South Korea 10-Year Zero-Coupon Bond Risk-Neutral Rate

The risk-neutral rate is the yield obtained from the no-arbitrage Affine Term Structure Model (ACM) when the market prices of risk are set to zero. It reflects the average of expected future short-term rates under the assumption that investors are risk-neutral, demanding no compensation for interest rate or inflation risk.

The zero-coupon yield $y_t(n)$ approximately equals the model-fitted yield and decomposes into the risk-neutral rate $y^Q_t(n)$ and the term premium $\text{TP}_t(n)$:

The model-fitted yield is the theoretical yield computed via affine recursion under the physical measure (P-measure), while the risk-neutral rate is the yield under the Q-measure with risk prices $\lambda = 0$.

This decomposition identifies whether movements in observed yields are driven by changes in monetary policy expectations (risk-neutral rate) or shifts in risk compensation (term premium). The trend in the risk-neutral rate reveals the future policy rate path that the market prices in.

Estimated using the five-step Affine Term Structure Model (ACM) of Adrian, Crump, and Moench (2013).

(1) Input Construction. Par yields from 5 key rates (MSB 91d, KTB 1Y/3Y/5Y/10Y) are bootstrapped into zero-coupon yields under the Actual/Actual (ICMA) day count convention, using simple interest for $\tau < 1$yr and semi-annual compounding for $\tau \geq 1$yr. PCHIP interpolation generates a monthly maturity grid $Y \in \mathbb{R}^{T \times 120}$ (1–120 months). Monthly data are extracted via month-end resampling.

(2) PCA. $K=5$ principal components are extracted from the demeaned yield matrix:

, where PC 1 = Level, PC 2 = Slope, PC 3 = Curvature, PC 4–5 = higher-order variation. Variance and sign normalization are applied.

(3) VAR(1). State dynamics follow a driftless VAR(1):

with $\mu = 0$ imposed post-estimation. The OLS estimate $\hat{\Phi}$ is then bias-corrected using the Bauer-Rudebusch (2012) iterated bootstrap procedure, which corrects for finite-sample downward bias in the persistence of yield curve factors and prevents systematic overestimation of term premiums.

(4) Risk Price Estimation. Excess holding-period returns are defined as:

These are regressed on

. After Jensen's inequality correction and orthogonal projection, the market prices of risk $(\lambda_0, \Lambda_1)$ are extracted via cross-sectional regression.

(5) Risk-Neutral Rate Computation. Setting $\lambda_0 = 0$ and $\Lambda_1 = 0$ in the affine recursion yields Q-measure dynamics, from which the risk-neutral rate $y^Q_t(n)$ is computed. The difference between the physical-measure fitted yield $y^P_t(n)$ and the risk-neutral rate gives the term premium.(6) Pricing Errors. Over the 6307 daily observations from 2000-12-18 to 2026-06-09 the mean absolute difference between the model-fitted yield and the observed zero-coupon yield is 4.99 basis points at twelve months, 1.05 at thirty-six months, 2.11 at sixty months and 1.04 at one hundred and twenty months. Those figures are a property of the input panel the estimation runs on rather than of the bias correction, and the same measurement on the same panel returns the same values to two decimal places when that correction is switched off.

(7) Second Configuration. A second KRED configuration of this estimator, which omits the small-sample persistence correction, publishes its own risk-neutral yields beside this family at the same four maturities. It is a different estimand rather than a second measurement of this one, and neither family validates, corroborates, or outranks the other in either direction (Adrian, Crump, and Moench 2013; Bauer, Rudebusch, and Wu 2012).

The risk-neutral rate reflects the bond market's embedded expectations for the future path of monetary policy. Under the ACM framework, it represents the average expected short-term rate over the bond's maturity with risk prices set to zero, effectively stripping away all risk compensation from observed yields. A decline in the risk-neutral rate suggests the market anticipates future rate cuts, while an increase signals tightening expectations.

Bernanke (2013) emphasized that longer-term interest rates are closely linked to market participants' expectations of how short-term rates will evolve, and that public expectations about future monetary policy matter because they affect financial conditions today. The risk-neutral rate provides the most direct measure of these embedded expectations. When a central bank engages in forward guidance (communicating the likely future path of interest rates), the risk-neutral component captures the signaling effect, distinguishing it from the portfolio balance effect that operates through the term premium (Woodford 2012; Bernanke 2020).

Gürkaynak, Sack, and Swanson (2005) demonstrate that monetary policy affects the yield curve through two distinct factors, namely a 'target' factor that captures surprise changes in the current policy rate, and a 'path' factor that reflects revisions to the expected future policy path. The risk-neutral rate is primarily responsive to the path factor, making it the key variable for assessing whether central bank communication has successfully shaped market expectations about the trajectory of future rates, rather than merely the current rate level.

The relationship between the risk-neutral rate and macroeconomic fundamentals is well established. Crump, Eusepi, and Moench (2018) show that risk-neutral rates derived from term structure models closely track survey-based measures of expected short rates from professional forecasters, validating their interpretation as genuine policy expectations rather than model artifacts. Furthermore, the long-run level of risk-neutral rates provides information about the market's assessment of the neutral rate of interest ($r^*$), the rate at which monetary policy is neither stimulative nor restrictive (Laubach and Williams 2003). A secular decline in risk-neutral rates across advanced economies has been interpreted as evidence of a falling neutral rate, driven by demographics, productivity slowdown, and global savings gluts (Rachel and Smith 2017).

