Volatility Paradox

Overview

A Bear Put Spread (also known as a Put Debit Spread) is the bearish version of the vertical spread. You buy a more expensive put (higher strike) and sell a cheaper put (lower strike) to offset the cost.

This strategy is favored by traders who want to capitalize on a downward move but are wary of the high "Theta" or "Vega" costs associated with buying naked options.

[!NOTE] This is a Debit Spread. You pay a net amount to enter, and that amount is your Maximum Risk.

The Setup

A Bear Put Spread consists of:

Long Put: Buy a put at Strike A ( $K_H$ ), which is higher (more expensive).
Short Put: Sell a put at Strike B ( $K_L$ ), which is lower (cheaper).

Mechanics of the Spread

By "selling the floor," you are saying: "I think the stock will go down, but I don't need to profit from it going past Strike B."

Capital Efficiency: You get a bearish position for a fraction of the price of the higher put.
Lower Break-even: The income from the short put brings your break-even price closer to the current stock price.

Payoff and Break-even

Max Profit

Your profit is the distance between the strikes minus the debit you paid:

\text{Max Profit} = (K_H - K_L) - \text{Net Debit}

Break-even Point

The stock needs to fall below:

\text{Break-even} = K_H - \text{Net Debit}

The "Hedged" Greeks

Because you have both a long and short put, your Greeks are "dampened."

1. Delta: Moderate Downside Exposure

Your Delta is negative (usually between -0.20 and -0.60). You benefit as the stock falls. Unlike a single put, your Delta will "shrink" toward zero if the stock falls too far (below the lower strike).

2. Theta: Reduced Decay

The short put you sold is losing value every day—and that's good for you! This "positive Theta" of the short leg helps cancel out the "negative Theta" of your long leg.

3. Vega: Lower Volatility Risk

Vertical spreads are "Vega-Neutral-ish." If you buy a put during a high-volatility event, a "Volatility Crush" after the event could destroy a naked put. In a spread, both legs crush together, protecting your net value.

Selection Tips

The ATM/OTM Spread: Buy at-the-money ( $100), sell out-of-the-money ($ 95). Good balance of risk/reward.
The OTM/OTM Spread: Buy OTM ( $95), sell further OTM ($ 90). Very high potential return on capital, but lower probability of success.

Checklist for Entry

Is my target price around or below the Lower Strike?
Have I calculated my Max Loss? (It's just the debit paid).
Is the stock in a clear downtrend or facing a bearish catalyst?

The Vertical Payoff MathRead more

At expiration ( $T$ ), the payoff is:

\text{Payoff} = \min(\max(K_H - S_T, 0), K_H - K_L) - \text{Debit}

This formula shows that once $S_T$ goes below $K_L$ , the term $K_H - S_T$ is capped by the short put's exercise, resulting in a flat line on your P&L diagram.

Bear Put Spread