QuanterLab · Research

Your beta is holding something different than it was, twenty lowest-beta names against twenty highest, across twenty sealed windows of the S&P 500

A point-in-time walk-forward investigation with hypotheses registered before scoring and the size of the search left unreconstructed rather than guessed.

By Serhat Girgin

Universe · S&P 500 (point-in-time constituents)

Method · Comparative: Low beta (Top-20 lowest β) vs High beta (Top-20 highest β)

Manipulated variable · Top-N selection direction on 252-day market beta: lowest (A) vs highest (B), construction held identical

Step size · 1 year per forward window

In-sample · 2 years before each anchor

Out-of-sample span · 2006-01-03 → 2025-12-31

Compiled · August 08, 2026

Search record · none (size unknown, see §2.3)

Abstract

Buy the twenty least volatile-looking stocks in the S&P 500, the twenty lowest market betas, hold them a year, re-select and repeat for twenty years. That portfolio returned +86.1% cumulative, 3.2% a year. The twenty highest-beta names, selected the same way on the same days, returned +692.1%, 11.1% a year. The equal-weight index did +324.8%. Across 5,011 paired trading days the probability that the low-beta book beats the high-beta book is 2.5%. Everything you have read about the low-beta anomaly says the first portfolio should not lose this badly. This study is about why it did, and about the part of the answer that lives not in the anomaly literature but in the beta estimate itself. Before 2020 the low-beta book earned two points a year less (4.4% vs 6.4% CAGR) with nothing like the same risk, vol 14% against 40%, worst drawdown −40% against −82%, which is the anomaly as the literature actually prices it: not more return, the same Sharpe (0.38 vs 0.36) for a third of the ride. Dividends narrow that raw-return gap, the low-beta book is the yield-heavy one, and the measured figures in the discussion say they do not close it across the full twenty windows, though before 2020 they very nearly do. From 2020 the picture inverts even risk-adjusted: the high-beta book earned 22.0% a year (Sharpe 0.68) while the low-beta book earned 0.4% (Sharpe 0.11). The composition record explains the break. What β selects changed identity: the high-beta book of 2008–2009 held zero technology, it was the levered financials of the last crisis; the high-beta book of 2020–2025 is 45% technology, reaching three-quarters of the basket by 2025, holding NVDA, AMAT and LRCX in every single window. When roughly a third of the index moves as one factor, the market return becomes that factor, and beta measured against it stops being a measure of diversified market risk and becomes a measure of loading on the dominant factor. The low-beta book is not ‘the market with less risk’; since 2020 it is the market minus its engine.

Author’s note

We usually split eras at 2010. This paper splits at 2020 because the data left no choice: fourteen windows of the anomaly behaving exactly as the literature describes, then six windows of inversion sharp enough to need its own name. The twenty windows were registered and sealed before any narrative existed, the era cut is my reading of the record, and the record is on the canvas for yours. Every window's frozen report, every quarterly basket, every beta estimation window is one click deep. If you think the story is wrong, fork the circuit and move the one field that matters, that is what this platform is for. The replication of the real BAB machine, at the borrowing costs retail actually pays, is next in this series.

1 Methodology

Two arms, identical in every field but one. Each arm selects from the point-in-time S&P 500 membership, computes each name's market beta, ordinary least squares on 252 trading days of daily returns against SPY, no shrinkage, as of the anchor, and hands the ranked list to a Top-N selector. Arm A keeps the twenty LOWEST betas, Arm B the twenty HIGHEST; that selector direction is the single manipulated variable, frozen at registration. Both books are equal-weighted and long-only, re-selected point-in-time quarterly inside each one-year out-of-sample window, with betas re-estimated at every re-selection from data available on that day only. Twenty sealed windows walk 2006–2025, one year per step, each step registered before it ran and bound to its frozen report. Costs are set to zero in both arms, the treatment is identical, and the measured turnover is nearly so (26.7% of the book per quarterly re-selection in the low-beta arm, 28.8% in the high-beta arm, 75 re-selections each), so the cost omission is close to neutral; the asymmetric omission is dividends, measured in the discussion. Sharpe ratios throughout use a zero risk-free rate, at the actual post-2020 cash rate the low-beta book's 2020+ Sharpe turns negative, which strengthens the era contrast. Cumulative figures in the text compound the paired daily construction (5,011 inner-joined days, the bootstrap's basis); the stitched figure compounds each arm's own series and lands one session apart, both are printed from the sealed record. The benchmark series is RSP (equal-weight S&P 500) to match the books' weighting scheme; SPY serves only as the market proxy inside the beta estimate, two different roles for two different questions. Deliberately absent, because their absence is the point: no leverage, no shorting, no rank-weighting, no beta-neutral scaling. This is the SELECTION CONTENT of betting-against-beta, the only part of the trade a retail hand can actually touch, measured on its own, so that what the construction adds can be measured separately when we replicate it.

Transaction costs are not modelled in this study; all results are gross of costs.

2 Results

2.1 Headline

Low beta (Top-20 lowest β), pooled Sharpe

0.28

5012 OOS bars

High beta (Top-20 highest β), pooled Sharpe

0.46

5012 OOS bars

P(Low beta (Top-20 lowest β) beats High beta (Top-20 highest β))

2.5%

5011 paired bars · CAGR gap (Low beta (Top-20 lowest β) − High beta (Top-20 highest β)) -7.9 pp

Figure 1. Both arms stitched through the identical windows, Low beta (Top-20 lowest β) (+86.3%), High beta (Top-20 highest β) (+694.0%), benchmark grey (+325.6%). Dotted verticals mark the step boundaries; the dashed horizontal is break-even. These figures compound each arm's own stitched daily series; the pooled statistics in the text inner-join both arms' trading days, one session apart, both are printed from the frozen record.

Figure 2. The same walk, re-based to 1.00x at the first window starting in 2020, 6 of the 20 windows above. Low beta (Top-20 lowest β) (+2.4%), High beta (Top-20 highest β) (+230.9%), benchmark grey (+67.9%). This is a subset of Figure 1, not a correction to it. The era boundary here is pinned by the author at 2020, a break this study's own record shows, not a chart-scaling choice, and the era rows below put a number on the two periods it separates. The full record is what the study claims.

2.2 Per-step results

**Table 1.** One row per step, raw out-of-sample results.
#	Out-of-sample window	Low beta (Top-20 lowest β) SR	High beta (Top-20 highest β) SR
1	2006-01-03 → 2006-12-29	0.52	0.04
2	2007-01-03 → 2007-12-31	0.60	0.16
3	2008-01-02 → 2008-12-31	-0.90	-0.45
4	2009-01-02 → 2009-12-31	0.80	1.06
5	2010-01-04 → 2010-12-31	0.46	0.94
6	2011-01-03 → 2011-12-30	0.75	-0.44
7	2012-01-03 → 2012-12-31	0.28	0.74
8	2013-01-02 → 2013-12-31	1.07	1.78
9	2014-01-02 → 2014-12-31	1.83	0.68
10	2015-01-02 → 2015-12-31	-0.74	-0.45
11	2016-01-04 → 2016-12-30	0.58	1.34
12	2017-01-03 → 2017-12-29	0.76	1.21
13	2018-01-02 → 2018-12-31	0.11	-0.29
14	2019-01-02 → 2019-12-31	1.88	1.30
15	2020-01-02 → 2020-12-31	-0.07	0.85
16	2021-01-04 → 2021-12-31	1.00	1.31
17	2022-01-03 → 2022-12-30	-0.05	-0.67
18	2023-01-03 → 2023-12-29	-0.55	1.62
19	2024-01-02 → 2024-12-31	0.61	0.53
20	2025-01-02 → 2025-12-31	0.20	1.13

Figure 3. Low beta (Top-20 lowest β): every step's out-of-sample curve overlaid, each rebased to 1× at its own start. Read alongside Table 1: consistent shape across steps is the walk-forward's evidence; a single lucky leg is not.

Figure 4. High beta (Top-20 highest β): the same windows, the other arm. Compare shape-for-shape with the previous figure: the two arms trade the identical out-of-sample legs.

2.3 Search accounting

No search record exists for this design. It was not promoted from a recorded evolving search, so the number of alternatives tried before it, on paper, in another tool, or in the author's head, is unknown. Unknown is a different fact from one: a study with no lineage is not a strategy with one trial, it is a strategy with an unrecorded number of them. Accordingly no count of alternatives tried is claimed, and nothing in this paper is corrected for a search that was never recorded; the number that stands is the raw out-of-sample result plus this disclosure. The registered per-step record below (§4) still guarantees each window's hypothesis was hashed and registered before that window was scored.

