Correlations are an easy technique to assess if a strategy is exposed to any given asset.

If the correlation is low, the strategy and the asset are unlikely to be related.

Unfortunately, the opposite is not true. If assets A and B are correlated, a fund may show an exposure to A simply because it is invested in B, while not invested in A.

Since many financial assets are correlated, correlations are often spurious.

As a result, correlations should be used with caution:

• They should be used as simple indicators, not conclusions.

• Correlation matrices give a good idea of co-exposures within groups of assets or strategies.

• Correlations are useful on a relative basis, to compare different strategies, e.g. Strategy 1 is much more correlated to asset A than strategy 2.

• Correlations are great as inputs to other techniques, notably Multinomial Logistic Regressions (MLR).

Pyrite has precalculated the correlations of any strategy or any fund to each of the ~2,000 time series (assets, styles, factors, economic indicators, currencies...), in 2Y, 3Y and 5Y horizons.

Is this manager invested in cotton? A uni-variate regression of the strategy's returns against cotton's returns will provide you with an explicit answer:

• The p-value: whether the exposure is statistically significant. If the p-value is below 0.05, there is only 5% chance that the strategy's returns are so closely related to cotton's returns.

• The beta: it is the manager's leverage if it were holding only this asset. If the manager gains 2% when the asset gains 1%, the beta will show this leverage of two.

• The filtered beta combines the two. It gives the beta only when p-value is below 0.05. It is a useful metric to list the exposures of a given fund.

• The R² measure the overall fit of the regression.

Uni-variate regressions are pre-calculated for all funds and strategies in your universe, against all 2,000 time series currently available.

The regressions are deployed in 2Y, 3Y and 5Y horizons.

Assets are correlated. If assets A and B are correlated, and your fund is invested in A but not in B, its mono-variate regressions will show exposures to both A and B. The apparent exposure to B is a side-effect of the exposure to A.

The multi-variate regression against A and B simultaneously tells you the likely exposure to both at the same time.

The multi-variate regression technique is valuable for groups of assets of fixed composition. Pyrite deploys the technique against:

• The main styles (10 exclusive styles).

• The Fama-French-Carhart factors.

• The Fung-Hsieh factors.

• Pyrite's own set of alternative factors (TED-spread, volatility, BTC...)

• The four sets of market factors are also analyzed together, in a single PCA regression (see PCA regressions below).

• The multi-variate regression is also deployed within the multi-step regressions.

The results:

• Betas, filtered betas, p-values indicate the likely exposures and quality metrics.

• The R² indicates how well a strategy is explained by a given set of factors.

• The Alpha is an indicator of the manager's performance.

Pyrite has precalculated all these regressions for the sets of input factors above, in 2Y, 3Y and 5Y horizons.

How do you regress a strategy against 30 assets with only 24 returns?

In theory, you can't. Practically, you can, to some extent.

The first solution is to decompose into subgroups and analyze in steps. We deploy this approach to detect the Main Asset Class exposures:

1. We regress against a low number of asset classes (equities, bonds, commos)

2. If commodities are detected, we regress against several commodities (precious metals, oil & gas, agriculture...), again in small numbers.

3. We then list all the assets that have been detected across all these preliminary regressions (based on p-values).

4. We run a multi-variate regression against those detected assets.

The results give you:

• The assets likely traded (p-values, betas, filtered betas).

• The R² tells you if the fund is well explained by main asset classes.

• The Alpha highlights the manager's skills beyond asset performance.

The technique is calculated with 2Y, 3Y and 5Y returns, and a fixed set of 14 leading assets.

Unfortunately, the selection of assets depends on each strategy at the specific moment. The R² and Alphas are therefore comparable across the whole universe, but the individual regression parameters are not.

How do you regress a strategy on 30 assets with only 24 returns?

In theory, you can't. Practically, you can, to some extent.

The second solution is to leverage the power of Principal Component Analysis (PCA).

How it works

1. Decompose. The selected series are reduced to their principal components. Pyrite keeps only the components that stand clearly above statistical noise, usually a handful.

2. Rotate. A Varimax rotation turns each component into a recognizable group of assets, such as developed-market equities or energy, so that results can be read.

3. Regress. The strategy is regressed on these few components, a regression the data can support.

4. Project back. The exposures to the components are translated back into a beta for each original asset.

The results: a beta for every asset and every component, the R², the alpha, and quality diagnostics on the fit.

Where Pyrite uses it

Main Asset Classes: Precalculated for every fund and strategy against the same [14] leading assets as the multi-step regressions, in 2Y, 3Y and 5Y horizons. Two methods on the same group of assets: where they agree, the exposure is robust; where they differ, it deserves a closer look.

Market Factors: Three separate multi-variate regressions (on the Fama-French-Carhart, Fung-Hsieh and Pyrite's alternative factors) are grouped together into a single PCA regression, alongside the separate regressions on each set. Factor families overlap; the combined regression shows which exposures survive once the overlaps are removed.

On demand: Choose your own set of assets, and ask. The Pyrite engine calculates the PCA regression and AI reports every beta. See The power of AI, part 2.

PCA regressions are precalculated or available in 2Y, 3Y and 5Y horizons.

Both mono- and multi-variate regressions give a linear exposure coefficient (beta) to asset(s).

Unfortunately, an explanatory model based on such regressions may give spurious results if the asset itself has atypical numbers (data error, large variations...)

Standardizing series is not a perfect solution, since abnormal returns (errors) can still impact regressions.

Logistic regressions limit the impact of abnormally large returns, by constraining results between bounds, with the use of the embedded sigmoid function.

