Synthetic Positions
Introduction: Put-Call Parity and Equivalence
Synthetic positions replicate stock ownership or shorting using options alone. They're based on the principle of put-call parity: the price of a call minus a put at the same strike equals the cost of owning the stock minus the risk-free rate. For traders, synthetics offer flexibility in margin usage, tax treatment, and position structure.
Synthetic Long Stock
The Basic Concept
Synthetic Long Stock = Buy Call + Sell Put (same strike, same expiration)
Equivalent to: Owning the stock outright
Cost: (Call price - Put premium) ≈ Stock price (roughly)
Risk: Same as owning stock (max loss = stake)
Equivalent to: Owning the stock outright
Cost: (Call price - Put premium) ≈ Stock price (roughly)
Risk: Same as owning stock (max loss = stake)
Real Example
Setup: AAPL at $195. You want stock exposure but prefer options.
Synthetic Long Stock:
Synthetic Long Stock:
- Buy 1 April 17 195 call for $7.40 = -$740
- Sell 1 April 17 195 put for $5.80 = +$580
- Net cost: $1.60 = $160
- Profit if stock rises to $205: $1,000 gain (same as owning stock)
- Loss if stock falls to $175: -$2,000 loss (same as owning stock)
When to Use Synthetic Long Stock
- Lower capital requirement: Synthetics use margin; stock requires full purchase price (for many brokers)
- Tax efficiency: May allow more favorable tax treatment (consult tax advisor)
- Dividend avoidance: Synthetics don't receive dividends, important for short-term positions
- Position structuring: Convert synthetics to other spreads easily
Synthetic Short Stock
The Basic Concept
Synthetic Short Stock = Sell Call + Buy Put (same strike, same expiration)
Equivalent to: Short-selling the stock
Benefit: No locate requirement (stock borrow), easier to execute
Equivalent to: Short-selling the stock
Benefit: No locate requirement (stock borrow), easier to execute
Real Example: Bearish Synthetic
Setup: You believe AAPL will decline but want to avoid short stock restrictions.
Synthetic Short Stock:
Synthetic Short Stock:
- Sell 1 April 17 195 call for $7.40 = +$740
- Buy 1 April 17 195 put for $5.80 = -$580
- Net credit: $1.60 = $160
- Profit if stock falls to $175: $2,000 gain
- Loss if stock rises to $215: -$2,000 loss
Put-Call Parity Explained
The Formula
Call Price - Put Price = Stock Price - Strike Price (approximately)
For the 195 AAPL options:
$7.40 - $5.80 = $1.60
Stock at $195 - Strike at $195 = $0
The difference of $1.60 represents the cost of carry (interest rates, dividends, time).
For the 195 AAPL options:
$7.40 - $5.80 = $1.60
Stock at $195 - Strike at $195 = $0
The difference of $1.60 represents the cost of carry (interest rates, dividends, time).
Arbitrage Opportunity
When call and put prices don't perfectly balance, arbitrageurs create risk-free profits:
Mispricing scenario:
Stock: $195
195 call: $8.00 (overpriced)
195 put: $5.60 (underpriced)
Difference: $8.00 - $5.60 = $2.40
Arbitrage:
Sell call ($800) + Buy put ($560) + Buy stock ($19,500)
= Net position: Synthetic short at profit if prices correct
Stock: $195
195 call: $8.00 (overpriced)
195 put: $5.60 (underpriced)
Difference: $8.00 - $5.60 = $2.40
Arbitrage:
Sell call ($800) + Buy put ($560) + Buy stock ($19,500)
= Net position: Synthetic short at profit if prices correct
Synthetic Covered Call
The Concept
A synthetic covered call replicates covered call income using only options:
Synthetic Covered Call = Long Call (ATM) + Short Call (OTM) + Short Put (OTM)
This three-leg position approximates owning stock and selling a call against it, but without the capital commitment.
This three-leg position approximates owning stock and selling a call against it, but without the capital commitment.
Real Example
Compare two covered call approaches:
Traditional Covered Call:
Buy 100 AAPL shares: -$19,500
Sell 1 April 17 200 call: +$250
Net capital: $19,250
Synthetic Covered Call:
Buy 1 April 17 195 call: -$740
Sell 1 April 17 200 call: +$250
Sell 1 April 17 190 put: +$300
Net capital: -$190 (actually a credit!)
