South Korea Composite Indicator of Systemic Stress

The Korea Composite Indicator of Systemic Stress is a daily, bounded measure that expresses contemporaneous stress in the Korean financial system as a single number on $(0, 1]$. Systemic stress is the state in which financial intermediation is impaired across several markets at once (de Bandt and Hartmann 2000), and KRCISS implements the portfolio-aggregation framework of Holló, Kremer, and Lo Duca (2012) for Korea almost verbatim, with a single disclosed substitution.

KRCISS aggregates five market-segment subindices, namely financial intermediaries, the money market, equity, bond, and foreign exchange, each the average of three raw stress measures homogenised to the unit interval. The five-subindex vector $s_t$ enters a portfolio-variance form through the segment weights $w$ and the time-varying cross-correlation matrix $C_t$:

where $\circ$ is the Hadamard product.

This portfolio weighting is what distinguishes KRCISS from a simple weighted average. The indicator rises only when stress is elevated and broadly correlated across segments, so a rise in KRCISS signals acute systemic stress that co-moves across segments rather than an isolated disturbance in one market.

(1) Fifteen raw stress measures. Each of the five market segments, namely financial intermediaries (FI), the money market (MM), equity (EQ), bond (BD), and foreign exchange (FX), contributes three raw daily stress measures, for fifteen in total, selected to mirror the measures of Holló, Kremer, and Lo Duca (2012) with jurisdiction-equivalent Korean instruments in the manner of Illing and Liu (2006) and Cardarelli, Elekdag, and Lall (2011). The certificate-of-deposit rate stands in for Euribor, a KOSPI non-financial basket serves the equity block, a bank-bond-versus-corporate-bond spread the bond block, and KRW realised volatilities the foreign-exchange block. Korea's marginal lending facility is not separately published, and the Bank of Korea loan-balance line is flat at roughly zero through every crisis and so carries no usable stress signal. The single disclosed substitution is therefore the MM third measure, where the call-rate-minus-KOFR basis replaces emergency central-bank lending, a price-based funding-strain proxy in the sense of Brunnermeier and Pedersen (2009).

(2) Recursive empirical-CDF homogenisation. Each raw measure $x_t$ is transformed to the unit interval by its recursively computed empirical cumulative distribution function, following equations (1a) and (1b) of Holló, Kremer, and Lo Duca (2012). Ordering the realisations through date $t$ as $x_{[1]} \le x_{[2]} \le \cdots \le x_{[n]}$, the homogenised value is $z_t = r/n$ for $x_{[r]} \le x_t < x_{[r+1]}$ with $r = 1, \dots, n-1$, and $z_t = 1$ for $x_t \ge x_{[n]}$, where the ranking sample expands recursively so that $z_t$ uses only information available at $t$. This order-statistic transform replaces the variance-equal and principal-component standardisations of Hakkio and Keeton (2009), Kliesen and Smith (2010), and Hatzius et al. (2010) with a scale-free and outlier-robust mapping.

(3) Segment subindices. Within each segment $i$ the three homogenised measures are averaged, $s_{i,t} = \tfrac{1}{3} \sum_{j=1}^{3} z_{ij,t}$, giving the five subindices $s_t = (s_{\text{FI},t}, s_{\text{MM},t}, s_{\text{EQ},t}, s_{\text{BD},t}, s_{\text{FX},t})'$, the equal-within-segment averaging of Holló, Kremer, and Lo Duca (2012) that the dynamic-weighting indices of Brave and Butters (2011) and Oet et al. (2011) implement with factor weights instead.

(4) Time-varying cross-correlations. The demeaned subindices $\tilde{s}_{i,t} = s_{i,t} - \bar{s}_i$ drive an exponentially weighted moving-average covariance $\sigma_{ij,t} = \lambda\, \sigma_{ij,t-1} + (1-\lambda)\, \tilde{s}_{i,t}\, \tilde{s}_{j,t}$ and correlation $\rho_{ij,t} = \sigma_{ij,t} / \sqrt{\sigma_{ii,t}\, \sigma_{jj,t}}$, the RiskMetrics recursion whose decay is set to $\lambda = 0.93^{1/5} \approx 0.9856$ so that the daily half-life matches the weekly $0.93$ of Holló, Kremer, and Lo Duca (2012), the optimal-decay calibration discussed by González-Rivera, Lee, and Yoldas (2007). The $5 \times 5$ matrix $C_t = [\rho_{ij,t}]$ collects these correlations.

(5) Portfolio aggregation. The indicator is the portfolio-variance form $CISS_t = (w \circ s_t)\, C_t\, (w \circ s_t)'$, where $w$ is the vector of segment weights, $\circ$ is the Hadamard product, and $C_t$ is the time-varying correlation matrix, so that simultaneous broad stress is weighted more heavily than isolated stress, the systemic emphasis that Holló, Kremer, and Lo Duca (2012) and Kremer (2016) formalise and that the survey of Bisias et al. (2012) places among correlation-based systemic-risk analytics. The real-impact weights are $w = (0.30, 0.15, 0.25, 0.15, 0.15)$ for FI, MM, EQ, BD, and FX, and $CISS_t$ is bounded in $(0, 1]$ and computed daily, with the weighting role read alongside the comparable summary constructions of Nelson and Perli (2007).

KRCISS is a macroprudential monitoring gauge that reads in real time where the Korean financial system sits between calm and crisis. This is the systemic-risk-monitoring purpose for which Holló, Kremer, and Lo Duca (2012) designed the original CISS, condensing fifteen market measures into one bounded series.

