---
ticker: "KRFXCTR3M"
title: "South Korean Won to U.S. Dollar 3-Month Carry-to-Risk Ratio"
unit: ""
frequency: "Weekly"
source: "Galati, Heath, and McGuire (2007); Aquilina et al. (2024)"
release: "Updated Weekly"
category: "Exchange Rates"
country: "KR"
language: "en"
canonical: "https://kred.dev/en/series/KRFXCTR3M"
license: "https://creativecommons.org/licenses/by-nc-nd/4.0/"
latest_value: -0.10
latest_date: "2026-10-23"
first_date: "2024-10-04"
observations_total: 108
observations_shown: 108
---

# South Korean Won to U.S. Dollar 3-Month Carry-to-Risk Ratio

## Overview

Weekly 3-month won-dollar carry per unit of option-implied volatility, a descriptive carry gauge.

## Key Figures

|  | Value | Date |
|---|---|---|
| Latest | -0.10 | 2026-10-23 |
| Change from previous | -0.02 | 2026-10-16 |
| Change over one year | +0.11 | 2025-10-17 |
| Highest on record | -0.04 | 2026-08-21 |
| Lowest on record | -0.24 | 2025-08-22 |
| Period covered | 2024-10-04 – 2026-10-23 |  |
| Observations | 108 |  |

