ratios. Nevertheless, these gains come at the cost of greater instability in other currencies: for example, CAD underperforms markedly, with negative Sharpe ratios across specifications and a large maximum loss exceeding 12 standard deviations. At the medium horizon (T = 60), linear regression consolidates its advantage. Significant gains emerge for GBP (SR=0.293, t = 1.961), NOK (SR=0.261, t = 1.746), and EUR (SR=0.237, t = 1.081), while AUD and JPY also show positive, though less significant, results. Ridge–RFF produces respectable outcomes for JPY (SR=0.274, t = 1.835) and AUD (SR=0.175, t = 1.174), but overall performance weakens elsewhere: GBP, NOK, and SEK all fall into negative territory, with drawdowns consistently higher than those observed under linear regression. For example, CAD records a maximum loss of 12.4 standard deviations under RFF versus a much smaller 10.9 standard deviations under LIN. These patterns highlight the fragility of complexity in medium-sized samples. At the longest horizon (T = 120), the contrast is most pronounced. Linear regression delivers its strongest and most statistically reliable results across all fundamentals. EUR achieves a Sharpe ratio of 0.528 (t = 2.094), while AUD also performs strongly (SR=0.354, t = 2.235). Positive and significant gains extend to CAD and NOK, while most other currencies remain at least weakly positive. Ridge–RFF, by contrast, deteriorates markedly. Apart from JPY (SR=0.284, t = 1.787) and CHE (SR=0.238, t = 1.406), most currencies 26

Table 7: Market timing performance metrics for single currency portfolios under Taylor rule fundamentals SR t IRv. t IRv. t IRv. t Skew Max Mkt RW LIN Loss PanelA:TrainingwindowsizeT =12 AUD 0.085 0.594 0.088 0.615 0.067 0.469 3.437 6.282 CAD −0.147 −1.027 −0.154 −1.076 −0.103 −0.719 −1.190 6.819 CHE −0.038 −0.251 −0.045 −0.295 −0.106 −0.702 0.794 6.075 EUR −0.018 −0.090 −0.020 −0.101 −0.056 −0.277 0.005 7.402 LIN GBP 0.136 0.952 0.137 0.955 0.061 0.425 1.662 4.356 JPY 0.249 1.740* 0.227 1.577 0.150 1.041 1.472 4.484 NOK 0.059 0.409 0.044 0.309 0.076 0.532 4.001 5.761 SEK 0.121 0.846 0.086 0.601 0.083 0.580 1.239 6.421 AUD 0.159 1.114 0.152 1.059 0.163 1.136 0.140 0.977 0.732 7.139 CAD −0.094 −0.656 −0.089 −0.620 0.130 0.904 −0.067 −0.464 −4.513 12.845 CHE 0.190 1.255 0.182 1.202 0.151 0.995 0.222 1.466 0.421 5.209 EUR 0.134 0.665 0.131 0.652 0.151 0.748 0.152 0.752 −0.539 4.787 RFF GBP 0.018 0.124 0.025 0.174 −0.084 −0.582 −0.044 −0.304 −0.796 6.812 JPY 0.257 1.796* 0.244 1.699* 0.074 0.515 0.167 1.158 −0.885 10.405 NOK −0.152 −1.059 −0.147 −1.022 −0.177 −1.236 −0.175 −1.218 −1.440 6.636 SEK −0.006 −0.041 −0.006 −0.040 −0.077 −0.534 −0.043 −0.302 −0.457 5.613 PanelB:TrainingwindowsizeT =60 AUD 0.120 0.801 0.110 0.738 0.042 0.280 2.612 6.044 CAD 0.053 0.355 0.070 0.469 0.142 0.951 0.645 10.855 CHE 0.047 0.294 −0.047 −0.293 0.025 0.160 −4.328 13.051 EUR 0.237 1.081 0.263 1.195 0.327 1.485 −3.892 10.332 LIN GBP 0.293 1.961** 0.280 1.873* 0.230 1.535 1.625 5.190 JPY 0.208 1.391 0.195 1.301 0.104 0.691 0.762 6.647 NOK 0.261 1.746* 0.248 1.653* 0.292 1.949* 0.724 4.689 SEK 0.100 0.669 0.079 0.530 0.032 0.213 −0.979 11.530 AUD 0.175 1.174 0.171 1.144 0.102 0.682 0.135 0.903 0.070 8.271 CAD −0.114 −0.765 −0.110 −0.734 0.074 0.496 −0.141 −0.941 −4.616 12.426 CHE 0.193 1.220 0.169 1.061 0.203 1.277 0.188 1.182 0.144 5.382 EUR −0.027 −0.123 −0.024 −0.110 0.033 0.150 −0.150 −0.679 −1.045 5.318 RFF GBP −0.065 −0.432 −0.048 −0.323 −0.167 −1.112 −0.157 −1.048 −0.796 6.287 JPY 0.274 1.835* 0.265 1.769* 0.089 0.595 0.212 1.411 −0.798 10.498 NOK −0.083 −0.557 −0.083 −0.554 −0.117 −0.779 −0.190 −1.268 −1.243 6.667 SEK 0.011 0.071 0.012 0.077 −0.084 −0.562 −0.025 −0.170 −0.310 5.489 PanelC:TrainingwindowsizeT =120 AUD 0.354 2.235** 0.351 2.212** 0.349 2.198** 2.173 6.429 CAD 0.147 0.930 0.159 0.999 0.228 1.433 2.181 10.080 CHE 0.080 0.470 0.052 0.307 0.067 0.396 −0.329 4.905 EUR 0.528 2.094** 0.572 2.259** 0.563 2.219** 0.926 4.678 LIN GBP 0.119 0.753 0.126 0.796 0.043 