Part X · Edges, one by one · Chapter 10A

Five kinds of edge

How the kind of edge sets its size and its kill rule

1 · One table cannot rank every edge

The Edge Book, the source of Part X, went through three versions. The first ranked every edge in a single table, which implied a false comparability. The equity risk premium (ERP) and an OPEX-week tilt, a change of positioning in the week of the monthly options expiration (OPEX), are different kinds of object. They should not compete against each other for the same capital.

The fix is a taxonomy of five categories. It separates what kind of edge something is from how strong the evidence for it is, and both from how much capital it should get. Once you know an edge's source (Chapter 1G) and have scored your conviction in it (Chapter 13B), the category tells you how it fits into a portfolio. Different categories need different sizing rules, different assumptions about how long the edge persists, and different kill criteria.

The key cognitive rule follows: before you can know how to size a strategy and how to kill it, you have to know what kind of edge it is.

The taxonomy has five categories, running from the most durable edges to the ones you should never trade:

1. Foundation premia: the risk premia that anchor the portfolio.
2. Equity factor tilts: systematic departures from weighting stocks by market capitalization that have produced excess returns.
3. Structural and tactical overlays: calendar or flow effects that modulate your exposure to the other premia.
4. Regime filters: variables that size other strategies and are never traded on their own.
5. Rejected or non-retail edges: those that decayed, were never robust, or can be traded only by institutions.

Each category has its own role and its own operating rules. The table gathers them, and the sections below take each row in turn.

"Portfolio risk" in the table means a share of the portfolio's volatility, not of its dollars. A dollar in a volatile sleeve carries more risk than a dollar in a calm one, so the two shares differ. Chapter 13G shows how to compute each sleeve's share of the risk.

The category matters most when something goes wrong, because it decides what you do next. The example applies the kill rule of one category to an edge from another.

The reverse mistake costs money too, because a foundation rule never switches an overlay off. It would keep an OPEX-week tilt running after its effect had diluted, paying trading costs every month for an edge that had gone.

2 · Category A: foundation premia

Foundation premia are compensated risk premia, payments for bearing risk that cannot be diversified away, and four of them anchor the portfolio:

• The equity risk premium, earned by holding equities (Chapter 10B).
• The index variance risk premium (VRP), earned by selling volatility on the index (Chapter 10C).
• Trend following, or time-series momentum (TSMOM), run systematically across asset classes (Chapter 10D).
• Cross-asset carry, earned by buying the assets that pay the most carry (Chapter 10E).

Almost all foundation premia are risk premia, Source 1 of Chapter 1G, which makes them the most durable category. Their premium exists for structural reasons, and those reasons do not disappear when capital exploits them. Their typical aggregate allocation is 60% to 70% of portfolio risk. Chapter 10E adds the four sleeves together and arrives at about 70% to 80%, a range from a different chapter of the Edge Book that meets this one only at 70%.

Four sizing principles follow from what a foundation premium is:

• Size each foundation sleeve from its long-run expectation, not from its recent performance.
• For a short-volatility foundation sleeve such as the VRP, assume the volatility of a stress period rather than a calm one.
• Assume drawdowns of 35% to 50%, which by Chapter 1E need gains of 54% to 100% to repair, and make sure the portfolio survives them.
• Do not cut the allocation during a drawdown, because drawdowns are the cost of the premium.

The persistence of foundation premia is high. These edges are documented across centuries, and they survive under different regulatory regimes. The ERP has been positive in 35 of 35 markets in the Dimson-Marsh-Staunton database. The VRP has been positive in roughly 80% of months for more than 30 years, and trend has been positive in every decade since 1880.

Their decay risk is limited: a premium compresses when investors' demand for the risk behind it shifts, but it does not go to zero. Higher equity allocations, for example, have compressed the forward ERP, the premium that equities are expected to pay from here on. So foundation premia are never switched off. They are sized down in adverse regimes, under the specific kill criteria of Chapter 13G.

