QuanterLab · Research

Lower risk without lower return, tested the way a private investor would have to run it

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 volatility: the twenty calmest names vs High volatility: the twenty wildest names

Manipulated variable · Top-N selection direction on three-year trailing volatility: lowest (A) against highest (B). Every other field is held identical, same point-in-time S&P 500, same equal weighting, same long-only book, same quarterly re-selection, same benchmark. This is the volatility effect of Blitz & van Vliet (2007) tested on the construction their own paper uses: large-cap, long-only, equal-weighted.

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

Blitz and van Vliet's 2007 paper is called "The Volatility Effect: Lower Risk Without Lower Return." It is one of the most cited results in equity investing. It is also, as published, something a private investor cannot run. The test sorts a market-wide universe into deciles and rebalances monthly. Nobody with a brokerage account and a job is doing that.

So I rebuilt the claim in a form somebody could actually hold. Twenty names, equal weighted, long only, drawn from the S&P 500 as it stood on each date rather than as it stands today, re-selected once a quarter, walked across twenty sealed one-year windows from 2006 through 2025. That construction is close to what Blitz and van Vliet use themselves, large cap and equal weighted, which is why the two can be compared at all. The point of running it this way is simple: if the effect only survives in a decile sort nobody can trade, it is a fact about the literature rather than about anyone's portfolio.

It survives, narrowly. The twenty calmest names returned 9.57% a year with dividends counted. The equal-weight index returned 9.87%. That is 0.30 points of a gap, earned at 54% of the index's year-to-year variation, with a worst year of -15.7% against the index's -39.7%. Per unit of annual variation the calm book returned 0.95 against the market's 0.54.

The arithmetic is worth stating plainly, because it is the whole mechanism. The calm book's average annual return is 1.53 points BELOW the market's. Compounded, it finishes only 0.30 behind, and the difference is variance drag, which it does not pay. Before 2020 that is enough to put it ahead outright: 10.73% against 9.60%.

Where this record departs from the paper is the other arm. Blitz and van Vliet find the highest-volatility decile earns poor returns. The twenty wildest names in the S&P 500 returned 12.06% a year, the best of the three. They did it at 34.1% volatility, an average worst drawdown of -28.4%, and a -46.7% year. The low-risk effect in this sample is a statement about risk taken, not about return foregone by the reckless.

1 Methodology

Two arms, identical in every field but one, 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 rather than today's. Each name's annualised volatility is computed from daily log returns over the trailing 756 trading days, the three-year window Blitz and van Vliet use, ending at the anchor. The ranked list goes to a Top-N selector that keeps twenty names. The book is equal weighted, long only, held for one year, and re-selected point-in-time at every quarterly rebalance from the membership as it stood then.

Arm A keeps the twenty LOWEST volatilities, Arm B the twenty HIGHEST. That selector direction is the single manipulated variable; every other parameter is identical, and the walk driver refuses to start if it is not.

The benchmark is RSP, the equal-weight S&P 500 ETF. The books are equal weighted, so a cap-weighted benchmark would import a size bet neither arm takes, and equal weighting is also what Blitz and van Vliet's own portfolios use, which is why this construction can be compared to theirs at all.

Returns as the engine computes them are price returns; dividends are not carried in the platform's price series. The calm book is yield-heavy and the wild book is not, 2.92% a year against 0.83%, so the omission is not neutral between arms and would decide this paper's headline on its own. Total returns are therefore measured separately: dividends per share taken from the payment record and applied against the entry price of each holding period, using the actual quarterly baskets and their weights. Every window was validated by rebuilding the price return from those same baskets and checking it against the engine's own figure; all forty arm-windows reconcile. Those total-return figures are an overlay on the sealed walk, not part of it, and both bases are reported throughout.

Twenty non-overlapping calendar years, one window each, no window reused.

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

2 Results

2.1 Headline

Low volatility: the twenty calmest names, pooled Sharpe

0.51

5012 OOS bars

High volatility: the twenty wildest names, pooled Sharpe

0.47

5012 OOS bars

P(Low volatility: the twenty calmest names beats High volatility: the twenty wildest names)

6.0%

5011 paired bars · CAGR gap (Low volatility: the twenty calmest names − High volatility: the twenty wildest names) -4.7 pp

Figure 1. Both arms stitched through the identical windows, Low volatility: the twenty calmest names (+251.8%), High volatility: the twenty wildest names (+729.7%), 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 volatility: the twenty calmest names (+252.5%), High volatility: the twenty wildest names (+806.7%), 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 volatility: the twenty calmest names SR	High volatility: the twenty wildest names SR
1	2006-01-03 → 2006-12-29	1.39	0.23
2	2007-01-03 → 2007-12-31	-0.01	0.80
3	2008-01-02 → 2008-12-31	-0.61	-0.46
4	2009-01-02 → 2009-12-31	0.84	0.85
5	2010-01-04 → 2010-12-31	0.57	0.89
6	2011-01-03 → 2011-12-30	0.98	-0.80
7	2012-01-03 → 2012-12-31	0.70	1.16
8	2013-01-02 → 2013-12-31	1.27	1.99
9	2014-01-02 → 2014-12-31	1.91	0.84
10	2015-01-02 → 2015-12-31	-0.02	-0.09
11	2016-01-04 → 2016-12-30	1.24	1.11
12	2017-01-03 → 2017-12-29	2.30	0.17
13	2018-01-02 → 2018-12-31	0.03	-0.28
14	2019-01-02 → 2019-12-31	2.23	0.67
15	2020-01-02 → 2020-12-31	0.29	0.89
16	2021-01-04 → 2021-12-31	1.20	1.20
17	2022-01-03 → 2022-12-30	-0.03	-0.14
18	2023-01-03 → 2023-12-29	-0.30	1.00
19	2024-01-02 → 2024-12-31	0.86	0.77
20	2025-01-02 → 2025-12-31	0.65	1.23

Figure 3. Low volatility: the twenty calmest names: 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 volatility: the twenty wildest names: 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 volatility: the twenty calmest names} − r_{High volatility: the twenty wildest names} 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 volatility: the twenty calmest names · Arm B = High volatility: the twenty wildest names.

