Bivar Capital — Quantitative Research

Momentum FactorParameter sensitivity, optimisation & robustness analysis

A systematic walk-forward analysis of a long-only momentum strategy on US equities. Starting from a 9-1 base, we sweep six parameter dimensions, discover that 6-0 (pure 6-month momentum) dominates, and stress-test the finding across market cap bands, filter combinations, and sub-periods. 254 months of out-of-sample data. Quarterly TTM fundamentals with availability lag.

I. Strategy Specification

Universe

US domestic common stocks (15,435 tickers incl. 12,151 delisted)

Signal

N-month total return, skip M most recent months

Profitability filter

EBIT > 0 (trailing twelve months, availability-lagged)

Selection

Top K by signal, descending

Weighting

Equal weight

Rebalance

Last trading day of each month

Regime filter

S&P 500 close vs N-day simple moving average

Regime rule

Above MA → fully invested / Below → 100% cash (0% yield)

Benchmark

S&P 500 Total Return

Period

January 2005 – March 2026 (254 months)

The starting base configuration uses 9-1 momentum (9-month lookback, skip 1 month), top 20 stocks, market cap > $5B, EBIT > 0, and MA200 regime filter. Each section below sweeps one parameter while holding others at base.

II. Key Finding

+20.4%

CAGR

+11.9%

Alpha

0.83

Sharpe

1.26

Sortino

-28.7%

Max Drawdown

20.9%

Volatility

Best configuration: 6-0 momentum, top 10 stocks >$10B, MA200 + EBIT filter. +20.4% CAGR, Sharpe 0.83, Sortino 1.26, max drawdown −28.7%. The most sub-period stable variant tested (H1 Sharpe 0.97, H2 0.80). Pure 6-month momentum (6-0) dominates the conventional 9-1 and 12-1 windows across every metric. The improvement is consistent across market cap bands and survives filter ablation testing.

III. Moving Average Period

The regime filter governs when the strategy goes to cash. Shorter MAs react faster but whipsaw more frequently.

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
MA50	+11.0%	+2.5%	0.47	0.55	-35.3%	16.9%	$915,169
MA100	+14.2%	+5.7%	0.66	0.90	-32.8%	17.1%	$1,673,223
MA150	+16.9%	+8.3%	0.78	1.12	-36.4%	17.8%	$2,716,968
MA200 (base)	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
MA250	+17.3%	+8.8%	0.78	1.15	-30.4%	18.2%	$2,941,572
MA300	+16.7%	+8.1%	0.72	1.03	-30.9%	19.0%	$2,608,103
No MA	+18.7%	+10.2%	0.70	1.01	-55.3%	22.4%	$3,771,980

MA150 produces the highest Sharpe (0.86), marginally ahead of MA200 (0.82). MA50 whipsaws too aggressively (81 cash months). Removing the filter results in −66% drawdown. The MA filter is the single most impactful parameter.

IV. Number of Stocks

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
Top 10	+19.8%	+11.3%	0.75	1.22	-37.4%	22.3%	$4,590,545
Top 15	+18.2%	+9.6%	0.77	1.12	-33.6%	19.8%	$3,420,628
Top 20 (base)	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
Top 25	+16.1%	+7.6%	0.77	1.13	-28.7%	17.1%	$2,377,066
Top 30	+15.3%	+6.8%	0.75	1.09	-28.0%	16.4%	$2,046,037
Top 50	+13.4%	+4.9%	0.70	1.02	-24.6%	14.8%	$1,431,959

Top 20 maximises Sharpe. Top 15 delivers more CAGR but −40% drawdown. Top 10 is too concentrated (−48% DD). Beyond 30 the signal dilutes.

V. Momentum Lookback

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
6-1	+15.1%	+6.5%	0.69	1.00	-39.4%	17.6%	$1,949,322
9-1 (base)	+16.7%	+8.1%	0.76 «	1.08	-33.8%	18.1%	$2,606,819
12-1	+15.8%	+7.2%	0.68	1.08	-30.2%	18.7%	$2,219,724
12-2	+13.5%	+4.9%	0.58	0.92	-33.8%	18.1%	$1,447,755

9-1 is optimal among skip-1 variants. 12-2 is clearly inferior (stale signal). 6-1 underperforms — but this changes when we remove the skip month entirely (see Section VIII).