2.4 The comparison

Both arms trade the same registered windows, so their returns can be PAIRED: inside each window the two return series are inner-joined date by date and the difference r_{Low beta (Top-20 lowest β)} − r_{High beta (Top-20 highest β)} is the object under test. Because this is ONE pre-declared contrast, frozen at registration before any window was scored, the paired statistic needs no multiple-testing deflation, and the per-arm pooled numbers above are likewise uncorrected, this design has no recorded search to correct against (§2.3). The paired contrast is the one statistic here that a missing search record does not weaken: it was declared in advance, and it is scored on the difference rather than on either arm's level.

In the table: Arm A = Low beta (Top-20 lowest β) · Arm B = High beta (Top-20 highest β).

**Table 2.** Window-by-window paired comparison. Δ is the growth gap (Arm A − Arm B) over the window's paired dates.
#	Window	Paired bars	Arm A	Arm B	Δ	Leader
1	2006-01-04 → 2006-12-29	250	+5.7%	-2.0%	+7.7 pp	Arm A
2	2007-01-04 → 2007-12-31	250	+6.2%	+0.6%	+5.6 pp	Arm A
3	2008-01-03 → 2008-12-31	252	-25.0%	-53.5%	+28.4 pp	Arm A
4	2009-01-05 → 2009-12-31	251	+11.0%	+68.5%	-57.5 pp	Arm B
5	2010-01-05 → 2010-12-31	251	+4.6%	+29.2%	-24.6 pp	Arm B
6	2011-01-04 → 2011-12-30	251	+9.3%	-25.8%	+35.1 pp	Arm A
7	2012-01-04 → 2012-12-31	249	+1.8%	+18.4%	-16.6 pp	Arm B
8	2013-01-03 → 2013-12-31	251	+10.8%	+39.2%	-28.5 pp	Arm B
9	2014-01-03 → 2014-12-31	251	+20.6%	+11.6%	+9.0 pp	Arm A
10	2015-01-05 → 2015-12-31	251	-11.7%	-13.2%	+1.6 pp	Arm A
11	2016-01-05 → 2016-12-30	251	+7.7%	+46.7%	-39.0 pp	Arm B
12	2017-01-04 → 2017-12-29	250	+6.4%	+18.0%	-11.5 pp	Arm B
13	2018-01-03 → 2018-12-31	250	+0.5%	-11.4%	+11.9 pp	Arm A
14	2019-01-03 → 2019-12-31	251	+23.1%	+32.2%	-9.1 pp	Arm B
15	2020-01-03 → 2020-12-31	252	-7.4%	+41.1%	-48.5 pp	Arm B
16	2021-01-05 → 2021-12-31	251	+11.7%	+39.8%	-28.1 pp	Arm B
17	2022-01-04 → 2022-12-30	250	-2.1%	-33.7%	+31.6 pp	Arm A
18	2023-01-04 → 2023-12-29	249	-6.2%	+54.1%	-60.4 pp	Arm B
19	2024-01-03 → 2024-12-31	251	+5.9%	+12.0%	-6.0 pp	Arm B
20	2025-01-03 → 2025-12-31	249	+1.7%	+46.4%	-44.7 pp	Arm B

Paired Sharpe of the difference track: -0.39 · block bootstrap (2000 paths, block 10, seed 1234): P(Low beta (Top-20 lowest β) beats High beta (Top-20 highest β)) = 2.5%.

Window win-rate. Low beta (Top-20 lowest β) led 8 of 20 windows (40.0%), High beta (Top-20 highest β) led 12 , and the mean window gap of -12.18 pp points the same way. Widest single window: 2023 at -60.4 pp.

**Table 3.** The same comparison split at 2020. Pooling the whole walk into one row hides which side of the split the difference came from.
Period	Windows	Low beta (Top-20 lowest β)	High beta (Top-20 highest β)	Mean gap	Low beta (Top-20 lowest β) led
All windows	20	+3.73%	+15.91%	-12.18 pp	8/20
Before 2020	14	+5.07%	+11.32%	-6.25 pp	7/14
2020 onward	6	+0.60%	+26.62%	-26.02 pp	1/6

Figure A1, mean window return per period. Low beta (Top-20 lowest β) above, High beta (Top-20 highest β) below, with the gap at right. The pooled bar and the post-2020 bar are the same comparison over different periods.

The two eras disagree by 19.77 pp. The pooled figure is therefore not a standing property of either method, it is dominated by the later period. Read the two rows, not the average.

3 The circuit

The strategy is a circuit of platform primitives, frozen when the study is registered. Below is the circuit as wired on the canvas, the objective it encodes and how the search runs through it, followed by the mathematics each primitive actually computes, the same formulas the execution engine runs. The complete parameterisation is preserved in the study ledger (Appendix A).

The hypothesis under test

A COMPARATIVE study, Low beta (Top-20 lowest β) vs High beta (Top-20 highest β), walked on the same registered out-of-sample windows. Low beta (Top-20 lowest β): S&P 500, selected by statistical / factor criteria, rebalanced quarterly across the selected basket, and run out-of-sample from the anchor, whatever the design estimates from history is re-estimated at each anchor from pre-anchor data only, and the walk advances through registered out-of-sample windows; its disposition is the realized forward path versus the benchmark. High beta (Top-20 highest β): S&P 500, selected by statistical / factor criteria, rebalanced quarterly across the selected basket, and run out-of-sample from the anchor, whatever the design estimates from history is re-estimated at each anchor from pre-anchor data only, and the walk advances through registered out-of-sample windows; its disposition is the realized forward path versus the benchmark. The arms differ in: Top-N, select: lowest → highest. The contrast under test: whether Low beta (Top-20 lowest β) generates better risk-adjusted returns than High beta (Top-20 highest β) over the identical out-of-sample windows.

Figure 5. The frozen circuit, every node a primitive, every wire a typed data-flow; the two arms are colour-coded (Low beta (Top-20 lowest β) green, High beta (Top-20 highest β) blue, shared feeds neutral). Each box is one step of the strategy; data flows along the wires left to right, and no box can see data dated later than the box feeding it. The whole diagram was frozen when the hypothesis was registered. Click any node to open what that step ran with and what it produced.

Envelopes show counts, ratios, dates, and the parameters the author chose. Full price and per-name data series are not republished: the underlying market data is licensed to QuanterLab. Point figures quoted in the prose, a named holding's return over a stated span, are summary facts derived from public market prices, not redistributed series.

What each part does

Universe, The starting set of tickers, resolved point-in-time from the index change-log, so names delisted or removed later still compete on the dates they traded.

Price Loader, Bulk OHLCV fetch for the whole universe, point-in-time, no future bars.

Filter Beta, CAPM market beta, how hard this stock moves when the market moves.

Top N, Keep the best N, rank, then cut.

Portfolio Backtest, Replay the portfolio forward, rebalanced, point-in-time. No transaction-cost overlay is wired in this circuit, so these results are gross of costs.

Portfolio Forward Autopsy, The post-mortem, where the forward test’s return actually came from.

The objective and the search

Low beta (Top-20 lowest β)

Universe	S&P 500 index constituents.
Selection	metric across Market beta (β) → lowest 20 kept by Market beta (β).
Validation & out-of-sample	portfolio forward test (buy-and-hold book) (1y horizon from the anchor, quarterly rebalance).

High beta (Top-20 highest β)

Universe	S&P 500 index constituents.
Selection	metric across Market beta (β) → highest 20 kept by Market beta (β).
Validation & out-of-sample	portfolio forward test (buy-and-hold book) (1y horizon from the anchor, quarterly rebalance).

What differs between the arms, one difference; the comparison is clean:

paramTop-N, select: lowest → highest

Everything else is held identical, so an out-of-sample gap between the arms is attributable to this one change.

No transaction-cost elements are wired into this circuit; results are gross of costs.

Show the mathematics, 6 primitives, formulas and parity notes

3.1 Universe

The starting set of tickers, resolved point-in-time from the index change-log, so names delisted or removed later still compete on the dates they traded.

Before any math, you need a list of stocks. An index preset (S&P 500, Nasdaq-100, Dow 30) is reconstructed as it stood ON your anchor date by replaying the historical add/drop change-log backwards, so a 2018 backtest sees the 2018 membership, not today's winners.

Point-in-time membership

Start from today's constituents and un-apply every membership change after the anchor t:

\mathcal{U}(t) = \mathcal{U}_{\text{now}} \;\ominus\; \{\text{adds after } t\} \;\oplus\; \{\text{drops after } t\}

Constituents resolved from the index change-log; the same point-in-time set the factor + screening modules use.

3.2 Price Loader

Bulk OHLCV fetch for the whole universe, point-in-time, no future bars.

Momentum, volatility, trend, every price-based metric needs history. This loads open/high/low/close/volume for all names in parallel, clipped so nothing after the anchor can leak in. The lookback window is derived automatically from the deepest metric you wired.

