Ten equal AI wealth providers would leave index tail selling unchanged in Kohli's simulation, compared with today's market where one provider holds 80.5% of usage. The measured difference is +0% (±5). Changing how the risk rules fire does move the result. The paper gives enough detail to rebuild that part. The headline fragility index is harder to test: its target is an agent-induced price deviation that no market reports. It also requires aggregate agentic flow, which nobody collects today. Kohli proposes collecting it through secure aggregation.
Inside Kohli's simulated market
An AI wealth platform consists of client agents, a few thousand in each simulated economy representing millions of clients. Every day, each agent builds a return view from four components: a shock common to all models, a provider-specific shock, a personal shock, and extrapolated trailing returns. Shrunk mean-variance then tilts its strategic allocation. A daily risk check follows, with half the agents using a volatility target. Thirty percent use a drawdown rule that halves exposure after losses exceed 15%.
Orders execute immediately. Aggregate flow affects prices through a square-root impact law applied to the outstanding imbalance, which decays 5% a day. The impact prefactor varies with exponentially weighted (EWMA) volatility.
The fundamentals come from block-bootstrapped returns for 20 S&P 500 constituents bundled with skfolio, covering 1990 to 2022 and 8,312 days. StatCounter supplies the consumer provider shares: the leading chatbot accounts for 80.5% of usage, an HHI of 0.66. For the enterprise scenario, Kohli uses Menlo Ventures API spend (40/27/21/12%, HHI about 0.28). His headline measure, SLaR99, is the 1% quantile of five-day agent-induced index moves in bps. Without agents, it is zero by construction.
At consumer concentration, the layer acts like about 2.0 independent investors. Enterprise concentration raises that to 2.7; perfect provider diversity gets it only to 3.5. SLaR99 is 62, 141 and 216 bps at agentic shares of 1%, 5% and 15%, implying an elasticity of 0.47 (±0.03). Feeding the same views through a monthly, staggered robo-adviser generates less tail selling. The agentic-to-robo ratio ranges from 1.47 to 1.90. At a 5% share it is 1.82 (±0.79). The uncertainty is substantial.
Why does provider diversity leave selling unchanged?
Views chiefly move money between stocks. Increasing tactical conviction from 0.8% to 3% tracking error raises rotation dislocation from 327 to 445 bps, while index liquidation barely changes: 195 against 186. Overlays, drawdown cuts and attention-driven execution drive the simultaneous reductions in the whole layer's exposure. Every volatility target reads the same realised volatility through a shared risk model.
Concentration actually has a negative coefficient on log SLaR99: -0.15 (±0.11) at baseline conviction and -0.34 (±0.14) at high conviction. Kohli argues that concentrated views create offsetting imbalances, absorbing common selling under concave impact. He tests that explanation. In the high-conviction economies, the coefficient is -0.34 (±0.17) with square-root impact and -0.10 (±0.17) with linear impact. The latter is indistinguishable from zero. For implementation, the portable finding is the null, no increase with concentration. The negative sign belongs to the square-root specification.
A poisoned provider is another matter. A 0.25 shock to the 80% provider causes a peak decline of 105 bps. Applied to one of ten equal providers, the same shock causes 19 bps, a blast-radius multiple of about 5.7.
The risk rule determines the useful intervention
The mitigation table offers the most usable findings. Execution spread over five days reduces SLaR99 by 24% (±6). Dispersing overlay parameters at strength 1.0 reduces it by 52% (±6). M7 combines both with a breaker: it trips when agentic flow reaches 20% of volume, then caps that flow at 10%. Across 18 paired seeds, M7 cuts SLaR99 by 63% (±4). With the other two measures already operating, the breaker binds on 0.7% of days.
The intervention has to fit the rule. As Kohli flags before testing it, the full model reverses a naive reading of Proposition 4. Consider economies with a 10% agentic share. When every agent uses only a volatility target, heterogeneity delivers -65% (±20) and slower execution -19% (±14). When every agent uses only a drawdown control, slower execution delivers -34% (±17), against -8% (±12) for heterogeneity.
Rebuilding this requires two judgment calls. Overlay heterogeneity at strength 1.0 spreads targets, risk-model memory and drawdown thresholds, but we did not find the dispersion distribution set out in the text. The released code must supply that detail. The other issue is seed noise: the 20%/10% breaker scores -35% in the mitigation table and -41% in the privacy section. Those are separate experiments, with 18 paired seeds in the mitigation table. A rebuild should expect variation on that scale.
Kohli is candid about cost. M7 changes welfare by +36 (±34) bps a year. Across 14 robustness variations, the estimates range from -103 to +273, with none distinguishable from zero. His conclusion is that M7 has no measurable cost; he explicitly declines to claim that it makes clients better off. Readers should keep that distinction intact.
A forecast waiting for flow data
The fragility index combines agentic flow volatility, public volatility and an impact prefactor, then divides by one minus an estimated loop gain. Across 240 random economies, it predicts second-half SLaR99 with a hold-out R² of 0.56. CV R² is 0.55, Spearman correlation is 0.80, and MAE is 39 bps against a median target of 87. Agentic share, the best conventional measure, reaches 0.23; agentic flow volatility alone reaches 0.35. Provider HHI scores -0.01, and view correlation scores 0.12.
Removing the loop gain leaves the index's score at 0.56, Kohli reports. He defends its inclusion on the grounds that gain becomes decisive near the critical share. The calibrated range never reaches that point. Even with linear impact and universal overlays, estimated gain gets only to 0.06. The denominator therefore remains untested.
The model's own amplification law supplies the index's form, and economies generated by that model supply its test. Kohli acknowledges the limitation: calibration covers the model's impact law and the range of economies in the ensemble. He proposes re-estimating the basis-point mapping when aggregate agentic-flow data become available. Nobody can take that step yet.
The 0.56 is a within-model result.
We could not backtest the index. It requires aggregate agentic order flow, and OHLCV volume cannot distinguish wealth-agent orders from other orders. Kohli proposes that platforms release noisy sums, combined through secure aggregation with differential privacy. With 10⁷ clients, a breaker using the private statistic matches the exact breaker (-41% at ε=0.5, 0.0 pp extra trips). With 10⁵ clients and ε=0.5, it delivers -24% (±15), accompanied by 23.4 pp of extra breaker days. Collection is solved in principle. Such data do not yet exist, and no real market reports the agent-induced price deviation used as the target.
We could build a local agent simulation and test heterogeneous thresholds, staged execution and participation caps on synthetic flows. Such a run would test our assumptions about behaviour and impact. It would leave both the index and crash amplification unvalidated. We have not run the paper's method.
COVID as a scenario
Replaying 2020 at a 10% agentic share adds 858 bps (±112) to drawdown. The largest induced decline is 939 bps. Slow bear markets show the opposite effect at the trough because agents de-risk early: the 2008 trough is 148 bps shallower, and the 2022 trough is 15 bps shallower (±100, indistinguishable from zero). Large induced declines still occur along the way, reaching 604 bps in 2008 and 213 bps in 2022.
M7 brings the 2020 figure down to 252 bps. Its interval, ±263, includes zero. These simulations all use 20 equal-cap large caps. With stronger liquidity withdrawal, a cap of 3 instead of 2, one of three baseline economies diverges without bound. All three M7 economies remain stable.
The overlay-design finding belongs in a platform's risk committee. The evidence that would change the verdict on the index is a supervisor calculating it from secure-aggregated platform flow and observing it track five-day tail moves.