0.270 0.005 7.143 JPY 0.040 0.255 0.036 0.224 −0.055 −0.344 −3.554 11.821 NOK 0.156 0.983 0.156 0.984 0.186 1.171 1.316 4.698 SEK −0.007 −0.042 0.001 0.008 0.000 −0.002 −1.364 7.251 AUD 0.179 1.132 0.177 1.115 0.135 0.853 0.027 0.172 0.175 7.937 CAD −0.125 −0.792 −0.125 −0.785 0.042 0.262 −0.174 −1.095 −4.496 11.805 CHE 0.238 1.406 0.227 1.333 0.253 1.488 0.225 1.324 0.539 5.624 EUR −0.234 −0.927 −0.233 −0.920 −0.156 −0.614 −0.372 −1.453 −1.180 4.823 RFF GBP −0.086 −0.542 −0.095 −0.600 −0.179 −1.128 −0.122 −0.767 −0.738 6.241 JPY 0.284 1.787* 0.267 1.676* 0.071 0.445 0.283 1.781* −1.241 10.610 NOK −0.089 −0.563 −0.089 −0.562 −0.079 −0.499 −0.135 −0.849 −1.222 6.306 SEK 0.011 0.071 0.013 0.080 −0.071 −0.445 0.013 0.081 −0.314 5.205 This table reports one-month-ahead out-of-sample market-timing strategy performance metrics for singlecurrency portfolios under Taylor rule fundamentals. See, notes for Table 5. 27

record negative Sharpe ratios, with especially poor results for EUR (SR=–0.234, t = −0.927). Moreover, maximum losses for RFF remain elevated, often exceeding those of linear regression, underscoring the higher tail risk associated with complexity. Overall, the Taylor rule results are consistent with a broader narrative: Ridge–RFF can provide isolated improvements in very small samples, particularly for JPY and AUD, but these advantages weaken and often reverse as the sample size expands. By contrast, linear regression steadily strengthens with longer histories, producing statistically significant gains for multiple major currencies at T = 120. Importantly, RFF strategies entail higher and more volatile drawdowns across all horizons, further reducing their appeal in practical portfolio settings. The evidence suggests that under Taylor rule fundamentals, parsimony dominates complexity: linear regression extracts the predictive content of these fundamentals in a stable and economically meaningful manner, while Ridge–RFF adds little and frequently introduces greater risk. Taken together, the single-currency results paint a consistent picture of the limited and fragile nature of complexity in exchange rate forecasting. Ridge–RFF offers selective benefits in very small samples with richer fundamentals, echoing the notion of “benign overfitting” whereby regularization allows complex models to exploit weak signals. Yet these advantages are narrow in scope: as sample sizes grow, Ridge–RFF not only fails to add value but often underperforms both linear regression and the random walk, with larger volatility and deeper drawdowns. By contrast, linear regression steadily improves with richer fundamentals and longer samples, culminating in robust, statistically significant gains under Taylor-rule fundamentals at T = 120. Thisprogression underscoresthe broaderlesson thatparsimonyand data availability ultimately dominate complexity in the context of exchange rate predictability. The “virtue of complexity,” while occasionally visible, does not translate into systematic or durable economic value; rather, the enduring strength lies in well-specified linear models and, in many contexts, the random walk benchmark. 5.2 Equal-Weighted Currency Portfolio Table 8 reports performance metrics for the equal-weighted market-timing strategy under RW, Linear regression, and Ridge-RFF.4 With the shortest training window of T = 12, Ridge-RFF demonstrates some promise in generating economically meaningful portfolio returns, while linear regression performs poorly relative to both RFF and the random walk. For example, 4Because the equal-weighted portfolio requires all eight currencies, the evaluation period begins only after the euro (EUR) enters the sample in 1999. Results using an alternative specification—where the portfolio includes seven currencies before 2000 and all eight thereafter—are very similar and therefore omitted for brevity, but available upon request. 28