The window is derived, not guessed

It loads exactly enough history for the hungriest downstream metric plus a warm-up buffer:

W = \max_k(\text{lookback}_k) + \text{buffer}, \qquad \text{bars} \le \text{anchor } t

3.3 Filter Beta

CAPM market beta, how hard this stock moves when the market moves.

Regress the stock’s daily returns on the market proxy’s over a trailing window. The slope is beta: 2.0 doubles the market’s move, 0.5 halves it, negative moves against it. One caution the estimate itself cannot give you: beta is measured AGAINST the index, so when one factor dominates index variance, a high beta is a high loading on that factor, whatever it happens to be that decade.

The regression slope

\hat\beta_i = \frac{\operatorname{Cov}(r_i, r_m)}{\operatorname{Var}(r_m)}

Daily simple returns, inner-joined dates, population moments (cov and var share the ddof, or the ratio drifts from OLS). Default window 252 trading days against SPY; fewer than 60 overlapping days returns no estimate rather than a guess.

Optional Vasicek shrinkage

\beta^{shrunk}_i = w\cdot 1 + (1-w)\,\hat\beta_i

Pulls extreme estimates toward 1.0 (Frazzini–Pedersen use w = 0.4 toward the cross-section). Default w = 0 keeps raw OLS, studies that rank on the extremes usually want the extremes unshrunk, and say so.

Reading it

The metric attaches to each stock for Composite Σ / Top-N ranking, “keep lowest” builds the defensive book, “keep highest” the aggressive one. The serial gate is OFF by default: this filter measures and ranks; it drops nothing unless you arm the gate.

Computed as-of the run anchor from anchor-clipped prices only, point-in-time at first selection and at every re-selection; the pure function is pinned by test_beta_filter (2×-market series → β = 2.0 to nine places).

3.4 Top N

Keep the best N, rank, then cut.

Sort the survivors by the Composite Σ (or, if none is wired, the last metric in the chain) and keep the top (or bottom) N. The final narrowing from a scored list to a committed basket.

Order statistic cut

\text{Top-}N = \{\, i : \operatorname{rank}(\text{score}_i) \le N \,\}

"Keep highest" for momentum; "keep lowest" for e.g. Hurst (mean reversion).

3.5 Portfolio Backtest

Replay the portfolio forward, rebalanced, point-in-time.

Holds the basket and rebalances on schedule, re-selecting and re-optimizing point-in-time at each rebalance (so it only ever uses information available then), and reports the equity curve, Sharpe, drawdown and trade stats, optionally net of cost and risk overlays.

Compounded equity

E_t = E_{t-1}\big(1 + \mathbf w_{t}^{\top}\mathbf r_t - \text{costs}_t\big)

Drawdown

\text{DD}_t = \frac{E_t}{\max_{\tau\le t}E_\tau} - 1, \qquad \text{MaxDD} = \min_t \text{DD}_t

Financing a levered book

\text{charge}_t \;=\; \text{loan}_t \cdot \frac{\text{spread}}{252}, \qquad \text{loan}_t = \begin{cases}\max(0,\,-\text{cash}_t) & \text{institutional (netted)}\\ \max(0,\,\text{long MV}_t - E_t) & \text{retail (no netting)}\end{cases}

A levered long/short book (the β-neutral Long/Short Select) borrows its excess notional. WHO you are decides the loan: a prime broker nets short-sale proceeds against the margin loan, a fully-netted BAB book carries almost none, while a retail margin account cannot net, so the same book borrows the long leg’s excess over equity. Profiles: institutional = 50 bps spread + 25 bps GC short borrow; retail = 350 bps + 150 bps (the BEST retail tier, so any verdict is conservative); custom = your own knobs, spread on negative cash. Charged daily, reported as financing_drag_pct, never silent.

3.6 Portfolio Forward Autopsy

The post-mortem, where the forward test’s return actually came from.

Runs after the Portfolio Forward Test and dissects its realized path: per-rebalance contributions, winners and losers, exposure and cash periods, and how the realized route compares to what the risk cones projected. It computes nothing new about the future, it explains the past the book just lived.

Reading it

Depth I–IV: headline attribution, per-segment breakdown, per-name contributions, and the calibration ledger (projected cone vs realized, segment by segment). In a study, this is the node that fills the appendices.

4 Projection calibration, pooled across the walk

Every rebalance carried a Monte Carlo cone and a 95% VaR estimated before the segment it is scored against. Two questions, pooled over the whole study: did realized outcomes land inside the band as often as the band claims, and were VaR breaches as frequent as 5%?

This section is produced by the forward tester itself: every portfolio backtest fits the cone and the VaR estimate at each rebalance and scores them against the segment that followed. It does not require, and this circuit does not contain, a Monte Carlo primitive; that primitive is a separate, standalone analysis.

Figure A2, projected range versus what occurred, at each of 160 scored rebalance segments, pooled across both arms. The final rebalance of each step has no following segment to score, the ledger marks those rows “no segment follows this rebalance”, which is why this count sits below the raw rebalance totals in the table beneath. Each vertical bar is that rebalance's P5–P95 Monte Carlo cone with the median ticked; the dot is the realized return of the segment that followed. Filled green = the outcome landed inside its own cone; red = it did not. The strip beneath repeats that as one mark per rebalance, so a run of misses in one period is visible as a run. Every cone was fitted only on data prior to the segment it is scored against.

Arm	Steps	Rebalances	In band	Coverage	Expected	VaR days	Breach rate	Expected
Low beta (Top-20 lowest β)	20	95	71 / 80	88.8% ±3.53	90.0%	4948	6.33% ±0.346	5.0%
High beta (Top-20 highest β)	20	95	70 / 80	87.5% ±3.7	90.0%	4951	6.34% ±0.346	5.0%

± values are binomial standard errors on the estimate. A coverage figure below the expected band means the projection was over-confident; a breach rate above 5% means the same of the risk model. Both forecasts used only data prior to the segment scored.

5 Discussion

5.1 Findings

1, The naive reading fails by a factor of five. Twenty years, twenty sealed windows, annual anchors, quarterly point-in-time re-selection: the twenty lowest-beta names compounded +86.1% (3.2%/yr); the twenty highest-beta names +692.1% (11.1%/yr); the equal-weight index +324.8% (7.5%/yr). On 5,011 paired out-of-sample days the sealed block bootstrap puts P(low beats high) at 2.5% with a paired Sharpe of −0.39; reconstructed from the stitched curves the figure is 3.0% at block length 10 and 2.2–2.8% at blocks 20 and 60, the conclusion does not depend on the block. Someone who read ‘low-beta stocks outperform’ and bought the calm twenty did not merely trail the wild twenty, they trailed the index itself by 4.3 points a year for two decades.

2, Before 2020 the anomaly was real, but it was never a raw-return claim. Over the first fourteen windows the low-beta book earned less (A +81.9% vs B +139.7% cumulative; 4.4% vs 6.4% CAGR; A still wins seven windows of fourteen) while carrying nothing like the same risk: annualized volatility 13.9% against 40.4%, worst drawdown −40.4% against −82.2%, and the Sharpe ratios come out level, 0.38 against 0.36. In 2008 the low-beta book lost 25.0% while the high-beta book lost 53.5%. Two points a year less at the destination, a third of the ride to get there, the same reward per unit of risk, that is the low-beta anomaly as Black (1972) and Frazzini–Pedersen (2014) actually state it: flat security-market line, better return PER UNIT OF BETA at the low end, monetizable only with leverage. Dividends narrow the raw gap, the low-beta book is the yield-heavy one, measured at 2.88% a year pre-2020 against the high-beta book’s 0.99%, and before 2020 they very nearly close it: total-return CAGRs of 7.37 against 7.53, 16 basis points apart. The pre-2020 anomaly in this record is a risk-adjusted fact and, on total returns, close to a level race.

3, From 2020 the anomaly inverts even on its own risk-adjusted terms. Six windows, 2020–2025: the low-beta book compounded +2.3% IN TOTAL (0.4%/yr, Sharpe 0.11, and a −35.1% drawdown anyway); the high-beta book +230.5% (22.0%/yr, Sharpe 0.68 at 42.3% vol); the equal-weight index +67.8%. The mean window gap is −26.0 points a year and the low-beta book wins one window of six (2022, +31.6 points, the one year the regime reversed). At a zero risk-free rate the low-beta book's era Sharpe is 0.11; at the actual post-2020 cash rate it is negative. The era boundary is anchored to index composition, not to these returns, information technology's S&P 500 weight first held above a quarter of the index around 2020 and kept rising (S&P DJ factsheets), and the break does not depend on the exact year: cutting at 2018, 2019, 2020 or 2021 leaves a post-cut cumulative gap of −550, −574, −550 or −438 points respectively. Our series' usual 2010 split stays in the report's own tables as a robustness row; it shows nothing, because nothing broke in 2010. A flat security-market line has an answer for same-return-less-risk. It has no answer for one side earning six times the Sharpe.