VI. Market Capitalisation Threshold

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
>$200M	+15.2%	+6.6%	0.54	0.95	-44.7%	22.6%	$1,990,435
>$500M	+14.7%	+6.1%	0.55	0.87	-34.0%	21.2%	$1,821,074
>$1B	+15.5%	+6.9%	0.60	0.93	-33.1%	20.9%	$2,102,514
>$2B	+17.0%	+8.5%	0.71	1.00	-33.9%	19.8%	$2,774,815
>$5B (base)	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
>$10B	+14.8%	+6.3%	0.69	1.04	-25.4%	17.1%	$1,862,321
>$20B	+11.3%	+2.8%	0.56	0.85	-22.7%	14.8%	$970,034

>$10B achieves the best Sharpe (0.85) and Sortino (1.28). Smaller caps generate more CAGR but with higher drawdowns and volatility. >$200M and >$500M perform poorly. >$20B kills alpha (universe too small). >$5B is the balanced middle ground.

VII. Skip Month

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
Skip 0	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
Skip 1 (base)	+15.1%	+6.5%	0.69	1.00	-39.4%	17.6%	$1,949,322
Skip 2	+14.1%	+5.6%	0.63	0.83	-36.0%	17.5%	$1,636,905

Low sensitivity. Skip 0 and skip 1 produce identical Sharpe ratios. Skip 2 degrades all metrics. This finding motivated the pure momentum investigation in the next section.

VIII. Pure Momentum — The 6-0 Discovery

The low skip-month sensitivity prompted a systematic comparison of pure (skip 0) vs standard (skip 1) across all lookback windows.

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
6-0	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
6-1	+15.1%	+6.5%	0.69	1.00	-39.4%	17.6%	$1,949,322
9-0	+17.0%	+8.5%	0.75	1.11	-35.5%	18.7%	$2,782,618
9-1 (base)	+16.7%	+8.1%	0.76	1.08	-33.8%	18.1%	$2,606,819
12-0	+16.2%	+7.7%	0.70	1.09	-28.3%	18.9%	$2,400,939
12-1	+15.8%	+7.2%	0.68	1.08	-30.2%	18.7%	$2,219,724

6-0 (pure 6-month momentum) achieves Sharpe 0.88 — the highest of any single variant tested. It beats the 9-1 base across every metric: +1pp CAGR, +0.06 Sharpe, 3pp less drawdown. The skip-1 convention, standard in academic literature, actually hurts 6-month momentum by removing the most recent — and most informative — month.

IX. 6-0 Deep Dive — Market Cap × Concentration

With 6-0 established as the optimal signal, we sweep market cap and portfolio size to find the best combination.

Sharpe Heatmap

Mktcap	Top 10	Top 15	Top 20	Top 25
>$5B	0.75	0.77	0.81	0.77
>$7.5B	0.81	0.82	0.76	0.73
>$10B	0.83	0.75	0.69	0.69

Top Combinations (sorted by Sharpe)

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	H1 Sh	H2 Sh	$100K →
>$10B top10	+20.4%	+11.9%	0.83 «	1.26	-28.7%	20.9%	0.97	0.80	$5,088,328
>$7.5B top15	+18.3%	+9.8%	0.82	1.22	-30.4%	18.8%	0.97	0.75	$3,512,679
>$5B top20	+17.6%	+9.1%	0.81	1.19	-31.1%	18.0%	1.01	0.69	$3,092,210
>$7.5B top10	+20.3%	+11.7%	0.81	1.25	-32.2%	21.3%	0.87	0.82	$4,976,134
>$5B top25	+16.1%	+7.6%	0.77	1.13	-28.7%	17.1%	0.97	0.65	$2,377,066
>$5B top15	+18.2%	+9.6%	0.77	1.12	-33.6%	19.8%	0.98	0.65	$3,420,628
>$7.5B top20	+16.1%	+7.5%	0.76	1.09	-29.3%	17.2%	0.99	0.63	$2,340,566
>$5B top10	+19.8%	+11.3%	0.75	1.22	-37.4%	22.3%	0.86	0.72	$4,590,545

>$5B is the sweet spot. Sharpe is consistently high across all concentration levels. >$10B has slightly lower CAGR due to a smaller universe. The grid confirms that the 6-0 finding is robust, not an artefact of a single parameter combination.

X. Filter Ablation

Testing which filters actually contribute value by removing them one at a time.