**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	+10.3%	+2.5%	+7.8 pp	Arm A
2	2007-01-04 → 2007-12-31	250	-0.9%	+18.2%	-19.1 pp	Arm B
3	2008-01-03 → 2008-12-31	252	-18.4%	-47.2%	+28.8 pp	Arm A
4	2009-01-05 → 2009-12-31	251	+11.8%	+43.0%	-31.2 pp	Arm B
5	2010-01-05 → 2010-12-31	251	+5.4%	+26.7%	-21.3 pp	Arm B
6	2011-01-04 → 2011-12-30	251	+12.9%	-33.8%	+46.7 pp	Arm A
7	2012-01-04 → 2012-12-31	249	+5.1%	+30.0%	-24.8 pp	Arm B
8	2013-01-03 → 2013-12-31	251	+13.6%	+47.2%	-33.6 pp	Arm B
9	2014-01-03 → 2014-12-31	251	+19.8%	+15.6%	+4.2 pp	Arm A
10	2015-01-05 → 2015-12-31	251	-1.2%	-4.4%	+3.1 pp	Arm A
11	2016-01-05 → 2016-12-30	251	+13.3%	+33.6%	-20.3 pp	Arm B
12	2017-01-04 → 2017-12-29	250	+14.5%	+1.4%	+13.0 pp	Arm A
13	2018-01-03 → 2018-12-31	250	-0.4%	-9.5%	+9.1 pp	Arm A
14	2019-01-03 → 2019-12-31	251	+25.7%	+13.5%	+12.1 pp	Arm A
15	2020-01-03 → 2020-12-31	252	+4.3%	+44.2%	-40.0 pp	Arm B
16	2021-01-05 → 2021-12-31	251	+12.8%	+40.2%	-27.4 pp	Arm B
17	2022-01-04 → 2022-12-30	250	-1.8%	-12.7%	+10.9 pp	Arm A
18	2023-01-04 → 2023-12-29	249	-4.0%	+26.3%	-30.3 pp	Arm B
19	2024-01-03 → 2024-12-31	251	+7.8%	+16.1%	-8.3 pp	Arm B
20	2025-01-03 → 2025-12-31	249	+7.9%	+41.8%	-33.9 pp	Arm B

Paired Sharpe of the difference track: -0.31 · block bootstrap (2000 paths, block 10, seed 1234): P(Low volatility: the twenty calmest names beats High volatility: the twenty wildest names) = 6.0%.

Window win-rate. Low volatility: the twenty calmest names led 9 of 20 windows (45.0%), High volatility: the twenty wildest names led 11 , and the mean window gap of -7.71 pp points the same way. Widest single window: 2011 at +46.7 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 volatility: the twenty calmest names	High volatility: the twenty wildest names	Mean gap	Low volatility: the twenty calmest names led
All windows	20	+6.92%	+14.63%	-7.71 pp	9/20
Before 2010	4	+0.70%	+4.12%	-3.42 pp	2/4
2010 onward	16	+8.48%	+17.26%	-8.78 pp	7/16

Figure A1, mean window return per period. Low volatility: the twenty calmest names above, High volatility: the twenty wildest names 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 5.36 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 volatility: the twenty calmest names vs High volatility: the twenty wildest names, walked on the same registered out-of-sample windows. Low volatility: the twenty calmest names: 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 volatility: the twenty wildest names: 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 volatility: the twenty calmest names generates better risk-adjusted returns than High volatility: the twenty wildest names 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 volatility: the twenty calmest names green, High volatility: the twenty wildest names 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 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 volatility: the twenty calmest names

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).

High volatility: the twenty wildest names

Universe	S&P 500 index constituents.
Selection	metric across Annualized volatility → highest 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:

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 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}}

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 volatility: the twenty calmest names	20	95	74 / 80	92.5% ±2.94	90.0%	4951	6.04% ±0.339	5.0%
High volatility: the twenty wildest names	20	95	72 / 80	90.0% ±3.35	90.0%	4951	5.84% ±0.333	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 title of the paper survives, narrowly. With dividends the calm book compounded at 9.57% a year against the equal-weight index's 9.87%, which is 0.30 points behind over twenty years. On price returns alone it is 6.48%. Whether that counts as "without lower return" is a judgement, but it is not a shortfall a holder would notice against what they were spared.

2. What they were spared is the finding. The calm book's annual returns varied by 10.0 points against the index's 18.4, which is 54% of the market's year-to-year variation. Its average worst drawdown was -10.7% against the wild book's -28.4%. In 2008 it lost -15.7% while the index lost -39.7% and the wild book lost -46.7%. Per unit of annual variation: calm 0.95, market 0.54, wild 0.45.

