Towards Financial World Modeling

Humzah Merchant; Alec Guthrie; Simon Mahns; Randall Balestriero; Bradford Levy

cs.LGOct 6, 2026

Towards Financial World Modeling

Authors: Humzah Merchant, Alec Guthrie, Simon Mahns, Randall Balestriero, Bradford Levy

Organizations: University of Chicago · Johns Hopkins University · Brown University

Abstract

Building a world model requires a state representation useful for planning and decision-making---potentially over tasks unknown at training time. In the context of financial markets, planning and decision-making may require a model to reason about market-wide conditions, asset-specific expected returns, liquidity, volatility, and cross-asset relationships. Yet financial representation learning has largely been evaluated on individual predictive tasks, oftentimes on a single time period using comparatively narrow datasets. We address this through three primary contributions. First, we introduce Market-1T, a dataset containing nearly one trillion observations across U.S. equities from 2008 to 2025 at 1 Hz resolution. Second, we develop and implement a rigorous evaluation protocol. Third, we conduct a systematic large-scale study of financial representation learning, comparing 18 encoder-training strategies across nearly two decades of market regimes. We evaluate learned representations both by their predictive utility on common finance tasks and through probes of latent structure. We find that encoders with similar predictive performance can organize market state very differently. Collectively, we establish a foundation for training and evaluating financial market representations in support of world models such as DINO-WM, V-JEPA 2, and LeWM.

Figures & tables

Figure 1 : Paper overview. Left: We systematically study how the pre-training objective and data augmentation shape the organization of the latent space and performance on downstream tasks such as return, volatility change, and spread change prediction. For example, matching views of the same stock at different times and resolutions yields latents that cluster tightly by firm but hardly at all by day, even though day-level structure, i.e., factor realizations, is arguably more important. Right: On tasks such as return and volatility prediction, ViT-Tiny outperforms larger ViTs while fixing the number of training FLOPs. Further scaling results are presented in Figures 6 and 10 .

Figure 2 : Rank IC for the same encoder configuration and training setup across Market-1T ’s 2008–2025 span. Performance varies substantially across market regimes, thus evaluation on narrow slices of time can lead to biased estimates of model performance with respect to it’s true performance. We address this by using a randomly sampled set of 32 months.

Figure 3 : We evaluate five different augmentation strategies using LeJEPA. As shown in Tables 2 and 3 , each augmentation learns different invariances about the market, e.g. same stock, diff. view primarily encourages memorization of firms through bid- and ask- size distributions, while cross-stock and cross-stock, same-industry emphasize more general market movements.

Dataset	Span	Min. Resolution	Universe / Coverage	Access
Market-1T	2008–2025	1 sec	All U.S.-traded equities; consolidated SIP NBBO + trades	Public
Kronos	–	1 min	45 exchanges; multiple asset classes	Partial
DELPHYNE	–2019	5 min	Global multi-asset; 15,817 securities in intraday-bar corpus	Proprietary
Qlib / Alpha158	2008–2020	Daily	CSI300 Chinese A-shares (canonical benchmark)	Public
FI-2010	10 days (2010)	Event-level	5 Nasdaq Nordic stocks; 10-level LOB	Public
LOBSTER / TotalView	2007–present	Event-level	Nasdaq; reconstructed order book up to 200 levels	Licensed

Table 1 : Comparison of representative financial market datasets and corpora.

Figure 4 : Predictive information retained by learned representations as a function of the number of samples used to fit the ridge probe. Probe performance improves substantially with sample size, indicating that large probe-training sets are required for reliable evaluation. LeJEPA ( 8 ) with time warping is among the strongest self-supervised methods. Full results are reported in Table 2 .

	Return	Volatility	Spread
Supervised
Return	$0.0272$ ( $0.0269$ )	$0.0695$	$0.1305$
Vol	$0.0197$	$0.0883$ ( $0.0891$ )	$0.1480$
Spread	$0.0178$	$0.0762$	$0.2517$ ( $0.2519$ )
Multihead	$0.0311$ ( $0.0317$ )	$0.0941$ ( $0.0952$ )	$0.2455$ ( $0.2441$ )
LeJEPA ( 8 )

Table 2 : Forecasting rank IC at the 15-minute horizon from a ridge probe, averaged over 32 eval months; a supervised arm’s own head IC follows in parentheses, red cells fail to beat the untrained Random ViT floor, and green marks the best two non-supervised arms per target. Finance baselines and TSFMs presented in Table 4 .

