The covariance matrix holds how much each instrument moves (its volatility) and how much each pair moves together (their correlation); methods such as Risk parity and MPT are built on it. An allocation method estimates it from past returns, and the Covariance matrix setting chooses how: the classic Sample estimate or one of seven corrected ones.
Also seen as: covariance estimator, covariance estimation, risk estimation, shrinkage estimator
Why does the sample covariance matrix need correcting?
Because it is noisy when there are many instruments and not much history. With 30 instruments the matrix holds 465 separate numbers — 30 volatilities and 435 correlations — and a 12-month window gives about 252 days to estimate them from. Some correlations then come out unusually low by pure chance, and an optimiser leans hard on exactly those. A corrected estimate pulls such accidents back toward something more plausible, which makes the weights steadier from one rebalance to the next, at the price of a small, deliberate bias.
How does Fincanva handle it?
The control is labelled Covariance matrix, with the hint "The covariance matrix (volatilities and correlations) the method estimates from history." How to change it, when an estimator has no effect and why a flat-priced instrument can stop the backtest are in Choose how a method estimates risk.
- A method you choose now starts on Ledoit-Wolf · constant correlation, marked Recommended. A strategy saved before this choice existed keeps Sample, so its results do not change by themselves.
- Marchenko-Pastur, Nonlinear Ledoit-Wolf and Regime-conditional (HMM) start at Ultimate: on a lower plan they stay in the list tagged with the plan that includes them, and choosing one opens a dialog naming it and leaves the current estimator in place. The five basic estimators come with the method. See what each plan includes.
- The Risk-On and Risk-Off profiles each keep their own estimator.
- The estimate is taken over the calculation window (In-sample), so the window and the estimator work together.
- Decay factor (EWMA only) accepts 0.90 to 0.99 and starts at 0.94; Shrinkage intensity (Manual shrinkage only) is required and accepts 0 to 1.
Which estimators can you choose?
The list names each one in the app's own words; the first five are the basic estimators, the last three sit in its Advanced group.
| Estimator | What it does |
|---|---|
| Sample | "The classic estimate, with no corrections." |
| Ledoit-Wolf · identity | "Reduces noise more firmly, treating every instrument the same way." |
| Ledoit-Wolf · constant correlation (Recommended) | "Reduces noise by pulling correlations toward their average." |
| Exponentially weighted moving average (EWMA) | "Gives more weight to recent days: reacts sooner when volatility changes." |
| Manual shrinkage | "You choose how much to correct, from 0 to 1." |
| Marchenko-Pastur | "Separates the signal from the noise and keeps only the signal." |
| Nonlinear Ledoit-Wolf | "A tailored correction for each part of the estimate." |
| Regime-conditional (HMM) | "Uses crisis correlations when the market is in crisis." |
- Ledoit-Wolf blends the sample estimate with a simple target, the amount worked out from the data. Identity treats every instrument alike; constant correlation keeps each instrument's volatility and pulls every pairwise correlation toward the average — suited to similar instruments such as stocks, less to a deliberately mixed basket (stocks, bonds and gold), where two very different correlation levels are real.
- EWMA weighs recent days more, so the estimate follows a change in volatility within weeks — and reacts to noise too, which can raise trading.
- Manual shrinkage is the constant-correlation blend with the amount set by you.
Which methods use the covariance matrix?
Only methods built on one show the Covariance matrix control: inside a strategy, Risk parity, MPT (Markowitz), Hierarchical risk parity, Hierarchical equal risk contribution, Nested clustered optimization and Max diversification; inside a Combined, Risk parity, MPT (Markowitz) and Max diversification. The tail-focused methods — Min CVaR, Min MAD, Conditional drawdown at risk, Entropic value at risk, Robust worst case and Stochastic programming — work on the returns themselves. In MPT the choice affects the risk side only: expected returns are the window's plain averages, and Black-Litterman replaces them with its own estimate.
What do the advanced estimators do?
- Marchenko-Pastur uses random-matrix theory to tell which parts of the correlation structure are indistinguishable from noise, flattens those, and keeps the rest — market-wide and sector-wide co-movement. It can discard weak structure that was real.
- Nonlinear Ledoit-Wolf corrects each part of the estimate by its own amount. It helps most with large baskets and short windows, and adds almost nothing when history is long compared with the number of instruments.
- Regime-conditional (HMM) estimates one covariance from calm periods and one from turbulent ones, and leans on the turbulent one when the market looks turbulent today, so the method sees crisis-level correlations while a crisis lasts.
How do shrinkage and EWMA work?
Shrinkage blends two estimates; Ledoit-Wolf works the blend out from the data, and Manual shrinkage lets you set it as Shrinkage intensity — "0 = no correction, 1 = all correlations equal."
- the blend, between 0 and 1
- the target — for constant correlation, each instrument keeps its own volatility and every pair gets the average correlation
- the sample covariance
EWMA updates each variance with a Decay factor — "The closer to 1, the more distant data counts."
- today's variance estimate
- the decay factor — how much of the old estimate survives each day
- yesterday's return, squared
At the default 0.94 the estimate's memory is about 1 ÷ (1 − 0.94) ≈ 17 trading days.
What does it look like in practice?
A strategy holds 25 stocks on a 12-month window. Most pairs show a correlation around 0.5, but the sample estimate puts one pair at 0.05 — very likely an accident of this particular year.
- Sample keeps the 0.05, and MPT leans on that pair as if it were a near-perfect diversifier.
- Manual shrinkage at 0.4 moves it to 0.6 × 0.05 + 0.4 × 0.5 = 0.23: still below the crowd, but no longer an outlier worth betting the portfolio on. Every other pair moves toward 0.5 in the same proportion, and each stock's own volatility is left as measured.
- Ledoit-Wolf · constant correlation does the same blend but picks the amount from the data — more when the estimate is noisier, for example with more stocks or a shorter window.