Worked examples: the portfolio

Step 1: haircut for skew. Far-OTM puts have a skewness well below −3.0, while the CBOE PUT Index, which sells at-the-money (ATM) puts, has −2.09 (Chapter 1D). Chapter 1D's rule cuts the Sharpe ratio of any short volatility strategy by 30% to 50% for that skew. At a cut of 35%, near the lenient end, the pitch becomes $0.85 \times 0.65 = 0.55$, its skew-adjusted equivalent.

Step 2: haircut for implementation. A live retail account typically keeps 0.6 to 0.7 times an academic-style number like this one (Chapter 13A), which at 0.65 gives $0.55 \times 0.65 = 0.36$.

Step 3: check the backtest period. The years from 2014 to 2023 include very few stress events: one quick spike in March 2020 and no extended bear market. The data do not reflect the full distribution of regimes, and a short volatility Sharpe ratio built on a benign decade is unreliable.

Step 4: project the tails. Far-OTM puts carry asymmetric exposure to a crash, and a rough mental stress test of the sleeve gives the losses in the table.

The strategy has been tested in none of these, so the backtest is silent on its real tail behavior.

Step 5: compare with the simpler alternative. Over the same years SPX returned about 12% a year at a volatility of about 16%, with full liquidity, efficient taxes and known tail behavior. Its Sharpe ratio of about 0.65 implies that a risk-free rate of about 1.6% was taken out. On the pitch's basis, with none taken out, it is $12/16 = 0.75$. After the haircuts, the candidate's realistic 0.36 is materially worse than simply holding SPX, at about 0.5 once SPX is adjusted for retail frictions.

Step 6: score the conviction. Every factor is weak, and sizing and evidence are the weakest:

The product is $C = 0.30 \times 0.50 \times 0.40 \times 0.55 \times 0.30 = 0.010$, far below the threshold of 0.3.

Step 1: choose the variant. Of the put-writing variants in Chapter 10C, ATM monthly cash-secured XSP puts come closest to the academic VRP with a reasonable retail implementation. This is what the book calls the VRP harvest. Holding the strike in cash eliminates margin risk, and XSP options are Section 1256 contracts, taxed 60% as long-term gains (Chapter 2E).

Step 2: size the position. Fifteen percent of $1 million is $150,000 of notional, against $600 \times 100 = \$60{,}000$ for each contract with XSP at 600. Each put is fully cash-secured at its strike, so each ties up about $60,000 of cash. The allocation is therefore $150{,}000/60{,}000 = 2.5$ contracts: 2 or 3, with $120,000 to $180,000 of collateral.

Step 3: project a typical month. An ATM monthly XSP put sells for roughly 2% to 3% of the strike, $12 to $18. Three contracts collect $36 to $54 of premium a month in index points, or $3,600 to $5,400 in dollars. That is 0.36% to 0.54% of the portfolio a month, and twelve months of it make 4.3% to 6.5% a year, gross.

Check the rule of thumb with the at-the-money approximation of Chapter 10C, which prices the put at about $0.4\,\sigma\sqrt{T}$ of the strike. Here $\sigma$ is the implied volatility and $T$ the time to expiry in years. At a VIX of 14 and one month, that is $0.4 \times 0.14 \times 0.289 = 1.6\%$, about $9.70 on a strike of 600. A premium of 2% to 3% fits a VIX of about 17 to 26, so this example's premiums are generous for a VIX of 14.

Premium is not profit either, because in the months when the index falls through the strike the puts pay much of it back. After those losses and the retail haircuts, the Edge Book's realistic net contribution is 2% to 4% a year, and Card 02 in Chapter 13F puts it at 3% to 5%. Read either as a return on the collateral. On $180,000, 2% to 4% is $3,600 to $7,200 a year, about 0.4% to 0.7% of the portfolio. As 2% to 4% of the whole $1 million, it would need the sleeve to earn 11% to 22% a year on its collateral, far above the PUT index's compound return of 9.54% (Chapter 10C).

Step 4: stress-test it. Each put is struck at 600, so in a stress it is worth at least its intrinsic value, the strike minus the index level. Your loss is that value less the premium you took in, times 100:

The low end of each row takes the $18 premium and no time value. The top of the S2 and S3 rows allows for the time value that a higher VIX adds, up to the Edge Book's own estimates of $12,000 and $20,000 a contract. The Edge Book's estimates start lower, at about $3,000 in S1, $8,000 in S2 and $15,000 in S3, which all fall below this floor.