3 · Category B: equity factor tilts

Factor tilts are systematic departures from market-capitalization weighting that have produced positive long-run excess returns within equity markets. A cap-weighted index such as the S&P 500 holds each company in proportion to its market value. A tilt leans away from those weights toward stocks with a chosen trait, and Chapter 10F examines the five tilts of this category:

• Quality or profitability, measured by the RMW ("robust minus weak") and QMJ ("quality minus junk") factors: long the high-quality stocks.
• Momentum, cross-sectional (CSMOM): long the recent winners, short the recent losers.
• Value, measured by the HML ("high minus low") factor: long the cheap stocks, short the expensive ones.
• Low volatility, or betting against beta (BAB): long the low-beta stocks, short the high-beta ones.
• Size conditional on quality: long the small companies of high quality.

By source the tilts are mixed: most are behavioral (Source 2), with risk-premium and institutional parts. Quality is the most risk-premium-flavored of them, and momentum the most behavioral. Tilts live within the equity sleeve, at a typical 15% to 30% of it, expressed through factor ETFs, exchange-traded funds that track a factor. On a $550,000 equity sleeve, a 20% tilt puts $110,000 into factor ETFs and leaves $440,000 in the broad index, so the total equity exposure does not change. Chapter 10F, building the tilt factor by factor, arrives at 25% to 40%, and the two ranges share only 25% to 30%.

Four sizing principles guard against the way factors fail:

• Tilt rather than concentrate: do not replace SPX with pure factor ETFs.
• Diversify across factors, since quality, momentum and low volatility together do better than any single factor.
• Plan for drawdowns that last several years.
• Do not try to time the rotation from one factor to another.

The persistence of tilts is medium, because behavioral edges decay after publication. Jensen, Kelly and Pedersen (2023) documented a decline of about 47% after publication. Quality has held up best, while size and naive value have struggled. The decay risk is therefore real: some factors have already decayed substantially, among them size on its own and naive value from 2010 to 2020. Others, such as quality and momentum, have decayed less but compressed.

Three kill criteria govern a tilt, and the first is the one the earlier example misapplied:

• If the 24-month rolling Sharpe ratio falls below 0, cut the allocation by 50%.
• If the vehicle's tracking error to the academic factor exceeds 4% annualized, switch vehicles. By the square-root-of-time rule of Chapter 1A, that is about $4\%/\sqrt{12} = 1.15\%$ a month.
• Multi-decade drawdowns are tolerable if you are committed to the long run. If you would panic and exit during one, do not allocate at all.

4 · Category C: structural and tactical overlays

Overlays are calendar or flow effects that modulate exposure to other premia rather than serving as strategies of their own. Chapter 10G examines the five overlays of this category:

• The Cieslak FOMC even-week cycle: the equity premium is concentrated in the even weeks of the cycle between meetings of the Federal Open Market Committee (FOMC).
• End-of-quarter (EOQ) rebalancing flow: pension funds rebalancing to their targets create predictable flow, as in the worked example of Chapter 1G.
• The Halloween effect, or "sell in May": a seasonal pattern in equity returns.
• The OPEX-week tilt: effects in the week of the monthly options expiration.
• The turn-of-the-month effect: the timing of cash flows around the end of each month.

By source, overlays are mostly institutional frictions (Source 3), with some behavioral effects (Source 2). Halloween is a mystery: the pattern persists, but no clean mechanism explains it.

How this book files OPEX and Halloween

The Edge Book files two of these effects differently in different chapters. Its chapter on sources lists seasonality among the behavioral edges and OPEX dynamics under microstructure. Its taxonomy calls the overlays mostly institutional with some behavioral. Its chapter on overlays files OPEX as microstructure and institutional, and finds no clean mechanism for Halloween.

This book uses one classification throughout, in which both effects are overlays by category. By source, the OPEX-week tilt is microstructure with an institutional part: dealers hedge into expiry, and option-related rebalancing concentrates around it. The Halloween effect is filed with the behavioral seasonality effects, as Chapter 1G files it. That filing stays provisional until someone finds a mechanism, and Chapter 10G examines both effects in full.

