South Korean Won to U.S. Dollar 3-Month Exchange-Rate-at-Risk

Exchange-Rate-at-Risk is a descriptive gauge that characterizes the conditional distribution of future KRW/USD returns given current financial conditions, applying the Growth-at-Risk idea of Adrian, Boyarchenko, and Giannone (2019) to the won. The object is the whole conditional distribution rather than a point forecast, and its informative content lies in the tails, where the dependence on financial conditions is strongest and a mean forecast would show little (Eguren-Martin and Sokol 2019).

The return is defined as:

Here $S$ is the won per U.S. dollar, so a positive return is a KRW depreciation and the upper quantiles are the depreciation-risk side. This ticker reports the 3-month-horizon 95th conditional quantile, namely the quarter-ahead depreciation-at-risk, as a percent headline, and it is a characterization of the conditional distribution rather than a forecast. Each daily point is still a 3-month-ahead at-risk value, so adjacent days overlap heavily and share roughly 91 of 92 days, and the daily output is the daily resolution of the same object rather than new daily information.

The conditional quantiles are estimated in four steps.

(1) Financial-conditions index. A single PCA financial-conditions index $x_t$ is formed as the first principal component of the cross-currency basis, the ACM term premium, the Wu-Xia shadow rate, and VIX.

(2) Quantile regression. The $h$-month-ahead return is regressed on this index quantile by quantile (Koenker and Bassett 1978):

where the return is given by:

and $S$ is the won per U.S. dollar.

(3) Estimation and daily scoring. Coefficients are estimated at monthly frequency, and the overlapping returns are handled by Newey-West HAC. The daily predictors are then projected onto the monthly loadings and the monthly betas are applied to score the series daily.

(4) Monotone rearrangement. The monotone rearrangement of Chernozhukov, Fernández-Val, and Galichon (2010) is applied each day.

It is a semiparametric conditional-quantile model with no parametric-distribution assumption.

This series characterizes the current conditional distribution of the won's return, not a point forecast. Tested out of sample against an unconditional historical-quantile benchmark, the conditional median modestly beats the benchmark while the upper-tail quantiles are essentially a tie, so it is a descriptive gauge that shows how present conditions tilt the distribution rather than a proven tail forecaster.

The at-Risk framework, introduced for output growth, models the conditional quantiles of an outcome as functions of a financial-conditions index rather than its mean, because the dependence on conditions concentrates in the tails (Adrian, Boyarchenko, and Giannone 2019). Quantile regression lets each quantile respond differently, while a mean regression averages that asymmetry away (Koenker and Bassett 1978). The construction generalizes to any risk measure built from the conditional quantiles and has become a standard surveillance tool, extended to macroeconomic downside risk (Adams et al. 2021) and applied to emerging-market capital flows (Gelos et al. 2019). Eguren-Martin and Sokol (2019) bring the same idea to exchange rates, showing that the whole distribution of currency returns responds to global financial conditions with the effect concentrated in the tails, which is exactly the object this gauge estimates for the won.

Why the won's depreciation tail matters is macroeconomic. In emerging-market economies a depreciation raises the upper quantiles of inflation more than the lower (Banerjee et al. 2020), so a fattening depreciation tail is also an imported-inflation upside-risk signal, and it bears on the servicing of foreign-currency obligations, on reserve adequacy, and on financial stability. The channel is Korea's structural dollar-funding vulnerability, which enters as the dominant loading of the conditioning index through the cross-currency basis (Du, Tepper, and Verdelhan 2018; International Monetary Fund 2019; Yu 2010). The q95 depreciation-at-risk widened sharply when dollar funding seized in the 2007–2009 crisis (Baba, Packer, and Nagano 2008; Baba and Shim 2010) and in the March 2020 dislocation, and its daily resolution pinpoints the peak day, which gives the gauge its face validity.

The headline q95 is a statistic of the conditional distribution, not a point forecast, and it is most useful read with the rest of the fan. The spread from q05 to q95 and its asymmetry show how current conditions tilt the won's return distribution rather than only its width. Because the at-Risk construction yields the full set of conditional quantiles, it feeds directly into a foreign-exchange Value-at-Risk and into the inputs of expected-shortfall and stress-testing frameworks (Adrian, Boyarchenko, and Giannone 2019), and the conditional q95 is a current-conditions Value-at-Risk for won depreciation rather than an unconditional historical one.