A first-order estimate explains the S1 figure: the put's delta of about −0.5 times the $60 fall gives $0.5 \times 60 \times 100 = \$3{,}000$ a contract, or $9,000 for three. That estimate ignores gamma, which pushes the put's delta toward −1 as the index falls through the strike (Chapter 5C). For a fall this large, the first-order estimate misses about a third of the loss.

The puts are cash-secured, so there is no margin breach and no forced liquidation. The maximum loss is bounded by the collateral, $180,000 for three contracts, which would need the index to go to zero, and an index does not do that.

Step 5: score the conviction. The table scores the strategy in each of the five domains, where it is strong throughout:

The product is $C = 0.85 \times 0.90 \times 0.85 \times 0.90 \times 0.85 = 0.497$, just under 0.5, so it is formally medium conviction. The Edge Book rounds it to 0.50, reads it as high conviction and allocates.

Step 1: check the filters of Chapter 10H. The first filter, VIX/VIX3M above 1.05 for 3 days, has failed, so the kill criterion has triggered. The second, 21-day realized volatility above implied, has failed too. With the VRP negative as well as the curve inverted, both filters say to halt new entries.

Step 2: ask whether a high VIX is a good time to sell. This is the most common retail misconception about the VRP. A high VIX tempts the trader because premiums are richer, but the richer premium comes with five changes:

• Realized volatility is higher still, at 32% against 28% implied.
• The distribution of the coming moves is wider than implied volatility prices.
• Margin expansion under portfolio margin (PM) has already begun.
• The path of mark-to-market (MTM) losses through this regime is severe.
• Even cash-secured positions face large drawdowns in their marks.

The rule of 16 (Chapter 5E) turns the gap into days. A VIX of 28 prices a typical day of $28/16 = 1.75\%$, while realized volatility of 32% delivers days of $32/16 = 2.0\%$, so the seller is paid for smaller days than the market is producing. The VRP exists when implied volatility exceeds realized. A negative VRP, with realized above implied, is the opposite of the structural premium, and selling premium into it is doing the wrong thing.

Step 3: score the conviction. The evidence and mechanism are unchanged from Example 2, while the other three factors fall:

The product is $C = 0.85 \times 0.90 \times 0.15 \times 0.65 \times 0.35 = 0.026$, an order of magnitude below the threshold.

Step 1: check the evidence (Chapters 1G and 10D). Hurst, Ooi and Pedersen (2017) cover 140 years of trend following, with every decade positive, and the effect is replicated across many asset classes. Its mechanism combines behavioral under-reaction, compensation for hedgers and the provision of liquidity, which makes the evidence T1.

Step 2: explain the drought. Trend goes through structural droughts in choppy, mean-reverting regimes. The years from 2011 to 2018 were the worst drought in modern history, lasting about 7 years. Trend does not "break": it goes through extended periods in which its signals do not line up across asset classes.

Step 3: weigh the case for waiting. The objection says to wait until trend works again and then allocate, but four facts stand against it:

• You cannot time the turn of the regime.
• Trend tends to recover in the same events that hurt other assets, as in 2008, 2020 and 2022.
• The recovery is fast, so by the time trend "works" you have missed the entry.
• Allocating during a drought is uncomfortable, but historically it has been a good entry.

Step 4: choose the size and the structure. Allocate 10% to 15% to DBMF, a single vehicle that is transparent and carries lower fees. Build the position over 3 months to avoid the timing risk of a single lump sum. For a $1 million portfolio targeting 12%, that is $120,000 bought as $40,000 a month. Do not try to time the turn of the regime.

Step 5: score the conviction. Four factors are strong, and the regime is the weak one:

The product is $C = 0.90 \times 0.85 \times 0.55 \times 0.95 \times 0.90 = 0.36$, medium conviction, with the regime score as the binding constraint.

Step 1: check the evidence (Chapter 10G). Cieslak, Morse and Vissing-Jorgensen (2019) ran their original sample from 1994 to about 2014. The evidence is T2: replicated, but with limited out-of-sample (OOS) data after 2019 and an uncertain hiking cycle in 2022.

Step 2: judge the mechanism. The Fed put and forward guidance give a plausible mechanism. But the effect could decay as the pre-FOMC drift did after 2015 (Chapter 10I), so it stays T2, not T1.