Figure 5 : Decomposition of variance for our tasks between random seed and month (

10\times 10

) along with the Random ViT baseline. We find that month contributes to 97.2%, 98.9%, and 99.9% of variation for the three tasks, respectively. Therefore we subtract off the Random ViT mean when calculating standard errors, substantially reducing month-to-month variance (Figure 9 ).

Figure 6 : We find that for every task and every amount of FLOPs the smaller models appear a better fit. On all three tasks, the ViT-Tiny beats out a ViT-Base that has been trained to 10

\times

the flops. We further expand the scaling in Figure 10 .

Figure 7 : We evaluate decay by comparing models to the same model trained closer to the evaluation date to control for change in the intrinsic difficulty of the task over time. We see that it is small but present on volatility change and spread change, relative to the base IC (

\approx 20\%

of the base IC on volatility change and

\approx 10\%

on spread change, over five years.

Panel of Table 3 — Table 3 : Evaluating the organization of learned market state. Top: We embed observations from six firms across three randomly selected industries within the same evaluation month and test whether proximity in representation space reflects shared day, firm, and industry structure, scored as T1–T4. Bottom: We estimate statistical factors from realized returns and measure both how well individual factor loadings can be decoded from the embeddings (F1) and how much of the factor subspace is captured by their principal directions (F2). Table: T1–T4 give the top-1 rate as a multiple of chance and the mean percentile rank of the target (lower is better), while F1 and F2 give a single score for which higher is better; green marks the top three trained methods in a column, and red values are no better than the untrained Random ViT.

Panel of Figure 8 — Figure 8 : Summary of Results: We rank all 19 encoders (including the Random ViT) from 1 to 19 on each task and show the Spearman correlation between every pair of task rankings, with bold marking $p<0.05$ (top). Averaging each encoder’s ranks within the forecasting and organization tasks shows the two are unrelated ( $\rho=-0.19$ ), with TimeMAE and Supervised Multihead drawing the efficient frontier.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 9 : If we subtract off the Random ViT baseline for each month, we can substantially reduce the amount of variation that is from the choice of month, allowing for better comparisons. In practice, we can use this to adjust our standard error calculation or make a more fair comparison between performance on different months.

Figure 10 : We train a single supervised multihead encoder on 2008-2017 and evaluated it on January 2018, compared to a standard multihead encoder. This run goes takes the top-end from ViT-Tiny from

3.33*10^{17}

3.33*10^{19}

FLOPs as compared to Figure 6 . Since the multihead encoder normalizes the gradient between all three tasks, it uses 3

\times

the FLOPs per data sample. We see that for return and volatility change the model does not yet saturate.

	Return	Volatility	Spread
Supervised
Return	$\mathbf{0.0272}$ ( $0.0269$ )	$0.0695$	$0.1305$
Vol	$0.0197$	$\mathbf{0.0883}$ ( $0.0891$ )	$0.1480$
Spread	$0.0178$	$0.0762$	$\mathbf{0.2517}$ ( $0.2519$ )
Multihead	$\mathbf{0.0311}$ ( $0.0317$ )	$\mathbf{0.0941}$ ( $0.0952$ )	$\mathbf{0.2455}$ ( $0.2441$ )
Classical forecasting models

Appendix

Table 4 : Forecasting rank IC at the 15-minute horizon for classical baselines, beside the supervised arms of Table 2 , averaged over evaluation months. The baselines are read off the normalised view tensor the encoder receives , not the raw order book. Based on the results on the Optimization Set, the frozen TSFMs were nearly uniformly optimal at the last layer for all three tasks. Supervised cells give the ridge probe with that arm’s own head IC in parentheses. Green marks the best two strongest supervised arms and the two strongest baselines.

Figure 11 : Sweeping all layers for the latent-space evaluations for the TSFMs. Stars show the optimal layer on the five month optimization set. We note that is not an entirely fair comparison, as all other methods are only presented on the last layer, and that other methods (both the default supervised models, and the SSL methods) will likely also have internal layers where performance is stronger than the last layer for each task.