3. Variance drag is the whole mechanism, and it is measurable here. The calm book's ARITHMETIC mean annual return is 1.53 points below the market's. Compounded, the gap is only 0.30. A calmer series keeps more of its average, and that recovery of 1.23 points a year is the entire economic case for the strategy. Before 2020 it is more than enough: the calm book compounds at 10.73% against the market's 9.60%, ahead outright while taking roughly half the risk.

4. The paper's other half does not replicate. Blitz and van Vliet find the highest-volatility names earn poor returns. Here the twenty wildest compounded at 12.06% with dividends, the best of the three books, on the back of 25.34% a year from 2020 to 2025. What they did not do is deliver it comfortably: 34.1% realised volatility, a -28.4% average worst drawdown, and a -46.7% year in 2008.

5. Neither difference is statistically distinguishable from zero. Calm against the market: 1.53 points a year behind, t = -0.55, ahead in 9 of 20 windows. Calm against wild: 5.56 points behind, t = -1.03, ahead in 9 of 20. The platform's own block bootstrap over 5011 paired out-of-sample days puts P(calm beats wild) at 6.0%. Twenty annual observations is a small sample for a return difference and this paper claims no more than it can carry.

6. On risk-adjusted terms the calm book wins on every measure available, which is the version of the effect this record supports without qualification: pooled out-of-sample Sharpe 0.51 against 0.469, return per unit of annual variation 0.95 against 0.45, and 38% of the wild book's drawdown.

7. There is no clean era break in the calm book's relationship to the market. Cutting the sample at any year from 2010 to 2022 leaves the calm book behind the market in BOTH halves, by between 0.1 and 4.1 points. The 2020 discontinuity that dominates the wild book, 25.34% a year against 6.81% before it, does not have a mirror on the calm side. Whatever changed in 2020 changed what risk paid, not what calm cost.

5.2 Interpretation

The low-volatility effect is usually sold as a free lunch: the same return for less risk, or better. This record supports the second half of that sentence emphatically and the first half only just. Thirty basis points a year is inside the width of every assumption in the study, the cost model, the dividend overlay and the vendor's coverage, so the honest reading is that the calm book matched the market rather than beat or lost to it, and did so while varying about half as much year to year.

The mechanism deserves to be stated in the open, because it is not the one most readers assume. The calm book does not earn more per year. It earns LESS per year, on average, and keeps more of what it earns. An average of 1.53 points below the market compounds to only 0.30 points below, because a series that does not fall -39.7% in 2008 has less ground to make up afterwards. Anyone evaluating this strategy on average annual return will reject it; anyone evaluating it on terminal wealth per unit of anxiety will not.

The wild book is the part that would have surprised the 2007 authors, and the composition tells the story better than the return does. It is not a portfolio of speculative small caps, because the S&P 500 does not contain those. It is a rotating position in whatever the market is currently most frightened of or most excited about: banks in 2008 through 2010, energy in 2016 and 2017, cruise lines and airlines in 2020 and 2021, speculative growth from 2022. Because the book re-selects quarterly on trailing volatility, it is mechanically a "buy whatever just blew up" rule, and in a sharp mean-reverting crash that is extremely profitable. It returned 25.34% a year from 2020. It also lost -46.7% in 2008 and 33.3% in 2011, a year the index barely moved.

That asymmetry is what the risk-adjusted numbers are describing. Both books can be defended; they are simply different products. One of them can be held through a crisis by an ordinary person and the other cannot, and no Sharpe ratio conveys that as well as the pair of 2008 numbers does: -15.7% against -46.7%.

A note on what this study does NOT settle, because it is the obvious next question. Low volatility and low beta are widely treated as the same defensive trade. They are not, and the same twenty windows say so, but that comparison needs its own sealed circuit rather than a paragraph borrowed from this one, and it has one.

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.

The comparison this study set up

The obvious question a defensive investor asks next is whether ranking on beta would have done the same job. It would not, and the difference is larger than the one this paper measures.

That comparison is its own sealed study rather than a paragraph here, because a claim of that size should rest on a circuit built to test it, not on two papers read side by side. The apparatus on this page, the figures, the tables, the bootstrap and the risk calibration, describes calm against wild and nothing else.

5.3 Limitations

No transaction costs are charged. The books turn over roughly 59% and 70% a year one way on the calm and wild sides, with quarterly re-selection. Costs at that turnover are small against the differences reported, but they are not zero and they fall harder on the wild book, which trades faster and holds wider-spread names.

The universe is point-in-time S&P 500 membership, which removes membership look-ahead but introduces the vendor's coverage as a limit: no delisted name is served at all. Lehman, Bear Stearns and General Motors return nothing. The pool that can be ranked runs from 344 names in 2006 to roughly five hundred by the 2020s, and the names missing from the early windows are disproportionately those that later failed, which is to say disproportionately volatile. The wild book is therefore missing its worst members, and its returns here flatter it. That bias runs AGAINST this paper's direction, so the risk contrast reported is conservative.

Twenty names a side is not a decile. Blitz and van Vliet sort into deciles across a market-wide universe; twenty of roughly five hundred is the top and bottom four percent, and the S&P 500 is already large, liquid and quality-filtered. The most volatile names available here are far tamer than the most volatile names in a market-wide sort, and the literature reports the effect strongest outside large caps. This is a narrower test than the published one, in the direction that weakens it.

The total-return figures are measured outside the sealed walk. The engine marks price returns; the dividend overlay is computed afterwards from the payment record and applied to the recorded baskets, with every window reconciled against the engine's own price return first. It is our arithmetic, not the walk's, and both bases are reported so the reader can use either.

