EntropyPooling/README.md

# EntropyPooling

Entropy pooling in native MQL5: keep every historical scenario, change only
the probability attached to each one, and let today's volatility and your own
views decide the weights instead of the length of a lookback array.

Companion code for the MQL5 article: https://www.mql5.com/en/articles/24757

## What it does

A 250-bar volatility or a historical VaR is a probability vector over the
history: weight 1/250 on the last 250 bars and exactly zero on everything
older. That choice forgets stress during calm periods, and it cannot take in
information the history does not contain. Entropy pooling, from Attilio
Meucci's *Fully Flexible Views*, replaces it with an explicit one. Choose the
probabilities closest to a prior, in relative entropy, that satisfy what you
want to be true: that today's volatility regime applies, that USDJPY
volatility is 50% higher, that a Swiss franc shock has at least a 1% chance.

`CEpSolver` solves the problem through its dual, so it works on one
multiplier per view rather than one unknown per scenario. The posterior is an
exponential tilt of the prior, found by projected Newton with a backtracking
line search, and inequality views are handled as bounds on their multipliers.
Each multiplier is also a price: the relative entropy a view costs per prior
standard deviation of its target, which shows which statement is fighting the
data hardest. `CEpViews` turns means, spreads, tail probabilities, volatilities
and correlations into the matrix the solver needs, re-solving volatility and
correlation views as second moments until they hold on their own terms.

The most useful statement for risk is not a subjective view at all. It is a
single mean view on a trailing-volatility state, solved exactly by a bracketed
scalar Newton iteration. On its own that condition collapses at the edge of
history: on 20 March 2020 a Gaussian kernel on the same state answers with 4
effective scenarios. `EpConditionState` gives conditioning a budget, pulling
the target back towards the prior mean until a minimum number of effective
scenarios survives, and reports the target it actually used.

`EP_Checks.mq5` tests the library against closed-form results on 200,000
Gaussian scenarios: the exponential tilt, its relative entropy of z^2/2, the
Black-Litterman mean, the unchanged covariance, the marginal cost against a
finite difference, and the budget. `EP_WalkForward.mq5` forecasts a five-pair
basket's next-day VaR and ES on 3,655 days using only the rows before each
one. Budgeted conditioning has the lowest joint VaR-ES loss and calibrated
coverage, beats the rolling window significantly, and improves on its own
decay prior only modestly, at the edge of significance. Against a Gaussian
kernel it is not significantly better: a mean and variance view on the state
is mathematically a kernel. What entropy pooling adds is that conditioning and
any number of views are one problem with one solution.

`EP_Sizer.mq5` holds the basket at a fixed daily expected-shortfall budget
sized by `EP_ViewCost`'s forecast. From 2011 to 2025, realised ES over budget
was closer to 1 under conditioned sizing than under the rolling window in 13
of 15 years, with a mean miss of 0.103 against 0.218. The window overshot by
more than 20% in the years when stress followed calm, 1.68 times the budget in
2020, when it entered March holding 1.70 times equity in gross notional.

## Layout

```
Include/EntropyPooling/Scenarios.mqh      joint scenario matrix: shared bar times, book and state columns, replay
Include/EntropyPooling/Probabilities.mqh  priors (uniform, rolling, decay, kernel), effective scenarios, relative entropy
Include/EntropyPooling/MinRelEntropy.mqh  CEpSolver: dual Newton solver with equality and inequality views
Include/EntropyPooling/Views.mqh          CEpViews, the scalar state tilt and budgeted state conditioning
Include/EntropyPooling/Posterior.mqh      weighted moments, exact weighted VaR and ES, blending, indicator buffer map
Scripts/EP/EP_Checks.mq5                  closed-form checks on synthetic Gaussian scenarios
Scripts/EP/EP_Demo.mq5                    priors, conditioning and three views on a basket, with a replay date
Scripts/EP/EP_WalkForward.mq5             walk-forward VaR and ES: coverage, FZ0 loss, Diebold-Mariano tests
Indicators/EP/EP_ViewCost.mq5             conditioned VaR and ES per bar, with a forming-bar panel
Experts/EP/EP_Sizer.mq5                   sizes a basket to an expected-shortfall budget from the indicator
```

Run `EP_Checks.mq5` first: every check should pass before anything else is
worth reading. `EP_Demo.mq5` then prints the book under each probability
vector for today, or for any past date through its replay input, and
`EP_WalkForward.mq5` produces the forecast comparison. `EP_Sizer.mq5` loads
`EP_ViewCost` through `iCustom`, so compile the indicator before the EA.

To use your own book, change the symbol list and the signed weights in the
inputs; the basket defaults to EURUSD, GBPUSD, AUDUSD, USDJPY and USDCHF on
D1. Any other state variable can replace trailing volatility by adding it as a
column with `AddColumn`, and any statement expressible as an expectation over
scenarios can be added as a view.

## Disclaimer

Educational code. `EP_Sizer` sizes a book; it does not choose one. The default
book is short the US dollar against the majors, the dollar rose for most of
the test period, and the account balance falls in every sizing mode. The
evidence concerns how closely the size keeps its risk budget, not
profitability. The views mode is not scored, because replaying the same fixed
views over sixteen years says nothing about them. Test on your own data and
broker conditions before drawing conclusions.