	Width	RankMe
Supervised
Return	$384$	$2.8\pm 0.1$
Vol	$384$	$3.0\pm 0.0$
Spread	$384$	$3.5\pm 0.2$
Multihead	$384$	$3.7\pm 0.1$
LeJEPA [ 8 ]

Appendix

Table 5 : RankMe [ 17 ] of each frozen embedding on the latent suite’s full-day panels of Table 3 , read at the same mean pooling, mean

\pm

SE over the eval months, beside the embedding width that bounds it. RankMe counts how many directions the embedding spends its variance on; it is not a score – the supervised models, the strongest forecasters, have the lowest – and a width far from 384 puts a row off the rest of the column’s scale. The frozen TSFMs are read at their last layer with the nine per-channel states averaged, the prediction evals’ readout; Figure 12 sweeps every layer.

Figure 12 : Sweep of RankMe across TSFM layers.

\pm

1 SE bands are narrower than the line width.

Universe	Selection	Weighting	Risk model	EFQ	Rebalance
All	All	Equal	Diagonal	$0\%$	Every decision
Tightest 50%	Quintile	Inverse vol.	Shrunk sample	$25\%$	Daily
Tightest 25%	Decile	Min. variance	Ledoit–Wolf [ 27 ]	$50\%$
	Long-only	ERC [ 32 ]	Embedding	$70\%$
		Rank		$88\%$
		Mean–variance [ 33 ]		$100\%$

Appendix

Table 6 : Six of the many choices that lie between a forward return prediction and a Sharpe ratio, and the options we sweep at each. Their product, less combinations that are degenerate by construction, gives the

2{,}448

configurations we use to demonstrate how wide a spread these choices induce. Execution quality is EFQ, the effective half-spread actually paid over the half-spread quoted when the order was sent [ 28 ] , at

0\%

a midpoint fill and at

100\%

the whole quoted spread.

Figure 13 : Annualized Sharpe of a dollar-neutral cross-sectional book as a function of EFQ, the effective-to-quoted half-spread ratio, where

0\%

is a midpoint fill and

100\%

pays the entire quoted spread. Once per day at 13:45 ET we take every name whose forecast edge exceeds the round trip it would actually be charged at that EFQ, equal-weight the long and short legs, and either unwind after fifteen minutes (left) or hold to the 16:00 ET closing auction (right); the shaded band is the EFQ range [ 28 ] measures for orders routed to the market rather than sold to a wholesaler,

55\%

for direct market access up to

88\%

on NYSE. We sweep past

100\%

because an order larger than the quoted depth walks the book, and because a signal others are trading moves the quote away before the order completes.

	IC vs. Sharpe		Sharpe range across each choice
EFQ	$r(\mathrm{IC},\bar{S})$	$\bar{r}(\mathrm{IC},S)$	Rebalance	Selection	Universe screen	Weighting	Risk model
$0\%$	+0.92	+0.52	2.3	1.6	1.6	2.4	0.4
$25\%$	+0.90	+0.49	4.9	2.3	2.2	1.4	1.4
$50\%$	+0.77	+0.41	11.9	6.1	5.7	1.3	2.2
$70\%$	+0.64	+0.36	17.2	9.1	8.4	2.9	2.7
$100\%$	+0.46	+0.29	24.7	13.3	11.9	5.5	3.4

Appendix

Table 7 : A Sharpe ratio is a property of the harness as much as of the forecast, and both halves of this table are read down the same axis of execution quality. EFQ is the effective half-spread actually paid over the half-spread quoted when the order was sent [ 28 ] , at

0\%

a midpoint fill and at

100\%

the whole quoted spread. Left:

r(\mathrm{IC},\bar{S})

correlates each method’s IC with its Sharpe averaged over every harness at that execution quality;

\bar{r}(\mathrm{IC},S)

correlates them inside one harness and then averages that correlation over harnesses.

r(\mathrm{IC},\bar{S})>\bar{r}(\mathrm{IC},S)

Right: how far each remaining choice moves the annualized Sharpe, over 18 methods and the 408 harnesses at each execution quality. The choice of backtest moves the score much more than the choice of model.

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