## Recent observations

| Date | Value | Change |
|---|---|---|
| 2024-10-04 | -0.20 |  |
| 2024-10-11 | -0.20 | +0.01 |
| 2024-10-18 | -0.19 | 0.00 |
| 2024-10-25 | -0.19 | 0.00 |
| 2024-11-01 | -0.17 | +0.02 |
| 2024-11-08 | -0.20 | -0.02 |
| 2024-11-15 | -0.18 | +0.01 |
| 2024-11-22 | -0.18 | 0.00 |
| 2024-11-29 | -0.17 | +0.01 |
| 2024-12-06 | -0.17 | 0.00 |
| 2024-12-13 | -0.15 | +0.02 |
| 2024-12-20 | -0.16 | -0.01 |
| 2024-12-27 | -0.16 | 0.00 |
| 2025-01-03 | -0.14 | +0.02 |
| 2025-01-10 | -0.15 | -0.01 |
| 2025-01-17 | -0.16 | -0.01 |
| 2025-01-24 | -0.18 | -0.02 |
| 2025-01-31 | -0.19 | -0.01 |
| 2025-02-07 | -0.17 | +0.02 |
| 2025-02-14 | -0.19 | -0.02 |
| 2025-02-21 | -0.21 | -0.02 |
| 2025-02-28 | -0.22 | -0.01 |
| 2025-03-07 | -0.21 | +0.02 |
| 2025-03-14 | -0.22 | -0.02 |
| 2025-03-21 | -0.23 | -0.01 |
| 2025-03-28 | -0.23 | 0.00 |
| 2025-04-04 | -0.22 | +0.01 |
| 2025-04-11 | -0.21 | +0.01 |
| 2025-04-18 | -0.22 | -0.01 |
| 2025-04-25 | -0.22 | -0.01 |
| 2025-05-02 | -0.22 | 0.00 |
| 2025-05-09 | -0.19 | +0.03 |
| 2025-05-16 | -0.22 | -0.03 |
| 2025-05-23 | -0.23 | 0.00 |
| 2025-05-30 | -0.23 | 0.00 |
| 2025-06-06 | -0.23 | 0.00 |
| 2025-06-13 | -0.23 | 0.00 |
| 2025-06-20 | -0.23 | 0.00 |
| 2025-06-27 | -0.19 | +0.04 |
| 2025-07-04 | -0.21 | -0.02 |
| 2025-07-11 | -0.21 | 0.00 |
| 2025-07-18 | -0.22 | -0.01 |
| 2025-07-25 | -0.23 | -0.01 |
| 2025-08-01 | -0.23 | 0.00 |
| 2025-08-08 | -0.22 | 0.00 |
| 2025-08-15 | -0.23 | -0.01 |
| 2025-08-22 | -0.24 | -0.01 |
| 2025-08-29 | -0.24 | 0.00 |
| 2025-09-05 | -0.23 | +0.01 |
| 2025-09-12 | -0.23 | 0.00 |
| 2025-09-19 | -0.23 | -0.01 |
| 2025-09-26 | -0.24 | -0.01 |
| 2025-10-03 | -0.23 | +0.01 |
| 2025-10-10 | -0.22 | +0.01 |
| 2025-10-17 | -0.20 | +0.02 |
| 2025-10-24 | -0.21 | 0.00 |
| 2025-10-31 | -0.20 | +0.01 |
| 2025-11-07 | -0.21 | -0.01 |
| 2025-11-14 | -0.22 | -0.01 |
| 2025-11-21 | -0.22 | 0.00 |
| 2025-11-28 | -0.22 | 0.00 |
| 2025-12-05 | -0.22 | 0.00 |
| 2025-12-12 | -0.21 | +0.01 |
| 2025-12-19 | -0.21 | -0.01 |
| 2025-12-26 | -0.19 | +0.03 |
| 2026-01-02 | -0.17 | +0.02 |
| 2026-01-09 | -0.17 | 0.00 |
| 2026-01-16 | -0.15 | +0.02 |
| 2026-01-23 | -0.15 | 0.00 |
| 2026-01-30 | -0.15 | +0.01 |
| 2026-02-06 | -0.14 | 0.00 |
| 2026-02-13 | -0.15 | 0.00 |
| 2026-02-20 | -0.15 | 0.00 |
| 2026-02-27 | -0.14 | +0.01 |
| 2026-03-06 | -0.12 | +0.02 |
| 2026-03-13 | -0.10 | +0.02 |
| 2026-03-20 | -0.10 | 0.00 |
| 2026-03-27 | -0.11 | -0.01 |
| 2026-04-03 | -0.09 | +0.01 |
| 2026-04-10 | -0.11 | -0.02 |
| 2026-04-17 | -0.11 | 0.00 |
| 2026-04-24 | -0.12 | -0.01 |
| 2026-05-01 | -0.11 | +0.01 |
| 2026-05-08 | -0.10 | +0.02 |
| 2026-05-15 | -0.09 | 0.00 |
| 2026-05-22 | -0.10 | 0.00 |
| 2026-05-29 | -0.10 | 0.00 |
| 2026-06-05 | -0.07 | +0.02 |
| 2026-06-12 | -0.07 | 0.00 |
| 2026-06-19 | -0.09 | -0.01 |
| 2026-06-26 | -0.07 | +0.02 |
| 2026-07-03 | -0.06 | +0.01 |
| 2026-07-10 | -0.08 | -0.02 |
| 2026-07-17 | -0.07 | +0.01 |
| 2026-07-24 | -0.07 | +0.01 |
| 2026-07-31 | -0.06 | +0.01 |
| 2026-08-07 | -0.05 | +0.01 |
| 2026-08-14 | -0.05 | 0.00 |
| 2026-08-21 | -0.04 | +0.01 |
| 2026-08-28 | -0.05 | 0.00 |
| 2026-09-04 | -0.05 | 0.00 |
| 2026-09-11 | -0.04 | +0.01 |
| 2026-09-18 | -0.06 | -0.01 |
| 2026-09-25 | -0.05 | +0.01 |
| 2026-10-02 | -0.06 | -0.01 |
| 2026-10-09 | -0.06 | 0.00 |
| 2026-10-16 | -0.08 | -0.01 |
| 2026-10-23 | -0.10 | -0.02 |