Step 3: count the implementation cost. Rotating SPY in and out of the account, about every 1.5 weeks, costs little in trading and a great deal in tax. The bid-ask spread for SPY is about 0.01%, and slippage is minimal. The cut moves 15 percentage points, $150,000, out and back in each odd week. With about eight meetings a year and three odd weeks in each cycle, that is 24 round trips a year. Crossing a 0.01% spread on $150,000 costs $15 each time, so the year's spread cost is about $24 \times \$15 = \$360$, under 4 bps of the portfolio.

The tax is what matters, because every sale realizes a gain or loss. In a taxable account the rotation is a disaster of tax acceleration: it pays tax now on gains that would otherwise be deferred.

Step 4: frame it by the account. In a tax-deferred account, such as an individual retirement account (IRA) or a 401(k) plan, the implementation cost is small. On cost alone, the rotation there looks worth doing. In a taxable account, the tax acceleration from rotating SPY can cost 20 to 40 bps a year, more than the expected 10 to 30 bps of alpha from the cycle.

Step 5: choose the operational form. Do not rotate the existing SPY position, and use one of three lighter forms instead:

• Time new contributions and rebalances to start in even weeks.
• Modulate exposure through the size of a futures position, in ES or the smaller MES. Futures are Section 1256 contracts, taxed 60% as long-term gains whatever the holding period (Chapter 2E).
• Hold a leveraged ETF on margin during even weeks only.

The lightest implementation of all is to time your discretionary purchases and sales to land in even weeks, with no rotation.

Step 6: score the conviction. Execution is the binding constraint, and it differs by account:

The score is $C = 0.50 \times 0.65 \times 0.65 \times 0.40 \times 0.85 = 0.072$ in the taxable account and $C = 0.50 \times 0.65 \times 0.65 \times 0.85 \times 0.85 = 0.153$ in the tax-deferred one, both below the threshold of 0.3.

Step 1: check the divergence threshold. Chapter 10G's rule requires a divergence of more than 1.5%, and 10% qualifies. Its approximation says a 60/40 portfolio drifts by about $0.6 \times 0.4 \times 10\% = 2.4\%$ of its value, a sizeable flow to trade ahead of.

Step 2: get the direction right. This is the corrected sign, and the chain runs as follows:

A reviewer of the Edge Book's first version caught this sign reversed in the original framework. Restated plainly: if equities outperformed bonds during the quarter, you go short equities and long bonds.

Step 3: size each leg. For the first few quarters of your own data, risk 0.5% of the portfolio per leg, which on $1 million is $5,000 a leg.

• ES: at a price of about 5,800 and $50 a point, one contract is $5{,}800 \times 50 = \$290{,}000$ of notional. A 1% adverse move costs $2,900, inside the $5,000 budget, while two contracts would risk $5,800, so hold 1 contract.
• ZN: at a price of about 110 and $1,000 a point, one contract is $110,000 of notional, and a 1% adverse move costs $1,100. The budget would allow up to $\lfloor 5{,}000/1{,}100 \rfloor = 4$ contracts, where the brackets take the floor function and round down, and the Edge Book holds 1, well inside it.

So for the first few quarters the position is short 1 ES contract and long 1 ZN contract.

Step 4: time it. Enter 5 trading days before the quarter ends and exit 1 to 3 trading days into the new quarter, giving the rebalancers time to execute.

Step 5: score the conviction. Evidence is the weakest of the five factors, as the table shows:

The product is $C = 0.55 \times 0.75 \times 0.85 \times 0.80 \times 0.80 = 0.224$, which Step 6 reads against the thresholds.

Step 6: read the score against its threshold. By the thresholds of Chapter 13B, 0.224 is below 0.3: insufficient conviction, so do not trade. The Edge Book's example calls it medium conviction and takes a test position anyway. Read as an exception, the trade is a pilot, sized so its worst quarter barely registers, whose purpose is to produce the personal evidence that could raise $E$. Read by the rule, it is a pass. Chapter 13D meets the same question in a swing trade scored at 0.282.

Step 1: read the kill rule. Chapter 10H's rule for a ratio above 1.05 for 3 closes is to halt new sales and to reduce the existing premium-selling sleeve by 50%. "Reduce by 50%" means closing half of the existing positions, not just stopping new entries.

Step 2: mark the position, and close half of it. Each put is now $24 in the money (ITM). With 22 days left and implied volatility raised, suppose each costs $30 to buy back: $24 of intrinsic value and $6 of time value. Each is down $30 - 15 = \$15$, or $1,500 a contract, and the three are down $4,500 together.

