MR-03 · Mean Reversion

Kalman Filter Mean Reversion

Uses Kalman Filter to dynamically estimate the 'fair value' of an asset. Enters long when price deviates significantly below the estimated value, expecting reversion. The filter adapts to changing market conditions.

Mean ReversionStatistical

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At a glance

Best onAssets with mean-reverting characteristics

Signal frequencyDaily

Typical holding periodDays

Asset classesIndex, Commodity, FX

Markets tested10

Data through2026-11-10

What the backtest shows

Beat buy-and-hold on 3 of 10 markets by annual return over 5 years.
Had a smaller maximum drawdown than buy-and-hold on 10 of 10 markets.
Best market by Sharpe ratio: USO (Sharpe 1.30, CAGR 23.5%).
Weakest market: ETH-USD (Sharpe -0.12, CAGR -16.3%).

Equity curve

Kalman Filter Mean Reversion Buy & hold · SPY, 2010-01-04 → 2026-11-10, growth of 1

Score and risk profile

Arena Score: 42.2SPY, 5 years

Return quality · 30%18

Drawdown control · 25%59

Consistency · 20%47

Robustness · 15%36

Significance · 10%72

Each bar is a percentile against every strategy on the same market and window (100 = best).

Time in market11%

Ulcer index2.0%

Longest drawdown585 days

Daily VaR (95%)-0.25%

Probability Sharpe > 072%

Beta vs buy & hold0.36

Alpha (annual)-1.9%

Positive months15%

CAGR after 10 bp costs1.8%

Deflated Sharpe (luck-adjusted)18%

CAGR, 90% bootstrap range-2.1% to 6.4%

Max drawdown, 90% bootstrap range-22.9% to -6.6%

How it held up in sell-offs (SPY)

Period	Strategy	Buy & hold
Q4 2018 sell-off	-7.0%	-19.2%
COVID crash (Feb–Mar 2020)	-14.0%	-33.7%
2022 bear market	-0.0%	-24.5%
Market above its 200-day average (annualized) · 81%	+0.5%	+12.5%
Market below its 200-day average (annualized) · 19%	+11.6%	+19.8%

Sell-off dates follow the US stock market. Above/below the 200-day average uses the previous day's position, so there is no look-ahead.

Out-of-sample check (SPY)

Check	Value
Chosen parameters on their 3-year training windows (average Sharpe)	0.45
Same parameters in the following 6 months, when traded (Sharpe)	0.22
Default parameters over the same months (Sharpe)	0.25
Parameter re-selections / changes	28 / 9
Parameter settings with a positive Sharpe (full history)	9 of 9
Sharpe across settings: worst / median / best	0.18 / 0.31 / 0.39

Out-of-sample periods start on 2013-01-04. Training-window figures are flattered by picking the best of 9 settings; the out-of-sample figure is what the strategy actually earned. A large drop, or a result that depends on one setting, points to overfitting. How walk-forward testing works.

Results by market (5 years)

Market	CAGR	Buy & hold CAGR	Sharpe	Max drawdown	Buy & hold max DD	Volatility	Arena Score
USOUnited States Oil Fund	23.5%	20.2%	1.30	-13.1%	-36.2%	17.5%	87
DBCInvesco DB Commodity Index	9.5%	10.8%	1.05	-8.9%	-27.3%	9.0%	81
SLViShares Silver Trust	6.8%	15.2%	0.49	-26.5%	-57.8%	16.2%	60
DBAInvesco DB Agriculture	2.1%	8.8%	0.40	-9.4%	-15.9%	5.6%	47
SPYSPDR S&P 500	2.1%	11.6%	0.25	-12.1%	-24.5%	10.4%	42
BTC-USDBitcoin	-0.3%	2.6%	0.13	-53.2%	-75.9%	27.2%	47
GLDSPDR Gold Shares	0.3%	16.4%	0.08	-12.8%	-28.3%	8.3%	32
EURUSD=XEUR/USD	-0.5%	-0.7%	-0.08	-10.9%	-17.2%	4.8%	45
UNGUnited States Natural Gas	-10.6%	-30.7%	-0.09	-68.0%	-93.3%	39.3%	58
ETH-USDEthereum	-16.3%	-15.1%	-0.12	-66.5%	-79.0%	38.6%	32

Strategy metrics use daily returns without trading costs. Buy-and-hold figures are for the same market and window. Rows are sorted by Sharpe ratio.

SPY across time windows

Window	Total return	CAGR	Sharpe	Sortino	Max DD	Win days	Trades
1 year	+3.1%	3.1%	0.53	0.31	-6.6%	5%	3
3 years	+2.2%	0.7%	0.12	0.04	-12.1%	3%	5
5 years	+11.0%	2.1%	0.25	0.13	-12.1%	5%	15
Full history	+52.0%	2.5%	0.29	0.12	-22.2%	5%	49

Rules

Entry

Buy when z-score < -Entry_Z (price undervalued)

Exit

Exit when |z-score| < Exit_Z

Indicators

Kalman state estimate
Standardized residual (z-score)

Inputs

Q = 0.001 (process noise)
R = 1.0 (observation noise)
Entry_Z = 2.0
Exit_Z = 0.5

Position sizing

Fixed 100% allocation

Risk controls

Adaptive Q based on recent volatility

Strategy evidence

Only available, validated bundles appear below. Missing evidence is not a passing validation result.

Evidence coverage

10 / 10 declared strategy–market pairs validated

Notes

Rudolf Kalman's 1960 optimal state estimation algorithm
Provides optimal linear estimate under Gaussian assumptions
Q/R ratio controls smoothness vs responsiveness tradeoff

Related strategies

MR-04 · SPY 5Y Sharpe 0.24Ornstein-Uhlenbeck Mean Reversion MR-06 · SPY 5Y Sharpe 0.86Z-Score Mean Reversion MR-07 · SPY 5Y Sharpe 0.37Hurst-Filtered Mean Reversion COMBO-04 · SPY 5Y Sharpe 0.38Trend + Mean Reversion Hybrid MOM-06 · GLD 5Y Sharpe 0.57Residual Momentum MR-01 · SPY 5Y Sharpe 0.77RSI Mean Reversion

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Backtests are historical simulations on daily data and do not include commissions or slippage. They do not guarantee future results and are not investment advice. See the methodology for how every strategy is tested.