QuanterLab · Research

Two ways to say calm - low beta and low volatility are not the same trade, and the difference is measurable

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 vs Low volatility

Manipulated variable · The ranking primitive, and nothing else. Both arms take the twenty LOWEST ranked names from the same point-in-time S&P 500, equal weighted, long only, re-selected point-in-time every quarter, measured against the same RSP benchmark. Arm A ranks on ordinary least squares market beta against SPY. Arm B ranks on annualised volatility of daily log returns. Both estimate over 252 trading days, so the estimation window is held fixed and the metric is the only difference between the two books. Low beta and low volatility are widely treated as the same defensive trade; this walk asks whether they are.

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 09, 2026

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

Abstract

Rank the S&P 500 by market beta and buy the twenty lowest. Rank it by trailing volatility and buy the twenty lowest. Both are called defensive, and they are widely treated as the same trade. This study runs them against each other across twenty sealed one-year windows, 2006 through 2025, in a circuit where the two arms are one node apart: same point-in-time membership, same equal weighting, same long-only book, same quarterly re-selection, same benchmark, and the same 252-bar estimation window. Only the ranking primitive differs.

They are not the same portfolio. At formation the two books share an average of 7.4 names out of twenty; in 2017 they shared 0.

The reason is arithmetic. Beta is correlation times the ratio of the stock's volatility to the index's, so a stock earns a low beta either by being quiet or by being decoupled, and the beta screen accepts both. Measured on this study's own formation baskets, the low-beta book carries 20.4% annualised volatility and 0.31 correlation against the low-volatility book's 16.6% and 0.50. It is the more volatile and the less correlated of the two in 20 of 20 windows, without a single exception. The low-beta screen is not buying calm. It is buying detachment, and detachment is a different product.

The books behaved accordingly. With dividends the low-volatility book compounded at 9.17% a year against the low-beta book's 6.44%, at a shallower average drawdown (-11.1% against -12.8%) and a higher mean per-window Sharpe (0.77 against 0.49). The return gap is 2.74 points a year with a t-statistic of 2.02 on twenty annual observations, supportive, not decisive, and reported here as such. The compositional difference is the finding; the return difference is its consequence.

Author’s note

I built this because I had been treating low beta and low volatility as the same trade, and two studies sitting next to each other suggested I was wrong. The honest way to check was not to write the paragraph, it was to build a circuit where the ranking primitive is the only thing that differs and let twenty sealed windows answer.

The answer came back smaller than the side-by-side reading implied. Three and a half points became 2.74, and the t-statistic became marginal. That is what a control is for, and it is why the paper leads with the composition rather than the returns: 20 of 20 windows is a fact about what the estimator selects, and it does not depend on how the market happened to pay over these particular twenty years.

If I had published the first version, the one where the two studies were read against each other without a matched window and without the same data gate, the headline number would have been larger and the paper would have been worse.

1 Methodology

Two arms, one node apart, each window registered and sealed before it ran.

At each annual anchor from 2006 to 2025 the point-in-time S&P 500 membership is the starting universe, the constituent list as it stood on that date, not today's. Both arms hand their ranked list to a Top-N selector that keeps the twenty LOWEST ranked names. Both books are equal weighted, long only, held for one year, and re-selected point-in-time at every quarterly rebalance. Both are measured against RSP, the equal-weight S&P 500 ETF, because equal-weighted books compared to a cap-weighted benchmark would import a size bet neither arm takes.

Arm A ranks on ordinary least squares market beta against SPY, no shrinkage. Arm B ranks on annualised volatility of daily log returns. Both estimate over 252 trading days.

That matched window is deliberate and it is what makes this study a test rather than an observation. The two published papers this grew out of rank beta over 252 bars and volatility over 756, so comparing them changes the metric AND the estimation window at once and cannot say which is responsible. Holding the window fixed leaves the ranking primitive as the only difference. The walk driver refuses to start if any other field differs between the arms, and it refuses arm labels longer than 24 characters, because those labels are interpolated into the result box and the page's link preview.

Beta requires a benchmark and volatility does not. That is not an imbalance in the comparison; it is the variable under test.

Returns as the engine computes them are price returns. Total returns are measured separately: dividends per share from the payment record, applied against the entry price of each holding period, using the actual quarterly baskets and weights, with every window reconciled against the engine's own price return first, all forty arm-windows agree. Unlike the volatility paper in this series, the overlay barely matters here: both books are defensive and yield almost identically, 2.86% against 2.91%, so the comparison is the same on either basis. Both are reported.

WHY THE GAP IS QUOTED AT SEVERAL SIZES. This study measures 2.65 points on price returns and 2.74 on total returns. An earlier note in this series put the difference near three and a half points; that figure compared volatility measured over 756 bars against a beta walk run before the platform's data-quality gate was widened. The number here is the like-for-like one: matched window, both arms walked under the current gate, in one sealed circuit. Where they disagree, this study governs.