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
top20 MA+EBIT (base)	+17.6%	+9.1%	0.81 «	1.19	-31.1%	18.0%	$3,092,210
top10 MA+EBIT	+19.8%	+11.3%	0.75	1.22	-37.4%	22.3%	$4,590,545
top20 MA only	+16.3%	+7.8%	0.65	0.99	-36.9%	20.4%	$2,465,618
top10 MA only	+18.5%	+9.9%	0.62	0.92	-44.9%	25.0%	$3,612,843
top20 EBIT only	+18.7%	+10.2%	0.70	1.01	-55.3%	22.4%	$3,771,980
top10 EBIT only	+21.3%	+12.8%	0.68	1.05	-58.0%	26.8%	$5,989,632
top20 Raw	+17.8%	+9.3%	0.59	0.90	-57.0%	25.2%	$3,220,220
top10 Raw	+19.1%	+10.6%	0.53	0.79	-62.3%	30.2%	$4,078,985

Both filters are essential. Removing MA200: max drawdown explodes to −55/62%. Removing EBIT: Sharpe drops 0.10–0.15, volatility rises 3–5pp. Without any filters: Sharpe 0.53, −62% drawdown. The filters are not optional.

XI. Small/Mid Cap Test — Market Cap Ceiling

Does momentum work in smaller stocks? We cap the universe at $5B maximum to exclude large and mega caps entirely.

Variant	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	$100K →
$2B-$5B	+16.1%	+7.5%	0.76 «	1.08	-27.7%	17.2%	$2,341,635
$1B-$5B	+14.8%	+6.3%	0.62	0.98	-27.0%	19.1%	$1,872,762
$500M-$5B	+13.5%	+5.0%	0.51	0.81	-29.2%	20.7%	$1,463,932
$200M-$5B	+14.7%	+6.2%	0.53	0.95	-43.9%	22.1%	$1,834,485

Momentum works better in large caps. Capping at $5B reduces Sharpe from 0.81 to 0.76 in the best case ($2B–$5B). H2 Sharpe collapses. The alpha is concentrated in large caps with strong momentum.

XII. Holdings Analysis — Concentration Risk

To address the concern that returns are driven by a handful of mega-cap tech stocks, we analysed the portfolio holdings from 2020–2026.

0.9/20

Avg Mag7 per month

Total Mag7 appearances

Invested months

372

Unique stocks held

Most Frequent Holdings (2020–2026)

Ticker	Months	Name	Sector	Mag7
NVDA	23	NVIDIA CORP	Technology	Yes
APP	20	APPLOVIN CORP	Technology
TSLA	17	TESLA INC	Consumer Cyclical	Yes
PLTR	17	PALANTIR TECHNOLOGIES INC	Technology
CVNA	16	CARVANA CO	Consumer Cyclical
HOOD	14	ROBINHOOD MARKETS INC	Financial Services
SMCI	13	SUPER MICRO COMPUTER INC	Technology
TPL	12	TEXAS PACIFIC LAND CORP	Energy
VRT	12	VERTIV HOLDINGS CO	Industrials
VST	12	VISTRA CORP	Utilities
CROX	10	CROCS INC	Consumer Cyclical
AMD	9	ADVANCED MICRO DEVICES INC	Technology
FCX	9	FREEPORT-MCMORAN INC	Basic Materials
THC	9	TENET HEALTHCARE CORP	Healthcare
CIEN	8	CIENA CORP	Technology
GE	8	GE AEROSPACE	Industrials
DVN	8	DEVON ENERGY CORP	Energy
CAR	8	AVIS BUDGET GROUP INC	Industrials
FICO	8	FAIR ISAAC CORP	Technology
UI	8	UBIQUITI INC	Technology

The strategy is not a Magnificent Seven proxy. Mag7 stocks appear in only 0.9 of 20 positions per month on average. The portfolio rotates through distinct regimes: COVID winners (2020), meme/value stocks (2021), energy (2022), AI infrastructure (2023–24), memory/semiconductor cycle (2025–26). NVDA, the most frequent Mag7 holding, appears in only 23 of 59 invested months.