4, The high-beta book changed identity underneath the estimator. Pre-2020, Arm B's baskets were 28% financials and 22% technology, and in the 2008 and 2009 windows they contained not a single technology name: the highest betas of that era were the levered banks and insurers of the crisis. From 2020 the same estimator, unchanged, fills the book with 45% technology, 18% across the 2020 window's formations rising to 74% by 2025, with AMAT, LRCX and NVDA present in all six windows and TSLA in five. (Sector labels are today's FMP classifications applied to historical baskets, GICS itself moved Google and Meta out of information technology in 2018 and Visa and Mastercard out in 2023, so the tech shares here are conservative for the early windows and definitional at the margins; the names, which are the evidence, are frozen in the ledger.) Arm A never changes clothes: consumer staples plus utilities are 69% of it before 2020 and 58% after; General Mills, Campbell, Kellogg, Kroger, Church & Dwight and Conagra appear in every 2020+ window. One arm is a stable habitat; the other is whatever the market's variance engine happens to be.

5, Beta is a rearview mirror pointed at the last regime. The 2009 high-beta book, zero tech, heavy financials, returned +68.5% in the recovery window: trailing beta had selected maximum exposure to the very sector the crash had just crushed, exactly in time for its rebound. The 2025 high-beta book is the semiconductor complex. A 252-day OLS beta does not measure a stable property of a company; it measures how hard the stock moved with whatever dominated index variance during the trailing year. Different decades load it with different cargo, and the portfolio it builds inherits that cargo, not the label.

6, When a third of the index is one factor, ‘market risk’ is that factor. Information technology grew to roughly a third of S&P 500 weight across 2020–2025 (S&P Dow Jones Indices factsheets put the sector above 30% from 2024). Beta is estimated against the index; as the index's variance became increasingly the tech factor's variance, a high beta became, mechanically, a high tech loading, finding 4 is the direct observation. The inversion in finding 3 then has a plain reading: from 2020, buying high beta meant concentrated exposure to the factor that carried the market, and buying low beta meant owning the market MINUS that engine, 0.4% a year while the equal-weight index did 9.0%. The estimate did not break; what it measures drifted. Your beta is measuring something other than what you think.

7, What betting-against-beta ACTUALLY does, none of which happened here, deliberately. Frazzini–Pedersen's BAB is not ‘buy calm stocks’: it rank-weights toward the extremes, goes LONG low-beta LEVERED UP to a beta of one and SHORT high-beta DELEVERED DOWN to a beta of one, and finances the leverage at institutional funding rates. It is a machine for converting a risk-adjusted edge (finding 2's kind) into raw return, and it needs cheap borrowing, cheap shorting and continuous rebalancing to exist. Novy-Marx & Velikov (2022) showed that much of its paper premium sits in those construction choices, rank weights, micro-caps, industry tilts, rather than in the anomaly itself. This study ran the unlevered selection content on liquid large caps precisely to isolate the part of the trade that exists BEFORE the machinery, because the machinery is exactly what a retail account cannot rent: margin at retail spreads instead of institutional funding, and a short leg that since 2020 means shorting the index's own engine.

8, Calibration, stated as calibration and nothing more. The evidence that the return gap is real is the paired bootstrap in finding 1; cone coverage speaks only to the projection model's honesty, and it was honest unevenly. Pooled across ninety-five rebalances per arm the low-beta book's band covered 88.8% of outcomes against a 90% target (VaR breaches 6.3% vs 5% expected), but the regime years stressed it: 2008 saw the low-beta cone cover just 25% of its segments (VaR breaches 19.3%), and 2020 did the same to the high-beta cone (25% coverage, 15.7% breaches). Trailing-window risk models miss regime breaks in exactly the windows this paper is about, which is consistent with the thesis, and every number is in the appendix ledger, including the ugly ones.

5.2 Interpretation

The era cut in this paper is 2020, not our usual 2010, and it is anchored to something the return series did not choose: index composition. Information technology's share of S&P 500 weight first held above a quarter of the index around 2020 and kept rising, the point at which, mechanically, beta against the index became substantially a loading on one sector. The sealed design, registered before any window ran, was the A/B contrast itself; the cut is interpretation, disclosed as such, and it is not fragile: any cut from 2018 to 2021 leaves a post-cut gap between −438 and −574 cumulative points. The customary 2010 split stays in the report as a robustness row; it shows nothing, because nothing broke in 2010, which is exactly why this paper does not use it.

Read in sequence, the record tells one coherent story. First: the popular sentence ‘low-beta stocks outperform’ was never true in raw returns, not even pre-2020, what was true was the same Sharpe at a third of the volatility, two raw points a year behind, which is a statement about the PRICE of beta, monetizable only with leverage. Second: from 2020 even the defensible version fails, and the composition ledger says why. The high-beta book stopped being ‘risky stocks’ in general and became THE index's dominant factor, the semiconductor-and-platform complex, while the low-beta book remained what it always was: staples, utilities, the pantry. Betting against beta in this regime is not a bet against risk appetite; it is a structural short of the market's engine, held for six years. Third: the estimator itself is the quiet culprit. Beta against an index that is one-third one factor is a factor loading wearing a risk-model costume. The same estimator loaded banks in 2009 and semis in 2025; anyone reading ‘beta’ as a stable risk dial across those decades was measuring two different things with one name.

Two honesty notes bound the headline, and the dividend one matters most before 2020. The platform computes price returns without dividends, and the omission always favors the high-beta side, because the low-beta book is the yield-heavy one. This passage originally carried stated-assumption bounds and said so. The dividends have since been measured, per share from the payment record, applied against the entry price of every recorded quarterly basket, with each window reconciled against the engine’s own price return before the overlay was applied, and the figures below are those measurements. The correction runs in the low-beta book’s favour, because the assumption that was wrong concerned the other arm. PRE-2020 the omission does not merely narrow the verdict, it very nearly erases it: the low-beta book yielded 2.88% a year across those fourteen windows and the high-beta book 0.99%, not the 2–2.5% originally assumed for a financial-heavy arm, because the banks that arm held through 2008–2010 had cut their payouts to almost nothing in exactly those windows. Crediting the measured yields moves the CAGRs from 4.37-vs-6.44 to 7.37-vs-7.53. The pre-2020 gap is 16 basis points, not two points and not one, which makes finding 2 stronger rather than weaker: on total returns the two books are level, and the low-beta book got there at a third of the volatility. POST-2020 it is immaterial, as originally stated, though for a slightly different reason, the low-beta book yielded 2.79% and the high-beta book 1.00%, so both era totals rise, the low-beta book’s to +21.1% and the high-beta book’s to +249.3%, and the gap is unchanged in character. Across the full twenty windows the low-beta book compounds at 6.11% against the high-beta book’s 12.00%, where the price-return figures were 3.15% and 10.90%: dividends take the headline gap from 7.75 points to 5.89 and come nowhere near closing it. Cost omission, the other candidate asymmetry, turns out nearly neutral by measurement: quarterly re-selection turnover is 26.7% of the book in Arm A and 28.8% in Arm B across 75 re-selections each, the staples core is stable, but the low-beta periphery churns as much as the high-beta book does. And the post-2020 era is six windows, six annual observations cannot carry a significance claim and we make none; the bootstrap's 2.5% is a full-period statement. What the six windows carry is composition: WHO was in the book is a fact per rebalance, not a statistic, and it is the composition that makes the mechanism legible.

The follow-up is committed: replicate the actual Frazzini–Pedersen construction, rank weights, both legs scaled to unit beta, the short leg live, under RETAIL financing: broker margin spreads instead of institutional funding, borrow fees on the short leg, the works. This study is the baseline that replication will be measured against: the selection content came free; everything the machinery adds must now pay for itself at the rates you and I actually face.

No search record exists for this study: the design was not promoted from a recorded evolving search, so the number of alternatives tried before it is UNKNOWN, which is a different fact from one. No count of alternatives tried is claimed, and nothing is corrected for a search that was never recorded; the number that stands is the raw out-of-sample result plus this disclosure. The out-of-sample windows are historical.