No search record exists for either design, so the number of configurations examined before them is unknown and no deflated Sharpe ratio is claimed.

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

2 Results

2.1 Headline

Low beta, pooled Sharpe

0.30

5012 OOS bars

Low volatility, pooled Sharpe

0.49

5012 OOS bars

P(Low beta beats Low volatility)

3.2%

5011 paired bars · CAGR gap (Low beta − Low volatility) -2.7 pp

Figure 1. Both arms stitched through the identical windows, Low beta (+97.6%), Low volatility (+226.8%), 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 2010, 16 of the 20 windows above. Low beta (+102.2%), Low volatility (+258.9%), benchmark grey (+362.5%). This is a subset of Figure 1, not a correction to it. The study is anchored before the 2007–09 crisis on purpose: a method that only works in calm markets should be caught doing it. But one crisis window and its equally singular recovery set the vertical scale for the whole of Figure 1, and everything after 2010 is compressed into the bottom of it. This figure shows the same windows, same method, same data, with that period outside the frame, so the post-crisis years can be read at their own scale. Neither figure stands on its own; the full record is what the study claims, and the era rows below put a number on how much of the gap came from which period.

2.2 Per-step results

**Table 1.** One row per step, raw out-of-sample results.
#	Out-of-sample window	Low beta SR	Low volatility SR
1	2006-01-03 → 2006-12-29	0.72	1.35
2	2007-01-03 → 2007-12-31	0.90	-0.28
3	2008-01-02 → 2008-12-31	-0.87	-0.76
4	2009-01-02 → 2009-12-31	0.78	0.72
5	2010-01-04 → 2010-12-31	0.51	0.74
6	2011-01-03 → 2011-12-30	0.75	0.86
7	2012-01-03 → 2012-12-31	0.24	0.68
8	2013-01-02 → 2013-12-31	1.07	1.47
9	2014-01-02 → 2014-12-31	1.83	1.48
10	2015-01-02 → 2015-12-31	-0.68	0.16
11	2016-01-04 → 2016-12-30	0.59	1.26
12	2017-01-03 → 2017-12-29	0.76	2.07
13	2018-01-02 → 2018-12-31	0.11	-0.12
14	2019-01-02 → 2019-12-31	1.88	2.04
15	2020-01-02 → 2020-12-31	-0.07	0.21
16	2021-01-04 → 2021-12-31	1.00	1.72
17	2022-01-03 → 2022-12-30	-0.05	-0.27
18	2023-01-03 → 2023-12-29	-0.55	-0.10
19	2024-01-02 → 2024-12-31	0.61	1.44
20	2025-01-02 → 2025-12-31	0.20	0.64

Figure 3. Low beta: 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. Low volatility: 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} − r_{Low volatility} 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.

**Table 2.** Window-by-window paired comparison. Δ is the growth gap (Low beta − Low volatility) over the window's paired dates.
#	Window	Paired bars	Low beta	Low volatility	Δ	Leader
1	2006-01-04 → 2006-12-29	250	+6.4%	+10.3%	-3.9 pp	Low volatility
2	2007-01-04 → 2007-12-31	250	+9.2%	-3.9%	+13.1 pp	Low beta
3	2008-01-03 → 2008-12-31	252	-24.0%	-21.7%	-2.3 pp	Low volatility
4	2009-01-05 → 2009-12-31	251	+10.6%	+9.7%	+1.0 pp	Low beta
5	2010-01-05 → 2010-12-31	251	+5.2%	+7.6%	-2.4 pp	Low volatility
6	2011-01-04 → 2011-12-30	251	+9.3%	+11.6%	-2.3 pp	Low volatility
7	2012-01-04 → 2012-12-31	249	+1.5%	+5.2%	-3.7 pp	Low volatility
8	2013-01-03 → 2013-12-31	251	+10.8%	+15.5%	-4.8 pp	Low volatility
9	2014-01-03 → 2014-12-31	251	+20.6%	+13.6%	+6.9 pp	Low beta
10	2015-01-05 → 2015-12-31	251	-10.8%	+1.3%	-12.1 pp	Low volatility
11	2016-01-05 → 2016-12-30	251	+7.9%	+13.3%	-5.4 pp	Low volatility
12	2017-01-04 → 2017-12-29	250	+6.4%	+14.2%	-7.7 pp	Low volatility
13	2018-01-03 → 2018-12-31	250	+0.5%	-2.3%	+2.8 pp	Low beta
14	2019-01-03 → 2019-12-31	251	+23.1%	+23.2%	-0.1 pp	Low volatility
15	2020-01-03 → 2020-12-31	252	-7.4%	+1.6%	-9.0 pp	Low volatility
16	2021-01-05 → 2021-12-31	251	+11.7%	+19.0%	-7.3 pp	Low volatility
17	2022-01-04 → 2022-12-30	250	-2.1%	-5.7%	+3.6 pp	Low beta
18	2023-01-04 → 2023-12-29	249	-6.2%	-1.6%	-4.7 pp	Low volatility
19	2024-01-03 → 2024-12-31	251	+5.9%	+13.6%	-7.6 pp	Low volatility
20	2025-01-03 → 2025-12-31	249	+1.7%	+7.8%	-6.1 pp	Low volatility

Paired Sharpe of the difference track: -0.38 · block bootstrap (2000 paths, block 10, seed 1234): P(Low beta beats Low volatility) = 3.2%.

