South Korea 10-Year Term Premium Contribution Ratio

The TP contribution ratio quantifies the signed fractional contribution of the 10-year term premium to the observed yield. It is defined as:

where $\text{TP}_n$ is the 10-year term premium and $\text{RN}_n$ is the risk-neutral yield, both estimated from the ACM affine term structure model. The denominator $|\text{RN}_n| + |\text{TP}_n|$ represents the total absolute contribution of the two yield components. The ratio $R_{TP} \in [-100, +100]$, where positive values indicate the term premium adds to the yield and negative values compress it below the risk-neutral rate. When $R_{TP} = +30$, approximately 30% of the yield level is attributable to the term premium.

Unlike the raw term premium expressed in percentage points, the contribution ratio normalizes by the total absolute decomposition, enabling meaningful comparisons across different interest rate regimes and time periods. During high-rate environments, a term premium of 100bp may represent a small fraction of yields, whereas the same 100bp in a low-rate regime constitutes a dominant share.

Cornish-Fisher confidence bands at the 1st, 5th, 50th, 95th, and 99th percentiles are computed directly in ratio space, adjusting the standard normal quantiles for the observed skewness and excess kurtosis of the $R_{TP}$ distribution via the expansion:

These are static bands based on the full sample. When the Cornish-Fisher quantiles fail monotonicity and thereby indicate extreme non-normality, empirical quantiles are used as a fallback.

Computed in two steps from the ACM model output.

(1) Term Premium Decomposition. The ACM model (Adrian, Crump, and Moench 2013), with bias-corrected VAR dynamics (Bauer and Rudebusch 2012), decomposes each $n$-maturity zero-coupon yield into a risk-neutral rate $y^Q_t(n)$ and a term premium:

Both are expressed in percent.

(2) Contribution Ratio and Real-Time CF Bands. The contribution ratio is:

The signed absolute ratio ensures that (a) the denominator never vanishes when both components are nonzero, (b) the sign preserves the direction of the term premium, and (c) the magnitude reflects relative importance regardless of the yield level. Confidence bands at levels $\{1\%, 5\%, 50\%, 95\%, 99\%\}$ are computed via a real-time expanding-window Cornish-Fisher expansion (Cornish and Fisher 1937) with a 1000-trading-day burn-in and month-end moment estimation frequency. The CF polynomial

uses the Maillard (2012) corrected coefficients $(S_c, K_c)$ obtained by numerically inverting the nonlinear moment-to-coefficient mapping (Amédée-Manesme, Barthélémy, and Maillard 2019). The Chernozhukov, Fernández-Val, and Galichon (2010) rearrangement procedure is applied to the resulting quantile function to ensure monotonicity. Bands are NaN within the burn-in period (approximately 2001–2005). Diagnostic columns record the expanding-window skewness, excess kurtosis, and a valid-domain indicator at each date.

The contribution ratio $R_{TP}$ helps distinguish monetary policy expectation shocks from term premium shocks in yield movements (Adrian, Crump, and Moench 2013). When $R_{TP}$ exceeds the 95th percentile CF band, it signals a historically extreme term premium contribution, potentially indicating supply/demand imbalances (Greenwood and Vayanos 2014), fiscal concerns (Laubach 2009), or uncertainty premia (Wright 2011) rather than policy rate expectations. Conversely, $R_{TP}$ near zero indicates a balanced regime, while strongly negative values indicate an expectations-dominated regime where yields primarily reflect anticipated policy paths.

$R_{TP}$ is used in monetary policy analysis to identify the source of yield movements. A rising yield accompanied by a stable or falling $R_{TP}$ suggests that rate expectations are driving the increase, consistent with anticipated tightening, while a rising yield with a rising $R_{TP}$ points to risk repricing. This distinction is critical for central bank communication and for calibrating the stance of monetary policy relative to the neutral rate (Bauer and Rudebusch 2014).

The contribution ratio informs bond portfolio duration decisions. TP-driven yield rises (high $R_{TP}$) may mean-revert faster than RN-driven rises (low $R_{TP}$), because the term premium reflects compensation for risk-bearing rather than a fundamental shift in the policy rate path. When $R_{TP}$ breaches the 95th percentile CF band, it signals historically extreme risk-premium dominance and can offer an attractive entry point for long-duration positions.

Comparing $R_{TP}$ across maturities, for instance 1Y and 10Y, reveals where the term premium concentrates on the curve, identifying whether curve steepening or flattening is TP-driven or expectations-driven. This informs butterfly and curve steepener/flattener strategies. The asymmetric CF bands, wider on the upside when skewness is positive, directly reflect the tendency of the TP contribution to spike upward more than it compresses downward, providing distribution-aware thresholds for relative value assessment.

KRTPCR10 publishes the term-premium contribution ratio at the ten-year maturity, the term premium expressed as a fraction of the fitted yield. This ratio is not a bounded object on the unit interval. Its numerator changes sign and its denominator can pass close to zero, so the ratio ranges far outside the unit interval into large positive and negative values and is heavy-tailed, a ratio of a variable-sign numerator over a near-zero-capable denominator whose second moment may fail to exist (Marsaglia 1965; Hinkley 1969).

For that reason the augmented Dickey and Fuller (1979) test with the Said and Dickey (1984) lag augmentation, the Phillips and Perron (1988) test, the KPSS test (Kwiatkowski et al. 1992), the DF-GLS refinement of Elliott, Rothenberg, and Stock (1996), and the Ng and Perron (2001) M-tests were deliberately not run. The prohibition here does not rest on bounded support, since the contribution ratio is not bounded, but on heavy tails, and it is inappropriate to read a finite-variance limit theory whose critical values collapse once the errors have infinite variance, so a mean-based integration battery on such a ratio is meaningless (Phillips 1990).

Persistence is therefore reported only descriptively, and even the descriptive lag-one autocorrelation is itself unreliable under heavy tails and is read with that reliability caveat. Over the 2000-12 to 2026-06 daily sample the estimated lag-one autocorrelation at the ten-year maturity is 0.997, with an implied half-life of about 256.2 trading days, so the ratio is strongly persistent near unity, a figure the small-sample downward bias of the estimator makes conservative (Andrews 1993). The level Ljung and Box (1978) portmanteau rejects the white-noise null, with Q(10) = 61346.6 and Q(20) = 119670.

The published Cornish-Fisher percentile bands at the first, fifth, fiftieth, ninety-fifth, and ninety-ninth percentiles are confirmed non-crossing at the ten-year maturity, so the distributional fan is internally coherent (Chernozhukov, Fernandez-Val, and Galichon 2010). No order of integration is assigned to this ratio, by ruling and not by an inconclusive test.