## Definition

The carry-to-risk ratio divides the interest rate differential implied by currency forwards by the option-implied volatility of the exchange rate, both at the 3-month horizon, and so records the carry a currency position accrues per unit of the exchange-rate risk priced in options. This series follows the definition of Galati, Heath, and McGuire (2007) and Aquilina et al. (2024) and applies it to the won against the dollar. The numerator is the forward-based carry of Koijen et al. (2018), namely what a forward position accrues if the spot rate stays unchanged, which equals the interest rate differential when covered parity holds, and the denominator is the at-the-money volatility that the pricing formulas of Black (1976) and Garman and Kohlhagen (1983) recover from option premiums.

$$\mathrm{CTR}_w=\frac{\bar c_w}{\sigma^{\mathrm{ATMF}}_w(3\mathrm{M})}$$

Here $w$ is a Monday–Friday week dated on its Friday, $\bar c_w$ is the mean of that week's daily 3-month carry, and $\sigma^{\mathrm{ATMF}}_w(3\mathrm{M})$ is the week's 3-month at-the-money-forward implied volatility. Both legs are in annualized percent, so the ratio is dimensionless, and each value is a weekly average rather than an end-of-day reading.

The sign is that of a position long the won and short the dollar, the side on which Aquilina et al. (2024) place the won in their carry basket. A positive value means the won's forward-implied interest rate exceeds the dollar's, and a negative value means that a long-won position pays carry, so that on forward prices the won sits on the funding side. The sign is never flipped with the regime, consistent with carry portfolios sorted on the same forward discount whatever its sign (Lustig, Roussanov, and Verdelhan 2011; Menkhoff et al. 2012).

The inputs are public trade records of offshore won-dollar non-deliverable forwards and options that are subject to U.S. reporting requirements, which makes them a subset of the offshore market rather than the whole of it. Offshore non-deliverable forwards trade apart from the onshore market and their implied yields can diverge from onshore interest rates (Ma, Ho, and McCauley 2004), so the numerator is an offshore forward-implied differential, and covered-parity deviations further separate it from an onshore money-market spread (Du, Tepper, and Verdelhan 2018). Weekly averaging smooths daily noise at the cost of positive autocorrelation in week-to-week changes (Working 1960), and non-overlapping weeks avoid the mechanical correlation of overlapping windows (Hansen and Hodrick 1980).

## Methodology

The ratio is computed each week from two separately estimated legs, following the definition of Galati, Heath, and McGuire (2007) and Aquilina et al. (2024), and both legs use transaction prices from public trade records rather than dealer mid quotes.

**(1) Daily 3-month carry.** Offshore non-deliverable forward trades, the market described by Ma, Ho, and McCauley (2004), are kept when they have 7–366 days to settlement, after cancellations, corrections and reinstatements are applied to the trade history and swaps, compressions, post-priced, non-standard and package trades are removed. Trades executed offshore on Korean holidays are kept. Each day the log forward prices are regressed on a quadratic in time to settlement $\tau$, measured in years on an ACT/365 basis, with a fixed effect for each 15-minute execution window $j$.

$$\ln F_i=a_{j(i)}+b_1\tau_i+b_2\tau_i^2$$

Residuals beyond four times the scaled median absolute deviation are trimmed iteratively. The window effects absorb the spot level, so no external spot series enters, and the carry is the annualized log forward premium at 3 months (Koijen et al. 2018), read from forwards alone because forward-implied and money-market differentials differ by the covered-parity basis (Du, Tepper, and Verdelhan 2018).

$$c_d=\frac{\ln F(0.25)-\ln F(0)}{0.25}=b_1+0.25\,b_2$$

**(2) Weekly numerator.** The numerator is the simple mean of the daily carries of a Monday–Friday week.

$$\bar c_w=\frac{1}{n_w}\sum_{d\in w}c_d,\qquad n_w\ge 3$$

A week with fewer valid days is left empty. Non-overlapping weeks avoid the overlap-induced serial correlation of rolling windows (Hansen and Hodrick 1980).

