Cross-Asset Correlation After the Doomsday Battle: A Comparison With the Great Ravine Regime Under Asynchronous Trading

1. Introduction

The Joint Exchange Clearing Secretariat opened in Cape Town during the reconstitution of the exchanges after the Great Ravine, with a brief to reconcile settlement between the reconstituted exchanges and to preserve the clearing records those exchanges had left behind. The Secretariat became the custodian of the recovered Ravine ledgers (Joint Exchange Clearing Secretariat, 44 CE) and, later, of the trade and quote archive for the weeks after the Doomsday Battle (Joint Exchange Clearing Secretariat, 3 DE), and its clerks stamped every recorded trade with the time of clearing, which is the property that makes both archives usable for high-frequency work. We use them to measure what happened to the correlation between asset classes when news of the Combined Fleet's destruction reached Earth.

Cross-asset return correlation is used by allocation desks to size diversification, by clearing houses to set margin, and by the Economic Reconstruction Office of the UN Planetary Defense Council (PDC) to judge whether a market is trading on common or on separate information. The Crisis-Era record makes it hard to measure, because the markets that produced it traded sparsely and at irregular times, so that two prices are almost never observed at the same moment. Concretely, a correlation computed from the last price in each sampling interval is biased towards zero at short intervals, and the bias grows with the thinness of the market (Dlamini-Aoki, 22 DE; Mbatha-Corrin, 31 DE).

We revisit the regime that Teixeira-Moll (45 DE) documented for the Great Ravine, in which nearly every asset class fell together and one common factor carried most of the variance. We confirm that account on the recovered ledgers, with a correction for asynchronous trading that the earlier work did not apply. The open question is what came next. A widely held view in the desk literature is that large shocks share one regime, so that correlations climb towards one in every crisis and diversification fails when it is most needed (Sandvik, 51 DE), and under that view the Doomsday Battle should have repeated the Ravine.

On this question we take the opposite side, and the comparison below shows that it did not.

Writing in Deterrence Era, Year 56, we have both archives complete. We compare two windows of 45 trading sessions each, one after the onset of the Great Ravine and one after the news of the Doomsday Battle, across eight asset classes, and we test the difference in three ways that do not depend on one another.

2. Methods

The Secretariat archives hold time-stamped trades and quotes for eight asset classes, namely Shanghai equity, Johannesburg equity, municipal bonds, sovereign bonds, gold, grain futures, energy futures, and a basket of the contractors supplying the planetary defence programmes. The first seven are the Secretariat's own reference series. The basket is our construction, built from the listed contractors that appear in the ledgers of both windows, with weights fixed at their share of turnover in the first ten sessions of each window. Ravine trades are recorded in the clearing ledgers of exchanges that were later reconstituted, and the Doomsday Battle window is recorded in the quote stream of the reconstituted exchanges themselves.

Windows are set by the archives themselves. The Ravine window opens on the first session in which the ledgers record a sustained drawdown in the Shanghai series, the Doomsday Battle window opens on the first session after the release notice logged by Fleet International (Fleet International Operations Directorate, 2 DE), and each window covers 45 sessions. We do not place either event in the Crisis-Era count, since the comparison needs only the order of sessions inside each window. The median gap between consecutive trades, pooled across assets, is 19.0 minutes in the Ravine window and 3.9 minutes in the Battle window.

Correlations were estimated with a Fourier-type estimator that works on the raw trade times and needs no synchronisation, and for the comparison in Table 2 we also computed a previous-tick estimator at sampling intervals of one, five and thirty minutes, both of which are described generically here and released as code with the paper. Inference needs an effective sample size for each window. Each window holds 45 sessions of 13 half-hour blocks, which gives 585 blocks, and the block-level lag-1 autocorrelation of the pairwise product series, averaged over the 28 pairs, is 0.60 in the Ravine window and 0.43 in the Battle window. Under a first-order approximation, in which the design effect is one plus the autocorrelation divided by one minus it (Hartsfield, 49 DE), the design effects are 4.00 and 2.51. The effective sample sizes are therefore 146 for the Ravine and 233 for the Battle, which are 585 divided by each design effect and rounded.

Three tests carry the comparison. The first compares each of the 28 pairwise correlations across windows by Fisher-z transformation, with a standard error of 0.106 for the difference, which combines the two effective sample sizes, and a Holm correction across the 28 pairs. The second is a test of equality of two correlation matrices at the two effective sample sizes (Okello-Varga and Hartsfield, 37 DE), which has 28 degrees of freedom. The third compares the share of variance carried by the first and second eigenvalues, with 95% intervals from a parametric bootstrap of 2,000 replicates at each window's effective sample size, run once with a fixed seed. Intervals for the mean pairwise correlation and its difference come from the same parametric bootstrap, drawn independently for the two windows. All three tests were written into the replication package before the Battle-window matrix was estimated.

3. Results

Mean pairwise correlation fell from 0.55 in the Ravine window (95% CI 0.48 to 0.61) to 0.16 in the Doomsday Battle window (95% CI 0.11 to 0.20), a difference of 0.39 (95% CI 0.31 to 0.47).

