Vega by structure and the portfolio Greeks table

Delta is the Greek everyone watches, and vega is the one that decides how a book behaves on the worst day of the year. Implied volatility does not drift; it jumps, and it jumps in the direction that hurts most positions that were collecting theta. This lesson gives you the sign of vega for every structure in this course, a way to compare vega across expirations, and the portfolio table you should be able to produce for your own book.

The sign table

XYZ at $50 in every case, structure centered at or near the money unless stated.

Two patterns are worth memorizing. First, any structure that collects theta is short vega except calendars and diagonals, which collect theta while being long vega; that is what makes them useful in low-IV environments. Second, butterflies change sign: at the center they behave like a short straddle, at the wings like a long strangle, so a butterfly's Greeks depend on where the stock is far more than a vertical's do.

Vega is not the same across expirations

A one-point rise in "IV" is not one event. When the market gets nervous, front-month IV rises much more than back-month IV; when things calm down, the front month collapses first. Raw vega treats a point of 7-day IV and a point of 90-day IV as the same, which overstates long-dated exposure and understates short-dated exposure.

The common fix is weighted vega: scale each leg's vega by √(30 ÷ days to expiration) so everything is expressed in 30-day-IV terms.

The raw number says you make $750 per IV point; the weighted number says the realistic exposure is closer to $180, because the 30-day leg's IV will move almost twice as much as the 90-day leg's IV in any real shock. Neither number is exact. The weighted one is the one to size by.

The portfolio Greeks table

Here is the table this module has been building toward, for a hypothetical book across three underlyings. Every row is the net of one position computed as in lesson 1; the totals are what you manage.

Reading the totals:

• Delta +331 across three different underlyings is not one number that means much yet; in Module 6 you will beta-weight it into a single index-equivalent figure. For now, you can see the book is net long.
• Gamma −7.4 is small, and it will not stay small: the ABC condor and XYZ put spread lose gamma fast as they approach 21 days.
• Theta +$5.80/day is the sum of collecting on the condor and calendar while paying on the long spreads and the hedge puts. It is modest because the book is balanced, which is fine.
• Vega +$10.70 says the book gains a little if IV rises across the board. That is a deliberate choice: the hedge puts and the calendar offset the condor and put spread. A book of only condors and credit spreads would show something like −$40 here, and a 10-point IV spike would cost it $400 on top of whatever delta and gamma cost.
• Max loss $4,185 is the sum of defined risk on the option legs, ignoring the shares. It should be compared with your account and your per-position limits (Module 7).

Stress grid for the book (approximate, one day, from Greeks only)

                 IV -5 pts    IV unchanged    IV +10 pts
  Stock -3%      -$2,120       -$2,070        -$1,960
  Stock  0%         -$50           +$6           +$113
  Stock +3%       +$2,020       +$2,070        +$2,180
  (each name moved 3%: ETF $12, XYZ $1.50, ABC $3.60; delta x move
   per name, plus gamma, theta and vega x IV change)

The grid is what the Greeks are for: not to predict, but to know in advance what a bad day roughly costs. Almost all of the −3% number is delta, and most of that is the 200 ETF shares; the option book barely moves it. Whether that is acceptable is a sizing question, not a Greeks question.

Key idea: Every theta-collecting structure except calendars and diagonals is short vega, and IV rises exactly when stocks fall. Weight vega by √(30/DTE) before summing, keep the whole book in one table, and run a simple stress grid so the worst day is a number you have already seen.

Try it: Build the portfolio table for your own book (or the hypothetical one above with your own sizes). Add a stress row: stock −3% with IV +10 points, using delta × move + ½ × gamma × move² + theta + vega × 10. Write the result as a percentage of your account. If it is more than you would accept losing in a day, the book is too big, whatever the individual positions look like.

Recap

• Long options and calendars are long vega; every other theta-collecting structure is short vega.
• Butterflies flip sign: short-straddle-like at the center, long-strangle-like at the wings.
• Weighted vega (× √(30/DTE)) corrects raw vega for the fact that front-month IV moves more than back-month IV.
• The portfolio table has one row per position and one total per Greek, plus summed max loss.
• A simple stress grid (stock ±3%, IV −5/+10) turns Greeks into the dollar number that actually matters.