Half of three is one and a half, so you close one contract or two. Neither is closer to the rule, since closing one leaves two open, a cut of a third, while closing two leaves one, a cut of two thirds. The Edge Book closes one and calls that the conservative rounding, because it trades less. If you read the rule as a limit on risk, closing two is the more cautious choice. Buying back one costs $3,000 and locks in $1,500 of loss on that contract.

Step 3: answer "if I hold, it might recover". The critical operational point is that the kill rule is pre-committed. It exists because in stress, intuition tells you to hold and hope, and it overrides intuition for three reasons:

• Stress regimes can deepen: in March 2020 the VIX went from 28 to 82 in 8 days.
• The rule is calibrated to cumulative outcomes across many cycles, not to individual trades.
• Following it is what allows the strategy to compound across those cycles.

If you override the rule once, you override it every time. Discipline exists only if it binds in stress.

Step 4: plan the return. Halt new entries until VIX/VIX3M has closed below 1.00 for 5 days, then re-enter in phases: 25%, then 50%, then 100% of the target size over 3 weeks. The premium you forgo during the halt is an opportunity cost, about 0.3% of the portfolio over a typical halt.

Step 5: score the halt itself. Every factor is high, because the regime the rule was written for has arrived:

The product is $C = 0.90 \times 0.85 \times 0.95 \times 0.85 \times 0.95 = 0.59$, high conviction in the halt.

Step 1: classify the source. This is single-name earnings short volatility, a category Chapter 10I rejects for retail accounts.

Step 2: recall the finding. Adams and Neururer (2020) found that for single names at retail size, naive earnings short volatility has a negative mean despite a positive median. Most of the time you collect a small premium, and occasionally you lose much more.

Step 3: lay out the distribution. Selling both options, a short straddle, collects $35 + 32 = \$67$, 7.9% of the price, so it breaks even at $850 \pm 67$: $783 and $917.

• The most likely outcome: the company beats and the stock moves $30. One option expires worthless and the other costs $30, so you keep $67 - 30 = \$37$, most of the premium.
• The tail outcome: guidance is cut and the stock drops 12%, or $102. The put then costs you $102 - 32 = \$70$ beyond its premium, and a deeper drop costs more.

The Edge Book's rough model treats each option sold as a bet, which wins about $15 on average in three cases out of four and loses about $60 in the fourth:

That is about −$4 per side: a negative expected value, which matches the Adams-Neururer finding.

Step 4: answer "the IV is high, so the market expects a big move". The framing that "IV is high" assumes you have an edge in predicting whether the move exceeds what is implied, and you have no systematic edge there. The negative mean that Adams and Neururer found is the average across many such earnings events with elevated IV.

Step 5: note the institutional version. Run across 200 or more names at once, as in the institutional study of Cao, Han, Tong and Zhan (2022), the strategy earns an edge built on the dispersion between names (Chapter 10I). That construction is what earns, and one name alone cannot reproduce it.

Step 6: score the conviction. Evidence and sizing are the weakest of the five factors:

The product is $C = 0.30 \times 0.40 \times 0.50 \times 0.70 \times 0.30 = 0.013$, effectively zero and far below the threshold of 0.3.

Step 1: decompose the structure. Each leg has its own Greeks and costs:

• The long LEAP call: a delta of about 0.50 and a cost of about $400, which is 8% of SPX's notional. Its embedded financing costs 50 to 150 bps a year in embedded leverage drag.
• The short put spread: positive theta, negative vega, a bounded loss and a delta of roughly +0.10.
• Combined: a total delta of about 0.60 for a net cost of $358. The exposure per dollar is $0.60 \times 5{,}000/358 = 8.4$ times the capital paid.

Chapter 10I calls the structure about 1.4 times SPX exposure, which describes an account holding several of them. One structure on SPX, at 100 times the index, costs $35,800 and carries $0.60 \times 5{,}000 \times 100 = \$300{,}000$ of exposure. A $1 million account that wants $1.4 million of exposure holds about 4.7 of them, for about $167,000, and keeps the rest in cash.

Step 2: compare with ES futures. At SPX 5,000, one ES contract is $50 \times 5{,}000 = \$250{,}000$ of notional, with margin of about $15,000. To match the structure's delta of 0.60 on that notional, hold 0.6 of a contract, $150,000 of exposure.

• Capital: ES needs about $9,000 of margin, 0.6 of $15,000, and it is a deposit you get back. The structure needs $150{,}000/3{,}000 \times 358 = \$17{,}900$ of premium, which is spent.
• Financing: futures build in a financing cost of about SOFR plus 10 to 20 bps, about 4.6% to 4.7% a year. On a full contract's $250,000 that is about $11,500 a year, and on $150,000 about $6,900 to $7,050. The LEAP's price carries the same rate plus its drag of 50 to 150 bps, an extra $750 to $2,250 a year on $150,000, where the futures' spread costs $150 to $300.