**(3) Implied volatility per trade.** Package trades are excluded, because a premium reported for one leg of a package need not be the price of that option. Each remaining option trade is priced at the forward prevailing at its execution time, taken from forward trades within minutes of it and carried to the option's maturity by that day's curve, and its implied volatility $\sigma$ solves the forward-based formula of Black (1976), which coincides with Garman and Kohlhagen (1983) for currency options.

$$\frac{P}{N}=\mathrm{DF}\,\frac{F\,\Phi(d_1)-K\,\Phi(d_2)}{F},\qquad d_{1,2}=\frac{\ln(F/K)\pm\tfrac{1}{2}\sigma^2\tau}{\sigma\sqrt{\tau}}$$

The formula is shown for a dollar call with premium $P$ per dollar notional $N$ and dollar discount factor $\mathrm{DF}$, with puts following by put-call parity. A trade whose two call-or-put indications disagree and whose price cannot settle the type is excluded, and near-simultaneous call and put trades of equal strike, maturity and notional are merged into one straddle, whose volatility does not depend on those indications.

**(4) Weekly surface.** Options with maturities of exactly 3 months trade thinly, so all of a week's observations are pooled and the 3-month point is interpolated from a quadratic smile in normalized moneyness with a linear maturity term.

$$\sigma_i=c_0+c_1(\tau_i-0.25)+c_2m_i+c_3m_i^2,\qquad m_i=\frac{\ln(K_i/F_i)}{\sqrt{\tau_i}}$$

The fit covers maturities of 21–213 days and $|m_i|\le 0.15$, with residuals beyond three times the scaled median absolute deviation trimmed. The denominator $\sigma^{\mathrm{ATMF}}_w(3\mathrm{M})$ is the fitted value $c_0$ at the point where the strike equals the forward, so at the money is defined at the forward, one of several at-the-money conventions in currency options (Reiswich and Wystup 2010), and it may differ from a delta-neutral-straddle quote. The arbitrage-free SVI parameterization of Gatheral and Jacquier (2014) is not used because a week supplies too few trades to pin its parameters, and a week whose surface fails fixed coverage minimums is left empty and never filled from other weeks.

**(5) Ratio and revisions.** The ratio divides the stored numerator by the stored denominator, so it reproduces exactly from the two companion series, and trades are processed in a fixed order because floating-point sums depend on the order of summation (Demmel and Nguyen 2013). Corrections, cancellations and late reports can arrive after a week closes, and the affected weeks are then recomputed, so values for past weeks can be revised and a first-published value can differ from the final one (Orphanides and van Norden 2002).

## Applications in Economics

The ratio places the won within the carry-trade literature, where a position borrows in a low-interest currency and lends in a high-interest one. Fama (1984) showed that the forward premium is a biased guide to subsequent spot changes, the forward-premium anomaly, so a forward-implied differential embeds a time-varying risk premium and is not a gauge of the depreciation to come, and Lustig, Roussanov, and Verdelhan (2011) trace the payoffs of currency portfolios sorted by forward discount to a common carry factor tied to global risk. Scaling the differential by option-implied volatility, as Galati, Heath, and McGuire (2007) do, restates carry in units of the risk the option market prices, the sense in which Bhansali (2007) describes a carry position as economically close to a short position in currency volatility.

The scaling matters because carry and volatility move against each other in stress. Brunnermeier, Nagel, and Pedersen (2008) document that carry positions build up gradually and unwind abruptly as risk and funding illiquidity rise, which leaves high-interest currencies exposed to crash risk, and Menkhoff et al. (2012) identify global foreign-exchange volatility as the risk to which high-interest currencies are exposed. A jump in implied volatility therefore moves the ratio toward zero even when the differential is unchanged, the configuration Aquilina et al. (2024) examine around a sharp unwinding of yen-funded carry positions in which the won sits on the long side of the basket, and Daniel, Hodrick, and Lu (2017) document how deep and prolonged carry drawdowns can be.