Table 8: Equal Weighted Portfolio Market timing trading strategy performance SR t IR v. t IR v. t IR v. t Skew Max Mkt RW LIN Loss Panel A: Training window size T =12 RW 0.232 1.181 0.232 1.149 −0.469 7.413 LIN −0.499 −1.953* −0.500 −1.946* −0.516 −2.008** −1.823 5.909 Trad RFF 0.446 1.747* 0.449 1.747* 0.351 1.349 0.475 1.851* −0.026 3.488 LIN −0.256 −1.276 −0.251 −1.242 −0.266 −1.318 −13.900 15.973 Mon+ RFF −0.020 −0.099 −0.006 −0.032 −0.240 −1.173 −0.003 −0.016 0.179 4.545 LIN 0.200 0.997 0.213 1.056 0.092 0.456 0.476 5.495 Taylor RFF 0.503 2.501** 0.516 2.557** 0.164 0.802 0.450 2.226** 0.039 3.891 Panel B: Training window size T =60 RW 0.345 1.701* 0.345 1.566 1.430 3.095 LIN −0.367 −1.236 −0.363 −1.213 −0.363 −1.213 0.272 3.894 Trad RFF 0.095 0.319 0.108 0.360 0.045 0.150 0.135 0.450 0.036 2.434 LIN 0.321 1.464 0.313 1.414 0.303 1.366 −0.233 3.665 Mon+ RFF −0.286 −1.303 −0.250 −1.133 −0.372 −1.667* −0.382 −1.715* 0.340 2.531 LIN 0.467 2.129** 0.505 2.287** 0.336 1.516 −0.113 3.551 Taylor RFF 0.387 1.761* 0.402 1.818* 0.084 0.377 0.217 0.974 0.275 3.321 Panel C: Training window size T =120 RW 0.361 1.413 0.361 1.427 1.671 2.858 LIN −0.032 −0.081 −0.030 −0.074 −0.049 −0.123 −0.535 3.802 Trad RFF −0.663 −1.669* −0.671 −1.658* −0.678 −1.682* −0.668 −1.659* 0.013 2.803 LIN 0.298 1.181 0.303 1.196 0.317 1.245 −0.048 5.237 Mon+ RFF −0.114 −0.452 −0.114 −0.452 −0.258 −1.008 −0.250 −0.972 0.449 2.359 LIN 0.220 0.875 0.217 0.856 0.164 0.646 −0.478 4.723 Taylor RFF 0.496 1.970** 0.506 1.997** 0.283 1.110 0.465 1.831* 0.544 2.906 This table reports performance metrics for equal-weighted currency market-timing portfolios constructed from one-month-ahead forecasts under the random walk (RW), linear (LIN), and Ridge–RFF (RFF) models across three sets of fundamentals, traditional monetary (Trad), monetary+ (Mon+), and Taylor rule (Taylor). Reported statistics include the Sharpe ratio (SR) with t-statistics for mean returns, the Information Ratio relative to the market (IR v. Mkt), the Information Ratio of LIN relative to RW, and the Information Ratio ofRFFrelativetobothRWandLIN,eachwith corresponding t-statistics. Wealsoreport skewness ofreturns (Skew) and the maximum portfolio loss (Max Loss) in standard deviation units. Statistical significance of t-statistics is denoted by *, **, and *** at the 10%, 5%, and 1% levels, respectively. 29

under Taylor rule fundamentals, Ridge-RFF achieves the highest Sharpe ratio (0.503) with a statistically significant t-statistic (2.501), clearly outperforming both the linear model and RW (SR = 0.232, t = 1.181). Similarly, under traditional fundamentals, RFF delivers a positive Sharpe ratio (0.446, t = 1.747) and significant information ratios relative to linear regression, while the linear model produces negative Sharpe ratios (–0.499, t = −1.953), substantially underperforming RW. By contrast, under monetary+ fundamentals, both models fail to improve upon RW: Ridge-RFF generates a near-zero Sharpe ratio (–0.020, insignificant), and linear regression produces strongly negative performance (–0.256, t = −1.276), while RW remains positive (SR = 0.232). Importantly, the drawdown evidence reinforces the fragility of these results. Ridge-RFF under Taylor fundamentals exhibits relatively modest losses (Max Loss ≈ 3.89), while linear portfolios under monetary+ fundamentals suffer extremely large drawdowns (Max Loss ≈ 15.97) with very large negative skew. Even under traditional fundamentals, linear timing strategy drawdowns are deeper than those of RFF or RW. Thus, while Ridge-RFF occasionally improves on linear timing strategy and even outperforms RW in settings such as Taylor fundamentals, these gains are neither broad-based nor robust across predictor sets, and the strategy remains vulnerable to sharp losses depending on model choice and information set. With larger samples, performance dynamics shift. In the evaluation period corresponding to T = 60 in Panel B of Table 8, the random walk benchmark sets a higher bar (SR = 0.345, t = 1.70). Linear regression begins to show meaningful economic value under Taylor rule fundamentals (SR = 0.467, t = 2.13), significantly outperforming both the random walk and RFF. Ridge-RFF continues to deliver moderate gains under Taylor rule fundamentals (SR = 0.387, t = 1.76), but its edge over linear regression largely disappears, with information ratios against linear model weak or insignificant. Under traditional and monetary+ fundamentals, RFF underperforms (Sharpe ratios near zero or negative), while linear regression strategies provide at best modest gains. Drawdowns provide further evidence of fragility: although linear portfolios under Taylor rule fundamentals and RW achieve positive Sharpe ratios in this training window, they also suffer moderate losses (≈ 3.55 to 3.10), while RFF portfolios show similar downside risk (≈ 3.32). In contrast, RFF under traditional or monetary+ fundamentals yields both weak returns and low information resilience, with even negative and statistically significant information ratios relative to both random walk and linear strategies. At the longest training horizon of T = 120 reported in Panel C of the Table, the reversal is stark. The random walk continues to yield stable if modest returns (SR = 0.361), while Ridge-RFF generally deteriorates, producing negative or insignificant Sharpe ratios under traditional and monetary+ fundamentals. For example, RFF under traditional fundamentals generates a Sharpe ratio of –0.66 (t = −1.67), significantly underperforming both the 30

random walk and linear regression, with drawdowns (≈ 2.8) comparable to linear but without compensating returns. By contrast, linear regression produces positive Sharpe ratios under monetary+ (0.30) and Taylor rule fundamentals (0.20). Importantly, Ridge-RFF under Taylor rule fundamentals still produces a positive and statistically significant Sharpe ratio (0.496, t = 1.97) with better information ratio relative to linear portfolio and relatively less elevated drawdown risk, suggesting some residual benefit of complexity in this setting. Overall, the portfolio results align closely with the out-of-sample forecast evidence. At short training windows (T = 12), Ridge-RFF can exploit extreme nominal complexity to deliver economically meaningful trading gains, particularly under Taylor rule fundamentals, with comparatively controlled drawdowns. At intermediate horizons (T = 60), the advantage shifts toward linear regression, which produces higher Sharpe ratios and stronger statistical significance,especiallyunderTaylorrulepredictors,thoughbothlinearandRFFportfoliosstill exhibit moderate downside risks. By T = 120, Ridge-RFF strategies generally underperform both linear regression and the random walk, with the exception of modest gains under Taylor fundamentals, and all models continue to be constrained by drawdowns that limit their practical applicability. Takentogether,theseresultsreinforcethebroaderconclusionthatthe“virtueofcomplexity” in FX prediction is fragile and sample-dependent. Complexity delivers relative improvements in very small samples, but these do not persist as sample size grows. Moreover, the drawdown evidence highlights that even when complexity improves Sharpe ratios, the resulting strategies remain vulnerable to sizeable losses, which undermines their appeal in practical portfolio settings. In terms of economic value, parsimony—captured by simple linear regression or even the random walk—remains more robust and reliable for constructing profitable and risk-managed market-timing portfolios. In comparing the equal-weighted portfolio performance with the single-currency portfolio results reported in Section 5.1, a consistent picture emerges. The equal-weighted portfolio tends to smooth out idiosyncratic gains and losses that appear in single-currency strategies, particularly for Ridge-RFF at short horizons. For example, while single-currency portfolios occasionally deliver strong Sharpe ratios under Ridge-RFF in small samples (e.g., JPY or CAD at T = 12), the equal-weighted portfolio translates these into only modest gains, with performance highly dependent on predictor choice. Likewise, linear regression strategies that perform reasonably well for select currencies under Taylor rule fundamentals in larger samples (T = 60 or T = 120) produce more muted gains once aggregated into the equal-weighted portfolio. Importantly, the drawdown evidence shows that portfolio aggregation reduces extreme tail risks present in single-currency strategies (e.g., very large losses for NOK or SEK), but at the same time it dilutes pockets of predictability that individual currencies 31

