The net Greeks of a position

In the fundamentals course you learned the Greeks one option at a time. From here on you will almost never hold one option at a time. A spread is two or four options, a book is several spreads, and what matters is what the whole thing does when the stock moves, when a day passes, and when implied volatility changes. That is the net Greek, and computing it is nothing more than adding, with the sign of each leg respected.

The rule

For every leg: position Greek = quantity × per-share Greek × 100, where quantity is positive for long contracts and negative for short. Then sum across legs, then across positions. Shares count too: 100 shares have delta +100 and zero for everything else.

Two things trip people up. First, a short put has positive delta (the per-share delta of a put is negative, and you multiply by a negative quantity). Second, theta and gamma always have opposite signs on the same leg: if you are long gamma you are paying theta, and if you collect theta you are short gamma. There is no structure that escapes this.

A bull call spread, leg by leg

XYZ at $50, 45 days to expiration, implied volatility 30%. Buy the $50 call, sell the $55 call.

Read the last row as plain English. This spread behaves like 30 shares of XYZ right now. If XYZ rises $1, the position gains about $30 and the delta grows to about 31.5. It loses about $0.80 a day to time decay if nothing else changes. If implied volatility rises one point (from 30% to 31%) the spread gains about $2.50.

Compare that with the long $50 call alone: delta 55, theta −$3.00/day, vega +$9.50. Selling the $55 call removed most of the theta bleed and most of the vega exposure, at the cost of capping the upside. That trade-off is the whole reason spreads exist, and you can now measure it instead of feeling it.

A whole book

The same arithmetic scales. Suppose you hold three XYZ positions:

Your XYZ exposure is equivalent to 383 shares, or about $19,150 of stock. Gamma is close to zero, so that 383 will stay roughly 383 for a $1 or $2 move. The book bleeds about $1.30 a day and would gain about $5.90 if IV rose a point. Most traders who "feel" hedged because they own a mix of spreads are surprised the first time they add it up and see 383.

Net delta of the book: what a $1 move does

  Position                       P&L for XYZ +$1
  5 x bull call spread            +$150
  3 x bull put spread             +$33
  200 shares                      +$200
  ---------------------------------------
  Book                            +$383  (plus a little from gamma)

What each net Greek is for

• Net delta answers "how much stock am I really long or short?" It is the number you hedge, and the number you compare with your intended directional bet. If you meant to be neutral and the book says +383, you are not neutral.
• Net gamma answers "how fast does that change?" Positive gamma means your delta moves with the stock (you get longer as it rises, shorter as it falls), which is comfortable. Negative gamma means the opposite and is the price of collecting theta.
• Net theta answers "what does one calm day cost or pay?" It is not free money; it is compensation for negative gamma and, usually, negative vega.
• Net vega answers "what does a one-point change in IV do?" This is the Greek most retail books ignore and the one that hurts them most in a sell-off, because IV jumps exactly when the stock falls.

Key idea: Net Greeks are sums: quantity × per-share Greek × 100 for every leg, shares included. A book is not "a few spreads"; it is one number for each of delta, gamma, theta and vega, and those numbers are the only honest description of what you own.

Where the numbers come from

Your broker's platform shows per-share Greeks for every option and usually a "position" or "beta-weighted" summary. Trust the platform's Greeks, but do the sum yourself at least once a week so you know the composition. The options profit calculator will show the Greeks of any structure you build there.

Greeks are also snapshots. They are correct for the current stock price, current IV and today's date and drift as all three change. The next three lessons look at how they drift: net delta as you adjust, gamma as expiration approaches, and vega across different structures.

Try it: Take every options position you currently hold (or a paper book of three spreads) and build the table above: quantity, per-share Greeks, net per contract, then book total. Write one sentence in plain English for each of the four totals. If any sentence surprises you, that is the exposure you did not know you had.

Recap

• Position Greek = quantity × per-share Greek × 100, short legs carry negative quantity, shares carry delta only.
• A 50/55 bull call spread on XYZ at $50 nets about +30 delta, +1.5 gamma, −$0.80/day theta and +$2.50 vega per contract.
• Summing across positions produces the book's Greeks; a "hedged" mix of spreads can still be several hundred deltas long.
• Theta and gamma always have opposite signs; theta is the payment for being short gamma.
• Greeks are snapshots and drift with price, time and IV; recompute them weekly at least.