The macroprudential value of such a gauge rests on the now-extensive evidence that financial stress carries real-economy consequences. Banking-centred stress episodes precede and deepen output contractions (Cardarelli, Elekdag, and Lall 2011), and high stress predicts weaker subsequent growth (Hakkio and Keeton 2009). Systemic-risk measures further skew the conditional distribution of future industrial-production shocks to the downside (Giglio, Kelly, and Pruitt 2016).

This downside-risk channel is the one that Adrian, Boyarchenko, and Giannone (2019) formalise as vulnerable growth, where tighter financial conditions and higher stress fatten the left tail of the growth distribution. The financial-accelerator mechanism of Bernanke, Gertler, and Gilchrist (1999) supplies it with structural foundations.

For Korea the real-activity link is strong. A threshold model of the CISS and industrial-production growth identifies a high-stress regime in which the production response turns sharply negative, consistent with the regime-dependent macro-financial dynamics that Hartmann et al. (2015) and Kremer (2016) estimate for the euro area.

KRCISS is therefore a natural input to the early-warning and systemic-risk frameworks of Lo Duca and Peltonen (2013) and de Bandt and Hartmann (2000) and to the medium-term financial-cycle monitoring of Borio (2014), read alongside KRED's credit-and-property-cycle series rather than in place of them.

KRCISS answers a different question from KRED's Financial Conditions Index (KRFCI). KRCISS measures acute systemic stress on a bounded scale that runs from calm to crisis and weights broad co-movement, whereas KRFCI measures financial conditions as a signed standardised score from a static principal-component analysis that runs from easing to tightening (Hatzius et al. 2010; Brave and Butters 2011). The two indicators therefore answer different questions, namely stress versus conditions.

A second Korean finding tempers the systemic interpretation. The average cross-segment correlation does not rise across Korea's crises, and only financial-centric pairs co-move strongly. Korea's episodes are heterogeneous, foreign-exchange-and-liquidity-led in 2008 and bond-and-credit-led in 2022, the cross-episode diversity that Reinhart and Rogoff (2009) and Patel and Sarkar (1998) document across countries and markets. This is a finding about Korea's financial system rather than a defect of the indicator.

For market participants KRCISS is a real-time market-stress thermometer for Korea. Its bounded scale and daily frequency make it a convenient single read on whether funding, equity, bond, and foreign-exchange markets are calm or strained, the market-monitoring use that Illing and Liu (2006) and Holló, Kremer, and Lo Duca (2012) intend for composite stress indices.

The chief operational advantage over a single headline number is the segment decomposition, where the five subindices and their contributions reveal which market is driving stress. The financial-intermediaries block tracks the health of banks and brokers (Adrian and Brunnermeier 2016; Acharya et al. 2017; Brownlees and Engle 2017), and the money-market block tracks the funding-liquidity strain at the heart of liquidity spirals (Brunnermeier and Pedersen 2009). The equity block tracks the volatility and drawdown of the kind Patel and Sarkar (1998) study, and the bond and foreign-exchange blocks track the cross-asset moves that accompany stress.

The portfolio weighting makes KRCISS most responsive precisely when stress becomes broad and correlated. This is the flight-to-quality and flight-to-liquidity dynamic in which capital flees equities for government bonds (Caballero and Krishnamurthy 2008; Baele et al. 2020), so a sharp rise in the indicator alongside a jump in the cross-segment correlations is the signature of a systemic rather than idiosyncratic episode.

Read this way KRCISS complements the connectedness and spillover measures of Diebold and Yilmaz (2014) and Billio et al. (2012) and sits within the broader toolkit of systemic-risk analytics catalogued by Bisias et al. (2012). Korea-focused desks thereby obtain a daily and decomposable gauge of where systemic stress is concentrated and how broadly it has spread.

KRCISS is a bounded composite indicator confined to the half-open unit interval (0,1] by the portfolio construction of Hollo, Kremer, and Lo Duca (2012), in which each raw stress measure is homogenised through a recursive empirical cumulative distribution function before aggregation. This bounded support determines which battery is legitimate, since a series that cannot leave a fixed interval is not the unbounded random walk that ordinary integration inference presupposes.

The augmented Dickey and Fuller (1979) test with the Said and Dickey (1984) lag augmentation and the trend-augmented form of Dickey and Fuller (1981), 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, because under known bounds the normalised partial-sum process converges to a regulated Brownian motion rather than to standard Brownian motion, the Dickey-Fuller null distributions become non-pivotal, and inference against ordinary critical values over-rejects the unit root toward spurious stationarity by a margin that does not shrink as the sample grows (Cavaliere 2005; Cavaliere and Xu 2014). No order of integration is therefore assigned to this series.

Over the 2008-02 to 2026-06 daily sample, persistence is reported descriptively, with no integration order attached. On the level KRCISS has a lag-one autocorrelation of 0.976 and a half-life of about 28.9 trading days, a figure read with the small-sample downward bias of the autocorrelation estimator in mind (Andrews 1993). The level Ljung and Box (1978) portmanteau rejects the white-noise null, with Q(10) = 36277.3 and Q(20) = 65274.1, a statement about serial correlation and not about integration order.

A reused Tsay (1998) threshold vector autoregression of monthly KRCISS against industrial-production growth, with the threshold estimated endogenously in the manner of Hansen (2000) over 219 months, locates a regime threshold near a CISS value of 0.13, and in the high-stress regime the industrial-production response is about −39.6 against about +9.3 in the low-stress regime, with a pseudo-F of about 5.04, so elevated systemic stress robustly coincides with depressed real activity. The construction's premise that cross-segment correlations rise in crises holds only partially for Korea, whose crises are heterogeneous, a finding about the domestic financial system and not a defect of the indicator (Hollo, Kremer, and Lo Duca 2012).