No search record exists for this study, so the number of configurations examined before it is unknown and no deflated Sharpe ratio can be computed. The twenty windows were registered and sealed one at a time before each ran; what is not evidenced is how many designs were considered before this one.

One vendor supplies every price. A data-quality gate rejects series carrying splice artifacts, sub-cent placeholder prices or sparse sampling, and it was widened on the morning this walk ran after a name with a tenfold unadjusted level shift was found in an earlier book. This walk ran entirely under the widened gate; the earlier papers in this series did not.

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?

Blitz, D. C., & van Vliet, P. (2007). The Volatility Effect: Lower Risk Without Lower Return. Journal of Portfolio Management, 34(1), 102-113.
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.
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.
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.
Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly. Financial Analysts Journal, 67(1), 40-54.
Blitz, D., van Vliet, P., & Baltussen, G. (2020). The Volatility Effect Revisited. Journal of Portfolio Management, 46(2), 45-63.
Frazzini, A., & Pedersen, L. H. (2014). Betting Against Beta. Journal of Financial Economics, 111(1), 1-25.
Novy-Marx, R. (2016). Understanding Defensive Equity. NBER Working Paper 20591.

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	43acd7fc0a05	675	2006-01-01	2006-01-03 → 2006-12-29
2	7d1fae0f375d	676	2007-01-01	2007-01-03 → 2007-12-31
3	4f84e3d69075	677	2008-01-01	2008-01-02 → 2008-12-31
4	d75cf5cedcbb	678	2009-01-01	2009-01-02 → 2009-12-31
5	f3e8d8a28082	679	2010-01-01	2010-01-04 → 2010-12-31
6	d43be0475304	680	2011-01-01	2011-01-03 → 2011-12-30
7	d804eb16697d	681	2012-01-01	2012-01-03 → 2012-12-31
8	a1d9d503b623	682	2013-01-01	2013-01-02 → 2013-12-31
9	a0b05cefebfa	683	2014-01-01	2014-01-02 → 2014-12-31
10	7c86f2006fdd	684	2015-01-01	2015-01-02 → 2015-12-31
11	7d29c65ac58f	685	2016-01-01	2016-01-04 → 2016-12-30
12	41d0ed9647c5	686	2017-01-01	2017-01-03 → 2017-12-29
13	90492fe55c6f	687	2018-01-01	2018-01-02 → 2018-12-31
14	68b6c3b50248	688	2019-01-01	2019-01-02 → 2019-12-31
15	fa51915dfd26	689	2020-01-01	2020-01-02 → 2020-12-31
16	ea944c7381b4	690	2021-01-01	2021-01-04 → 2021-12-31
17	6d1bc181ae33	691	2022-01-01	2022-01-03 → 2022-12-30
18	bab1e61ed54e	692	2023-01-01	2023-01-03 → 2023-12-29
19	c33b8f9afaae	693	2024-01-01	2024-01-02 → 2024-12-31
20	a12150fe2c9d	694	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 volatility: the twenty calmest names vs High volatility: the twenty wildest names, walked on the same registered out-of-sample windows. Low volatility: the twenty calmest names: 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 volatility: the twenty wildest names: 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 volatility: the twenty calmest names generates better risk-adjusted returns than High volatility: the twenty wildest names 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 21:06:54	2026-08-08 22:28:42
2	2007-01-01	2026-08-08 22:28:47	2026-08-08 22:30:47
3	2008-01-01	2026-08-08 22:30:52	2026-08-08 22:32:33
4	2009-01-01	2026-08-08 22:32:38	2026-08-08 22:34:38
5	2010-01-01	2026-08-08 22:34:43	2026-08-08 22:36:43
6	2011-01-01	2026-08-08 22:36:49	2026-08-08 22:38:29
7	2012-01-01	2026-08-08 22:38:34	2026-08-08 22:40:14
8	2013-01-01	2026-08-08 22:40:19	2026-08-08 22:42:20
9	2014-01-01	2026-08-08 22:42:25	2026-08-08 22:44:25
10	2015-01-01	2026-08-08 22:44:30	2026-08-08 22:46:31
11	2016-01-01	2026-08-08 22:46:36	2026-08-08 22:48:16
12	2017-01-01	2026-08-08 22:48:21	2026-08-08 22:50:21
13	2018-01-01	2026-08-08 22:50:27	2026-08-08 22:52:27
14	2019-01-01	2026-08-08 22:52:32	2026-08-08 22:54:32
15	2020-01-01	2026-08-08 22:54:37	2026-08-08 22:56:18
16	2021-01-01	2026-08-08 22:56:23	2026-08-08 22:58:23
17	2022-01-01	2026-08-08 22:58:29	2026-08-08 23:00:29
18	2023-01-01	2026-08-08 23:00:34	2026-08-08 23:02:35
19	2024-01-01	2026-08-08 23:02:40	2026-08-08 23:04:20
20	2025-01-01	2026-08-08 23:04:25	2026-08-08 23:06:26

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 volatility: the twenty calmest names

Portfolio book, rebalanced quarterly · 5 constructions · 19 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