What betting-against-beta actually is, and why your broker breaks it

The trade the literature defends is not the trade the sentence ‘low-beta outperforms’ suggests. Frazzini–Pedersen's BAB portfolio: rank every stock by beta; overweight the extremes by rank; go LONG the low-beta half and lever it UP until its portfolio beta equals one; go SHORT the high-beta half and scale it DOWN to a beta of one; the two legs finance each other, and the leverage is funded near institutional rates. The bet is not that calm stocks beat wild ones, it is that the security-market line is too flat, so a dollar of beta bought at the calm end earns more than a dollar of beta sold at the wild end. Leverage is the engine that converts that per-unit edge into raw return. Now price the engine at retail. The long leg needs roughly 1.4x exposure: margin at a mainstream broker runs several points over the benchmark rate, the spread alone consumes an edge measured in single points. The short leg needs to be short the highest-beta names continuously: since 2020 that is a standing short of the semiconductor complex, the +230% side of this study, plus borrow fees. And the whole construction rebalances monthly, at spreads, forever. Novy-Marx & Velikov (2022) put numbers on the institutional version's implementation drag; the retail version is not a degraded copy of the trade, it is a different trade with the same name. What a retail account CAN hold is the selection content, the two books this study ran. Unlevered, long-only, the content said: the same Sharpe for a third of the ride before 2020, two raw points a year behind, and ‘you sold the engine’ after.

Next in the series

The replication paper will build the actual machine: rank weights, both legs scaled to unit beta, the short leg live, monthly rebalancing, run once at frictionless institutional assumptions to reproduce the published shape, and once at retail reality: broker margin spreads on the levered long, borrow fees on the short, spreads on every rebalance. The gap between those two runs is the price of the machinery; this study is the baseline that says what the raw material was worth before any machinery touched it. If the anomaly survives its own construction at retail prices, that is worth knowing. If it does not, that is worth knowing precisely.

What the twenty highest betas were, window by window. Sector shares of the high-beta basket at every formation, 2006–2025: financials collapse after 2009; technology climbs from zero in the crisis windows to three-quarters of the basket by 2025. Sector labels are current FMP classifications (see Lim

The cumulative gap, window by window, low-beta minus high-beta, compounded across the twenty sealed windows. Flat through 2016, a slow drift into 2019, then the break draws itself. Any cut from 2018 to 2021 leaves a post-cut gap between −438 and −574 points.

5.3 Limitations

Price returns, not total returns, platform-wide, and the omission favors the high-beta arm (the low-beta book is the yield-heavy one); the discussion now carries MEASURED dividends rather than the stated-assumption bounds it originally used, pre-2020 the effect is larger than that bound allowed, taking the two books from 4.37-vs-6.44 to 7.37-vs-7.53, and across the full twenty windows it narrows the gap from 7.75 points to 5.89 without flipping it. The universe is point-in-time S&P 500 membership, so Novy-Marx–Velikov's micro-cap critique of BAB is dissolved by construction rather than tested, nothing here speaks to small-cap behavior. Beta is a 252-day raw OLS estimate against SPY with no Vasicek shrinkage; Frazzini–Pedersen shrink toward one, which compresses the extremes both books select from, a replication knob, deliberately left at zero here. Sector labels for the composition analysis come from current FMP company profiles, not point-in-time GICS history, sector membership as of today is applied to holdings of the past, and twenty of the 308 names that ever entered a book (delisted tickers) were classified by hand from public record. Both books ran at zero transaction costs; the contrast is symmetric but absolute levels are gross. The 2020 era cut is descriptive, chosen after seeing the window table, and is labelled as such wherever it appears; the sealed, pre-registered object is the twenty-window A/B walk itself. Six post-2020 windows support narrative and composition facts, not statistical claims. Books occasionally held fewer than twenty names for a quarter when a selected name lacked a usable entry bar, the engine's honest behavior, disclosed in the per-window reports.

References

QuanterLab reference architecture

Gelman, A., & Loken, E. (2013). The garden of forking paths: Why multiple comparisons can be a problem, even when there is no “fishing expedition.” Working paper, Columbia University.
Harvey, C. R., Liu, Y., & Zhu, H. (2016). … and the Cross-Section of Expected Returns. Review of Financial Studies, 29(1), 5–68. doi:10.1093/rfs/hhv059
Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36–52. doi:10.2469/faj.v58.n4.2453

Author’s references?

Black, F. (1972). Capital Market Equilibrium with Restricted Borrowing. Journal of Business, 45(3), 444–455.
Black, F., Jensen, M. C., & Scholes, M. (1972). The Capital Asset Pricing Model: Some Empirical Tests. In Studies in the Theory of Capital Markets. Praeger.
Haugen, R. A., & Heins, A. J. (1975). Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles. Journal of Financial and Quantitative Analysis, 10(5), 775–784.
Frazzini, A., & Pedersen, L. H. (2014). Betting Against Beta. Journal of Financial Economics, 111(1), 1–25.
Novy-Marx, R., & Velikov, M. (2022). Betting Against Betting Against Beta. Journal of Financial Economics, 143(1), 80–106.
Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly. Financial Analysts Journal, 67(1), 40–54.
Asness, C., Frazzini, A., Gormsen, N. J., & Pedersen, L. H. (2020). Betting Against Correlation: Testing Theories of the Low-Risk Effect. Journal of Financial Economics, 135(3), 629–652.
Vasicek, O. A. (1973). A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Betas. Journal of Finance, 28(5), 1233–1239.
S&P Dow Jones Indices (2024–2025). S&P 500 Factsheet, sector weights; information technology above 30% of index weight.
Published retail margin rate schedules of major U.S. brokers (2024–2025), vs. overnight benchmark rates, the retail financing spread referenced in §7.

Appendix A Reproducibility in QuanterLab

Each step is backed by a frozen run report. The study is re-derivable from the ledger below.

#	Commit	Report	Anchor	OOS window
1	5f9784202c0d	591	2006-01-01	2006-01-03 → 2006-12-29
2	e293a3aeee7d	592	2007-01-01	2007-01-03 → 2007-12-31
3	9283fdbc0b32	593	2008-01-01	2008-01-02 → 2008-12-31
4	07a67d15b84d	594	2009-01-01	2009-01-02 → 2009-12-31
5	ca486f527f9b	595	2010-01-01	2010-01-04 → 2010-12-31
6	07ca4ba18587	596	2011-01-01	2011-01-03 → 2011-12-30
7	61c2e745988f	597	2012-01-01	2012-01-03 → 2012-12-31
8	154de9f02996	598	2013-01-01	2013-01-02 → 2013-12-31
9	1124c963e8b2	599	2014-01-01	2014-01-02 → 2014-12-31
10	449c52a5c87e	600	2015-01-01	2015-01-02 → 2015-12-31
11	35c635f804c4	601	2016-01-01	2016-01-04 → 2016-12-30
12	3cda82a1d48d	602	2017-01-01	2017-01-03 → 2017-12-29
13	2b0130c5003c	603	2018-01-01	2018-01-02 → 2018-12-31
14	5b68c6fedc20	604	2019-01-01	2019-01-02 → 2019-12-31
15	796d7e0f0580	605	2020-01-01	2020-01-02 → 2020-12-31
16	c69d3909b13b	606	2021-01-01	2021-01-04 → 2021-12-31
17	0dcd07af6edb	607	2022-01-01	2022-01-03 → 2022-12-30
18	c76d4b584182	608	2023-01-01	2023-01-03 → 2023-12-29
19	29617393c8ab	609	2024-01-01	2024-01-02 → 2024-12-31
20	2c9d884f2238	611	2025-01-01	2025-01-02 → 2025-12-31

Appendix A2 Registration record

What this record does and does not establish. Every window in this study is historical: the data existed before the study began, so this is sequential sealing on past windows, not pre-registration in the clinical-trial sense, and no procedure could make it so. What the platform does enforce is order, each step's specification was frozen and hashed before that step was scored, and the walk cannot advance past a step that was never run or close one with a result registered for a different window. The two timestamp columns below are the evidence: read them together and each seal precedes its own run, and each run precedes the next seal. A study whose seals all post-date its runs would show it here. Wall-clock spacing between seals varies with the author's schedule and queue latency; the ordering, not the tempo, is the claim.

“A COMPARATIVE study, Low beta (Top-20 lowest β) vs High beta (Top-20 highest β), walked on the same registered out-of-sample windows. Low beta (Top-20 lowest β): S&P 500, selected by statistical / factor criteria, rebalanced quarterly across the selected basket, and run out-of-sample from the anchor, whatever the design estimates from history is re-estimated at each anchor from pre-anchor data only, and the walk advances through registered out-of-sample windows; its disposition is the realized forward path versus the benchmark. High beta (Top-20 highest β): S&P 500, selected by statistical / factor criteria, rebalanced quarterly across the selected basket, and run out-of-sample from the anchor, whatever the design estimates from history is re-estimated at each anchor from pre-anchor data only, and the walk advances through registered out-of-sample windows; its disposition is the realized forward path versus the benchmark. The arms differ in: Top-N, select: lowest → highest. The contrast under test: whether Low beta (Top-20 lowest β) generates better risk-adjusted returns than High beta (Top-20 highest β) over the identical out-of-sample windows.”

