Volatility Paradox

Overview

The Risk Reversal is a core strategy for professional traders and institutions. It is a way to express a bullish view while often paying zero (or very little) for the position.

By selling a put and using that money to buy a call, you are essentially hiring the market to pay for your upside.

[!CAUTION] This is a high-conviction trade. Because you sold a naked put, you have the same downside risk as someone who bought 100 shares of stock. If the stock crashes, you are on the hook.

The Setup

A Bullish Risk Reversal consists of:

Short Put: Sell 1 Put at Strike $K_P$ .
Long Call: Buy 1 Call at Strike $K_C$ .

Usually, $K_P < K_C$ , which creates a "gap" where the position doesn't move much. This is known as a Synthetic Long with a wider range.

Mechanics: The Synthetic Stock

Why do institutions love this?

Capital Efficiency: You can control 100 shares of a $200 stock for a fraction of the$ 20,000 it would cost to buy them outright.
The Gap: As long as the stock stays between your two strikes, the position stays relatively flat. But once it breaks out, you participate in the full rally.

Payoff and Break-even

Max Profit

Unlimited to the upside.

Max Loss

Significant. If the stock goes to zero, you lose Strike $K_P$ minus the credit collected.

\text{Max Loss} \approx K_P \times 100

Break-even Point

If you enter for zero cost (even money), your break-even is essentially $K_C$ for the upside and $K_P$ for the downside.

The "Pure Delta" Greeks

Risk Reversals are designed to isolate direction.

1. Delta: Driving the Trade

At initiation, a Risk Reversal has high positive Delta (often +0.50 to +0.80). This makes the position move in lockstep with the stock.

2. Gamma: The Flat Curve

Because you have one long option and one short option, their Gammas tend to cancel each other out near the money. This makes the position "Synthetic Stock"—it doesn't have the convex "pop" of a simple call.

3. Vega: Skew Sensitive

Risk Reversals are sensitive to Volatility Skew. In many markets, puts are more expensive than calls. This means you can often "sell high" (the put) and "buy low" (the call), resulting in a net credit.

When to Use?

High-Conviction Bullishness: You would be happy to own the shares if they dropped to the put strike.
Speculative Substitution: You want to bet on a stock rally without using all your available cash.

Checklist for Entry

Am I willing to buy the stock at Strike $K_P$ ?
Is the "Skew" in my favor (can I get a credit or near-zero cost)?
Does my broker allow naked put selling in this account?

The Put-Call Parity LinkRead more

The Risk Reversal is a practical application of Put-Call Parity:

C - P = S - K e^{-rT}

If you choose the same strike for both the call ( $C$ ) and the put ( $P$ ), you have created a Synthetic Forward. The Risk Reversal simply widens the "gap" between these two instruments to reduce the probability of assignment while maintaining the directional bias.

Risk Reversal