The technique is also very useful to assess probabilities, where results must be within [0,1].

Pyrite deploys this technique in its multinomial version, in 2Y, 3Y and 5Y horizons.

The Multinomial Logistic Regressions (MLR) technique assigns probabilities to several mutually exclusive outcomes, based on any input parameters.

It is critical to calculate probabilities of mutually exclusive situations, notably style or geographical focus.

Pyrite has created a classification of 10 mutually exclusive styles (Long/Short equities, CTA, Emerging, MultiStrat...) and deploys the MLR technique with multiple inputs to provide multiple style quantifications of any given fund.

For example: CTAs rarely have a Sharpe above 1. If a fund has a Sharpe of 3.5, it is most likely a multi-strategy (whose diversification permits such performance).

In a similar fashion, max drawdowns, return kurtosis, CVaR or MPPM can all be indicators of a fund's strategy.

By deploying an MLR model, on a fund's entire set of performance and risk metrics, and trained on all fund strategy disclosure statements, Pyrite created an objective assessment of the strategy's likely styles. In the example above, it could indicate 4% chance of being a CTA, 9% a LS equity and 73% chance of being a multistrat.

Pyrite deploys this technique on a dozen sets of input parameters to analyze and cross check any fund's stated style.

Pyrite deploys the Multinomial Logistic Regression (MLR) technique against a dozen sets of inputs.

• Each deployment gives an independent quantitative and objective indicator of a strategy's most likely style.

• Pyrite aggregates the different results into a global style determination.

• This aggregate model is a solid indicator of the fund's most likely style.

• The dispersion of the dozen models has significance as well. A fund that is detected as a CTA based on performance should not be detected as Global Macro based on exposures to Main Asset Classes. The different methods should generally be congruent.

Pyrite deploys the MLR technique to determine fund style against all the following sets of inputs:

1. Performance and risk metrics.

2. Correlations to investment styles.

3. Betas in regressions to styles.

4. t-Stats in regressions to styles.

5. Correlations to Main Asset Classes.

6. Betas to Main Asset Classes.

7. t-Stats to Main Asset Classes.

8. Correlations to Main Market Factors.

9. Betas to main Market Factors.

10. t-Stats to main Market Factors.

11. Overall model.

These sets of probabilities are pre-calculated for all strategies and funds, in 2Y, 3Y and 5Y time-horizons.

(In progress)

In the same fashion, Pyrite deploys the Multinomial Logistic Regression (MLR) technique against several sets of geographically sensitive inputs to determine the most likely geographical focus of a given fund.

We use as inputs:

• A set of geography-sensitive equity indices.

• A set of geography-sensitive fixed-income indices.

• Correlations to these assets.

• The outputs of the multi-variate regressions (t-Stats, betas...) to these assets.

• An overall model.

This model will be deployed in the near future.

All the metrics and results above (correlations, betas, R², probabilities...) are provided as raw values. They are also provided in percentiles in comparison to

1. all other funds in the universe, as well as

2. to all other funds in the same stated style.

These two extra dimensions offer interesting insights. For instance, a fund's Sharpe Ratio is a key piece of information in itself, but styles and periods have a significant impact on that same assessment:

• A Sharpe of 5 is suspicious for a CTA, but not so much for a structured credit fund. Style matters.

• A 50% Max Drawdown impacts a portfolio, whatever the style. Investors need to compare MDDs across all fund strategies, independently of styles. Cross-sectional comparisons sometimes matter more.

• A Sharpe of 1 for a CTA may be likely during sustained trends but would be surprising at a market inflection point (CTAs are generally long momentum). Timing matters. Both the time-chart and the benchmarking inside the stated style give valuable comparisons to investors.

Pyrite pre-calculates the percentiles of every metric, both across the universe of all funds, and the given fund's stated style, for every strategy and fund.

Percentiles are calculated in 2Y, 3Y and 5Y horizons.

Note: ranking and distribution are sometimes better explained by charts. They let you know where your fund is in a distribution, or if a metric tends to be lognormal or not.

At the last count, Pyrite offers ~480,000,000,000 pre-calculated metrics. Half a trillion is a lot of risk and exposure metrics. An awful lot.

No website using tables can display all of this; you need queries.

And even with queries, one can only sift through so much. Unless you have an SQL engineer sitting next to you, even querying that much data is difficult.

Pyrite has leveraged the power of AI to help you. You can ask the question in plain English; AI will convert your question into database queries and provide the answer you need for just a few tokens.

For example: let's say you have a triple market conviction, that

1. oil is underpriced,

2. rates will go down,

3. and the euro is to too cheap to sterling.

How can you identify which funds hold those views? Searching through your emails will be challenging.

An AI query can handle the selection very easily; you only need to ask which funds hold these exposures (filtered betas). AI will write the query, search the database, and provide you with the result in a few seconds.

You can even ask AI to sort the funds by Sharpe, or ask for the chart of their historical performance over the last three years. AI will execute the request in seconds.

AI can calculate.

How many metrics can you derive from 480 billion data points? Far more than anyone could precalculate. When the number you need is not in the database, ask for it, and the AI computes it from the data:

• The average Sharpe ratio of CTAs that trade copper.

• A fund's percentile within a peer group you define.

• Each answer states the metric, the period and the group of funds used, so you can see exactly what was compared.

We do not charge for computation time, so AI calculations stay within simple arithmetic.

With one exception: PCA/Varimax regressions. Choose your own set of assets and ask, for example: "Run a PCA regression of this fund on gold, silver, copper, Brent and the S&P 500, over 3 years." The Pyrite engine calculates the regression, and the AI reports every beta, the R² and the alpha.