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 3.24% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2006-01-01	-5.3373%	1.1075%	8.644%	-2.3667%	yes	0.8693%	2 / 61
2006-04-01	-5.9545%	0.9182%	8.3375%	2.2052%	yes	0.8932%	5 / 62
2006-07-01	-5.9036%	1.1295%	8.7338%	5.0855%	yes	0.9008%	0 / 62
2006-10-01	-5.1074%	1.8504%	9.3634%	3.8931%	yes	0.8445%	1 / 62
2007-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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 5.67% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2006-01-01	-15.5329%	2.2555%	25.9742%	20.4229%	yes	2.5586%	1 / 61
2006-04-01	-15.0787%	4.4369%	28.5919%	-12.6258%	yes	2.5879%	5 / 62
2006-07-01	-9.8756%	7.9802%	29.5095%	-10.9967%	no	2.1445%	8 / 62
2006-10-01	-14.5289%	4.7925%	28.634%	10.151%	yes	2.6067%	0 / 62
2007-01-01	no segment follows this rebalance, not scored

Step 2 · 2007-01-03 → 2007-12-31

Low volatility: the twenty calmest names

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	-5.0157%	2.0301%	8.8836%	-2.1975%	yes	0.8134%	5 / 60
2007-04-01	-5.4594%	1.2083%	8.3892%	-0.3355%	yes	0.7966%	6 / 62
2007-07-01	-5.138%	1.3233%	8.2662%	3.1102%	yes	0.8055%	13 / 62
2007-10-01	-5.5857%	2.2302%	9.922%	-3.1518%	yes	0.9181%	9 / 63
2008-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-13.2273%	5.8546%	26.8059%	6.7412%	yes	2.3193%	4 / 60
2007-04-01	-12.1043%	6.4934%	29.1703%	7.2155%	yes	2.3404%	1 / 62
2007-07-01	-9.5185%	9.1958%	31.9248%	7.3172%	yes	2.2007%	8 / 62
2007-10-01	-11.6622%	9.774%	33.8317%	-10.6447%	yes	2.6096%	8 / 63
2008-01-01	no segment follows this rebalance, not scored

Step 3 · 2008-01-02 → 2008-12-31

Low volatility: the twenty calmest names

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 50.0% 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	-5.7855%	2.2076%	10.056%	-4.2423%	yes	0.9423%	12 / 60
2008-04-01	-7.0996%	1.8866%	10.839%	-9.0765%	no	1.0548%	9 / 63
2008-07-01	-8.5935%	0.991%	10.6069%	5.2419%	yes	1.2677%	5 / 63
2008-10-01	-9.2009%	1.2101%	11.7435%	-13.1607%	no	1.2925%	22 / 63

High volatility: the twenty wildest names

Portfolio book, rebalanced quarterly · 4 constructions · 19 names held · selection: reselect · 0.0% in cash · 2 names dropped at load (36 names actually held across the window), weights renormalised onto the rest

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2008-01-01	-17.5502%	2.1916%	24.1976%	-6.7828%	yes	2.5388%	11 / 60
2008-04-01	-28.1028%	-3.9166%	25.1744%	-22.6175%	yes	3.2128%	7 / 63
2008-07-01	-32.4047%	-7.5831%	22.927%	5.6149%	yes	3.7745%	14 / 63
2008-10-01	-47.6666%	-11.1986%	43.839%	-30.5279%	yes	5.6757%	14 / 63

Step 4 · 2009-01-02 → 2009-12-31

Low volatility: the twenty calmest names

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	-15.6889%	-0.8658%	14.8493%	-10.2831%	yes	1.6662%	9 / 60
2009-04-01	-16.9811%	-2.3429%	14.9849%	7.7817%	yes	1.9558%	0 / 62
2009-07-01	-17.0767%	-1.2131%	15.8884%	5.7176%	yes	1.8695%	0 / 63
2009-10-01	-16.0429%	0.0866%	17.486%	9.0182%	yes	1.8915%	0 / 63
2010-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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

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	-51.9165%	-14.7004%	43.5905%	-32.3033%	yes	5.728%	16 / 60
2009-04-01	-57.3008%	-17.8013%	58.8417%	72.5024%	no	7.5727%	3 / 62
2009-07-01	-58.8352%	-12.2112%	75.1635%	44.8039%	yes	8.2851%	0 / 63
2009-10-01	-56.054%	-5.9277%	88.3442%	-2.259%	yes	8.3323%	0 / 63
2010-01-01	no segment follows this rebalance, not scored

Step 5 · 2010-01-04 → 2010-12-31

Low volatility: the twenty calmest names

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	-15.1556%	0.2626%	16.6868%	1.4282%	yes	1.8808%	1 / 60
2010-04-01	-13.8675%	0.4912%	17.3487%	-5.3465%	yes	1.8218%	2 / 62
2010-07-01	-15.1045%	0.0929%	16.315%	7.1077%	yes	1.881%	0 / 63
2010-10-01	-14.1322%	1.1715%	17.4966%	1.8708%	yes	1.851%	0 / 63
2011-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-54.6141%	-5.4358%	84.2341%	22.0276%	yes	8.4802%	0 / 60
2010-04-01	-51.359%	-2.787%	95.0718%	-19.0954%	yes	8.4553%	0 / 62
2010-07-01	-54.404%	-3.2165%	92.2851%	11.0639%	yes	8.6232%	0 / 63
2010-10-01	-51.5317%	1.8826%	100.6248%	15.3937%	yes	8.6232%	0 / 63
2011-01-01	no segment follows this rebalance, not scored