For the won the ratio condenses two Korea-specific features into one number. Its numerator is an offshore non-deliverable forward-implied differential, and because the offshore market trades apart from the onshore one its implied yields can diverge from onshore rates (Ma, Ho, and McCauley 2004), while the covered-parity basis further separates it from the onshore money-market spread (Du, Tepper, and Verdelhan 2018). Its sign records whether, on forward prices, the won is a target or a funding currency against the dollar, so a negative reading means that a position long the won pays carry. Koijen et al. (2018) stress that carry is what accrues only if prices stay unchanged, and Burnside et al. (2011) relate carry payoffs to peso problems, rare adverse states that a short sample may not contain, so the ratio characterizes current pricing and is not a forecast.

The ratio is an exact identity, the forward-implied differential divided by the at-the-money implied volatility, so every weekly change is fully accounted for by changes in those two companion series, which show which of them moved. The three series are one construction and are not independent evidence about one another.

## Applications in Financial Markets

For currency desks and investors with won exposure, the ratio states on one scale how much forward-implied rate differential a won position carries relative to the exchange-rate volatility that options price, whose global component Menkhoff et al. (2012) identify as the risk priced in carry. A reading near zero means the differential is small relative to priced volatility, and a change of sign marks a switch in which side of a won-dollar forward receives the carry (Koijen et al. 2018).

Carry and option protection are two sides of one trade-off. Burnside et al. (2011) and Jurek (2014) hedge carry positions with currency options and find that removing crash exposure leaves part of the average carry payoff in place, and Bhansali (2007) shows that the carry position itself behaves like a short volatility position, whose exposure is priced by the implied volatility in the denominator. A won-based holder of dollar assets hedges by selling dollars forward, a position long the won, so a negative differential is a hedging cost and a positive one a hedging pickup, and the ratio sets that 3-month forward-hedge carry against the price of hedging with options at the same horizon (Garman and Kohlhagen 1983; Reiswich and Wystup 2010).

The series is a descriptive record and is not a forecast, nor a trading rule. Regressions of asset payoffs on persistent financial ratios suffer the small-sample bias documented by Stambaugh (1999), rules chosen after inspecting a sample invite the data-snooping biases analyzed by Lo and MacKinlay (1990) and White (2000), and carry strategies have suffered deep and prolonged drawdowns (Daniel, Hodrick, and Lu 2017) that a short sample may not contain.

The records cover only offshore trades subject to U.S. reporting requirements, a subset of the offshore market, and recent weeks can be revised as late reports arrive, so their values are provisional in the sense of Orphanides and van Norden (2002). Desks that read the ratio beside the forward-implied differential and the implied volatility should treat the three as one identity and attribute a change in the ratio by checking which leg moved.

## Statistical Tests

KRFXCTR3M is the weekly carry-to-risk ratio of Galati, Heath, and McGuire (2007) and Aquilina et al. (2024) for the won against the dollar, and it is an exact identity, the published forward-implied rate differential divided by the published at-the-money option-implied volatility of the same week, so the object tested is the dimensionless weekly level on the pinned sample of 104 complete weeks from 2024-10-04 to 2026-09-25 recorded for sign-off. A ratio acquires heavy tails only when its denominator carries material probability near zero (Hinkley 1969; Marsaglia 1965), and the denominator here is a currency volatility that stays well away from zero in this sample, so the ratio is tested as an ordinary unbounded level, with the deterministic term pinned to a constant because a trend in a ratio of a rate differential to a volatility would be a specification error rather than a finding.

Over this span of about two years the three procedures agree, and they agree against the stationary prior that a spread-type object would suggest. The augmented Dickey and Fuller (1979) test, lag-augmented as in Said and Dickey (1984) with the lag chosen by an information criterion (Ng and Perron 2001), does not reject a unit root with a statistic of −0.125348 at p = 0.946855, the Phillips and Perron (1988) test concurs at −0.0739713 with p = 0.95197, and the KPSS test rejects level stationarity at 1.0157 with p < 0.01 (Kwiatkowski et al. 1992), an honest agreement that carries a clean I(1) verdict. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous readings and was not needed here. Unit-root power depends on the time span of the sample rather than on the number of observations (Shiller and Perron 1985), so weekly rather than daily sampling costs little power, but two years is short relative to the cycles that move rate differentials. The verdict therefore says only that over this window the ratio cannot be told apart from a series carrying a stochastic trend.

