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):

$$\text{Portfolio Greek} = \sum_{i} \text{Position}_i \times \text{Greek}_i$$

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

Delta	Interpretation
+10 BTC	Long 10 BTC equivalent. Bull position.
-5 BTC	Short 5 BTC equivalent. Bear position.
~0	Delta-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

Gamma	Interpretation
Positive	Long convexity. Moves in either direction help you.
Negative	Short 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

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

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

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

Theta: Time Cost

Theta	Interpretation
-50	Losing $50 per day to time decay
+30	Gaining $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:

Position	Gamma	Theta	What 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 delta	Trade spot or ATM options
Reduce gamma	Trade short-dated ATM options
Reduce vega	Trade options (any strike)
Balance theta	Adjust 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

Mistake	Correction
Only looking at delta	Gamma and vega often matter more.
Ignoring theta for long positions	Time decay is relentless. Know your bleed.
Not scenario-testing	Run "what if" scenarios, not just Greek snapshots.
Forgetting second-order effects	Vanna can flip your delta in a vol spike.
Over-hedging	Transaction costs from constant re-hedging eat profits.

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

• Greeks 101 (Options Explainers)
• Lesson 7: Advanced Greeks
• Lesson 9: What the Market is Telling You →

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