The Edge Book's rough estimate is that the structure costs 50% to 100% more than ES futures for the same exposure. The capital comparison supports the upper end, at about twice as much. The financing gap is smaller, but it runs the same way.

Step 3: look for the "VRP edge". The short put spread collects $42, and the Edge Book's rough distribution for it is in the table.

At the middle of each range the expected value is $0.65 \times 42 - 0.275 \times 55 - 0.075 \times 158 = +\$0.33$, about zero. The most favorable reading, with the highest chance of a win and the smallest losses, gives $0.70 \times 42 - 0.25 \times 30 - 0.05 \times 158 = +\$14$, and the least favorable −$14.60. The Edge Book's own estimate of +$15 to +$20 before friction, and about +$10 after it, sits above even the favorable reading. Grant it anyway: $10 is $10/358 = 2.8\%$ a year on the $358 outlay. Against the LEAP's drag of 50 to 150 bps, the net edge over simple leverage runs from −1.5% to +2.3% a year for a spread earning between nothing and 2.8%, which is within noise.

Step 4: follow the path through S2. Take SPX down 20% and the VIX up 25 points.

• ES: one contract loses 20% of its $250,000 of notional, which is $50,000. Its margin requirement roughly triples, from about $15,000 to about $45,000, but in a $1 million account the cushion is clear.
• The structure: the LEAP call loses on its delta, a fall that its positive vega only partly offsets, and the Edge Book puts the loss at about 80% of its value, $320. The short put spread, now deep in the money, loses $116 of its $158 maximum. Together that is $320 + 116 = \$436$, 122% of the $358 outlay, so the position is essentially destroyed and a forced close is likely.

ES handles the stress much better, because its loss is the index's loss, with no second leg whose margin grows as it loses.

Step 5: score the conviction. Three of the five factors sit at 0.30, as the table shows:

The product is $C = 0.30 \times 0.30 \times 0.60 \times 0.50 \times 0.30 = 0.008$, effectively zero and far below the threshold of 0.3.

Step 1: estimate the S2 loss per contract. Take an ATM XSP put struck near the current price of 600. In S2 the index falls 20%, so XSP falls to 480, and the put is deep in the money with an intrinsic value of $120. Sold for $12 of premium, it has lost about $120 - 12 = \$108$ per unit at S2.

Step 2: compute the maximum count. With the multiplier of 100, the loss is about $10,800 a contract. The budget allows $50{,}000/10{,}800 = 4.6$ contracts, so round down to 4.

Step 3: verify against S3. In S3, SPX falls 35%, XSP falls to 390, and the put's intrinsic value is $210. The loss is about $210 - 12 = \$198$, close to $200, or about $20,000 a contract, so four contracts lose about $80,000, 8% of the portfolio. That exceeds the S2 budget, but it should still be recoverable: by Chapter 1E a loss of 8% needs a gain of $0.08/0.92 = 8.7\%$ to repair. If 8% would cause operational trouble, such as a margin breach or a behavioral capitulation, reduce to 3 contracts.

Step 4: verify the cash collateral. Each contract needs its strike in cash, $600 \times 100 = \$60{,}000$, and the $1,200 premium you receive supplies part of it, leaving $58,800 of your own. Four contracts tie up $240,000 of collateral, 24% of the portfolio. That is operationally feasible: it reduces the portfolio's effective exposure, but it eliminates the path risk of margin.

Step 5: write the sizing equation. A reviewer of the Edge Book proposed the rule that turns the budget into a count. The number of units $n$ you may hold is

Here $B_\text{exp}$ is the explicit loss budget in dollars and $L_\text{max}$ the maximum loss per unit, per contract in the stress. The floor brackets $\lfloor\ \rfloor$ round down to a whole number. With $B_\text{exp} = \$50{,}000$ and $L_\text{max} = \$10{,}800$, the rule gives $n \le 4.6$, so you may hold $n = 4$ contracts. Chapter 13C runs the same budget with the round $10,000 a contract of Card 02 and also arrives at 4.

Step 6: score the conviction. The sizing score rises because the size now comes from the budget:

The product is $C = 0.85 \times 0.90 \times 0.85 \times 0.90 \times 0.90 = 0.53$, high conviction, so allocate.