Step 6 · 2011-01-03 → 2011-12-30

Low volatility: the twenty calmest names

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	-9.5535%	1.9204%	16.1121%	1.72%	yes	1.5779%	0 / 61
2011-04-01	-6.5661%	3.0486%	13.7174%	3.3758%	yes	1.0908%	0 / 62
2011-07-01	-4.4295%	4.3287%	13.0151%	-1.4967%	yes	0.9329%	11 / 63
2011-10-01	-6.3815%	2.697%	12.7166%	9.1303%	yes	1.0575%	6 / 62
2012-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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 6.85% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2011-01-01	-40.737%	4.2961%	93.2961%	1.7076%	yes	7.2136%	0 / 61
2011-04-01	-29.9003%	14.8664%	88.7629%	-8.1192%	yes	5.0183%	0 / 62
2011-07-01	-18.0883%	9.884%	43.6509%	-39.8876%	no	3.3111%	10 / 63
2011-10-01	-23.901%	0.8538%	33.8804%	25.1462%	yes	3.6236%	7 / 62
2012-01-01	no segment follows this rebalance, not scored

Step 7 · 2012-01-03 → 2012-12-31

Low volatility: the twenty calmest names

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	-6.2909%	2.6543%	13.3956%	1.5746%	yes	1.0915%	0 / 61
2012-04-01	-6.9472%	2.3194%	12.5709%	3.5793%	yes	1.0677%	1 / 62
2012-07-01	-6.8748%	2.5939%	13.0889%	0.9387%	yes	1.0738%	0 / 62
2012-10-01	-5.6508%	2.4308%	12.0442%	-2.1453%	yes	0.9872%	1 / 61

High volatility: the twenty wildest names

Portfolio book, rebalanced quarterly · 4 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

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2012-01-01	-23.7157%	0.8066%	36.6538%	11.0773%	yes	3.8614%	0 / 61
2012-04-01	-25.4505%	0.3861%	35.4109%	-12.687%	yes	3.7515%	2 / 62
2012-07-01	-28.2921%	-3.1215%	31.1134%	10.4868%	yes	3.7155%	0 / 62
2012-10-01	-24.6499%	-0.83%	33.8429%	17.3578%	yes	3.4429%	0 / 61

Step 8 · 2013-01-02 → 2013-12-31

Low volatility: the twenty calmest names

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	-7.0504%	1.8868%	10.2336%	11.9738%	no	1.0088%	0 / 59
2013-04-01	-5.6403%	3.7859%	13.2023%	-0.8157%	yes	0.9839%	9 / 63
2013-07-01	-7.0689%	2.7477%	12.603%	-1.9681%	yes	1.0413%	4 / 63
2013-10-01	-6.9465%	2.8692%	12.7224%	4.4156%	yes	1.0651%	2 / 63
2014-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-26.2712%	0.4856%	31.0485%	6.2417%	yes	3.5731%	1 / 59
2013-04-01	-28.057%	-1.9258%	30.105%	15.4665%	yes	3.4542%	2 / 63
2013-07-01	-26.2246%	0.0886%	32.1948%	4.2468%	yes	3.513%	1 / 63
2013-10-01	-12.15%	9.4195%	33.6801%	12.2057%	yes	2.5366%	1 / 63
2014-01-01	no segment follows this rebalance, not scored

Step 9 · 2014-01-02 → 2014-12-31

Low volatility: the twenty calmest names

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	-5.8444%	2.4994%	10.7192%	7.354%	yes	0.9752%	3 / 60
2014-04-01	-4.9645%	2.6401%	10.9028%	4.7637%	yes	0.9249%	3 / 62
2014-07-01	-4.7407%	3.3866%	11.4028%	-2.053%	yes	0.8849%	5 / 63
2014-10-01	-4.904%	2.9316%	10.6401%	9.8917%	yes	0.8033%	4 / 63
2015-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-7.7093%	13.0919%	36.0286%	1.8096%	yes	2.2392%	3 / 60
2014-04-01	-3.6252%	14.8115%	36.9143%	4.8464%	yes	1.9656%	4 / 62
2014-07-01	-4.5947%	14.6385%	35.5434%	2.4655%	yes	1.9264%	3 / 63
2014-10-01	-4.8659%	13.7349%	33.855%	4.2366%	yes	1.8715%	6 / 63
2015-01-01	no segment follows this rebalance, not scored

Step 10 · 2015-01-02 → 2015-12-31

Low volatility: the twenty calmest names

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	-4.425%	3.5338%	11.3377%	-1.9668%	yes	0.9396%	7 / 60
2015-04-01	-4.8276%	3.2313%	12.0256%	-3.9813%	yes	1.0352%	2 / 62
2015-07-01	-6.5133%	2.003%	10.4456%	-2.1619%	yes	1.025%	10 / 63
2015-10-01	-7.9273%	1.0846%	10.0715%	6.69%	yes	1.0441%	6 / 63
2016-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-8.2378%	9.5924%	28.7782%	5.166%	yes	1.9979%	5 / 60
2015-04-01	-7.8907%	9.5932%	30.5276%	-0.6372%	yes	2.0117%	1 / 62
2015-07-01	-10.8813%	5.5465%	23.1574%	-12.6499%	no	1.9666%	8 / 63
2015-10-01	-17.6994%	-1.0586%	17.0373%	5.3306%	yes	2.1982%	2 / 63
2016-01-01	no segment follows this rebalance, not scored

Step 11 · 2016-01-04 → 2016-12-30

Low volatility: the twenty calmest names

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	-8.1436%	1.5924%	11.3297%	9.1326%	yes	1.114%	6 / 60
2016-04-01	-6.4982%	3.9621%	14.5203%	5.9198%	yes	1.1448%	3 / 63
2016-07-01	-7.0749%	3.3348%	13.8431%	-3.2859%	yes	1.1477%	2 / 63
2016-10-01	-7.2525%	2.6259%	13.6232%	1.4346%	yes	1.1967%	1 / 62