The same hypothesis was registered independently at every step, hashed before each step's out-of-sample window was scored:

**Table 4.** Registration audit, one row per registered step, with the time each specification was frozen and the time its window was scored. The hypothesis is identical on every row by design: it was registered once and re-registered unchanged at each anchor. Rows that differ would mean the specification moved mid-walk, which is the thing this record exists to rule out. The timestamps are the separate claim: each seal precedes its own run, and each run precedes the next seal.
#	Anchor	Registered at (UTC)	Run completed (UTC)
1	2006-01-01	2026-08-08 10:39:45	2026-08-08 10:43:03
2	2007-01-01	2026-08-08 10:43:08	2026-08-08 10:44:48
3	2008-01-01	2026-08-08 10:44:53	2026-08-08 10:46:14
4	2009-01-01	2026-08-08 10:46:19	2026-08-08 10:47:59
5	2010-01-01	2026-08-08 10:48:04	2026-08-08 10:49:45
6	2011-01-01	2026-08-08 10:49:50	2026-08-08 10:51:30
7	2012-01-01	2026-08-08 10:51:35	2026-08-08 10:52:56
8	2013-01-01	2026-08-08 10:53:01	2026-08-08 10:54:41
9	2014-01-01	2026-08-08 10:54:46	2026-08-08 10:56:27
10	2015-01-01	2026-08-08 10:56:32	2026-08-08 10:58:13
11	2016-01-01	2026-08-08 10:58:18	2026-08-08 10:59:38
12	2017-01-01	2026-08-08 10:59:43	2026-08-08 11:01:23
13	2018-01-01	2026-08-08 11:01:28	2026-08-08 11:03:09
14	2019-01-01	2026-08-08 11:03:14	2026-08-08 11:04:34
15	2020-01-01	2026-08-08 11:04:39	2026-08-08 11:06:00
16	2021-01-01	2026-08-08 11:06:05	2026-08-08 11:07:45
17	2022-01-01	2026-08-08 11:07:50	2026-08-08 11:09:11
18	2023-01-01	2026-08-08 11:09:16	2026-08-08 11:09:56
19	2024-01-01	2026-08-08 11:10:01	2026-08-08 11:11:21
20	2025-01-01	2026-08-08 11:11:26	2026-08-08 11:13:07

Appendix B Per-step diagnostics

What each step's run actually did beyond its return: capital allocation across lanes and regimes, the portfolio book's rebalancing and cost drag, and how positions were sized. Harvested from the frozen run reports, present where the circuit produced them.

Step 1 · 2006-01-03 → 2006-12-29

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (40 names actually held across the window), weights renormalised onto the rest

Projection accuracy, realized outcome fell inside the P5–P95 cone in 100.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 9.84% of 244 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2006-01-01	-6.2423%	0.7644%	9.0115%	2.5693%	yes	0.9315%	3 / 58
2006-04-01	-5.4674%	1.5077%	9.0425%	0.1678%	yes	0.8592%	10 / 62
2006-07-01	-5.9965%	0.7713%	8.07%	4.0675%	yes	0.7852%	5 / 62
2006-10-01	-4.7368%	1.965%	9.1814%	6.3028%	yes	0.8633%	6 / 62
2007-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (31 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2006-01-01	-11.7541%	5.9051%	29.2379%	10.6998%	yes	2.402%	1 / 61
2006-04-01	-11.0797%	8.4706%	32.4721%	-10.8641%	yes	2.4626%	8 / 62
2006-07-01	-12.3097%	8.0393%	33.2718%	-9.3681%	yes	2.6259%	3 / 62
2006-10-01	-14.2984%	6.0577%	31.4116%	8.1255%	yes	2.6478%	1 / 62
2007-01-01	no segment follows this rebalance, not scored

Step 2 · 2007-01-03 → 2007-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2007-01-01	-4.4569%	2.4542%	9.1655%	2.1338%	yes	0.7934%	4 / 60
2007-04-01	-4.8979%	1.384%	8.1209%	-1.1623%	yes	0.7468%	9 / 62
2007-07-01	-4.2277%	1.8152%	8.2778%	1.7276%	yes	0.7403%	10 / 62
2007-10-01	-5.1538%	2.0974%	9.1936%	1.3828%	yes	0.8664%	7 / 63
2008-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 9.31% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2007-01-01	-13.0054%	6.7969%	28.6702%	3.6013%	yes	2.4111%	4 / 60
2007-04-01	-10.4734%	7.8689%	30.1102%	8.2707%	yes	2.2659%	1 / 62
2007-07-01	-10.3923%	7.6269%	29.4073%	-4.9912%	yes	2.0761%	10 / 62
2007-10-01	-11.4127%	8.5307%	30.612%	-12.0923%	no	2.4027%	8 / 63
2008-01-01	no segment follows this rebalance, not scored

Step 3 · 2008-01-02 → 2008-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 4 constructions · 19 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (37 names actually held across the window), weights renormalised onto the rest

Projection accuracy, realized outcome fell inside the P5–P95 cone in 25.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 19.28% of 249 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2008-01-01	-5.1466%	2.2391%	9.4466%	-7.7864%	no	0.8246%	12 / 60
2008-04-01	-8.0864%	0.6435%	9.3272%	-9.3658%	no	1.1049%	8 / 63
2008-07-01	-9.3723%	-0.0117%	9.3667%	1.6941%	yes	1.2139%	8 / 63
2008-10-01	-8.4453%	0.9268%	10.3093%	-10.709%	no	1.2194%	20 / 63

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 4 constructions · 19 names held · selection: reselect · 0.0% in cash · 4 names dropped at load (31 names actually held across the window), weights renormalised onto the rest

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 21.69% of 249 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2008-01-01	-21.0797%	-0.3418%	23.1879%	-5.9781%	yes	2.6122%	15 / 60
2008-04-01	-32.998%	-7.0434%	25.3067%	-34.5033%	no	3.6703%	12 / 63
2008-07-01	-36.9891%	-10.5473%	23.1391%	16.1815%	yes	4.4435%	13 / 63
2008-10-01	-49.8384%	-13.3364%	42.7022%	-35.5781%	yes	5.6225%	14 / 63

Step 4 · 2009-01-02 → 2009-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (24 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2009-01-01	-14.5928%	-0.1383%	15.1043%	-10.3909%	yes	1.7534%	9 / 60
2009-04-01	-16.1601%	-1.8743%	14.9507%	7.8138%	yes	1.9177%	0 / 62
2009-07-01	-16.638%	-0.7925%	16.2728%	5.5239%	yes	1.9553%	0 / 63
2009-10-01	-15.8259%	0.0522%	17.1328%	8.9255%	yes	1.9504%	0 / 63
2010-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (28 names actually held across the window), weights renormalised onto the rest

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 7.66% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2009-01-01	-47.6932%	-10.4986%	45.802%	-29.4574%	yes	5.3861%	16 / 60
2009-04-01	-57.1102%	-17.9221%	57.6657%	79.1532%	no	7.9587%	3 / 62
2009-07-01	-57.8888%	-11.2371%	75.2276%	47.4253%	yes	9.1557%	0 / 63
2009-10-01	-54.1991%	-5.0542%	84.6082%	3.3441%	yes	8.7637%	0 / 63
2010-01-01	no segment follows this rebalance, not scored

Step 5 · 2010-01-04 → 2010-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (39 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2010-01-01	-15.995%	0.8735%	19.1186%	2.8514%	yes	1.9707%	1 / 60
2010-04-01	-15.9901%	0.3372%	19.9614%	-10.4229%	yes	2.0047%	3 / 62
2010-07-01	-15.6675%	0.223%	17.3141%	9.0656%	yes	1.8842%	0 / 63
2010-10-01	-15.4609%	1.2098%	19.2662%	2.9529%	yes	1.9898%	0 / 63
2011-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2010-01-01	-55.6214%	-5.7916%	86.6819%	22.3295%	yes	8.5029%	0 / 60
2010-04-01	-49.2333%	-2.3482%	88.5531%	-20.3775%	yes	8.1789%	0 / 62
2010-07-01	-48.4545%	-2.6292%	73.9354%	9.9004%	yes	7.6282%	0 / 63
2010-10-01	-45.6404%	0.8847%	77.3252%	19.3458%	yes	7.9409%	0 / 63
2011-01-01	no segment follows this rebalance, not scored

Step 6 · 2011-01-03 → 2011-12-30

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 6.45% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2011-01-01	-10.4299%	1.5783%	16.5305%	2.0963%	yes	1.5185%	0 / 61
2011-04-01	-7.0356%	3.0066%	14.2017%	5.0784%	yes	1.1384%	2 / 62
2011-07-01	-4.0326%	5.0673%	14.1177%	-6.2642%	no	0.9677%	11 / 63
2011-10-01	-6.1864%	2.7917%	12.6889%	7.94%	yes	1.1286%	3 / 62
2012-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 8.87% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2011-01-01	-32.8792%	9.0865%	85.3491%	9.2885%	yes	6.3351%	0 / 61
2011-04-01	-24.7285%	16.4946%	80.7523%	-10.4146%	yes	5.0736%	0 / 62
2011-07-01	-21.252%	9.5313%	47.9932%	-37.6113%	no	3.4787%	13 / 63
2011-10-01	-28.5424%	-2.2463%	33.9704%	27.7714%	yes	3.954%	9 / 62
2012-01-01	no segment follows this rebalance, not scored