Window win-rate. Low beta led 5 of 20 windows (25.0%), Low volatility led 15 , and the mean window gap of -2.60 pp points the same way. Widest single window: 2007 at +13.1 pp.

**Table 3.** The same comparison split at 2010. Pooling the whole walk into one row hides which side of the split the difference came from.
Period	Windows	Low beta	Low volatility	Mean gap	Low beta led
All windows	20	+4.01%	+6.62%	-2.60 pp	5/20
Before 2010	4	+0.55%	-1.40%	+1.95 pp	2/4
2010 onward	16	+4.88%	+8.62%	-3.74 pp	3/16

Figure A1, mean window return per period. Low beta above, Low volatility below, with the gap at right. The pooled bar and the post-2010 bar are the same comparison over different periods.

The two eras disagree by 5.69 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 vs Low volatility, walked on the same registered out-of-sample windows. Low beta: 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. Low volatility: 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: Market Beta → Volatility, substituted (its parameters change with the swap). The contrast under test: whether Low beta generates better risk-adjusted returns than Low volatility 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 green, Low volatility 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.

Filter Volatility, Annualized volatility, the size of the wiggle.

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

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).

Low volatility

Universe	S&P 500 index constituents.
Selection	metric across Annualized volatility → lowest 20 kept by Annualized volatility.
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:

substitutedMarket Beta → Volatility, substituted (its parameters change with the swap)

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, 7 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.

3.7 Filter Volatility

Annualized volatility, the size of the wiggle.

The standard deviation of daily log-returns, scaled to a yearly number by √252 (trading days). A risk and regime descriptor used everywhere downstream.

Annualized standard deviation

\sigma_{\text{ann}} = \operatorname{std}(r_t)\,\sqrt{252}, \qquad r_t = \ln\frac{P_t}{P_{t-1}}

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	20	95	71 / 80	88.8% ±3.53	90.0%	4951	5.96% ±0.336	5.0%
Low volatility	20	95	73 / 80	91.2% ±3.16	90.0%	4951	5.55% ±0.326	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, Two screens both called defensive select mostly different stocks. At formation the low-beta and low-volatility books share an average of 7.4 names out of twenty, ranging from 15 down to 0 in 2017. A practitioner substituting one for the other is not making a methodological refinement; they are buying a substantially different portfolio.

2, The mechanism is visible in every window, without exception. Beta is correlation times the ratio of volatilities, so a low beta can be bought two ways. On this study's own formation baskets the low-beta book carries 20.4% annualised volatility and 0.31 correlation with the index; the low-volatility book carries 16.6% and 0.50. The low-beta book is the more volatile AND the less correlated in 20 of 20 windows. That is not a tendency, it is a property of what the estimator selects for.

3, Detachment is not safety, and the risk numbers say so. The low-beta book realised 13.7% volatility in-window against the low-volatility book's 13.0%, and its average worst drawdown was -12.8% against -11.1%. The screen that explicitly targets low market sensitivity delivered MORE portfolio risk than the screen that targets low portfolio risk. Mean per-window Sharpe: 0.49 against 0.77.

4, The return difference supports the mechanism without carrying the paper. With dividends the low-volatility book compounded at 9.17% a year (+478.6% cumulative) against the low-beta book's 6.44% (+248.2%). On price returns, 6.10% against 3.46%. The gap is 2.74 points a year, t = 2.02, with the low-volatility book ahead in 14 of 20 windows. On twenty annual observations that is supportive evidence, not a decisive result, and this paper does not present it as one.

5, It is not an artifact of when you cut the sample, with one honest exception. Splitting at any year from 2011 to 2022 leaves the low-volatility book ahead in BOTH halves, the later half by between 3.15 and 4.90 points. The single exception is the earliest available cut, 2010, where the first four windows favour low beta by 1.03 points. Twelve of thirteen breaks agree; the one that does not is the one with the least data behind it.

6, Against the index, neither defensive book was a free lunch. Counting dividends on every side, the equal-weight benchmark returned 9.87% a year. The low-volatility book trailed it by 0.70 points and the low-beta book by 3.43, both at roughly 60% of the index’s year-to-year variation. (On price returns the same ordering holds: 7.50% for the index against 6.10% and 3.46%.) The low-volatility book in this study is not quite the one in the replication paper, that book ranks over 756 bars and returned 9.57%, this one ranks over 252 to match beta and returned 9.17%. The estimation window costs the calm book about four tenths of a point a year; it is held fixed here because the comparison, not the level, is what this study measures. The question this study answers is not whether defensive equity beats the market. It is which of two screens that claim to build a defensive book actually builds one.