occasionally display. Taken together, the results indicate that while individual currencies may at times exhibit local predictability under complex models, these signals are too weak or inconsistent to scale into robust portfolio-level profits, leaving the random walk and simple linear benchmarks difficult to beat in practice. Overall, market timing portfolio results align closely with the out-of-sample forecast evidence. At short training windows (T = 12), Ridge-RFF can exploit extreme nominal complexity to deliver economically meaningful trading gains, particularly under Taylor rule fundamentals. At intermediate horizons ( T = 60), the advantage shifts toward linear regression, which produces higher Sharpe ratios and stronger statistical significance, especially under Taylor rule predictors. By T = 120, Ridge-RFF strategies generally underperform both linear regression and the random walk, with the exception of modest gains under Taylor fundamentals. These results reinforce the broader conclusion that the “virtue of complexity” in FX prediction is fragile and sample-dependent. Complexity delivers relative improvements in very small samples, but these do not persist as sample size grows. In terms of economic value, parsimony—captured by simple linear regression or even the random walk—remains more robust and reliable for constructing profitable market-timing portfolios. These findings connect tightly to the evolving debate on complexity in equity return prediction. First, Kelly and Malamud (2025) respond to recent critiques by clarifying that the central object is the complexity ratio c = P/T, distinguishing nominal from effective complexity and emphasizing how implicit regularization can allow large models to learn even in small samples; they further stress that VoC is a theory of out-of-sample performance under misspecification and is not about recovering a “true” model. They also highlight data features—“concentration” and “alignment”—that govern whether performance should rise with complexity. In our FX setting, the absence of systematic gains relative to RW as T grows suggests that either concentration, alignment, or both, differ materially from the equity contexts where VoC curves slope upward, consistent with their framework. Second, Nagel (2025) argues that with P >> T and highly persistent predictors, ridgeless RFF forecasts mechanically approximate a volatility-timed momentum rule—weights become a similarity kernel over the last T returns—so apparent small-sample “learning” largely reflects recency and volatility timing rather than extraction of genuine signals. Our FX results are potentially consistent with this interpretation: at T = 12, Ridge–RFF can outperform OLS (a local advantage) but does not consistently defeat RW; at larger T, the momentum-like edge recedes and parsimony wins, aligning with the view that small-T overparameterization explores only a thin subspace and cannot reliably uncover stable predictability. 32

