South Korean Won to U.S. Dollar 1-Month Exchange-Rate-at-Risk

Exchange-Rate-at-Risk 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 is in the tails, where the dependence on financial conditions is strongest and a mean forecast would see little (Eguren-Martin and Sokol 2019). With

and $S$ the won per U.S. dollar, a positive return is a KRW depreciation, so the upper quantiles are the depreciation-risk side, and this ticker is the 1-month horizon headlined by its 95th conditional quantile, the one-month-ahead depreciation-at-risk, in percent. It is a conditional-distribution characterization, not a forecast. Each daily point is still a 1-month-ahead at-risk value, so adjacent days overlap and the daily output is the daily resolution of the same object rather than daily-resolution information.

Conditional quantiles come from quantile regression (Koenker and Bassett 1978) of the h-month-ahead return on a single PCA financial-conditions index (PC1 of the cross-currency basis, ACM term premium, Wu-Xia shadow rate, and VIX), estimated per quantile,

with

and $S$ the won per U.S. dollar. Coefficients are ESTIMATED at monthly frequency (overlapping returns handled by Newey-West HAC); the series is then SCORED DAILY by projecting the daily predictors onto the monthly-fitted loadings and applying the monthly betas, with Chernozhukov, Fernández-Val, and Galichon (2010) monotone rearrangement per day. It is a semiparametric conditional-quantile model with no parametric-distribution layer.

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 indicator of how present conditions tilt the distribution rather than a validated tail predictor, and it warrants the same caution as the quarter-ahead headline.

The at-Risk framework, introduced for output growth by Adrian, Boyarchenko, and Giannone (2019), models the conditional quantiles of an outcome as functions of a financial-conditions index rather than its mean, since the dependence on conditions concentrates in the tails, where quantile regression (Koenker and Bassett 1978) lets each quantile respond differently. The construction generalizes to any risk measure built from the conditional quantiles and has become a standard surveillance tool (Adams et al. 2021; Gelos et al. 2019), and Eguren-Martin and Sokol (2019) bring it to exchange rates, where the whole distribution of currency returns responds to global financial conditions in the tails. As the one-month companion this ticker moves faster than the quarter-ahead gauge and is more sensitive to acute, short-lived funding spikes than to the slower structural signal.

The macroeconomic implications trace the same channel as the quarterly gauge at a shorter horizon. A depreciation raises the upside risk to import prices (Banerjee et al. 2020) and strains the near-term servicing of foreign-currency debt. The one-month tail is sharpest when dollar funding seizes suddenly, since the 2007 money-market turmoil spilled into the swap markets within weeks (Baba, Packer, and Nagano 2008) and the won's short-horizon swap deviations track global risk and funding conditions closely (Yu 2010). Here the cross-currency basis acts as the largest conditioning signal (Du, Tepper, and Verdelhan 2018; International Monetary Fund 2019).

The headline q95 is a conditional-distribution statistic, not a point forecast, and it is most useful read together with the rest of the fan. The one-month spread from q05 to q95 shows how current conditions tilt the near-term return distribution. Because the at-Risk construction yields the full set of conditional quantiles, the one-month fan supplies a current-conditions foreign-exchange Value-at-Risk and a stress-test input at the funding-rollover horizon (Adrian, Boyarchenko, and Giannone 2019).

This series' comparative advantage is monitoring short-term funding stress. The one-month fan reacts faster than the three-month gauge to acute dollar-funding spikes, so reading the two horizons together separates a transient spike from a more persistent widening of the depreciation distribution. This feeds directly into short-dated hedge and rollover decisions on dollar obligations.

It pairs with the cross-currency basis and dollar-liquidity series, and is read together with the three-month headline rather than in isolation.

KRFXAR1M is an estimated conditional quantile path, $\hat{q}_t(\theta)=x_t^{\top}\hat{\beta}(\theta)$ fit by quantile regression of the one-month KRW/USD log return on the PCA financial-conditions index, so its persistence is inherited from the conditioning variables and the object that carries forecast quality is the violation-indicator sequence rather than the path. Unit-root, structural-break, and level Ljung and Box (1978) batteries on the path were therefore deliberately not run, since coverage is a property of the joint forecast-outcome distribution that a univariate path diagnostic cannot speak to (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 unit-root inference over-rejects toward spurious stationarity (Cavaliere 2005; Cavaliere and Xu 2014). The appropriate evidence is coverage backtesting at the two pinned extreme tails, the fifth and ninety-fifth conditional quantiles, and because the one-month horizon is sampled monthly and non-overlapping the independence tests are informative here.

Over 292 monthly-sampled observations from 2002-02-28 to 2026-05-31 the Kupiec (1995) unconditional-coverage test fails to reject correct coverage at both tails, with fifteen exceedances at each tail and identical statistics of 0.011 at p = 0.915. The Christoffersen (1998) independence test fails to reject at the lower tail, 0.068 at p = 0.794, and is uninformative at the upper tail where no two exceedances are consecutive, and the joint conditional-coverage test fails to reject at both tails, 0.083 at p = 0.959 and 1.646 at p = 0.439. Because the monthly hit sequence is non-overlapping at this horizon, the full out-of-sample dynamic-quantile test of Engle and Manganelli (2004) is feasible and fails to reject at both tails, 1.209 at p = 0.976 and 10.664 at p = 0.099, and the cross-quantile monotonicity check confirms a non-crossing fan (Chernozhukov, Fernandez-Val, and Galichon 2010).

The reading is that the one-month depreciation tails are well calibrated on this sample at both the lower and upper quantiles, with the independence tests confirming no residual clustering at the non-overlapping monthly horizon. Two cautions attach in the register the density-forecast literature sets for coverage evaluation (Diebold, Gunther, and Tay 1998; Rosenblatt 1952; Berkowitz 2001), namely that the upper-tail dynamic-quantile statistic sits closest to its threshold and that these are estimated quantiles whose parameter uncertainty is not folded into the reference distribution (Campbell 2005; Escanciano and Olmo 2010), so a non-rejection is read as descriptive calibration rather than a validated forecast.