Yoon's breakpoint requires a price-impact coefficient of about 53 for SK Hynix and about 62 for Samsung Electronics, compared with an assumed long-run mean of 15. Those are the numbers a desk can watch. In the model, realized volatility is the stock's own volatility divided by (1 minus lambda times theta times omega times L). Once that product reaches one, the closing auction loses its fixed point. The calibration uses Korea in July 2026. Beyond the descriptive Seibro statistics, every other quantitative result comes from simulation.

A disclosure comes first. The paper studies Korean single-stock leveraged ETFs and their Korean underlying shares. We have US minute bars, without quotes or closing-auction imbalance, so no run of ours tests the paper's mechanism. Adapting the exercise to a US equity and ETF would mean a different market structure, a different concentration of product AUM and a different closing-auction mechanism. Yoon's calibration depends on two names accounting for 55.68% of the KOSPI 200, with about KRW 14.9tn of single-stock product concentrated in them.

The flow always runs with the day's move. Daily rebalancing demand for a leveraged fund is proportional to (x squared minus x) times NAV times the day's return. Every multiple except plain passive has a positive coefficient. A 2X long carries 2, while a 2X inverse carries 6. Yoon assigns 6 to a 3X long and 12 to a 3X inverse. Long and inverse funds therefore send orders with the same sign as the return. Their flows add.

Around 88 to 90% of Samsung Electronics and SK Hynix single-stock derivative assets are held in 2X long products. Another 11 to 12% sit in 2X inverse. Yoon calculates the effective multiplier as 0.9 times 2 plus 0.1 times 6, producing 2.4.

Cheng and Madhavan (2009) supply the starting point. Yoon extends their setup by inserting rebalancing demand into a linear price-impact equation, then solving for the fixed point. The result is the 1/(1 minus lambda theta omega L) amplifier and its associated breakpoint condition.

All further quantitative work uses Monte Carlo simulation: 3,000 paths covering 252 business days. The price-impact coefficient mean-reverts around long-run 15, with reversion speed 10, own volatility 15% and a floor of 1. Its correlation with the fundamental shock is either 0 or -0.60. Fund NAV compounds at the leverage multiple, allowing omega to move with price. The paper estimates no return panel. Its calibration uses Korea Securities Depository (Seibro) ETF statistics as of 9 July 2026 and KOFIA-disclosed KOSPI 200 weights, scaling one underlying to SK Hynix.

Annualized realized volatility moves from 34.94% in the control to 47.83% with the products when rho = 0. With rho = -0.60, it reaches 45.96%. Kurtosis rises from 3.0156 to 10.9053 in the first case, versus only 3.3272 in the second. The second correlation produces the worst mean maximum drawdown, at -42.38%, compared with -32.61% for the control.

How distant is 53 from 15?

The paper's descriptive work is persuasive. Korea had 1,152 ETFs with NAV of KRW 469.6455tn as of 9 July 2026. Derivative-type products accounted for 146 listings and KRW 55.4511tn. Leveraged funds within that group held KRW 29.4137tn, against KRW 3.4479tn for inverse funds, a ratio of 8.53 times. Over three months, the leveraged category received KRW 12.3795tn while the inverse category took in KRW 0.1774tn.

Leveraged shares outstanding stayed near 1.0bn from mid-April to mid-May 2026. They passed 1.2bn after single-stock products started listing on 27 May, then reached 1,961,505,000 by 9 July. The count climbed as the underlyings declined. Yoon attributes the pattern to authorised participants arbitraging a retail-driven market premium at zero creation fees.

Now apply the inequality. SK Hynix has about KRW 11.7tn of derivative-linked exposure, comprising KRW 3.5tn implied through index products and KRW 8.2tn single-stock, against a KRW 1,480tn market cap. Omega is therefore 0.0079. Samsung has KRW 10.9tn against KRW 1,622tn, giving omega of 0.0067. With L at 2.4 and execution on the same day, one divided by 0.0079 times 2.4 equals 52.7. Hence 53. The breakpoint follows directly from AUM share and the multiplier, placing lambda at more than triple its assumed normal level.

Yoon's footnote on effective closing liquidity matters more than the simulation here. Begin with a KRW 1,000tn free float and natural daily turnover of about KRW 10tn. Ten to fifteen per cent trades through the 15:20 to 15:30 auction, leaving just KRW 1 to 1.5tn of actual absorption capacity.

Deferral has an awkward result

Two findings carry more weight than the volatility headline. Deferring part of the rebalance until the next morning pushes return autocorrelation toward positive values. Yet the simulated realized-volatility curve continues to fall as the deferred share rises, since relief from price impact outweighs the added momentum. Daily tracking-error rules requiring 100% same-day execution would therefore maximize volatility.

The dangerous state follows a rally. On declines, NAV falls faster than the underlying, reducing omega and the absolute order size. In the median stress path around business days 90 to 100, the crash arrives with lambda between 10 to 12, below its long-run mean of 15, while several hundred billion won of mechanical sell orders strike a thinned book.

Swollen exposure at ordinary liquidity.

Inverse products also defeat the familiar sell-side case for balance. A 2X inverse fund has a coefficient of 6, versus 2 for the 2X long. Each unit of inverse AUM therefore triples the short-gamma shock rather than offsetting it.

The source of 47.83%

Use the simulation's own inputs in the amplifier. Omega of 0.008, L of 2.4 and lambda of 15 produce 1/(1 minus 0.288), or 1.40. Multiplying 34.94% by 1.40 gives 49.1%. The reported 47.83% sits close to that closed-form result, with mean reversion and the price-impact floor of 1 reducing it.

The formula at assumed inputs explains the control-versus-treatment gap. Long-run lambda of 15 is assumed, along with the -0.60 correlation between the fundamental shock and illiquidity. The 90/10 long-inverse split producing the 2.4 multiplier is assumed as well. The paper contains no empirical estimate of lambda from Korean order-book or closing-auction data. I found no regression, t-statistic or standard error anywhere in it.

Baseline theta equals 1, maximizing the loop. The simulation excludes primary-market creation and redemption, even though Yoon's account of AP arbitrage identifies creation as the force that expands AUM. As specified, it also includes no LP inventory response and no contrarian liquidity supply leaning against publicly known, predictable flow.

Abstract versus footnote

Yoon makes most of these qualifications himself. The conclusion says the simulated quantitative values should be read as indications of structural tendency rather than absolute benchmarks. A footnote acknowledges that Kyle (1985) logic places lambda above 50 near a theoretical extreme for mega-caps of this kind. It also supplies the defence: the grid extends beyond 50 to examine vulnerability during a flash-crash scenario, when ordinary LP function is paralysed and order-book depth collapses. The reference is the 2010 US flash crash.

That defence suits an extreme-scenario grid. The abstract reaches further, saying the study "provides evidence" that the limit order book's liquidity breakdown threshold declines steeply as AUM grows. Yet a threshold calculated as 1/(omega L) declines steeply because omega appears in the denominator. Extending the grid into a regime the author describes as close to a theoretical extreme leaves the result as arithmetic rather than evidence about Korean closes. We found no event study of a Korean close in the paper.

The useful prescription is narrow. Monitor omega times L against effective auction turnover instead of nominal market cap, and regard post-rally exposure as the risky state. One estimate of lambda from Korean auction data would change my view of the remaining claims. If normal-state lambda for these two names is anywhere near 30, the policy conclusions arrive early. At 5, they do not arrive at all.