Third, Buncic (2025) revisits Kelly et al. (2024)’s empirics and shows that two implementation choices—zero-intercept and aggregation of RFF draws—shape the monotone VoC patterns; when an intercept is included and aggregation is handled coherently, simpler (or mildly regularized) models often dominate. Our FX evidence parallels that spirit without including an intercept: as T expands, OLS (parsimonious, with effectively lower c) overtakes RFF, and portfolio performance improves without escalating nominal complexity. Notably, all three equity-based papers debate buy-and-hold versus timing and do not employ the RW forecasting benchmark we adopt in FX; thus, our findings contribute new evidence under a benchmark that is notoriously difficult to surpass in currencies. In FX, complexity’s benefits are not universal: when c = P/T is extreme and T is short, Ridge–RFF can look relatively good versus OLS but not versus RW; as effective sample size grows, parsimony becomes economically preferable. This pattern is consistent with theories that allow small-sample learning under high complexity but predict datadependent VoC curves, and with critiques highlighting the mechanical momentum content of overparameterized, short-window RFF. The upshot is that domain (FX vs. equities), sample length, and the benchmark all matter. Our results therefore refine the “virtue of complexity” claim by showing its limits in FX: when judged against a strong RW comparator, complexity delivers—at most—localized advantages that do not generalize into durable economic value. 6 Conclusions This paper investigates whether the recently proposed “virtue of complexity”—originally documented in equity return prediction—extends to foreign exchange rate forecasting. Using nonlinear Ridge regressions augmented with Random Fourier Features (RFF), we conduct a comprehensive 1-month ahead out-of-sample forecasting exercise under alternative sets of economic fundamentals, across rolling training windows of 12, 60, and 120 months. Benchmarks include both traditional linear regression models and the random walk, with additional evaluation through market-timing portfolio strategies. The results provide a measured perspective on the role of complexity in FX forecasting. With short training windows, where nominal complexity (T = c/T) is highest, Ridge–RFF can deliver relative gains over linear regression, including lower MSPE ratios and improved Diebold–Mariano statistics in select currencies. Yet, these improvements are fragile and never translate into robust gains against the random walk benchmark. As the training window expands, Ridge–RFF performance deteriorates—first losing parity with linear regression at T = 60 and then decisively underperforming at T = 120. In contrast, linear models gradually improve with larger samples, occasionally outperforming the random walk under richer 33

predictor sets (especially under Monetary+ fundamentals, supporting recent results in Engel and Wu, 2024), though the benchmark remains difficult to beat consistently. Market-timing portfolio results reinforce this message: RFF-based strategies show local gains in very small samples, especially under Taylor rule fundamentals, but linear strategies provide more stable and economically meaningful returns as sample sizes grow. Relative to the recent literature, our findings add several insights. Consistent with Kelly et al. (2024), we observe that complexity can yield localized benefits in small samples with richer fundamentals, reflecting the idea of “benign overfitting.” However, our results show that these benefits are limited in scope and highly sensitive to training sample size, predictor choice, and benchmark. Importantly, the random walk—absent from equity-based studies—remains the dominant comparator in FX, and neither Ridge–RFF nor linear regression consistently surpass it. This highlights the domain-specific limits of complexity’s appeal. Our evidence also connects to the evolving debate. Kelly and Malamud (2025) clarify that the key distinction is between nominal complexity (p/T) and effective complexity (parameters effectively used after shrinkage). In their framework, nominal complexity remains central for understanding out-of-sample performance. Our results suggest that, in FX, high nominal complexity does not translate into effective predictive gains against the random walk, particularly as sample size grows. Instead, parsimony appears to dominate at longer training