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Lesson 9: Reading Your Greeks

Promise: Learn to interpret portfolio-level Greeks and understand what your actual exposures are.

From Single Options to Portfolios​

So far we've discussed Greeks for individual options. But real traders hold portfolios: multiple options across strikes and expiries, often with underlying hedges.

The key skill is reading your aggregate Greeks and understanding what scenarios hurt or help you.

Aggregating Greeks​

Greeks are additive across positions (with appropriate signs):

Portfolio Greek=∑iPositioni×Greeki\text{Portfolio Greek} = \sum_{i} \text{Position}_i \times \text{Greek}_i
Position
Delta
Gamma
Vega
Theta
Long 10x 100k Call
+5.2
+0.8
+120
-45
Short 10x 110k Call
-2.1
-0.3
-50
+22
Short 5 BTC (hedge)
-5.0
0
0
0
**Portfolio Total**
**-1.9**
**+0.5**
**+70**
**-23**

This portfolio is:

  • Nearly delta-neutral (-1.9 BTC exposure)
  • Long gamma (benefits from moves)
  • Long vega (benefits from vol increase)
  • Paying theta (time decay costs $23/day)

Reading Your Greek Profile​

Delta: Directional Exposure​

DeltaInterpretation
+10 BTCLong 10 BTC equivalent. Bull position.
-5 BTCShort 5 BTC equivalent. Bear position.
~0Delta-neutral. No directional bet.

Question to ask: "If BTC moves $1,000, what happens to my P&L?"

Answer: Approximately $1,000 × Delta.

Gamma: Convexity​

GammaInterpretation
PositiveLong convexity. Moves in either direction help you.
NegativeShort convexity. Moves hurt you. You want stability.

Question to ask: "Do I want the market to move or stay still?"

💡

Positive gamma + negative theta = "Paying for lottery tickets." Negative gamma + positive theta = "Selling insurance."

Vega: Vol Exposure​

VegaInterpretation
+100Gain $100 per 1% vol increase
-50Lose $50 per 1% vol increase

Question to ask: "What happens if vol spikes 10 points?"

Answer: Approximately 100×Vega×10=100 × Vega × 10 = 1,000 gain (if +100 vega).

Theta: Time Cost​

ThetaInterpretation
-50Losing $50 per day to time decay
+30Gaining $30 per day from time decay

Question to ask: "What's my daily bleed/income if nothing moves?"

The Gamma-Theta Tradeoff​

This is the fundamental tradeoff in options:

PositionGammaThetaWhat It Means
Long options+-Pay theta, hope for moves
Short options-+Collect theta, fear moves
Delta-hedged long+-Pure vol bet
Delta-hedged short-+Pure vol sale

You can't have positive gamma and positive theta (without taking on other risks).

💡

Theta is the price you pay for gamma. There's no free lunch.

Scenario Analysis​

The most practical way to read Greeks: scenario analysis.

Scenario 1: Spot +5%, Vol unchanged​

  • Delta P&L: +5% × Spot × Delta
  • Gamma P&L: 0.5 × Gamma × (5% × Spot)²
  • Vega P&L: ~0 (vol unchanged)
  • Theta P&L: Depends on time elapsed

Scenario 2: Spot -5%, Vol +10 points​

  • Delta P&L: -5% × Spot × Delta
  • Gamma P&L: 0.5 × Gamma × (5% × Spot)²
  • Vega P&L: +10 × Vega
  • Vanna effect: Additional delta change from vol spike

Scenario 3: Weekend, nothing moves​

  • Delta P&L: ~0
  • Theta P&L: Theta × 2 or 3 days
  • Charm effect: Delta drifted (need to re-hedge Monday)

Risk Management with Greeks​

Setting Limits​

Professional desks set Greek limits:

Greek
Example Limit
Why
Delta
±50 BTC
Limit directional exposure
Gamma
±5 BTC/1%
Limit convexity risk
Vega
±$10,000/1vol
Limit vol exposure
Theta
-$5,000/day max
Limit daily bleed

Hedging Decisions​

If You Want To...Hedge With...
Reduce deltaTrade spot or ATM options
Reduce gammaTrade short-dated ATM options
Reduce vegaTrade options (any strike)
Balance thetaAdjust option positions

Reading Second-Order Greeks​

For advanced portfolios, also track:

Net Vanna​

"How will my delta change if vol moves?"

  • Positive vanna: Delta increases with vol
  • Negative vanna: Delta decreases with vol

If you're delta-neutral but have large vanna, a vol spike will make you directional.

Net Volga​

"How will my vega change if vol moves?"

  • Positive volga: Long convexity in vol space
  • Negative volga: Short convexity in vol space

High volga portfolios (long wings) benefit disproportionately from vol explosions.

Common Greek Profiles​

Strategy
Delta
Gamma
Vega
Theta
Long straddle
~0
++
++
--
Short straddle
~0
--
--
++
Long call spread
+
+/-
+/-
+/-
Iron condor
~0
-
-
+
Calendar spread
~0
-
+
+/-

Common Mistakes​

MistakeCorrection
Only looking at deltaGamma and vega often matter more.
Ignoring theta for long positionsTime decay is relentless. Know your bleed.
Not scenario-testingRun "what if" scenarios, not just Greek snapshots.
Forgetting second-order effectsVanna can flip your delta in a vol spike.
Over-hedgingTransaction costs from constant re-hedging eat profits.

Greeks are often expressed in "dollar" terms for easier P&L estimation:

Dollar Delta:

$Δ=Δ×S×Multiplier\$\Delta = \Delta \times S \times \text{Multiplier}

Dollar Gamma:

$Γ=0.5×Γ×S2×Multiplier×(0.01)2\$\Gamma = 0.5 \times \Gamma \times S^2 \times \text{Multiplier} \times (0.01)^2

Dollar Vega:

$ν=ν×Multiplier\$\nu = \nu \times \text{Multiplier}

These let you directly estimate P&L in currency terms for given moves.

Test your understanding before moving on.

Q: A portfolio has +50 vega. What happens if IV increases 5 points?
Q: Why can't you have positive gamma and positive theta simultaneously?
Q: What does it mean to be 'delta-neutral with positive vanna'?

💡 Tip: Try answering each question yourself before revealing the answer.

See Also​

Navigation: ← Lesson 8: Advanced Greeks | Lesson 10: What the Market is Telling You →