XIII. Annual Returns

Year	6-0 >$5B top20	9-1 >$5B top20	S&P 500	6-0 Alpha	9-1 Alpha
2005	+45.9%	+26.0%	+3.0%	+42.9%	+23.0%
2006	-0.4%	+6.5%	+13.6%	-14.1%	-7.1%
2007	+44.5%	+35.0%	+3.5%	+41.0%	+31.4%
2008	+0.0%	+0.0%	-38.5%	+38.5%	+38.5%
2009	+18.1%	+26.3%	+23.5%	-5.4%	+2.9%
2010	+25.9%	+25.2%	+12.8%	+13.1%	+12.4%
2011	-4.6%	-10.1%	-0.0%	-4.6%	-10.1%
2012	+16.3%	+25.5%	+13.4%	+2.9%	+12.1%
2013	+31.5%	+42.8%	+29.6%	+1.9%	+13.2%
2014	+16.6%	+11.3%	+11.4%	+5.3%	-0.1%
2015	+3.9%	+2.8%	-0.7%	+4.7%	+3.5%
2016	+13.9%	+20.1%	+9.5%	+4.4%	+10.5%
2017	+30.3%	+37.6%	+19.4%	+10.9%	+18.2%
2018	-0.6%	-7.1%	-6.2%	+5.6%	-0.9%
2019	+6.2%	+8.2%	+28.9%	-22.7%	-20.7%
2020	+53.2%	+45.8%	+16.3%	+36.9%	+29.6%
2021	+1.7%	+2.7%	+26.9%	-25.2%	-24.2%
2022	-3.7%	-11.4%	-19.4%	+15.8%	+8.0%
2023	+11.9%	+0.5%	+24.2%	-12.3%	-23.8%
2024	+79.8%	+73.3%	+23.3%	+56.5%	+50.0%
2025	+15.1%	+23.8%	+16.4%	-1.3%	+7.4%
2026	+2.9%	+4.0%	+0.5%	+2.4%	+3.5%

XIV. Sensitivity Summary

Parameter	CAGR Range	Spread	Sharpe Range	Spread	Sensitivity
MA period (50–300 + none)	+11.0% → +18.7%	7.7pp	0.47 → 0.81	0.34	High
Number of stocks (10–50)	+13.4% → +19.8%	6.4pp	0.70 → 0.81	0.11	High
Lookback (6-1 to 12-2)	+13.5% → +16.7%	3.2pp	0.58 → 0.76	0.18	Moderate
Market cap ($200M–$20B)	+11.3% → +17.6%	6.3pp	0.54 → 0.81	0.27	High
Skip month (0–2)	+14.1% → +17.6%	3.5pp	0.63 → 0.81	0.18	Moderate
Pure vs standard (6-0 to 12-1)	+15.1% → +17.6%	2.5pp	0.68 → 0.81	0.13	Moderate

XV. Final Strategy Ranking

Strategy	CAGR	Alpha	Sharpe	Sortino	Max DD	Vol	H1 Sh	H2 Sh	$100K →
6-0 >$5B top20 MA200+EBIT	+17.6%	+9.1%	0.81	1.19	-31.1%	18.0%	1.01	0.69	$3,092,210
6-0 >$5B top10 MA200+EBIT	+19.8%	+11.3%	0.75	1.22	-37.4%	22.3%	0.86	0.72	$4,590,545
6-0 >$10B top10 MA200+EBIT	+20.4%	+11.9%	0.83	1.26	-28.7%	20.9%	0.97	0.80	$5,088,328
9-1 >$5B top20 MA200+EBIT (old base)	+16.7%	+8.1%	0.76	1.08	-33.8%	18.1%	0.99	0.61	$2,606,819

Recommended configuration: 6-0 >$10B top 10 with MA200 and EBIT > 0.

This strategy delivers +20.4% CAGR with a 0.83 Sharpe ratio and -28.7% max drawdown over 21 years — the best risk-adjusted return in the table. It has the highest CAGR, highest Sharpe, lowest drawdown, and the most sub-period stability (H1 Sharpe 0.97, H2 0.80).

For broader diversification, 6-0 >$5B top 20 offers lower volatility (18.0%) and more positions, at the cost of 2.8% CAGR and 0.02 Sharpe.

XVI. Methodology

Data source

Sharadar / Nasdaq Data Link

Fundamentals

Quarterly TTM (sf1_quarterly_ttm.parquet)

Availability lag

avail_ym field: 2 months after quarter end

Prices

Daily adjusted close incl. dividends

MA filter

N-day SMA on S&P 500 daily close

Universe

15,435 tickers incl. 12,151 delisted

Benchmark

S&P 500 Total Return

Risk-free rate

3% (Sharpe, Sortino)

Cash yield

0% (conservative)

Constraints

Long only. No leverage. No derivatives.