Overlays sit on top of existing positions. Their typical aggregate allocation is 10% to 15% of portfolio risk as modulation, not as separate sleeves, because they scale equity exposure up or down rather than run strategies of their own. Three sizing principles follow from that role:

• Express an overlay through instruments you already hold, by rotating ETFs or changing the size of a futures position, rather than through a new strategy.
• Do not add transaction costs that eat the small premium.
• Most overlays add 10 to 30 bps of Sharpe, in the Edge Book's phrase, so check that implementing one costs well below that.

The last principle compares a gain in Sharpe ratio with a cost in money, so the gain has to be turned into return first. The Sharpe ratio is $\text{SR} = \mu/\sigma_p$, where $\mu$ is the portfolio's expected return above the risk-free rate and $\sigma_p$ is its volatility. At a fixed volatility, a rise of $\Delta\text{SR}$ in the Sharpe ratio is therefore a rise in expected excess return of

Read literally, a basis point of Sharpe ratio is 0.0001, so 10 to 30 bps would be 0.001 to 0.003. Chapter 10G adds the five overlays together and puts their combined gain at 0.10 to 0.30 of Sharpe ratio if all are implemented well. Whichever scale is meant, (10A.1) turns the gain into return, the only number a cost can be compared with.

The persistence of overlays varies with how well their mechanism is understood. The FOMC cycle and EOQ rebalancing have clear mechanisms and seem persistent. OPEX and Halloween show empirical patterns without clear mechanisms, so their persistence is uncertain. Their decay risk is real: the S&P 500 inclusion effect has already decayed from 7% to under 1%, and the OPEX effect may be diluting as weekly and 0DTE options spread. Track every overlay for evidence of decay, under three kill criteria:

• If the effect underperforms its baseline by more than 50% over 4 cycles, suspend it. The baseline is what the evidence leads you to expect: an overlay expected to earn 0.3% a quarter has a baseline of 1.2% over 4 quarters, so earning less than 0.6% triggers the rule.
• If the implementation costs exceed the expected edge, simplify the overlay or stop it.
• If the mechanism changes, through regulation or through the structure of a product, reassess the overlay.

5 · Category D: regime filters

A regime filter is a variable used to size exposure to other strategies up or down. It is not a standalone edge, and Chapter 10H examines five of them:

• The VIX term structure, whether it is in contango or in backwardation (Chapter 9A).
• Realized against implied volatility, the gap behind the VRP (Chapter 7A).
• The liquidity regime, read from the TED spread, the MOVE index and corporate credit spreads, which gauge strain in funding and bond markets (Chapter 10E).
• The sign of dealer gamma, read at low confidence (Chapter 8D).
• Breadth and internals, which measure how many stocks take part in a move.

Filters are informational signals about the regime, not edges to trade. The "edge" they create takes the form of avoided losses on other strategies rather than direct returns. So a filter gets zero direct allocation, and its whole use is to modulate other allocations under three principles:

• Define the rule explicitly, for example: "if the VIX divided by the VIX3M exceeds 1.05 for 3 days, halt new put sales".
• Phase changes in and out over several days to avoid whipsaw, being pushed in and out repeatedly by a signal that flickers across its threshold.
• Do not trade the filter itself: for example, do not buy VXX, an exchange-traded product (ETP) that holds VIX futures, because the VIX is in contango. VXX has lost 99.84% of its value to roll decay.

The persistence of filters is high at the level of information: the fact that the VIX term structure backwardates in stress is structural and persistent, even though specific threshold rules may need recalibrating. So the decay risk is low for the underlying signal but meaningful for particular rules, and a filter has two kill criteria:

• If the rule produces persistent false positives, with more than 50% of its "stress" calls followed by no stress, recalibrate it.
• If the underlying signal becomes unavailable or unreliable, switch to another source.