Step 7 · 2012-01-03 → 2012-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (24 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2012-01-01	-5.7273%	2.9842%	13.4144%	0.8802%	yes	1.1048%	0 / 61
2012-04-01	-6.4188%	2.5387%	12.4133%	2.0837%	yes	1.0994%	1 / 62
2012-07-01	-7.0554%	1.9216%	11.8257%	1.3046%	yes	1.1325%	0 / 62
2012-10-01	-5.7726%	2.0571%	11.3478%	-3.3079%	yes	0.9417%	3 / 61

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2012-01-01	-27.8893%	-1.2199%	39.2668%	19.5197%	yes	4.3498%	0 / 61
2012-04-01	-28.5432%	-0.1543%	39.7848%	-18.3149%	yes	4.4012%	2 / 62
2012-07-01	-31.9187%	-4.3586%	34.6239%	7.1895%	yes	4.3927%	0 / 62
2012-10-01	-27.9012%	-3.0043%	34.0812%	12.0172%	yes	3.9012%	1 / 61

Step 8 · 2013-01-02 → 2013-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 5.24% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2013-01-01	-7.1813%	2.1132%	10.8227%	12.2712%	no	0.9912%	1 / 59
2013-04-01	-6.3277%	3.2923%	12.9257%	-2.2599%	yes	1.0054%	7 / 63
2013-07-01	-8.168%	2.5065%	13.3212%	-0.1649%	yes	1.0876%	3 / 63
2013-10-01	-7.9983%	2.2456%	12.5806%	1.3429%	yes	1.0951%	2 / 63
2014-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2013-01-01	-27.1846%	0.3876%	32.2174%	1.6275%	yes	3.7153%	1 / 59
2013-04-01	-27.5661%	-0.1913%	33.7082%	9.4791%	yes	3.7107%	1 / 63
2013-07-01	-25.8032%	1.5807%	35.2839%	8.6523%	yes	3.6078%	0 / 63
2013-10-01	-20.4531%	7.1367%	40.5682%	13.5286%	yes	3.4893%	0 / 63
2014-01-01	no segment follows this rebalance, not scored

Step 9 · 2014-01-02 → 2014-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2014-01-01	-7.1529%	0.8584%	8.7346%	7.3048%	yes	0.9406%	3 / 60
2014-04-01	-6.0532%	1.3056%	9.2887%	3.4654%	yes	0.9319%	1 / 62
2014-07-01	-6.9139%	1.7335%	10.3194%	-2.8623%	yes	1.0243%	5 / 63
2014-10-01	-8.5738%	0.5297%	9.6212%	11.2089%	no	1.0834%	5 / 63
2015-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2014-01-01	-11.6388%	9.3264%	32.6571%	0.5022%	yes	2.2907%	3 / 60
2014-04-01	-9.5147%	8.6322%	30.557%	5.4973%	yes	2.1956%	2 / 62
2014-07-01	-6.6275%	12.3605%	33.0277%	0.6897%	yes	2.0126%	3 / 63
2014-10-01	-7.545%	12.6653%	34.9285%	5.2322%	yes	1.9104%	7 / 63
2015-01-01	no segment follows this rebalance, not scored

Step 10 · 2015-01-02 → 2015-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2015-01-01	-7.4389%	2.3212%	12.0779%	-3.8699%	yes	1.1405%	7 / 60
2015-04-01	-8.1843%	1.3123%	11.8551%	-7.1315%	yes	1.0794%	7 / 62
2015-07-01	-9.0248%	-0.0816%	8.8399%	-4.1233%	yes	1.0243%	9 / 63
2015-10-01	-9.6954%	0.6733%	11.1654%	2.571%	yes	1.1816%	6 / 63
2016-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2015-01-01	-8.8061%	11.2211%	33.2053%	6.5931%	yes	2.1502%	4 / 60
2015-04-01	-10.3267%	7.9882%	30.1843%	-0.7357%	yes	2.3299%	1 / 62
2015-07-01	-11.7907%	7.2506%	28.1811%	-19.3469%	no	2.2171%	8 / 63
2015-10-01	-16.615%	2.0199%	22.626%	2.0946%	yes	2.5128%	3 / 63
2016-01-01	no segment follows this rebalance, not scored

Step 11 · 2016-01-04 → 2016-12-30

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (33 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2016-01-01	-8.6914%	1.5048%	11.7522%	8.977%	yes	1.1728%	3 / 60
2016-04-01	-7.0468%	4.2886%	15.829%	7.9001%	yes	1.2299%	4 / 63
2016-07-01	-8.7434%	4.4093%	18.0524%	-6.7359%	yes	1.5936%	4 / 63
2016-10-01	-8.9481%	3.5156%	17.7732%	-0.5655%	yes	1.6158%	5 / 62

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2016-01-01	-19.1849%	-0.3344%	20.5784%	-1.4546%	yes	2.4318%	13 / 60
2016-04-01	-25.762%	-2.5689%	24.8508%	16.2137%	yes	3.5169%	3 / 63
2016-07-01	-26.7211%	-2.9699%	25.348%	13.4433%	yes	3.4426%	1 / 63
2016-10-01	-25.9798%	-3.1232%	26.9897%	15.7834%	yes	3.5881%	0 / 62

Step 12 · 2017-01-03 → 2017-12-29

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2017-01-01	-9.4432%	2.2908%	16.8408%	5.6808%	yes	1.6163%	0 / 61
2017-04-01	-10.392%	1.2621%	14.5133%	0.9798%	yes	1.4978%	0 / 62
2017-07-01	-9.2192%	1.8738%	14.3991%	0.189%	yes	1.5391%	1 / 62
2017-10-01	-8.7745%	2.2089%	14.5903%	-0.5345%	yes	1.3966%	1 / 62
2018-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2017-01-01	-24.5553%	-2.7618%	28.2719%	3.7568%	yes	3.5444%	0 / 61
2017-04-01	-20.593%	1.5033%	29.9336%	-4.1669%	yes	2.9471%	1 / 62
2017-07-01	-20.5233%	-0.0494%	25.8665%	8.4642%	yes	2.9489%	0 / 62
2017-10-01	-14.2534%	5.6659%	30.3709%	8.0375%	yes	2.7124%	0 / 62
2018-01-01	no segment follows this rebalance, not scored

Step 13 · 2018-01-02 → 2018-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2018-01-01	-8.092%	2.473%	13.1208%	-3.126%	yes	1.2638%	7 / 60
2018-04-01	-10.2298%	0.4888%	11.3775%	3.2228%	yes	1.4123%	2 / 63
2018-07-01	-9.9515%	0.4609%	12.1485%	0.1933%	yes	1.4363%	2 / 62
2018-10-01	-10.4903%	-0.3508%	11.0064%	0.8658%	yes	1.3809%	5 / 62
2019-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 10.53% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2018-01-01	-11.991%	7.6111%	29.1811%	1.5721%	yes	2.1833%	6 / 60
2018-04-01	-5.748%	14.4299%	36.579%	9.6585%	yes	2.2423%	4 / 63
2018-07-01	-6.9889%	10.34%	31.0275%	5.2509%	yes	2.1305%	2 / 62
2018-10-01	-6.773%	9.8307%	29.5149%	-23.5999%	no	1.991%	14 / 62
2019-01-01	no segment follows this rebalance, not scored

Step 14 · 2019-01-02 → 2019-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Projection accuracy, realized outcome fell inside the P5–P95 cone in 75.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 3.63% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2019-01-01	-9.7781%	1.3028%	12.5458%	13.1051%	no	1.4395%	1 / 60
2019-04-01	-8.4122%	1.4445%	12.4287%	4.4845%	yes	1.3047%	4 / 62
2019-07-01	-8.1456%	2.494%	13.2696%	7.2894%	yes	1.3091%	2 / 63
2019-10-01	-7.792%	3.1013%	14.1556%	-1.1743%	yes	1.3347%	2 / 63
2020-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2019-01-01	-13.4917%	6.6263%	28.9331%	22.9006%	yes	2.709%	4 / 60
2019-04-01	-12.9389%	7.2266%	32.2231%	-1.002%	yes	2.9237%	1 / 62
2019-07-01	-14.7947%	7.3301%	32.4844%	-9.5142%	yes	2.8964%	4 / 63
2019-10-01	-17.4776%	4.7768%	30.2702%	18.6204%	yes	3.0907%	0 / 63
2020-01-01	no segment follows this rebalance, not scored