5.2 Interpretation

The identity beta = rho x (sigma_i / sigma_m) is not controversial, and neither is the conclusion that follows from it. What the measurement adds is how consistently it bites: in every one of the 20 windows, the book selected for low beta was the more volatile and the less correlated of the two. There is no era in this sample where the beta screen behaved like a volatility screen.

The names make it concrete. Gold miners, for-profit education, pipeline operators, assets whose correlation with the S&P 500 sits near zero and occasionally below it, are exactly what a low-beta screen reaches for, and none of them are calm. The names a volatility screen holds instead are the ones anybody would list if asked to describe a defensive portfolio, and they are disqualified from a beta screen precisely because they are correlated. Consumer staples move with the market. That is not a defect in them; it is a defect in using beta as a proxy for calm.

This matters most where it is least examined. Low-beta and minimum-volatility products are sold into the same allocation slot, often to the same investor, on the same sentence about downside protection. The two books here share about a third of their names and differ in realised drawdown by nearly two points. An allocator treating them as interchangeable is not making a fine distinction; they are choosing between two different bets and being told there is only one.

On the return gap: 2.74 points a year with t = 2.02 is the kind of number that would be over-claimed by almost anyone with an incentive to. Twenty annual observations cannot carry a strong significance claim and this paper makes none. What the returns do is agree with the mechanism rather than contradict it, the book that took more risk without meaning to also earned less, which is what the decomposition predicts and what the drawdown numbers independently show. If the return gap vanished tomorrow, findings 1 through 3 would stand, because they are measurements of what the screens select, not of what the market paid.

The relationship to the low-risk literature is worth stating precisely. Asness, Frazzini, Gormsen and Pedersen decompose the low-risk effect into volatility and correlation components and argue the correlation component is what makes betting against beta work. In this sample, on long-only twenty-name books inside the S&P 500, the correlation component is what makes it underperform. Their construction is levered, long-short and market-wide and ours is none of those, so this is not a refutation. It is a disagreement about which component carries the effect, in a setting where an ordinary investor actually operates.

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 would settle this

The decomposition points at a test this study does not run. If the damage is the correlation term, a third screen, the twenty LOWEST correlations to the index, volatility ignored, should sit on the far side of the decomposition from the volatility screen and behave worse than either book here. That would pin the mechanism from both ends rather than one.

The other open question is shrinkage. A Vasicek-shrunk beta pulls the extremes toward one and would select a different low-beta book, plausibly a less decoupled one. Whether shrinkage repairs the estimator or merely blunts it is answerable with the same twenty windows.

5.3 Limitations

Twenty annual observations. The return gap's t-statistic is 2.02, which is marginal at conventional thresholds, and findings 1 through 3 are compositional measurements rather than statistical claims, they are stated that way deliberately. Nothing here should be read as establishing a return premium.

One era break disagrees. Cutting at 2010, the earliest split with at least four windows a side, puts the low-beta book ahead by 1.03 points in the early half. Every other break from 2011 to 2022 favours low volatility in both halves. The disagreeing cut is the one with the fewest observations, but it exists and is reported.

No transaction costs are charged. Both books turn over at broadly similar rates with quarterly re-selection, so the omission is close to symmetric between arms, but absolute levels are gross.

The universe is point-in-time S&P 500 membership. There is no membership look-ahead, but the vendor serves no delisted names, so the rankable pool runs from 344 in 2006 to roughly five hundred by the 2020s. Both arms draw from the same pool each window, so this is close to neutral for the comparison while it bounds the absolute returns.

Beta is a raw 252-day OLS estimate against SPY with no Vasicek shrinkage. Frazzini and Pedersen shrink toward one, which compresses the extremes the book selects from. That is a replication knob deliberately left at zero, and a shrunk estimator would produce a different low-beta book.

The total-return overlay and the sigma/rho decomposition are both measured outside the sealed walk, from the recorded formation baskets, after the fact. Each window was reconciled against the engine's own price return before the overlay was applied, but the arithmetic is ours, not the walk's. The decomposition is measured at formation and not through the holding period.

This comparison was not pre-registered as an idea. Each walk was sealed window by window before it ran, and this circuit was built and sealed specifically to test the claim, which is the right order, but the claim itself came from reading two earlier studies side by side. An earlier note in this series quoted the gap near three and a half points, from a comparison that varied the estimation window and the data-quality gate alongside the metric; this study is the controlled version and its numbers govern.