The figure counts the same hundred months, one square each. Lower the share of stress months and watch the hit rate fall, while the net value stays positive.

stress months

10%

sensitivity

80%

specificity

90%

loss in stress

8%

flags = 17 (8 true, 9 false)

hit rate = 8/17 = 47%

net = 64 − 9 = +55 points

Recalibrate, do not drop. Only 8 of 17 flags are followed by stress, below the 50% line. Standing aside still avoids 64 points of loss and gives up 9 points of gain.

6 · Category E: rejected or non-retail

An edge is rejected because it has decayed, because its evidence was never robust, or because it is real but open only to institutions. Chapter 10I examines the seven examples of this category, each with the evidence that rejects it:

• Pre-FOMC announcement drift has decayed. Kurov, Halova, Wolfe and Gilbert (2021) document that it disappeared after 2015, because of reforms to the Federal Reserve's forward guidance.
• The S&P 500 inclusion premium has decayed. Greenwood and Sammon (2024) document an effect under 1% after 2010, against 7% or more in the 1990s.
• Naive single-name earnings short volatility is institutional-only and carries high tail risk. Adams and Neururer (2020) show a negative mean despite a positive median. An institutional cross-sectional version exists (Cao, Han, Tong and Zhan 2022), but it needs infrastructure covering 200 names.
• GEX-level scalping is driven by narrative and has not validated since 2022. Gamma exposure (GEX) estimates the dealers' net gamma, strike by strike (Chapter 8A), and a Cboe study of 2025 estimates that 0DTE hedging by market makers is about 0.2% of liquidity. That study measures same-day hedging only, so using it against levels built mostly from longer-dated open interest extends the measurement.
• Systematic iron condors in the style of Cboe's CNDR index empirically underperform massively. The CNDR returned about 690% from 1986 to 2024, against about 5,500% for the SPX Total Return index (SPX TR), compound rates of about 5.5% and 11% a year (Chapter 1D).
• A 1-year put spread combined with a LEAP, a listed option with a year or more to expiry, is leverage with extra steps rather than edge. A worked example in Chapter 13E shows it to be economically equivalent to about 1.4 times SPX exposure, with worse path properties (Chapter 1E).
• VIX ETPs, long or short, have catastrophic tails. VXX has lost 99.84% to roll decay. A short position in VIX futures held for its roll yield, through products such as XIV and SVXY, carries the opposite danger: XIV was terminated after losing 96% in a day in 2018.

Most retail trading content focuses on Category E strategies. They are vivid, with specific narratives and dramatic claims, and easy to backtest, because their data is clean. They are also frequently traded, with high volume in trading communities. But they do not survive an evaluation by evidence tier.

Knowing what not to trade is half the battle, and a textbook should teach that negative space explicitly. With an allocation of zero, the category's members are documented for reference and to inoculate you against narrative-driven retail bait.

Some Category E items still have legitimate informational uses, even though the trade is rejected:

• The directional sign of GEX, used as low-confidence regime context and never as a set of specific levels.
• Awareness of the earnings calendar, used for risk management, so that you are not caught holding bought options into a report.
• The VIX term structure, used as a filter in Category D and never as a trade.

The trades themselves stay rejected: the information is useful, and the implementations are not.

Where this book's two traditions disagree

Two items on the rejected list are taught elsewhere in this book, in the chapters drawn from the Dealer Mechanics Lab:

• Trading GEX levels: Chapter 8C builds the gamma exposure profile and its walls. The market dashboard of Chapter 11A reads the call wall above spot as potential resistance and the put wall below as potential support. The conviction score of Chapter 13B asks whether dealer positioning supports a trade's path. The Edge Book gives three reasons for caution: vendor models disagree, 0DTE changed who holds what, and the measured hedging flow is small. Both sides agree that scalping level by level is not supported (Chapter 13F).
• Iron condors: Chapter 12C teaches the condor for when you expect realized volatility to come in below implied, and Chapter 5E counts condor writing among the short-premium strategies with positive long-run returns. The Edge Book rejects running condors systematically on the CNDR record (Chapters 1D and 10I). Chapter 12C reports that record too, so the open question is whether a condor chosen for the regime escapes it.