High volatility: the twenty wildest names

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	-21.6922%	-4.4633%	14.4553%	9.7205%	yes	2.4701%	10 / 60
2016-04-01	-28.7196%	-6.1986%	20.4947%	18.3682%	yes	3.4528%	3 / 63
2016-07-01	-28.9223%	-4.0046%	26.2688%	3.3513%	yes	3.6885%	2 / 63
2016-10-01	-27.7849%	-2.6975%	31.3325%	1.0381%	yes	3.7958%	0 / 62

Step 12 · 2017-01-03 → 2017-12-29

Low volatility: the twenty calmest names

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	-7.4291%	1.4117%	12.0282%	4.3781%	yes	1.225%	0 / 61
2017-04-01	-6.6405%	2.2616%	12.0719%	1.9315%	yes	1.1365%	0 / 62
2017-07-01	-5.8881%	2.8076%	12.3644%	1.918%	yes	1.0808%	0 / 62
2017-10-01	-5.6438%	2.7954%	12.0452%	5.12%	yes	1.056%	0 / 62
2018-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-25.194%	-2.1534%	31.168%	-2.1498%	yes	3.5828%	0 / 61
2017-04-01	-22.8797%	-0.2895%	29.1104%	-7.9201%	yes	3.3721%	0 / 62
2017-07-01	-22.9956%	-1.2214%	26.8933%	7.8284%	yes	3.2695%	0 / 62
2017-10-01	-15.1726%	5.7534%	32.0108%	3.6207%	yes	2.5629%	0 / 62
2018-01-01	no segment follows this rebalance, not scored

Step 13 · 2018-01-02 → 2018-12-31

Low volatility: the twenty calmest names

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	-3.8405%	3.5944%	10.8464%	-3.0737%	yes	0.9215%	10 / 60
2018-04-01	-4.6035%	3.1993%	10.8715%	1.3189%	yes	0.8773%	3 / 63
2018-07-01	-5.2042%	1.9228%	9.6319%	5.2967%	yes	0.9278%	2 / 62
2018-10-01	-4.5418%	2.4363%	9.9695%	-2.3442%	yes	0.7884%	11 / 62
2019-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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 11.74% of 247 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2018-01-01	-15.5777%	3.5265%	24.6067%	-3.634%	yes	2.1962%	7 / 60
2018-04-01	-12.0088%	6.7764%	27.3869%	19.0908%	yes	2.1291%	2 / 63
2018-07-01	-9.4582%	6.6858%	25.8284%	2.468%	yes	1.9856%	2 / 62
2018-10-01	-9.8282%	4.5577%	21.3432%	-22.3375%	no	1.7445%	18 / 62
2019-01-01	no segment follows this rebalance, not scored

Step 14 · 2019-01-02 → 2019-12-31

Low volatility: the twenty calmest names

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 4.44% of 248 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2019-01-01	-6.8071%	2.4454%	11.6456%	13.9865%	no	1.0429%	0 / 60
2019-04-01	-6.5602%	2.7468%	13.0431%	4.9366%	yes	1.1585%	3 / 62
2019-07-01	-7.0043%	3.0947%	13.2594%	6.8247%	yes	1.1813%	5 / 63
2019-10-01	-7.2492%	3.3453%	14.0605%	-0.8893%	yes	1.2419%	3 / 63
2020-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-15.5767%	1.1778%	19.2659%	18.707%	yes	2.1885%	5 / 60
2019-04-01	-14.5093%	3.0011%	24.2324%	-3.0558%	yes	2.3247%	1 / 62
2019-07-01	-16.5065%	2.8828%	24.4693%	-8.5118%	yes	2.5546%	6 / 63
2019-10-01	-18.7721%	1.3479%	24.0158%	11.583%	yes	2.9135%	0 / 63
2020-01-01	no segment follows this rebalance, not scored

Step 15 · 2020-01-02 → 2020-12-31

Low volatility: the twenty calmest names

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 8.84% of 249 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2020-01-01	-6.6827%	2.5926%	13.7721%	-10.485%	no	1.2512%	13 / 61
2020-04-01	-13.6496%	0.8911%	17.9871%	9.8722%	yes	1.4703%	7 / 62
2020-07-01	-11.9261%	4.2139%	21.5013%	9.8301%	yes	1.5834%	1 / 63
2020-10-01	-12.5276%	3.7849%	21.3027%	1.912%	yes	1.5632%	1 / 63

High volatility: the twenty wildest names

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 25.0% of 4 scored rebalances (a well-calibrated 90% band contains ~90.0%) · 95% VaR breached on 12.85% of 249 days (expected ~5.0%)

Rebalance	P5	Median	P95	Realized	In band	VaR 95 (1d)	Breaches
2020-01-01	-17.2803%	0.3933%	24.0217%	-36.9915%	no	2.7283%	13 / 61
2020-04-01	-39.9189%	-14.2981%	22.501%	68.1179%	no	3.2714%	14 / 62
2020-07-01	-43.4057%	-8.7441%	41.0952%	-0.8873%	yes	4.5683%	3 / 63
2020-10-01	-44.3501%	-8.6132%	43.6709%	47.1707%	no	4.7184%	2 / 63