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.
Blitz, D. C., & van Vliet, P. (2007). The Volatility Effect: Lower Risk Without Lower Return. Journal of Portfolio Management, 34(1), 102-113.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The Cross-Section of Volatility and Expected Returns. Journal of Finance, 61(1), 259-299.
Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly. Financial Analysts Journal, 67(1), 40-54.
Frazzini, A., & Pedersen, L. H. (2014). Betting Against Beta. Journal of Financial Economics, 111(1), 1-25.
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.
Novy-Marx, R. (2016). Understanding Defensive Equity. NBER Working Paper 20591.
Novy-Marx, R., & Velikov, M. (2022). Betting Against Betting Against Beta. Journal of Financial Economics, 143(1), 80-106.
Clarke, R., de Silva, H., & Thorley, S. (2006). Minimum-Variance Portfolios in the U.S. Equity Market. Journal of Portfolio Management, 33(1), 10-24.

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	d4723792a457	715	2006-01-01	2006-01-03 → 2006-12-29
2	bd8228163f4c	716	2007-01-01	2007-01-03 → 2007-12-31
3	8fe42f9dbaeb	717	2008-01-01	2008-01-02 → 2008-12-31
4	d3a6cdd9abdf	718	2009-01-01	2009-01-02 → 2009-12-31
5	480fb1f0425e	719	2010-01-01	2010-01-04 → 2010-12-31
6	eec567a5cc30	720	2011-01-01	2011-01-03 → 2011-12-30
7	cd264df3b849	721	2012-01-01	2012-01-03 → 2012-12-31
8	c81ef41b49b8	722	2013-01-01	2013-01-02 → 2013-12-31
9	d69257aa6f6e	723	2014-01-01	2014-01-02 → 2014-12-31
10	c86bd506bb63	724	2015-01-01	2015-01-02 → 2015-12-31
11	8414a1ee152f	725	2016-01-01	2016-01-04 → 2016-12-30
12	0f0f5230bc5d	726	2017-01-01	2017-01-03 → 2017-12-29
13	205e1cd3a2a4	727	2018-01-01	2018-01-02 → 2018-12-31
14	0c64ee4f3371	728	2019-01-01	2019-01-02 → 2019-12-31
15	a2411c707b56	729	2020-01-01	2020-01-02 → 2020-12-31
16	69f07b6f86e4	730	2021-01-01	2021-01-04 → 2021-12-31
17	128cff0686b2	731	2022-01-01	2022-01-03 → 2022-12-30
18	f418f06c68c3	732	2023-01-01	2023-01-03 → 2023-12-29
19	18b0f7423696	733	2024-01-01	2024-01-02 → 2024-12-31
20	7022673f3c25	734	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 vs Low volatility, walked on the same registered out-of-sample windows. Low beta: 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. Low volatility: 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: Market Beta → Volatility, substituted (its parameters change with the swap). The contrast under test: whether Low beta generates better risk-adjusted returns than Low volatility 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	2026-08-09 11:14:46	2026-08-09 11:19:31
2	2007-01-01	2026-08-09 11:19:36	2026-08-09 11:24:20
3	2008-01-01	2026-08-09 11:24:25	2026-08-09 11:27:26
4	2009-01-01	2026-08-09 11:27:31	2026-08-09 11:30:53
5	2010-01-01	2026-08-09 11:30:58	2026-08-09 11:34:39
6	2011-01-01	2026-08-09 11:34:44	2026-08-09 11:38:44
7	2012-01-01	2026-08-09 11:38:49	2026-08-09 11:51:30
8	2013-01-01	2026-08-09 11:51:35	2026-08-09 12:15:17
9	2014-01-01	2026-08-09 12:15:22	2026-08-09 12:28:23
10	2015-01-01	2026-08-09 12:28:28	2026-08-09 13:15:55
11	2016-01-01	2026-08-09 13:16:00	2026-08-09 13:18:00
12	2017-01-01	2026-08-09 13:18:05	2026-08-09 13:20:46
13	2018-01-01	2026-08-09 13:20:51	2026-08-09 13:23:12
14	2019-01-01	2026-08-09 13:23:17	2026-08-09 13:25:37
15	2020-01-01	2026-08-09 13:25:42	2026-08-09 13:27:43
16	2021-01-01	2026-08-09 13:27:48	2026-08-09 13:30:09
17	2022-01-01	2026-08-09 13:30:14	2026-08-09 13:31:55
18	2023-01-01	2026-08-09 13:32:00	2026-08-09 13:33:41
19	2024-01-01	2026-08-09 13:33:46	2026-08-09 13:35:07
20	2025-01-01	2026-08-09 13:35:12	2026-08-09 13:36:53

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

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 4.86% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2006-01-01	-6.08%	0.7837%	8.8494%	0.7113%	yes	0.9244%	3 / 61
2006-04-01	-5.7205%	1.3599%	9.018%	-0.4054%	yes	0.9382%	5 / 62
2006-07-01	-5.7567%	0.9084%	8.0877%	0.3334%	yes	0.8033%	4 / 62
2006-10-01	-4.6594%	1.9715%	9.1063%	5.7081%	yes	0.8546%	0 / 62
2007-01-01	no segment follows this rebalance, not scored