Step 15 · 2020-01-02 → 2020-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2020-01-01	-7.2011%	2.6303%	14.554%	-11.6745%	no	1.368%	13 / 61
2020-04-01	-11.8871%	0.9858%	15.8312%	11.2799%	yes	1.5811%	1 / 62
2020-07-01	-9.9999%	4.338%	19.3985%	3.925%	yes	1.4502%	5 / 63
2020-10-01	-10.887%	3.5675%	18.7868%	-3.2397%	yes	1.594%	2 / 63

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2020-01-01	-17.972%	1.0437%	26.8656%	-38.7593%	no	2.9378%	15 / 61
2020-04-01	-39.4942%	-14.0319%	22.3951%	60.5663%	no	3.1249%	19 / 62
2020-07-01	-41.4567%	-7.4284%	40.6006%	5.2187%	yes	4.291%	3 / 63
2020-10-01	-41.8736%	-6.837%	43.2541%	47.3493%	no	4.4451%	2 / 63

Step 16 · 2021-01-04 → 2021-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (38 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2021-01-01	-11.7799%	2.8127%	18.153%	1.5426%	yes	1.582%	1 / 60
2021-04-01	-11.2504%	3.3901%	20.5525%	1.5569%	yes	1.4538%	0 / 62
2021-07-01	-14.4535%	2.3395%	20.5154%	-3.3382%	yes	1.587%	1 / 63
2021-10-01	-13.3407%	2.6402%	19.7732%	12.7357%	yes	1.4191%	2 / 63
2022-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2021-01-01	-40.4281%	-3.0074%	51.0328%	23.3549%	yes	4.4835%	0 / 60
2021-04-01	-35.6731%	3.7788%	67.8927%	6.8913%	yes	4.5041%	0 / 62
2021-07-01	-21.4927%	16.0406%	65.7276%	-2.7586%	yes	4.0718%	0 / 63
2021-10-01	-29.8754%	10.7285%	67.9621%	4.3813%	yes	4.1393%	1 / 63
2022-01-01	no segment follows this rebalance, not scored

Step 17 · 2022-01-03 → 2022-12-30

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2022-01-01	-10.7018%	3.9256%	22.64%	-0.8951%	yes	1.5245%	4 / 61
2022-04-01	-12.4591%	1.8239%	20.087%	-3.3726%	yes	1.5254%	5 / 61
2022-07-01	-9.9669%	1.8941%	14.0701%	-11.4327%	no	1.4413%	7 / 63
2022-10-01	-10.5594%	-0.3289%	11.1417%	10.4872%	yes	1.3796%	3 / 62
2023-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2022-01-01	-18.2605%	15.0068%	66.9504%	-7.8656%	yes	3.7102%	5 / 61
2022-04-01	-23.6749%	8.1408%	58.184%	-28.2271%	no	4.0126%	9 / 61
2022-07-01	-22.5067%	8.7488%	48.1325%	-0.4595%	yes	3.9895%	3 / 63
2022-10-01	-25.808%	2.0941%	40.7506%	0.2405%	yes	4.0227%	5 / 62
2023-01-01	no segment follows this rebalance, not scored

Step 18 · 2023-01-03 → 2023-12-29

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2023-01-01	-7.2896%	2.6744%	14.7765%	-2.3206%	yes	1.2593%	2 / 61
2023-04-01	-7.5996%	2.4254%	14.6136%	-2.7784%	yes	1.2539%	2 / 61
2023-07-01	-8.4829%	1.9357%	13.6116%	-5.0296%	yes	1.1962%	1 / 62
2023-10-01	-9.1137%	1.4885%	13.4002%	3.4017%	yes	1.2374%	4 / 62
2024-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2023-01-01	-26.8744%	-0.2954%	39.8571%	27.762%	yes	4.0622%	0 / 61
2023-04-01	-28.0571%	-2.0069%	37.3051%	9.7462%	yes	4.0147%	2 / 61
2023-07-01	-28.0939%	-0.958%	36.6726%	-9.0873%	yes	4.0281%	1 / 62
2023-10-01	-28.8189%	-2.18%	34.6769%	14.0541%	yes	3.7559%	0 / 62
2024-01-01	no segment follows this rebalance, not scored

Step 19 · 2024-01-02 → 2024-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2024-01-01	-9.6629%	1.5695%	12.9807%	4.6366%	yes	1.2053%	0 / 60
2024-04-01	-8.9378%	1.2442%	12.634%	-1.9738%	yes	1.1808%	4 / 62
2024-07-01	-9.7595%	1.2817%	12.5264%	10.2406%	yes	1.1895%	2 / 63
2024-10-01	-7.6273%	2.3788%	12.4477%	-5.3518%	yes	1.1168%	4 / 63

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 4 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2024-01-01	-29.4624%	-2.1784%	31.6614%	5.6064%	yes	3.7517%	1 / 60
2024-04-01	-23.3089%	3.2117%	39.1435%	1.589%	yes	3.5513%	0 / 62
2024-07-01	-22.0615%	7.1628%	43.2786%	3.8606%	yes	3.4864%	6 / 63
2024-10-01	-20.9195%	7.7365%	42.841%	1.1156%	yes	3.3717%	4 / 63

Step 20 · 2025-01-02 → 2025-12-31

Low beta (Top-20 lowest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2025-01-01	-8.3952%	1.4106%	10.6529%	9.5421%	yes	1.1598%	7 / 59
2025-04-01	-7.9655%	0.9691%	11.7143%	-5.4627%	yes	1.2303%	5 / 61
2025-07-01	-9.1611%	1.8134%	12.9755%	-2.2836%	yes	1.3345%	1 / 63
2025-10-01	-8.8808%	2.1647%	13.403%	0.0732%	yes	1.2946%	3 / 63
2026-01-01	no segment follows this rebalance, not scored

High beta (Top-20 highest β)

Portfolio book, rebalanced quarterly · 5 constructions · 20 names held · selection: reselect · 0.0% in cash

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2025-01-01	-15.5191%	12.4503%	43.7097%	-10.5239%	yes	3.1528%	8 / 59
2025-04-01	-17.2144%	7.5737%	43.1755%	34.43%	yes	3.4437%	4 / 61
2025-07-01	-19.1699%	12.8958%	53.1188%	20.5694%	yes	3.4816%	0 / 63
2025-10-01	-17.1889%	15.4437%	56.3041%	0.8701%	yes	3.284%	6 / 63
2026-01-01	no segment follows this rebalance, not scored

QuanterLab · Study 90ca825ab77f · compiled August 08, 2026. Point-in-time constituents and hypothesis-registration timestamps are enforced by the platform; transaction costs are not modelled in this study. This report is generated from the frozen study artifact and is reproducible from the ledger above. Educational research, not investment advice: every result on this page is simulated, and nothing here is a recommendation to buy or sell any security.

Your beta is holding something different than it was, twenty lowest-beta names against twenty highest, across twenty sealed windows of the S&P 500

1 Methodology

2 Results

2.1 Headline

2.2 Per-step results

2.3 Search accounting

2.4 The comparison

3 The circuit

The objective and the search

3.1 Universe

3.2 Price Loader

3.3 Filter Beta

3.4 Top N

3.5 Portfolio Backtest

3.6 Portfolio Forward Autopsy

4 Projection calibration, pooled across the walk

5 Discussion

5.1 Findings

5.2 Interpretation

What betting-against-beta actually is, and why your broker breaks it

Next in the series

5.3 Limitations

References

Appendix A Reproducibility in QuanterLab

Appendix A2 Registration record

Appendix B Per-step diagnostics

Step 1 · 2006-01-03 → 2006-12-29

Step 2 · 2007-01-03 → 2007-12-31

Step 3 · 2008-01-02 → 2008-12-31

Step 4 · 2009-01-02 → 2009-12-31

Step 5 · 2010-01-04 → 2010-12-31

Step 6 · 2011-01-03 → 2011-12-30

Step 7 · 2012-01-03 → 2012-12-31

Step 8 · 2013-01-02 → 2013-12-31

Step 9 · 2014-01-02 → 2014-12-31

Step 10 · 2015-01-02 → 2015-12-31

Step 11 · 2016-01-04 → 2016-12-30

Step 12 · 2017-01-03 → 2017-12-29

Step 13 · 2018-01-02 → 2018-12-31

Step 14 · 2019-01-02 → 2019-12-31

Step 15 · 2020-01-02 → 2020-12-31

Step 16 · 2021-01-04 → 2021-12-31

Step 17 · 2022-01-03 → 2022-12-30

Step 18 · 2023-01-03 → 2023-12-29

Step 19 · 2024-01-02 → 2024-12-31

Step 20 · 2025-01-02 → 2025-12-31

Run a study like this one