Pairs trading on Korean equities: cointegration that actually held

If you have ever tried running a statistical arbitrage book on global equities, you know the painful cycle of backtesting a promising pairs trading strategy, deploying it live, and watching the cointegration relationship disintegrate immediately.

In late 2022, I set out to build a systematic pairs trading book specifically targeted at the South Korean market (KRX). The thesis was straightforward: the unique, highly concentrated corporate structure of South Korea—dominated by chaebols (family-run conglomerates)—creates deep, structurally driven economic dependencies between parent holding companies, their listed subsidiaries, and primary suppliers. Theoretically, these entities should exhibit exceptionally tight, long-term cointegrating relationships.

In practice, I nearly blew up my account in the first quarter of 2023.

This is the breakdown of why the standard textbook approach failed miserably on Korean equities, how I re-engineered the strategy using a dynamic state-space model (Kalman Filtering) instead of static rolling OLS, how I navigated the regulatory minefield of the Korean short-selling ban, and the production-grade Python implementation that actually turned a profit.

The structural trap of naive rolling OLS

My initial mistake was relying on the classic Engle-Granger two-step method using a 60-day rolling window to estimate the hedge ratio. I selected Hyundai Motor Company (005380 KS) and Kia Corporation (000270 KS) as my primary pair. They share platform architectures, powertrains, and global supply chains, and their revenues are highly correlated.

The standard model assumes:

$$\text{Price}{\text{Hyundai}, t} = \beta \cdot \text{Price}{\text{Kia}, t} + \alpha + \epsilon_t$$

Where we monitor the residual series $\epsilon_t$ for mean reversion. If $\epsilon_t$ diverges significantly from zero (measured by a Z-score), we long the cheap asset and short the expensive one.

Here is the exact point where this approach shattered. In early 2023, the Korean market experienced a massive, retail-driven thematic wave. Retail investors on forums like Naver Financial and various YouTube channels began aggressively buying specific names based on EV battery supply chain narratives. Kia surged on EV-related momentum, while Hyundai Motor lagged.

Using a 60-day rolling OLS regression, the model responded to this divergence by constantly shifting the hedge ratio ($\beta$).

Because the rolling OLS window had a memory length of 60 days, it was too slow to adapt to the regime shift, yet fast enough to “chase” the trend. By the time the rolling $\beta$ adjusted down to $1.95$, the spread had widened so far that I hit my hard stop-loss limits, crystallizing a -14.8% draw on allocated capital.

The fundamental problem with rolling OLS is its uniform weight distribution over the historical window. It treats data from 59 days ago with the same importance as yesterday’s data, leading to a lagging hedge ratio that systematically enters trades too early during structural shifts and exits them too late.

The Architecture: Kalman Filters and Single-Stock Futures

To fix this, I abandoned rolling regressions entirely and pivoted to a state-space model where the hedge ratio is treated as a hidden, dynamic state variable that evolves according to a random walk. We observe this state through noisy market prices.

$$\theta_t = \begin{bmatrix} \beta_t \ \alpha_t \end{bmatrix}$$

$$\theta_t = \theta_{t-1} + \eta_t, \quad \eta_t \sim N(0, Q)$$

$$y_t = H_t \theta_t + \epsilon_t, \quad \epsilon_t \sim N(0, R)$$

Where $y_t$ is the price of the dependent asset (Hyundai), $H_t = [x_t, 1]$ represents the independent asset price (Kia) and an intercept, $Q$ is the process noise covariance matrix, and $R$ is the measurement noise variance.

The Kalman Filter recursively updates its estimate of the true relationship $\theta_t$ with every new 1-minute bar, allowing us to compute a dynamic, lag-free prediction error (the spread) and its variance (to compute a dynamically scaling Z-score).

Additionally, I had to solve a structural execution problem unique to South Korea: short-selling restrictions. In Korea, shorting physical equities is highly regulated, expensive, and subject to sudden regulatory bans (such as the sweeping ban imposed by the Financial Services Commission in November 2023).

To make this strategy viable and robust to regulatory intervention, I shifted the execution layer from physical equities to Single-Stock Futures (SSFs) traded on the KRX. SSFs offer several distinct advantages:
1. They are immune to the physical short-selling ban.
2. The transaction tax on derivatives is orders of magnitude lower than the 0.18% (formerly 0.20%) tax on physical stock sales in Korea.
3. Leverage is built-in, requiring significantly less capital allocation.

Here is how the data and trade signals flow through my production setup:

flowchart TD
 A["Raw KRX Market Data"] -->|"1-Min Bar Websocket"| B["Kalman Filter State Estimator"]
 B -->|"Dynamic Beta & Alpha"| C["Dynamic Hedge Ratio"]
 C -->|"Prediction Error Calculation"| D["Spread Calculation & Z-Score"]
 D -->|"Z-Score Threshold Check"| E["Execution Logic (Futures/L/S)"]
 E -->|"Limit Orders via Koscom API"| F["Risk Management & Circuit Breaker"]

The Production Implementation

Below is the complete, self-contained implementation of the Kalman Filter-based pairs trading engine. It includes a synthetic data generator that models a structural regime shift (the exact failure mode that blew up my OLS model) to demonstrate how the state-space model adapts without lagging.

Let’s look at the console output from this exact run to see how the Kalman Filter adapts compared to the naive rolling OLS:

Performance breakdown and results

The difference in tracking accuracy between the state-space model and the static OLS was stark during the regime shift.

While the rolling OLS beta lagged for nearly 80 business days—clinging to the historical relationship and generating catastrophic false entry signals—the Kalman Filter converged on the new, true hedge ratio ($\beta \approx 1.8$) within 15 periods of the shift’s completion.

Here is the performance comparison of the two execution regimes when applied to actual historical 1-minute data of the Hyundai/Kia pair during the turbulent 2023–2024 period:

Because the Kalman Filter dynamically adjusts the variance matrix $S_t$, our threshold limits expand during periods of high market volatility. This automatically filtered out bad entry signals during the peak retail FOMO periods on the Korean Exchange, as shown by the low Max Drawdown profile of the KF strategy.

Lessons from the KRX trenches

Developing and operating statistical arbitrage engines in the South Korean market taught me several expensive lessons that you will not find in academic papers on cointegration.

1. The FX hazard and the KOSPI correlation

If you are trading Korean equities from a USD-denominated fund, you are implicitly running a heavy overlay trade on the KRW/USD exchange rate. During periods of risk-off sentiment in emerging markets, Korean stocks drop while the KRW depreciates sharply against the USD. If your hedge ratios are computed on nominal KRW values but your risk limits are calculated in USD, your portfolio risk limits will trigger prematurely. Always denominate your spread computations and stop-losses in the native execution currency (KRW), and hedge the currency exposure separately at the portfolio level.

2. Single-Stock Futures liquidity limits

While SSFs insulate you from short-selling restrictions and cut transaction taxes to almost zero, they suffer from highly concentrated liquidity. On the KRX, only the near-month contract has active market makers. When transitioning from the current month to the next, the spread wide-opens during roll week.

If you attempt to run a pairs strategy using a position size larger than 5% of the average daily volume of the target SSF, your execution slippage during the roll will erase all theoretical statistical arbitrage edge. For larger capacity, you must implement a hybrid execution layer: trade the liquid leg using physical equity (long) and the illiquid leg using the SSF (short), dynamically rebalancing via a multi-asset execution router.