Low volatility

Portfolio book, rebalanced quarterly · 5 constructions · 19 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (35 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	-5.4236%	1.1053%	8.7472%	-0.3743%	yes	0.882%	1 / 61
2006-04-01	-6.3422%	0.79%	8.5115%	0.7492%	yes	0.9188%	6 / 62
2006-07-01	-5.9333%	1.0025%	8.4945%	4.6247%	yes	0.8783%	0 / 62
2006-10-01	-5.0276%	2.122%	9.8562%	3.8575%	yes	0.8619%	1 / 62
2007-01-01	no segment follows this rebalance, not scored

Step 2 · 2007-01-03 → 2007-12-31

Low beta

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	-4.7815%	1.483%	8.1998%	1.4496%	yes	0.7419%	5 / 62
2007-07-01	-4.2277%	1.8152%	8.2778%	1.7276%	yes	0.7403%	10 / 62
2007-10-01	-5.0674%	2.0348%	8.975%	1.3828%	yes	0.8493%	7 / 63
2008-01-01	no segment follows this rebalance, not scored

Low volatility

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	-5.0868%	1.9395%	8.7729%	-2.653%	yes	0.8313%	4 / 60
2007-04-01	-6.0364%	1.0274%	8.668%	-0.3058%	yes	0.8971%	6 / 62
2007-07-01	-4.8958%	1.481%	8.3262%	0.4271%	yes	0.7677%	12 / 62
2007-10-01	-5.0881%	2.1107%	9.1518%	-3.2125%	yes	0.8242%	10 / 63
2008-01-01	no segment follows this rebalance, not scored

Step 3 · 2008-01-02 → 2008-12-31

Low beta

Portfolio book, rebalanced quarterly · 4 constructions · 19 names held · selection: reselect · 0.0% in cash · 1 name dropped at load (36 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 18.47% of 249 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2008-01-01	-5.4828%	1.8875%	9.0806%	-9.0763%	no	0.8865%	11 / 60
2008-04-01	-8.0864%	0.6435%	9.3272%	-9.3658%	no	1.1049%	8 / 63
2008-07-01	-9.1129%	0.1966%	9.5169%	2.0937%	yes	1.246%	7 / 63
2008-10-01	-8.4453%	0.9268%	10.3093%	-10.709%	no	1.2194%	20 / 63

Low volatility

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
2008-01-01	-5.8516%	2.0176%	9.7358%	-9.1835%	no	0.9657%	10 / 60
2008-04-01	-7.2636%	1.5011%	10.2158%	-8.1268%	no	1.0949%	7 / 63
2008-07-01	-8.0705%	1.3822%	10.8491%	6.038%	yes	1.2277%	5 / 63
2008-10-01	-8.6657%	1.5843%	11.9333%	-14.3831%	no	1.2862%	22 / 63

Step 4 · 2009-01-02 → 2009-12-31

Low beta

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
2009-01-01	-14.6664%	-0.193%	15.0741%	-10.8108%	yes	1.8708%	6 / 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

Low volatility

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
2009-01-01	-15.2178%	-0.5189%	15.0338%	-10.2147%	yes	1.6049%	9 / 60
2009-04-01	-16.5238%	-2.0183%	15.115%	7.0368%	yes	1.9673%	0 / 62
2009-07-01	-17.0934%	-1.1469%	16.0583%	4.3786%	yes	1.8544%	0 / 63
2009-10-01	-17.0554%	-0.2412%	18.0507%	9.1997%	yes	2.1273%	0 / 63
2010-01-01	no segment follows this rebalance, not scored

Step 5 · 2010-01-04 → 2010-12-31

Low beta

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	-15.995%	0.8735%	19.1186%	2.8514%	yes	1.9707%	1 / 60
2010-04-01	-15.7491%	0.3913%	19.7456%	-9.8891%	yes	1.9211%	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

Low volatility

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	-16.3925%	-0.3075%	16.974%	1.2771%	yes	2.0446%	1 / 60
2010-04-01	-15.3991%	-0.0146%	18.2824%	-4.8376%	yes	2.0657%	3 / 62
2010-07-01	-15.9744%	0.06%	17.3391%	7.9795%	yes	1.9999%	0 / 63
2010-10-01	-15.8011%	0.8425%	18.8763%	2.4409%	yes	2.0238%	0 / 63
2011-01-01	no segment follows this rebalance, not scored

