Welcome to Explore DQT’s Proprietary Crypto Factor Models
WELCOME to explore our proprietary statistical/PCA factor models for cryptos! These are the first set of publicly released crypto factor models with rigorous mathematics and statistics, and also with numerous analytical and technological intricacies handled meticulously.
Recall for the equities market in TradFi, vendor factor models (e.g., Axioma or MSCI-Barra) provide indispensable tools for trading, investment, and modern portfolio management, including but not limited to the following areas.
- Correlation-based trading and investment of portfolios and indices, e.g., various bespoke equity baskets or index options based on correlations, best-of or worst-of, and so on.
- Optimal portfolio or index construction, hedging, and management, including index tracking and swaps
- Optimal portfolio Algos or electronic trading, including market-neutral or risk-neutral portfolio liquidation
- Multi-name market making systematic trading with optimal inventory control and futures-based hedging
- General risk management on market risks, VaR calculations, and Central Risk Book (CRB) management
All these apply equally to crypto trading, investment, and risk management!
At the very forefront of this exciting field, we are presenting two PCA-based statistical factor models:
- DQT-CRPT-FM-SH120F11, with horizons of 120 days/4 months (short-horizon or SH) and 11 factors, and
- DQT-CRPT-FM-LH240F13, with horizons of 240 days/8 months (long-horizon or LH) and 13 factors.
Recall for equities in TradFi, in order to achieve desired statistical stability, vendors typically settle for a horizon of 12 months and 20 PCA factors. Vendors often market PCA factor models as “statistical risk models.”
Before proceeding, we strongly recommend reading the section on Cautions and Limitations of Factor Models.
Disclaimer: Here or anywhere else on this site, any mention of external vendors and companies does not imply any outbound endorsement of them from DQT, nor any inbound endorsement of DQT from them. The nature of mentioning is purely for being professional and transparent.
Cautions and Limitations of Factor Models
- (Limitation of History) Factor models are calibrated from history, and Mark Twain said “History Doesn’t Repeat Itself.” For cryptos, the entire investment ecosystem seems forever evolving and far from reaching the quasi-equilibrium observed in the stock/equity market. One should be cautious about projecting the future using the past, as always.
- (Illusory Nature of Hidden Variables) The second half of Mark Twain’s comment is “But It Often Rhymes,” the very spirit that invigorates factor models. Beyond all the ups and downs, and convergence and divergence, it is hoped that the crypto universe and its dynamics at least share a set of hidden driving factors, or “rhythms.” Accepting and utilizing the notions of “hidden” variables, however, requires the same amount of caution because they are purely conceptual and can never be directly observed.
- (Ignorance of Jump Risks) The basic assumption supporting factor models is normality (or Gaussianity) of coin returns. Consequently, using factor models to project VaRs and market risks may suffer underestimation as there are no built-in jump risks. From the infamous incidents of TerraUSD to FTX in 2022, the costly lesson has taught us that the hidden tigers could jump out anytime.
- (Educated Decision) But to forecast the strength of the tigers and their attacking timelines is perhaps even more illusory. It does not necessarily carry less model risks to handcraft the non-stationary dynamics of a yet-to-be-settled asset class. Therefore, one could still turn to the old wisdom – making educated decisions based on the minimalist assumptions about the past.
- (About PCA) Similar to the more matured equity asset class, there are two approaches to constructing factor models: fundamental vs. PCA (principle component analysis). DQT expects a waiting time of at least another several years before fundamental crypto models could prevail meaningfully. Construction of technical factors like size or liquidity is relatively easier. But the most important fundamental factors equivalent to sector and industrial groups or balance-sheet financials are much foggier in the near future. PCA is more phenomenological and does not require fundamental details of any coin project. It is relatively handy to construct and maintain, which is why in-house equity factor models in TradFi investment banks are mostly PCA-based. PCA is a powerful analytic tool to compress massive data and capture core trends, and to efficiently weed out idiosyncratic noises. Beyond that, PCA perhaps should not be overinterpreted.
Short-Horizon Model: DQT-CRPT-FM-SH120F11
The short-horizon factor model has the following attributes
| Factor Types | #Factors | Covered Universe | Calibration Horizon |
|---|---|---|---|
| 1Market + 10PCA | 11 | About 170~180 coins | 120 days (4 months) |
The covered universe remains stable, especially for all the major coins. The algorithm automatically updates the universe every month or quarter, mainly based on the rolling dynamics of market capitals and trading volumes across the entire crypto landscape. Currently the number of factors is based on expert judgement, and the single market factor is constructed by a proprietary algorithm. Please read the White Paper for more details.
