Investment Strategy Explanation
Advanced concepts and formulas for trading strategies
Black-Scholes Formula
The Black-Scholes model is a mathematical model used for pricing options contracts. It provides a theoretical estimate of the price of European-style options.
The call and put option prices are given by:
C = S0N(d1) − Ke−rtN(d2)
P = Ke−rtN(−d2) − S0N(−d1)
where:
d1 = (ln(S0/K) + (r + σ2/2)T) / (σ√T)
d2 = d1 − σ√T
Parameters:
- S0 = 270 (Current Stock Price)
- K (Strike Price): 230 for the put, 300 for the call
- r (Risk-Free Rate): 5% (0.05)
- σ (Volatility): 30% (0.30)
- T (Time to Expiration): 3 months (0.25 years)
The Black-Scholes formula assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. It's particularly useful for European-style options that can only be exercised at expiration.
Collar Strategy Explained
A collar strategy is used to protect against a significant drop in price while still allowing for some upside potential. It's essentially a protective strategy that combines multiple positions.
Traditional Collar Strategy:
- Buy the stock at $270
- Buy a protective put at $230 (cost: $2.29) → Limits downside risk
- Sell a covered call at $300 (premium received: $6.93) → Caps upside profit
1. Strategy Concept
We will split your €10,000 into a long position and a short hedge to protect against a 15% drop while allowing for potential profits if the price rises.
| Position | Entry Price | Alloc.(€) | Lev. | Take Profit | Stop Loss |
|---|---|---|---|---|---|
| Long (Main Trade) | €270 | €7,000 | 3x | €320 | €230 |
| Short (Hedge Trade) | €270 | €3,000 | 5x | €230 | €300 |
2. Leverage & Margin Usage
- Long Trade (3x Leverage) → Controls €21,000 worth of stock
- Short Trade (5x Leverage) → Controls €15,000 worth of stock
The goal is to hedge against a potential 15% drop while keeping upside potential open.
Profit & Loss Scenarios
| Stock Price | Long P&L (3x) | Short P&L (5x) | Total P&L | Outcome |
|---|---|---|---|---|
| €200 (-25%) | -€5,250 | +€5,000 | -€250 | ✅ Minimal Loss |
| €230 (-15%) | -€3,150 | +€3,000 | -€150 | ✅ Minimal Loss |
| €270 (Entry Price) | €0 | €0 | €0 | Neutral |
| €300 (+11%) | +€3,150 | -€3,000 | +€150 | ✅ Small Profit |
| €320 (+18%) | +€5,250 | -€5,000 | +€250 | ✅ Small Profit |
4. Key Adjustments & Benefits
- Replaces options with direct long/short positions
- Short position acts as protection against a 15% drop
- Allows flexibility to close hedge if stock moves favorably
- Risk is controlled, while upside remains open
Strategy Implementation
5. Execution Steps
Advantages of this Strategy
This approach provides several benefits compared to traditional options strategies:
- No time decay issues that affect options
- Lower transaction costs in many markets
- Ability to close positions individually as market conditions change
- Clear risk/reward profiles at different price points
- No option premium lost if stock remains flat
Important: Always consider your risk tolerance and investment goals before implementing any strategy. This approach uses leverage which can amplify both gains and losses.
Use the simulator to test different scenarios and allocation amounts to find the optimal setup for your risk tolerance.