Correlation and Portfolio Construction

A portfolio of options positions is not a portfolio of independent bets. Two positions on the same underlying, both bullish, are not "two bullish bets" — they are one bullish bet with twice the size. The portfolio's risk is determined by the correlation between the positions, not just the sizes of the individual positions. The journal's portfolio construction rules are designed to limit the total exposure to any single underlying thesis, regardless of how many positions are deployed.

Correlation basics

The correlation between two positions is a measure of how their returns move together. A correlation of 1.0 means the positions move in lockstep; a correlation of -1.0 means they move in opposite directions; a correlation of 0.0 means they are independent. For options on the same underlying, the correlation is high (often 0.7-0.95 for similar structures); for options on different underlyings in the same sector, the correlation is moderate (0.4-0.7); for options on different sectors, the correlation is low (0.1-0.3).

The portfolio's variance is the weighted sum of the individual variances plus the weighted sum of the pairwise covariances. For a portfolio of N positions with equal size, the variance is:

σ²_portfolio = (1/N) × σ²_avg + (N-1)/N × ρ_avg × σ²_avg

Where σ²_avg is the average variance of the positions and ρ_avg is the average correlation. When ρ_avg is 1.0, the portfolio variance is σ²_avg (the entire portfolio moves as one). When ρ_avg is 0.0, the portfolio variance is (1/N) × σ²_avg (the diversification reduces the variance by a factor of N). The reality is somewhere in between, and the journal's portfolio construction rules are designed to keep ρ_avg low enough to deliver meaningful diversification.

Name-level vs. market-level correlation

The journal distinguishes between two types of correlation:

Name-level correlation is the correlation between two positions on the same underlying. Two call spreads on SPX with the same strike and expiration have a name-level correlation of essentially 1.0; the journal treats them as a single position with twice the size. The 6% rule per underlying is the cap on this kind of concentration.

Market-level correlation is the correlation between two positions on different underlyings that are driven by the same factor. A long call on SPX and a long call on QQQ are different underlyings, but both are bets on the broad equity market. A market selloff will hurt both positions; the journal treats them as a correlated basket for the purpose of total exposure.

The distinction matters because the journal's 6% rule applies to the underlying, but the total exposure to the broad-market factor across all positions is a separate calculation. The journal's rule for the broad-market factor is: total long delta exposure across all index and equity positions should not exceed 8% of NLV. The 8% is a separate cap from the 6% per underlying, and the journal monitors both.

The 6% rule in practice

The 6% rule says: total risk in any single underlying (or highly correlated basket) should not exceed 6% of NLV. The rule allows the journal to have three positions at the 2% sizing in the same underlying, or two positions at 2% and one position at 2% on a correlated name, or one position at 4% with no other positions in the basket. The rule is not a hard cap on the number of positions; it is a cap on the total risk.

The journal's most common application of the rule is the credit-spread portfolios on SPX and XSP. The journal frequently runs 3-4 short-premium positions on SPX at the same time, sized to 1.5%-2% each, with the total exposure at 5-7%. The 6% rule is the cap; the journal prefers to be at 5-6% rather than 6% in case an additional position is added.

The rule is also the reason the journal does not run a "diversified" portfolio of 20 small positions across 20 underlyings. The correlation across the 20 positions is not zero — the broad-market factor is common to all of them, and the sector factors are common to many of them. A 20-position portfolio with 0.5% sizing each has a total exposure of 10% to the broad-market factor, which is more than the journal's 8% cap. The journal prefers a smaller number of larger positions.

Basket exposure

The journal groups underlyings into baskets for the purpose of the correlation analysis. The baskets are:

• Broad market: SPX, XSP, SPY, QQQ, IWM, XND. The journal treats these as a single basket for the purpose of the broad-market exposure cap.
• Sector ETFs: XLK, XLF, XLE, XLV, XLY, XLP, XLI, XLU, XLB, XLRE, XLC. The journal treats these as separate baskets (each sector is its own basket), but applies a cross-sector concentration cap: total risk in any two sectors should not exceed 10% of NLV.
• Single names: Each individual stock is its own basket. The journal caps single-name exposure at 3% of NLV per position, with a 6% total cap across all single-name positions.

The basket definitions are not scientific — the journal uses the sector ETF definitions as a rough proxy for the factor exposure of individual stocks in the same sector. The cap on cross-sector exposure is the journal's way of saying "we don't want to be heavily long cyclicals and short defensives at the same time, because that's two bets on the same factor."

Concentration vs. diversification

The journal's portfolio construction rules favor concentration over diversification. The reasoning is that the journal's edge is in the playbook's specific structures, not in a broad-based market view. A 20-position portfolio has more diversification benefit than a 5-position portfolio, but the diversification is achieved by adding positions that the journal has lower conviction in, which dilutes the expected value of the book.

The trade-off is between the variance reduction of diversification and the expected value of concentration. The journal's preference is to run a smaller number of higher-conviction positions, with the sizing rule (2% per position, 6% per underlying) controlling the total exposure. The portfolio is not optimized for the lowest possible variance; it is optimized for the highest expected value subject to the risk constraints.

The exception is the broad-market factor. The journal's directional bias on the broad market is provided by the forecast methodology published on Dependability, and the journal translates that bias into specific structures rather than running a long-beta portfolio. The broad-market exposure is concentrated in the SPX/XSP positions, not spread across the book.

Risk reversals and correlation

The journal uses risk reversals (long call + short put at the same expiration, slightly OTM) to take advantage of the volatility skew on SPX. The structure is delta-neutral at entry, and the cost is the difference between the call's premium and the put's premium. On SPX, the put is more expensive than the equivalent call, so the risk reversal is a net credit.

The risk reversal is a position that benefits from the underlying moving up or down by a small amount, and is hurt by the underlying staying near the center. The structure is correlated with the directional bias of the forecast, but the correlation is weak because the position is delta-neutral at entry. The journal uses the risk reversal as a low-cost directional bet when the directional thesis is clear, and the structure is sized to 1% of NLV rather than the usual 2% because the position's risk profile is more complex than a vertical spread.

The risk reversal is the journal's most-skewed structure. The position's payoff is asymmetric: the position loses the most if the underlying stays near the center, and the position's max-loss is the width of the spread minus the net credit. The journal sizes the risk reversal smaller than other structures to account for the asymmetric payoff.