windows. Meanwhile, the critiques of Nagel (2025) and Buncic (2025) resonate strongly with our findings. Nagel argues that RFF-based forecasts often mimic volatility-timed momentum rulesinshortsamples, whichalignswithourevidencethatRidge–RFFadvantagesfadequickly as T expands. Buncic shows that methodological restrictions can exaggerate complexity’s benefits, and when relaxed, simpler models often prevail—mirroring our result that OLS reasserts itself in larger samples. Takentogether, ouranalysissuggeststhreekeylessons. First, complexityinFXforecasting is conditional and fragile, offering advantages only in small samples with specific predictor sets, and never consistently over the random walk. Second, linear regression retains relevance: with richer fundamentals and larger samples, it often provides more robust statistical and economic performance. Third, the persistence of the random walk benchmark underscores the challenges of FX predictability and the risks of overstating the benefits of nonlinear complexity. For researchers, these findings highlight the importance of benchmarking complex models against both linear regressions and the random walk, and of linking statistical performance to economic value. For practitioners and policymakers, they underscore the enduring appeal of transparency, parsimony, and robustness in FX forecasting—where signals are weak, benchmarks are strong, and the supposed virtue of complexity proves sharply limited. 34

Future research should build on these insights by probing further into the specific mechanisms behind complexity gains, investigating alternative nonlinear structures beyond RFF, and more carefully accounting for methodological artifacts that may confound empirical results. Moreover, adaptive or hybrid models that intelligently blend simplicity and complexity in response to data conditions may hold promise for improving forecast accuracy in a robust and interpretable manner. 35

References Amat, O. (2018). Forecasting exchange rates using fundamentals and machine learning. International Journal of Forecasting, 34(1):123–142. Bacchetta, M. and van Wincoop, E. (2004). Exchange rate misalignment in emerging market economies. Journal of International Economics, 62(1):67–95. Buncic, D. (2025). Simplified: A closer look at the virtue of complexity in return prediction. Working Paper. Cartea, A., Jin, Q., and Shi, Y. (2025). The limited virtue of complexity in a noisy world. Working Paper. Cheung, Y. L., Chinn, M. D., and Pascual, A. (2005). Exchange rate forecasting: The role of fundamentals. Journal of International Economics, 65(2):123–144. Cheung, Y. L., Chinn, M. D., and Pascual, A. (2017). Exchange rate forecasting revisited: New evidence on fundamental models. Journal of International Money and Finance, 72:150–170. Engel, C. and West, K. D. (2012). Exchange rates and fundamentals: A panel data approach. Journal of Political Economy, 120(2):351–376. Engel, C. and Wu, S. P. Y. (2024). Exchange rate models are better than you think, and why they didn’t work in the old days. Technical Report Working Paper 32808, National Bureau of Economic Research. NBER Working Paper Series. Filippou, I., Rapach, D. E., Taylor, M. P., and Zhou, G. (2025). Economic fundamentals and short-run exchange rate prediction: A machine-learning perspective. Working Paper. Gilchrist, S. and Zakrajsek, E. (2012). Credit spreads and business cycle fluctuations. American Economic Review, 102(4):1692–1720. Ince, U. and Kubler, F. (2014). Panel data approaches in exchange rate forecasting. Journal of International Money and Finance, 38:125–140. Kelly, B. and Malamud, S. (2025). Understanding the virtue of complexity. Kelly, B., Malamud, S., and Zhou, K. (2024). The virtue of complexity in return prediction. Journal of Finance, 79(1):451–486. 36