For South Korea, the risk-neutral rate reflects not only expectations for Bank of Korea base rate decisions but also spillovers from Federal Reserve policy expectations and global financial conditions. Obstfeld (2015) documents that U.S. monetary policy shocks transmit to emerging market yield curves through the expectations channel, shifting risk-neutral rates even in the absence of domestic policy changes. The Korean risk-neutral rate is therefore jointly determined by the domestic monetary policy stance and the global interest rate environment, making it a useful indicator for analyzing the interaction between Bank of Korea policy autonomy and external financial conditions.

The decomposition of yields into risk-neutral rates and term premiums is fundamental for fixed income portfolio management, as it enables practitioners to separate directional rate bets from risk compensation harvesting, two conceptually distinct sources of bond returns. When the risk-neutral rate exceeds the current short-term rate, the market expects future rate hikes; when it is lower, rate cuts are anticipated. This information is critical for positioning along the yield curve.

The risk-neutral yield curve provides a cleaner measure of the market's expected rate path than raw forward rates, which embed both expectations and risk premia. Cochrane and Piazzesi (2005) show that a tent-shaped linear combination of forward rates predicts excess bond returns with an $R^2$ of approximately 44%, and much of this predictability stems from time-varying risk premia rather than expectations. By using risk-neutral rates instead of raw forwards, investors can isolate the expectations component and avoid conflating risk premia signals with genuine rate expectations when constructing views on the rate cycle.

The slope of the risk-neutral yield curve (the difference between long-term and short-term risk-neutral rates) summarizes the market's expectations for the monetary policy cycle in a single number. A steeply upward-sloping risk-neutral curve signals expected tightening, while an inverted risk-neutral curve signals expected easing. Unlike the observed yield curve slope, which can be distorted by supply-demand dynamics and time-varying risk premia (Greenwood and Vayanos 2014), the risk-neutral slope offers a purer reading of policy expectations. This makes it the preferred input for curve trading strategies (flatteners/steepeners) that seek to express views on the direction and pace of monetary policy.

The divergence between the model-fitted yield and the actual observed yield (the pricing error) serves as a gauge of model fit and carries its own information content. Persistent pricing errors may indicate the presence of market microstructure factors such as liquidity premia, supply-demand imbalances from preferred-habitat investors (Vayanos and Vila 2021), or regulatory-driven demand (e.g., bank and insurance capital requirements). Monitoring these residuals helps identify bonds that are trading rich or cheap relative to the model-implied fair value, supporting relative value strategies.

In the Korean Treasury Bond (KTB) market context, the risk-neutral rate is particularly valuable for foreign investors managing both duration and currency risk. By comparing KTB risk-neutral rates with U.S. counterparts (from the New York Fed ACM model or the Kim-Wright three-factor model), investors can isolate the cross-country differential in expected policy paths from the differential in risk compensation. This decomposition is essential for determining whether observed yield spread changes between the two markets represent shifting monetary policy expectations (suggesting potential convergence or divergence trades) or merely reflect fluctuations in relative term premiums.

For liability-driven investors (LDI) such as insurers and pension funds, the level and trajectory of risk-neutral rates have direct implications for discount rate assumptions and liability valuation. A structurally declining risk-neutral rate implies that the market expects persistently lower policy rates, challenging the ability to match long-duration liabilities through traditional fixed-income strategies. In such environments, these institutions may need to extend duration further into the curve or supplement bond holdings with alternative duration-providing instruments, decisions that the risk-neutral yield curve helps inform (Ilmanen 2011).

This is a model-derived series, the output of the Adrian-Crump-Moench affine term-structure decomposition, so the unit-root reading describes the fitted curve rather than a directly observed price, and the serial-correlation and break diagnostics run on the first difference. The series is tested over its own span from 2000-12-18 to 2026-06-09.

The ten-year risk-neutral rate is integrated of order one on the level, with the Dickey and Fuller (1979) test in the Said and Dickey (1984) form not rejecting at p = 0.8552, the Phillips and Perron (1988) test concurring at p = 0.7483, and the Kwiatkowski et al. (1992) test rejecting stationarity. On the first difference the Ljung and Box (1978) portmanteau rejects white noise at lags 10 and 20, Q = 68.36 and Q = 100.22 at p = 0.000 and p = 0.000, and the automatic portmanteau of Escanciano and Lobato (2009) concurs with a statistic of 12.55 at p = 0.000. The Bai and Perron (1998, 2003) procedure finds no break in the mean, a reading consistent with the parameter-instability inference of Andrews (1993) on the differenced object (Perron 1989).

This is a daily model output with no low-integer seasonal period, so the seasonal-unit-root and seasonal-stationarity machinery of Hylleberg et al. (1990) and Canova and Hansen (1995) is deliberately not run (Beaulieu and Miron 1992; Ghysels and Osborn 2001).