A third disagreement concerns the VRP, which both traditions keep. The Dealer Mechanics Lab calls it the most important source of edge available to retail traders (Chapters 4C and 5E). The Edge Book is more guarded about what it is worth to a retail account (Chapters 1D and 10C).

7 · How sources map onto categories

Chapter 1G gave a rough mapping from the four sources to the five categories. The matrix shows it edge by edge, with parentheses marking a partial fit:

Read by rows, the matrix says that risk premia tend to become foundation sleeves, the most durable category. Behavioral edges tend to become factor tilts, which carry decay risk. Institutional frictions tend to become overlays, which carry regulatory risk. Microstructure edges tend to be rejected for retail accounts, for reasons of capacity.

The mapping is not deterministic, but it is predictive. The VRP is a risk premium that is sometimes implemented as a tilt, and BAB is institutional but often classified as a factor. But if you find an edge that is purely microstructure and are trying to make it a foundation sleeve, you are doing something wrong.

8 · Three questions, three tables

The Edge Book's first version ranked every edge in one table. Its second separated three independent questions, and its third, the textbook behind Part X, keeps them apart, one table to a question:

The three questions have different answers for different strategies. The index VRP has T1 evidence and an acceptable retail implementation, with a user-account Sharpe ratio of about 0.30. Its tail beta of about 1.0 in the left tail still makes it a problem for portfolio construction. Trend following has a middling Sharpe ratio but uniquely diversifying behavior, so its value to a portfolio sits in the third table, not the second (Chapter 10D). Keep all three answers in view: a single ranked number would let a strong answer to one question hide a failing answer to another.

9 · Using the taxonomy

When you evaluate a candidate move, take four steps in order. These four steps are the full pipeline:

1. Source first: which of the four sources is it (Chapter 1G)?
2. Category second: where in the taxonomy does it fit?
3. Conviction third: how does the move score on the conviction score of Chapter 13B?
4. Implementation fourth: which vehicle, sizing and kill rule does its category call for?

Each category has its own style of implementation. A foundation premium gets the foundation style: long-term, sized for stress and executed mechanically. An overlay gets the overlay style of ETF rotation or a simple change of size, with no derivatives unless your capital justifies them. A filter gets the filter style: never traded directly, and used only to size other things. The dossiers of Chapters 10B to 10I fill the taxonomy edge by edge, and the worked examples of Chapter 13E put the whole pipeline to work.

A second common mistake is to stack several edges in one sleeve and expect their Sharpe ratios to add. Chapter 1F showed how correlation governs the gain from combining two strategies, and the same algebra covers any number of them.

The Sharpe ratio of N stacked strategies

Hold $N$ strategies in equal weights, each with expected excess return $\mu$, volatility $\sigma$ and correlation $\rho$ with every other. Averaging equal means leaves the mean unchanged, so the mix also has expected excess return $\mu$.

Its variance is the variance of an average. Each weight is $1/N$, and there are $N$ variance terms of $\sigma^2$ and $N(N-1)$ covariance terms of $\rho\sigma^2$, each multiplied by $1/N^2$:

$$\begin{aligned} \sigma_p^2 &= \frac{N\sigma^2 + N(N-1)\rho\sigma^2}{N^2} \\ &= \sigma^2\,\frac{1 + (N-1)\rho}{N} \end{aligned}$$ (10A.2)

Dividing $\mu$ by $\sigma_p$ gives the Sharpe ratio of the mix, $\text{SR}_N$, in terms of each strategy's own ratio, $\text{SR} = \mu/\sigma$:

$$\text{SR}_N = \text{SR}\,\sqrt{\frac{N}{1 + (N-1)\rho}}$$ (10A.3)

With $N = 2$ this is the formula of Chapter 1F. As $N$ grows without limit, the fraction under the root approaches $1/\rho$, so no number of such strategies can lift the mix above $\text{SR}/\sqrt{\rho}$.

10 · Check yourself