Kouwenberg, R. et al. (2017). Time-varying predictability in exchange rates. Journal of International Economics, 108:509–517. Meese, R. and Rogoff, K. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14(1-2):3–24. Meng, F. et al. (2024). Deep learning for exchange rate forecasting: A transformer approach. Journal of Financial Data Science, 6(1):45–67. Molodtsova, I. and Papell, D. (2009). Exchange rate forecasting: Model evaluation and fundamentals. Journal of International Money and Finance, 28(3):465–487. Nagel, S. (2025). Seemingly virtuous complexity in return prediction. Working Paper. Pfahler, B. (2022). Machine learning models for exchange rate forecasting. Working Paper, IMF. Rahimi, A. and Recht, B. (2007). Random features for large-scale kernel machines. Advances in neural information processing systems, 20. Rahimi, A. and Recht, B. (2008). Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in neural information processing systems, 21. Rossi, B. (2013). Exchange rate predictability: Recent evidence. Journal of International Money and Finance, 34(4):987–1003. Zorzi, A. C., Muck, T., and Rubaszek, A. (2015). The role of purchasing power parity in exchange rate forecasting. Journal of International Economics, 96:150–167. 37

Appendices A Data As discussed in Section 3, our empirical analysis employs three sets of economic fundamentals to analyze U.S. dollar exchange rates against eight major currencies. End-of-month nominal exchange rate series are obtained from the IMF International Financial Statistics (IFS). Consumer Price Index (CPI) and industrial production index data for the United States (home country) and foreign countries are also sourced from IFS. Inflation rates are calculated as the log-difference of the CPI over the preceding 12-month period. Monthly industrial production indices serve as proxies for each country’s output level. To measure the money supply, we utilize the monetary aggregate M0, chosen for its consistent availability across the countries in our study. The end-of-month money supply data are retrieved from Haver Analytics. Nominal 3-month government bond interest rates are obtained from the Global Financial Database (GFD) and Federal Reserve Economic Data (FRED). The specific interest rate series from GFD include ITAUS3D (AUD), ITCAN3D (CAD), ITEUR3D (EUR), ITJPN3D (JPY), ITNOR3D (NOK), ITSWE3D (SEK), ITCHE3D (CHF), and ITGBR3D (GBP), while DTB3 (US) is obtained from FRED. We construct a global risk aversion variable, denoted as Risk, by extracting the first principal component from the same five risk measures utilized by Engel and Wu (2024). These risk measures include spreads from Gilchrist and Zakrajsek (2012), Moody’s Aaa and Baa corporate bond yields minus the Federal Funds rate spreads (FRED series: AAAFF and BAAFF), and Moody’s Aaa and Baa corporate bond yields minus the 10-Year Treasury yield (FRED series: AAA10Y and BAA10Y). The Gilchrist and Zakrajšek (2012) spreads are available from https://www.federalreserve.gov/econres/notes/feds-notes/updatin g-the-recession-risk-and-the-excess-bond-premium-20161006.html, whereas the remaining four spreads (AAAFF, BAAFF, AAA10Y, BAA10Y) are downloaded from FRED. Additionally, U.S. trade balance and GDP data are sourced from FRED. The trade balance data is available at monthly frequency starting from 1992 (FRED series: BOPGSTB) and quarterly prior to 1992 (BOPBGS). Quarterly trade balance and GDP series are converted into monthly frequency through linear interpolation. Finally, we compute the output gap for the United States and foreign countries using quarterly GDP data. We first apply the Hodrick-Prescott (HP) filter with a smoothing parameter of 1600, then convert the quarterly output gap series into monthly frequency through linear interpolation. The availability of a complete dataset varies by currency, depending on data availability for the included variables across the three fundamental sets. For all currencies, the sample 38

period ends in October 2024. The start dates differ as follows: January 1974 for GBP and JPY, February 1975 for AUD, March 1975 for CAD, January 1980 for CHF, January 1998 for SEK, January 1999 for EUR, and January 2008 for NOK. 39