On the level the first-order autoregressive coefficient is 0.997085, which puts the implied half-life beyond the length of the sample, a descriptive persistence summary and not an integration claim, read with the small-sample downward bias of Andrews (1993) in mind. The Ljung and Box (1978) portmanteau on the level, refining the Box and Pierce (1970) form, rejects the no-autocorrelation null on the weekly ladder at lags 13 and 26, with Q = 862.424 and Q = 1053.98 and p = 0.000 in both cases, which on a level with a unit-root reading restates that persistence rather than revealing further structure. Because the triplet gave a clean integrated reading, the Bai and Perron (1998) search, computed by the Bai and Perron (2003) algorithm, moves to the 103 weekly differences from 2024-10-11 to 2026-09-25, and it finds no break in the mean of the differenced series (Perron 1989). Those differences are changes in weekly averages, which carry an induced positive first-order autocorrelation even when the underlying daily path has none (Working 1960).

The persistence is the differential's. The carry leg's own battery also gives a clean integrated reading while the volatility leg's is ambiguous, and because the ratio is their quotient in every week, its persistence is inherited largely from the numerator. This is the dependence the identity imposes, since the ratio equals the differential divided by the volatility, so the three verdicts of this group are not independent evidence and are not to be read as agreeing or disagreeing with one another. Values can also be revised after first publication as late trade reports arrive. Replaying the archive in file-date order over 104 weeks, the 95th percentile of the absolute gap between each week's first-published and final ratio is 0.0014, and no week was empty at first publication, so the pinned sample is a record of values that were themselves subject to small data-vintage revisions (Orphanides and van Norden 2002).

The series is weekly and no seasonal quantity is posited for a ratio of a rate differential to a volatility, so the seasonal-unit-root machinery of Hylleberg et al. (1990) and the Canova and Hansen (1995) seasonal-stationarity test are not applicable and were deliberately not run (Beaulieu and Miron 1992; Ghysels and Osborn 2001).

## Frequently Asked Questions

### What is the won-dollar carry-to-risk ratio?

It divides the 3-month interest rate differential implied by won-dollar forward prices by the 3-month at-the-money volatility implied by option prices. It shows how much carry a won position receives or pays per unit of the exchange-rate risk that options price.

### Why can the ratio be negative?

The sign is that of a position long the won and short the dollar. When the won's forward-implied interest rate is below the dollar's, that position pays carry and the ratio is negative, which means the won sits on the funding side on forward prices. The sign is never flipped.

### Can the ratio be read as a signal of where the won is heading?

No. It is a descriptive record of current forward and option pricing, not a forecast. Carry accrues only if the exchange rate stays where it is, and carry positions are known for gradual gains and abrupt losses, so the ratio makes no statement about subsequent exchange-rate moves or the payoff of any position.

### How do the three series in this group relate to each other?

The ratio equals the forward-implied rate differential divided by the at-the-money option-implied volatility, week by week and exactly. The three are one construction seen from three sides, so a move in one is not independent evidence about another, and a change in the ratio is explained by checking which of the other two moved.

### Why are the values weekly rather than daily?

Won-dollar options near three months do not trade every day, so a daily volatility would leave many gaps or borrow prices from other days. Each weekly value uses only trades from Monday to Friday of that week, is dated on the Friday, and a week without enough trades is left empty rather than filled.

### Can past values change after they are published?

Yes. The series is built from publicly disseminated trade reports, and corrections, cancellations and late reports can arrive after a week closes. The affected weeks are then recomputed, so recent values in particular are provisional.