Advantage: Uses 100x less capital while generating same income potential
Traditional Covered Call:
Buy 100 AAPL shares: -$19,500
Sell 1 April 17 200 call: +$250
Net capital: $19,250
Synthetic Covered Call:
Buy 1 April 17 195 call: -$740
Sell 1 April 17 200 call: +$250
Sell 1 April 17 190 put: +$300
Net capital: -$190 (actually a credit!)
Advantage: Uses 100x less capital while generating same income potential
Conversion and Reversal (Advanced)
Conversion (Long Stock → Short via Options)
Convert a long stock position to synthetic short by:
- Sell call at strike
- Buy put at strike
Reversal (Short Stock → Long via Options)
Convert a short position to synthetic long by:
- Buy call at strike
- Sell put at strike
Advantages of Synthetics vs. Actual Stock
| Factor | Stock Purchase | Synthetic Long |
|---|---|---|
| Capital Required | 100% of stock price | ~5-10% (via margin) |
| Dividends | Received by owner | Not applicable |
| Voting Rights | Shareholder rights | None |
| Margin Interest | Variable rate | Included in option pricing |
| Liquidity | Instant (market hours) | Depends on option liquidity |
| Expiration | None (permanent) | Must roll monthly or hold to expiration |
Practical Example: Synthetic vs. Stock Trade
Scenario: You want $10,000 exposure to AAPL for 6 weeks. Stock at $195.
Option 1: Buy stock
Buy ~51 shares: $9,945 capital
Earn dividends: ~$25
Sell after 6 weeks at $200: +$255 gain
Total return: 2.6% in 6 weeks
Option 2: Synthetic long with margin
Buy 50-share equivalent (buy 1 call, sell 1 put): ~$500 capital (leveraged 20x)
No dividends
Sell calls every month: Collect $200/month income (rolling)
Stock appreciation: +$255
Total return: 4.6% in 6 weeks (income + appreciation)
Advantage of synthetic: Better ROI via leverage + income, but with higher risk
Option 1: Buy stock
Buy ~51 shares: $9,945 capital
Earn dividends: ~$25
Sell after 6 weeks at $200: +$255 gain
Total return: 2.6% in 6 weeks
Option 2: Synthetic long with margin
Buy 50-share equivalent (buy 1 call, sell 1 put): ~$500 capital (leveraged 20x)
No dividends
Sell calls every month: Collect $200/month income (rolling)
Stock appreciation: +$255
Total return: 4.6% in 6 weeks (income + appreciation)
Advantage of synthetic: Better ROI via leverage + income, but with higher risk
Key Takeaways
1. Synthetics create stock-like exposure using only options. Useful for margin efficiency and flexibility.
2. Synthetic long = Buy call + Sell put. Replicates stock ownership with same profit/loss profile.
3. Synthetic short = Sell call + Buy put. Easier than short stock; no locate needed.
4. Put-call parity ensures pricing consistency. Call price - Put price ≈ Stock price - Strike price.
5. Synthetics require rolling at expiration. Unlike stock, they don't exist forever.
6. Margin efficiency is the biggest advantage. Control more shares with less capital, but accept higher risk.
2. Synthetic long = Buy call + Sell put. Replicates stock ownership with same profit/loss profile.
3. Synthetic short = Sell call + Buy put. Easier than short stock; no locate needed.
4. Put-call parity ensures pricing consistency. Call price - Put price ≈ Stock price - Strike price.
5. Synthetics require rolling at expiration. Unlike stock, they don't exist forever.
6. Margin efficiency is the biggest advantage. Control more shares with less capital, but accept higher risk.
Test Your Knowledge
1. What option combination creates a synthetic long stock position?
A) Sell call + Sell put
B) Buy call + Sell put (same strike, same expiration)
C) Buy call + Buy put
D) Sell call + Buy put
2. What does put-call parity state?
A) Calls and puts always cost the same
B) Call price - Put price equals the difference between stock and strike price
C) Calls and puts are never related
D) Put prices are always higher than call prices
3. What is the primary advantage of using synthetics instead of buying stock?
A) No risk involved
B) You receive dividends automatically
C) Lower capital requirement due to leverage
D) Infinite profit potential
4. What is a synthetic covered call?
A) Just owning stock and selling a call
B) A three-legged position replicating covered call income without owning stock
C) Buying both calls and puts
D) A position with unlimited profit
5. How does a synthetic long position expire?
A) It never expires (like stock)
B) It must be rolled at each expiration like all options
C) Only the call expires, put is permanent
D) Synthetics never expire