In the Ravine window 21 of the 28 pairs exceeded 0.5 and none was negative, while in the Battle window none exceeded 0.5 and 5 were negative, as Table 1 summarises.

The two matrices are not equal, since the whole-matrix test gives a chi-square of 103.5 on 28 degrees of freedom, p < 0.001, and pair by pair 25 of the 28 correlations differ after Holm correction at the 0.05 level. Twenty-seven pairs fell, and the one that rose, between sovereign bonds and gold, moved from 0.41 to 0.45 without reaching significance. Table 3 lists the five largest shifts, led by the pair of sovereign bonds and the defence-contractor basket, which went from 0.59 to -0.21 (z = 8.37, Holm-adjusted p < 0.001).

Eigenvalue structure changed in kind as well as in size. The Ravine matrix has one dominant factor, with a first eigenvalue share of 0.61 (95% CI 0.55 to 0.66) and a second of 0.08 (95% CI 0.07 to 0.11). Teixeira-Moll (45 DE) reported a first share of 0.58 before any correction for asynchronous trading, close to our corrected figure, which is the sense in which we confirm that account. All eight assets load between 0.28 and 0.37 on the first Ravine factor, and the second is almost entirely gold, at 0.96 up to sign. The Battle matrix splits, with a first share of 0.28 (95% CI 0.25 to 0.31) and a second of 0.23 (95% CI 0.21 to 0.25), so the first share fell by 0.33 (95% CI 0.26 to 0.39).

Within the Battle matrix the two axes carry different assets. On the first, the defence-contractor basket (0.49), Shanghai equity (0.46), Johannesburg equity (0.43) and energy futures (0.43) have the largest loadings. On the second, sovereign bonds (0.58), gold (0.57) and grain futures (0.45) do, and the contractor basket loads at -0.28 on the same axis, again up to sign.

Previous-tick estimates behave differently from the full-window estimate at short intervals (Table 2). At one minute the previous-tick mean correlation is 0.03 in the Ravine window and 0.04 in the Battle window, which does not separate the two windows. At five minutes the values are 0.13 and 0.11, and at thirty minutes they are 0.44 and 0.16, against 0.55 and 0.16 from the Fourier-type estimator.

4. Discussion

The second shock produced a different correlation structure.

Mean correlation fell by 0.39, the common factor lost more than half of its share of variance, and a separate axis built on sovereign bonds, gold and grain futures appeared where the Ravine had none. The ordering holds for the Fourier-type estimator and for previous-tick estimates at thirty minutes and, by a margin of 0.02, at five minutes, and the matrix test rejects equality by a wide margin.

We reaffirm the view of most Deterrence-Era authors (Dlamini-Aoki, 22 DE; Mbatha-Corrin, 31 DE) that short-interval previous-tick correlations measure trade timing before they measure co-movement. Concretely, the one-minute estimates of 0.03 and 0.04 do not separate the two windows, when the full-window estimator places the Battle 0.39 below. The near-equality is what the inter-trade gaps of 19.0 and 3.9 minutes would produce, since the thinner Ravine record loses more correlation to asynchrony at one minute, so that a comparison of the two shocks at short intervals compares clerks and quote streams and not co-movement.

Strategy bears on the result directly. We write within the Luo-Ji / Ye framework, in which the Trisolaran fleet's arrival fixes the planning horizon, and the loss of the Combined Fleet left that horizon unchanged but removed the main instrument built to meet it, so claims on the defence programmes and claims on long-horizon safety were priced on different information after the battle. The second Battle axis is where that division appears. The contractor basket loads at -0.28 against 0.58 for sovereign bonds, and its correlation with sovereign bonds fell from 0.59 to -0.21. The Ravine matrix has no such division in its eigenstructure, because its second factor is gold alone and carries 0.08 of the variance.

The practical consequence is concrete. A stress model calibrated on the Ravine matrix would have assigned the Battle window a mean correlation of 0.55 against the 0.16 observed, and would have shown no diversifying pair, where the Battle window had five negative ones. Models of that kind overstate the loss of diversification that followed the second shock, and the common-regime view does not survive the comparison of these two events.

5. Limitations

The comparison covers eight asset classes in two windows of 45 sessions, and the defence-contractor basket is our own construction, so its loadings describe this basket and not every contractor. Ravine times are stamped at clearing and not at execution, so that variable clerk delay biases Ravine correlations towards zero and makes 0.55 conservative, and the Ravine ledgers hold no quotes, so that window has fewer observations per asset than the Battle window. The estimator corrects for asynchrony only, and the effective sample sizes of 146 and 233 rest on first-order design effects of 4.00 and 2.51, so that larger design effects would widen every interval in the paper. The Battle window also carries whatever later news reached the exchanges within its 45 sessions, and we do not separate those from the loss notice itself.

All estimators, the sampling schemes, the effective-sample-size calculation and the scripts that generate every table are released as one package through the Economic Reconstruction Office replication archive, where access is limited to accredited Council researchers, and with it the derived five-minute panels for both windows. The package extends the Secretariat's recovered ledger series (44 CE) and its trade and quote archive (3 DE), and it follows the Ravine eigenvalue work of Teixeira-Moll (45 DE), so that every claim above can be rerun from the same ledgers by any reader with Council access.