Step 16 · 2021-01-04 → 2021-12-31

Low volatility: the twenty calmest names

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	-12.7661%	2.9985%	19.7781%	0.6029%	yes	1.5126%	2 / 60
2021-04-01	-12.0319%	2.7169%	20.0467%	3.2504%	yes	1.5659%	0 / 62
2021-07-01	-12.6857%	2.9136%	19.5598%	-2.7006%	yes	1.4737%	2 / 63
2021-10-01	-12.9058%	2.6443%	19.2366%	11.692%	yes	1.454%	1 / 63
2022-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-41.5098%	-3.3666%	52.4849%	31.3804%	yes	4.8561%	0 / 60
2021-04-01	-34.3592%	5.8149%	71.051%	8.0697%	yes	4.6782%	0 / 62
2021-07-01	-35.3535%	8.1683%	72.984%	-3.2428%	yes	4.8003%	0 / 63
2021-10-01	-31.7%	12.1295%	76.2366%	-3.9493%	yes	4.5318%	2 / 63
2022-01-01	no segment follows this rebalance, not scored

Step 17 · 2022-01-03 → 2022-12-30

Low volatility: the twenty calmest names

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	-11.1937%	2.73%	20.4313%	0.3249%	yes	1.4449%	1 / 61
2022-04-01	-12.1206%	1.8417%	19.6258%	-1.634%	yes	1.4545%	3 / 61
2022-07-01	-8.3179%	3.5456%	15.7%	-9.7852%	no	1.3443%	8 / 63
2022-10-01	-9.464%	1.2338%	13.2692%	5.4991%	yes	1.3786%	5 / 62
2023-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-28.3748%	10.4683%	77.2689%	8.0204%	yes	4.5306%	1 / 61
2022-04-01	-30.532%	8.9348%	78.0047%	-26.6538%	yes	4.5153%	7 / 61
2022-07-01	-21.707%	12.3227%	56.1115%	-0.2675%	yes	3.9328%	1 / 63
2022-10-01	-19.2372%	7.5766%	43.5318%	5.0684%	yes	3.4272%	3 / 62
2023-01-01	no segment follows this rebalance, not scored

Step 18 · 2023-01-03 → 2023-12-29

Low volatility: the twenty calmest names

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	-8.2393%	2.0047%	14.4959%	-0.8474%	yes	1.3904%	1 / 61
2023-04-01	-8.3795%	1.821%	14.2557%	0.6102%	yes	1.3816%	0 / 61
2023-07-01	-9.8572%	0.5936%	12.3277%	-7.9844%	yes	1.3013%	1 / 62
2023-10-01	-10.4582%	-0.0306%	11.6829%	5.8651%	yes	1.327%	5 / 62
2024-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-21.4782%	4.4433%	42.5968%	14.7673%	yes	3.6747%	1 / 61
2023-04-01	-26.3539%	-1.6638%	34.8246%	-0.1303%	yes	3.952%	3 / 61
2023-07-01	-27.2727%	-1.1642%	34.5567%	-12.5844%	yes	3.6557%	1 / 62
2023-10-01	-29.8848%	-3.5678%	32.8728%	16.7092%	yes	3.8803%	1 / 62
2024-01-01	no segment follows this rebalance, not scored

Step 19 · 2024-01-02 → 2024-12-31

Low volatility: the twenty calmest names

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	-9.7411%	1.1353%	12.1489%	5.5548%	yes	1.2759%	0 / 60
2024-04-01	-9.3487%	0.9455%	12.4791%	-0.4034%	yes	1.2933%	2 / 62
2024-07-01	-8.7047%	1.9046%	12.653%	8.8581%	yes	1.2136%	1 / 63
2024-10-01	-6.7653%	2.9143%	12.6168%	-4.4334%	yes	1.0631%	2 / 63

High volatility: the twenty wildest names

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	-31.1645%	-3.5299%	31.0886%	5.3379%	yes	3.8864%	0 / 60
2024-04-01	-26.0441%	0.2689%	36.1847%	-2.2278%	yes	3.6202%	0 / 62
2024-07-01	-23.3955%	2.2295%	33.0095%	8.6589%	yes	3.3912%	4 / 63
2024-10-01	-19.4125%	3.8446%	30.8644%	6.3299%	yes	3.0305%	1 / 63

Step 20 · 2025-01-02 → 2025-12-31

Low volatility: the twenty calmest names

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	-5.4181%	3.1068%	11.028%	10.9445%	yes	0.9414%	7 / 59
2025-04-01	-4.2345%	3.3562%	12.33%	-2.1781%	yes	0.988%	6 / 61
2025-07-01	-6.1511%	3.3934%	12.9431%	1.1333%	yes	0.9999%	2 / 63
2025-10-01	-6.5775%	3.2539%	13.1207%	-1.0802%	yes	1.069%	4 / 63
2026-01-01	no segment follows this rebalance, not scored

High volatility: the twenty wildest names

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	-15.5886%	6.6218%	30.2724%	-7.8858%	yes	2.7129%	7 / 59
2025-04-01	-15.2009%	3.3377%	28.2287%	21.8926%	yes	2.5103%	8 / 61
2025-07-01	-17.6981%	8.5435%	39.712%	26.6693%	yes	2.8749%	0 / 63
2025-10-01	-15.7923%	12.2382%	45.8684%	-0.4798%	yes	2.9195%	5 / 63
2026-01-01	no segment follows this rebalance, not scored

QuanterLab · Study ed03eee24bdd · 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.

Lower risk without lower return, tested the way a private investor would have to run it

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 Volatility

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

The comparison this study set up

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