Step 6 · 2011-01-03 → 2011-12-30

Low beta

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

Low volatility

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
2011-01-01	-10.2593%	1.6369%	16.429%	0.7949%	yes	1.5849%	0 / 61
2011-04-01	-7.4669%	2.571%	13.7659%	4.248%	yes	1.2043%	0 / 62
2011-07-01	-5.5831%	4.2612%	14.1326%	-2.2092%	yes	1.0495%	11 / 63
2011-10-01	-6.7465%	2.2866%	12.255%	9.3698%	yes	1.0856%	4 / 62
2012-01-01	no segment follows this rebalance, not scored

Step 7 · 2012-01-03 → 2012-12-31

Low beta

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	-5.7273%	2.9842%	13.4144%	0.8802%	yes	1.1048%	0 / 61
2012-04-01	-6.6924%	2.3203%	12.2637%	1.7846%	yes	1.1355%	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

Low volatility

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	-6.2143%	2.6354%	13.2509%	1.3295%	yes	1.0922%	0 / 61
2012-04-01	-6.1832%	2.9087%	12.9424%	3.395%	yes	1.1192%	1 / 62
2012-07-01	-7.2795%	2.1319%	12.5618%	1.4116%	yes	1.0583%	0 / 62
2012-10-01	-6.9859%	1.7552%	12.2366%	-2.0845%	yes	1.0489%	2 / 61

Step 8 · 2013-01-02 → 2013-12-31

Low beta

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

Low volatility

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
2013-01-01	-7.8316%	1.8084%	10.8757%	12.6192%	no	1.045%	0 / 59
2013-04-01	-6.5035%	3.8769%	14.3468%	-1.1602%	yes	1.0521%	7 / 63
2013-07-01	-8.0285%	2.4367%	13.0172%	-0.6016%	yes	1.1055%	1 / 63
2013-10-01	-8.602%	2.7619%	14.3547%	4.9063%	yes	1.2794%	1 / 63
2014-01-01	no segment follows this rebalance, not scored

Step 9 · 2014-01-02 → 2014-12-31

Low beta

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

Low volatility

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	-5.5391%	3.738%	12.9542%	0.1588%	yes	0.9938%	4 / 60
2014-04-01	-4.7613%	2.6624%	10.713%	5.253%	yes	0.8663%	1 / 62
2014-07-01	-4.8162%	3.4567%	11.6279%	-1.2558%	yes	0.8547%	4 / 63
2014-10-01	-4.638%	3.3854%	11.2908%	9.6095%	yes	0.9018%	5 / 63
2015-01-01	no segment follows this rebalance, not scored

Step 10 · 2015-01-02 → 2015-12-31

Low beta

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	-7.5966%	1.9412%	12.5278%	-7.2416%	yes	1.1154%	8 / 62
2015-07-01	-8.3836%	0.4158%	9.1768%	-3.2259%	yes	0.9633%	11 / 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

Low volatility

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	-4.7489%	3.6183%	11.8556%	0.3394%	yes	0.9463%	8 / 60
2015-04-01	-4.58%	3.9286%	13.252%	-2.5797%	yes	1.054%	3 / 62
2015-07-01	-5.9559%	2.8011%	11.4976%	-2.9728%	yes	1.0588%	10 / 63
2015-10-01	-7.8864%	1.1151%	10.0904%	6.5281%	yes	1.0576%	5 / 63
2016-01-01	no segment follows this rebalance, not scored

Step 11 · 2016-01-04 → 2016-12-30

Low beta

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	-8.6717%	1.5665%	11.8599%	9.1767%	yes	1.1848%	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

Low volatility

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	-7.2557%	1.6041%	10.3853%	7.8683%	yes	1.0123%	6 / 60
2016-04-01	-5.8235%	3.9081%	13.6588%	5.5567%	yes	1.0532%	3 / 63
2016-07-01	-6.4531%	3.3137%	13.1087%	-3.5682%	yes	1.1693%	2 / 63
2016-10-01	-6.9932%	2.5558%	13.1495%	3.0577%	yes	1.2565%	0 / 62

Step 12 · 2017-01-03 → 2017-12-29

Low beta

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

Low volatility

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	-7.4534%	1.6831%	12.6884%	6.6992%	yes	1.2778%	0 / 61
2017-04-01	-7.1668%	2.5879%	13.4335%	4.4209%	yes	1.2281%	0 / 62
2017-07-01	-6.3274%	2.8599%	13.0098%	1.3236%	yes	1.0874%	1 / 62
2017-10-01	-6.3671%	2.8793%	13.1006%	0.3948%	yes	1.1932%	1 / 62
2018-01-01	no segment follows this rebalance, not scored

Step 13 · 2018-01-02 → 2018-12-31

Low beta

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

Low volatility

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	-5.6609%	2.7988%	11.1405%	-5.1791%	yes	1.0558%	8 / 60
2018-04-01	-7.2534%	1.943%	11.1241%	2.9616%	yes	1.1843%	1 / 63
2018-07-01	-6.7813%	1.5697%	10.724%	1.3485%	yes	1.0702%	2 / 62
2018-10-01	-5.2011%	2.1533%	10.1261%	0.2489%	yes	0.8976%	7 / 62
2019-01-01	no segment follows this rebalance, not scored

