Portfolio-Level Greeks: Managing Aggregate Delta, Vega, and Gamma Across Multiple Overlays
Abstract
Five micro-cap positions. Five proxy baskets. Ten options layers — five put-spread hedges, five short-call premium legs. Each overlay looks balanced alone: net delta −0.07, positive carry, defined tail. Together the options portfolio is short $58,000 of vega per vol point. A 10-point spike costs $580,000 before delta losses. Nobody sized that position. It accumulated one overlay at a time. This note covers portfolio Greeks aggregation across overlays — delta, vega, and gamma — plus the dashboard and budget rule that keep the total inside a fixed limit.
1. The Accumulation Problem: Five Overlays, One Short-Vol Bet
Take a five-position book. Micro-cap notional: $9.2M. Proxy notional: $7.8M. Each overlay repeats the standard template: long 60-DTE put spread, short 30-DTE 30Δ calls.
Per-overlay Greeks, measured against proxy notional:
| Overlay | Proxy ($M) | Net Δ ($/1%) | Net Γ ($/1%²) | Net Vega ($/1 vol) | Net Theta ($/day) |
|---|---|---|---|---|---|
| 1 — Industrials | 1.70 | −11,900 | −4,100 | −12,500 | +2,100 |
| 2 — Healthcare | 1.55 | −10,200 | −3,800 | −11,000 | +1,900 |
| 3 — Energy | 1.60 | −10,900 | −4,400 | −13,000 | +2,200 |
| 4 — Tech SC | 1.45 | −9,600 | −3,200 | −9,500 | +1,700 |
| 5 — Materials | 1.50 | −10,100 | −3,600 | −12,000 | +1,950 |
| Portfolio total | 7.80 | −52,700 | −19,100 | −58,000 | +9,850 |
Each row is defensible. Overlay 4 is short only $9,500 per point against $1.45M — ~0.65% per 10 vol points. Risk signs off. Then the fifth overlay goes on and the book carries −$58,000 per point.
That number is P&L. A 5-point IV expansion — a normal risk-off week — marks the options book down ~$290,000. A 10-point expansion costs ~$580,000, or 6.3% of NAV, before delta losses on the idiosyncratic residual. Theta at +$9,850/day needs 59 days to earn back the 10-point shock. Carry accrues monthly. Vega loss lands in an afternoon.
The mechanism is structural. Each short-call layer contributes roughly −$14,000 to −$16,000 of vega; each put spread offsets only +$2,000 to +$4,000 because its legs partially cancel. Net per overlay is always short. In portfolio Greeks terms, short vega stacks linearly with overlay count. Delta gets watched because it moves daily P&L. Vega sits quiet until vol reprices, then dominates the options portfolio.
2. Delta Aggregation: Sum in Dollars Across the Options Portfolio
Portfolio Greeks start with delta. Convert every leg to dollar-delta, add basket share delta, and subtract the factor-implied hedge (micro-cap notional × blended beta). Express the residual in $/1% basket move, not delta points — points hide size differences.
The example book nets −$52,700 per 1% decline, roughly −0.68% of proxy notional. That mild short bias is intentional: each overlay is designed to run −0.05 to −0.10 delta versus its basket.
Two rules. Recompute on current betas — a healthcare beta drifting 1.28 to 1.45 overstates the hedge ~$2,600 per 1% if the proxy is not resized. Re-estimate monthly on the rolling 252-day window. And never net cross-basket deltas at face value: apply a 20–30% haircut or show gross and net side by side.
3. Vega Aggregation: The Binding Constraint
Vega is where delta vega gamma management succeeds or fails. Every short-call layer is short vega; every put spread is only weakly long vega because its legs partially cancel. The net is short, always, and it scales with overlay count.
Sum vega as dollars per 1-point IV change with no diversification benefit. In a vol event, single-name and ETF volatilities spike together; assuming they diversify fails exactly when the number matters.
Normalize two ways: per $1M proxy, and as days of theta to cover a defined shock. Here: −$58,000 / $7.8M = −$7,440 per point per $1M. A 10-point shock costs ~$580,000 against +$9,850/day theta — 59 days to earn back. Any options portfolio where a 10-point shock costs more than 30–45 days of theta is a carry trade funded by tail risk. That ratio is the most informative number in the dashboard.
Also split vega by tenor. Five overlays short 30-DTE into the same window cannot be rolled cheaply into a spike. Stagger 30/45/60 DTE so no more than 40% of short vega expires in any 2-week bucket. Tenor concentration belongs in every portfolio Greeks review.
4. Gamma Aggregation: Small Until It Is Not
Gamma sums the same way: dollars of delta change per 1% move. The book totals −$19,100 per 1%², so a 5% drop adds ~−$95,500 of incremental short delta.
Short gamma is quiet in calm markets and mechanical past a 3–4% gap: put spreads hit their short-strike caps and go gamma-flat while the premium leg stays short gamma throughout, and the micro-cap falls faster than the proxy hedge gains. Report gamma at spot, −5%, and −10% by bump-and-revalue. A book at −$19,100 spot but −$31,000 at −10% has convexity working against it. Any overlay that breaches stressed gamma must include a far-OTM long wing.
5. The Greeks Dashboard: One Table, Updated Weekly
One table, recomputed weekly and on any overlay, roll, or beta rebalance. Columns per overlay: proxy notional, net Δ ($/1%), net Γ ($/1%²), net vega ($/1 vol), net theta ($/day), max short-vega share in any 2-week bucket. Bottom row: totals plus budget utilization. Side panel: shock P&L at +5/+10 vol, −5%/−10% spot, and joint −7%/+8 vol. Flag beta drift above 0.15 or sector IV moved ±5 points.
Broker exports in a spreadsheet suffice at this scale. Cadence is the constraint: monthly misses tenor concentration. Weekly minimum; daily when VIX exceeds 25.
6. The Budget Rule: Fixed Vega Cap With a Mechanical Rebalance
Aggregate net vega may not exceed −$40,000 per vol point on this $7.8M proxy book (~−$5,100 per $1M). Gamma may not exceed −$15,000 per 1%² at spot. Above 80% utilization, no new short-vol layers.
The example book breaches both. Rebalance in fixed order until both clear with 10% headroom:
- Trim nearest-expiry shorts. Buy back 30–40% of the closest 30Δ calls, starting with the highest-vega overlay. A one-third trim on one overlay recovers ~$3,500 vega.
- Roll up and out. Move 30Δ 30-DTE to 20Δ 45-DTE — cuts vega 20–30% per contract, keeps 60–70% of theta.
- Add long wings. Far-OTM puts (15–20Δ) on the two largest baskets: ~$2,000–3,000/month each for +$3,000–4,000 vega plus flatter stressed gamma.
Here that sequence — trims on Overlays 1 and 3, one roll, two wings — moves vega from −$58,000 to ~−$39,500. Daily theta falls from +$9,850 to ~+$8,400, a 15% carry sacrifice. That stated exchange rate is the cost of keeping the program a hedging book rather than a volatility carry fund. New overlays inherit the constraint: above 80% utilization they go on at 20Δ/45-DTE with a paired wing, or they wait.
7. What the Framework Delivers
Ten individually sensible layers become one visible number with a binding cap. Delta stays mildly short. Gamma is precomputed under stress, not discovered in it. Vega is summed without diversification credit, quoted as shock cost over daily theta, and capped with a trim-roll-wing sequence on breach. Carry falls 10–15% versus the unconstrained book; the 10-point shock falls from ~59 days of theta to ~40. That is the trade, priced weekly.