For hedging, the q95 gauges how far the won could depreciate over the quarter in an adverse scenario consistent with current conditions. It thereby informs the hedge ratio for dollar liabilities and the cost-benefit of forward cover, and a wider upper tail argues for more complete hedging of near-term dollar obligations.

The gauge also informs portfolio currency allocation and the foreign-exchange risk capital that Korean insurers hold under the K-ICS regime, because a conditional depreciation-risk measure maps more directly to required capital than an unconditional one. Because the conditioning index is anchored on the cross-currency basis, the gauge co-moves with the forces that drive won dollar-funding and FX-swap stress, so it is best read alongside the basis ticker and the dollar-liquidity indicators.

KRFXAR3M is an estimated conditional quantile path, $\hat{q}_t(\theta)=x_t^{\top}\hat{\beta}(\theta)$ from quantile regression of the three-month KRW/USD log return on the PCA financial-conditions index, so the path inherits its persistence from the conditioning set and the evaluation object is the violation-indicator sequence, not the path. Unit-root, structural-break, and level Ljung and Box (1978) batteries on the path were deliberately not run, because coverage is a property of the joint forecast-outcome distribution beyond the reach of a univariate path diagnostic (Christoffersen 1998; Engle and Manganelli 2004; Murphy and Winkler 1987), and a bounded estimated quantile cannot be an unbounded unit-root process on which standard inference would over-reject (Cavaliere 2005; Cavaliere and Xu 2014). The evidence is coverage backtesting at the two pinned extreme tails, the fifth and ninety-fifth conditional quantiles.

At a three-month horizon the violation sequence overlaps across adjacent months, so no size-correct unconditional-coverage test exists on the full sample. A literal Kupiec (1995) likelihood-ratio test on the overlapping sample and a Newey and West (1987) autocorrelation-robust coverage statistic constructed to repair it were both found materially oversized in a pre-registered Monte-Carlo size check recorded in the model specification, so a formal unconditional-coverage verdict is withheld on the full sample and the full-sample record is reported descriptively. Over 290 monthly-sampled observations from 2002-02-28 to 2026-03-31 the lower depreciation tail records fifteen exceedances at a rate of 0.052 and the upper tail sixteen at 0.055, both near the nominal five percent.

The one size-correct formal check is the Kupiec test on the offset-zero non-overlapping subsample, where independent Bernoulli sampling is restored by construction, and on that subsample of ninety-six observations with an expected 4.8 exceedances it records four lower-tail and seven upper-tail exceedances, 0.148 at p = 0.700 and 0.936 at p = 0.333, and fails to reject correct coverage at either tail. The subsample check is exact under the hypothesis of correct conditional coverage, which renders the spaced violation indicators independent Bernoulli draws (Christoffersen 1998), and it does not claim size control for exceedances of a fixed unconditional quantile of a persistent process, where dependence can cross the non-overlapping window boundaries. The exceedance rate ranges from 0.041 to 0.072 at the lower tail and from 0.042 to 0.072 at the upper tail across the three admissible offsets, reported to preclude offset selection.

The Christoffersen (1998) independence test rejects at both tails, 13.022 at p = 0.000 and 11.620 at p = 0.001, and the joint conditional-coverage test likewise rejects, 13.044 at p = 0.001 and 11.789 at p = 0.003, the mechanical clustering that the overlapping three-month target induces in the hit sequence rather than a coverage failure and consistent with the withheld full-sample verdict. The full out-of-sample dynamic-quantile test of Engle and Manganelli (2004), run at lags at or beyond the horizon to respect the overlap, fails to reject at both tails, 2.164 at p = 0.904 and 7.657 at p = 0.264, and the cross-quantile monotonicity check confirms a non-crossing fan (Chernozhukov, Fernandez-Val, and Galichon 2010).

The honest reading is that the non-overlapping subsample and the overlap-respecting dynamic-quantile test both fail to reject correct coverage at the lower and upper depreciation tails while the independence tests reject through the overlap, so the calibration claim rests on those two overlap-aware checks and is read in the register the density-forecast literature sets for coverage under dependence (Diebold, Gunther, and Tay 1998; Rosenblatt 1952; Berkowitz 2001). Because these are estimated quantiles whose parameter uncertainty is not absorbed into the reference distribution, the reading is descriptive calibration of how current conditions place the quarter-ahead depreciation distribution rather than a validated forecast (Campbell 2005; Escanciano and Olmo 2010; Kupiec 1995).