Step 14 · 2019-01-02 → 2019-12-31

Low beta

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	-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

Low volatility

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 4.03% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2019-01-01	-6.3792%	2.0335%	10.3302%	12.0526%	no	1.0051%	0 / 60
2019-04-01	-6.3014%	2.8664%	12.9924%	4.1582%	yes	1.1084%	3 / 62
2019-07-01	-6.4245%	3.3658%	13.1862%	7.651%	yes	1.0593%	4 / 63
2019-10-01	-7.0588%	3.4969%	14.1669%	-1.3242%	yes	1.2101%	3 / 63
2020-01-01	no segment follows this rebalance, not scored

Step 15 · 2020-01-02 → 2020-12-31

Low beta

Portfolio book, rebalanced quarterly · 4 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 8.43% of 249 days (expected ~5.0%)

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

Low volatility

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	-6.4909%	2.6054%	13.547%	-11.7939%	no	1.1652%	15 / 61
2020-04-01	-12.4292%	1.3514%	17.4004%	12.707%	yes	1.6634%	2 / 62
2020-07-01	-11.0792%	4.3831%	20.8195%	6.9305%	yes	1.5431%	3 / 63
2020-10-01	-11.6023%	3.2566%	18.9772%	0.4392%	yes	1.5906%	2 / 63

Step 16 · 2021-01-04 → 2021-12-31

Low beta

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

Low volatility

Portfolio book, rebalanced quarterly · 5 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
2021-01-01	-12.9236%	3.198%	20.4188%	1.632%	yes	1.5431%	2 / 60
2021-04-01	-13.7756%	2.7131%	22.4794%	4.1127%	yes	1.5601%	1 / 62
2021-07-01	-14.4729%	2.6466%	21.2329%	-0.9749%	yes	1.6141%	0 / 63
2021-10-01	-15.7197%	2.21%	21.8704%	13.1213%	yes	1.6709%	1 / 63
2022-01-01	no segment follows this rebalance, not scored

Step 17 · 2022-01-03 → 2022-12-30

Low beta

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 7.69% of 247 days (expected ~5.0%)

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

Low volatility

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	-13.6872%	2.2407%	22.9997%	0.3503%	yes	1.6139%	1 / 61
2022-04-01	-15.9571%	1.5127%	24.7515%	-5.8445%	yes	1.8422%	5 / 61
2022-07-01	-9.5849%	2.6608%	15.271%	-10.7737%	no	1.3818%	9 / 63
2022-10-01	-9.1841%	1.0507%	12.5089%	6.2509%	yes	1.4303%	4 / 62
2023-01-01	no segment follows this rebalance, not scored

Step 18 · 2023-01-03 → 2023-12-29

Low beta

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

Low volatility

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	-7.0986%	2.4599%	14.0192%	-1.7362%	yes	1.3579%	3 / 61
2023-04-01	-7.8299%	2.0443%	14.0335%	0.857%	yes	1.2656%	2 / 61
2023-07-01	-9.1928%	1.2016%	12.8569%	-7.1323%	yes	1.3212%	0 / 62
2023-10-01	-10.5561%	0.3157%	12.5841%	6.9847%	yes	1.3683%	3 / 62
2024-01-01	no segment follows this rebalance, not scored

Step 19 · 2024-01-02 → 2024-12-31

Low beta

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

Low volatility

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	-9.5532%	1.7684%	13.2785%	7.6972%	yes	1.3448%	0 / 60
2024-04-01	-8.9579%	2.4814%	15.4374%	1.0629%	yes	1.3579%	1 / 62
2024-07-01	-9.1785%	2.0605%	13.5202%	9.9011%	yes	1.3012%	1 / 63
2024-10-01	-7.2733%	3.5649%	14.5515%	-3.9052%	yes	1.311%	3 / 63

Step 20 · 2025-01-02 → 2025-12-31

Low beta

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

Low volatility

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	-6.935%	3.0013%	12.3643%	11.7307%	yes	1.1887%	4 / 59
2025-04-01	-5.2041%	3.4354%	13.7668%	-2.3346%	yes	1.2548%	5 / 61
2025-07-01	-7.4626%	2.8328%	13.2189%	2.6341%	yes	1.2872%	1 / 63
2025-10-01	-8.3367%	3.221%	15.029%	-2.9043%	yes	1.4317%	2 / 63
2026-01-01	no segment follows this rebalance, not scored

QuanterLab · Study b6d25a9de61b · compiled August 09, 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.

Two ways to say calm - low beta and low volatility are not the same trade, and the difference is measurable

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

3.7 Filter Volatility

4 Projection calibration, pooled across the walk

5 Discussion

5.1 Findings

5.2 Interpretation

What would settle this

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

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