Chart I – Entropy of the Crypto World
The entropy metric exemplifies DQT’s deeply innovative approach to even traditional financial practices. In Tradfi, no leading vendors of equity factor models have defined, proposed or published such a metric.
Based on Shannon’s information theory and the way a factor model is constructed, we have discovered a unique way to define the entropy of the crypto market, i.e., a single index that can reveal whether the crypto market as a whole is more diverging or converging (or “flocking”). Scaled between 0 and 100, a high entropy index (e.g., 75) indicates that individual coins are more diverging or tend to “doing their own individual things,” while a low entropy index (e.g., 30 ) may reveal that they are more converging or “flying as a coherent flock,” so to speak.
As emphasized earlier in the Cautions section, all factor models and derived analytics are based on history. Their prediction power should be assessed cautiously. At the minimum, they offers a valuable diagnostic reading.
To benchmark, also plotted are the correlations between bitcoin and ethereum (blue line) against the daily entropy line (red line). The correlation window coincides with the model data window.
Chart II – Total Volatilities (Vols), Systematic Vols, and Idiosyncratic Vols
Plotted in this chart are the total vols (blue), systematic vols (green), and idiosyncratic or specific vols (red) of individual coins under the short-term factor model. These are all daily vols (in percent), and can be easily annualized by a multiplier of 19 ( square root of 365). The systematic vol (green) measures the portion of the total vol (blue) that can be captured by the systematic factors. Only the specific vol is independent information and the other two can be derived. Please read the White Paper for more details. (Format: non-overlapping stacking bars.)
Chart III – Ratios of Specific Variance/Total Variance
Plotted in this chart are the ratios (in percent) of specific variance over total variance for individual coins.
Variance is the squared vol. The chart gives an empirical observation that coins with ratios above 40% are highly volatile in their own specific or idiosyncratic ways.
Long-Horizon Model: DQT-CRPT-FM-LH240F13
The long-horizon factor model has the following attributes
| Factor Types | #Factors | Covered Universe | Calibration Horizon |
|---|---|---|---|
| 1Market + 12PCA | 13 | About 170~180 coins | 240 days/8 months |
The covered universe in general remains stable, especially for all the major coins. The algorithm will automatically update the universe every month or quarter, mainly based on the rolling dynamics of market capitals and trading volumes across the entire crypto landscape. Currently the number of factors is based on expert judgement, and the single market factor is constructed by a proprietary algorithm. Please read the White Paper for more details.
Chart I – Entropy of the Crypto World
The entropy metric exemplifies DQT’s deeply innovative approach to even traditional financial practices. In TradFi, no leading vendors of equity factor models have defined, proposed or published such a metric (so far).
Based on Shannon’s information theory and the way how a factor model is constructed, we have discovered a unique way to define the entropy of the crypto market, i.e., a single index that can reveal whether the crypto market as a whole is more diverging or converging (or “flocking”). Scaled between 0 and 100, a high entropy index (e.g., 75) indicates that individual coins are more diverging or tend to “doing their own individual things,” while a low entropy index (e.g., 30 ) reveals that they are more converging or “flying as a coherent flock,” so to speak.
As emphasized earlier in the Cautions section, all factor models and derived analytics are based on history. Their prediction power should be assessed cautiously. At the minimum, they offers a valuable diagnostic reading.
To benchmark, also plotted are the correlations between bitcoin and ethereum (blue line) against the daily entropy line (red line). The correlation window coincides with the model data window.
Chart II – Total Volatilities (Vols), Systematic Vols, and Idiosyncratic Vols
Plotted in this chart are the total vols (blue), systematic vols (green), and idiosyncratic or specific vols (red) of individual coins under the long-term factor model. These are all daily vols (in percent), and can be easily annualized by a multiplier of 19 ( square root of 365). The systematic vol (green) measures the portion of the total vol (blue) that can be captured by the systematic factors. Only the specific vol is independent information and the other two can be derived. Please read the White Paper for more details. (Format: non-overlapping stacking bars.)
Chart III – Ratios of Specific Variance/Total Variance
Plotted in this chart are the ratios (in percent) of specific variance over total variance for individual coins.
Variance is the squared vol. The chart gives the empirical observation that coins with ratios above 40% are highly volatile in their own specific or idiosyncratic ways.
- “Linear Factor Models,” a friendly online page by Nobel Laureate Prof. William F. Sharpe at Stanford.
- “Factor Models“, MIT’s Open Course, Math 18.S096, by Dr. Kempthorne.