What is a risk reversal, and how does it express a view on both direction and volatility skew?

A risk reversal is a powerful strategy that simultaneously expresses a directional view and a view on volatility skew. It's widely used by institutional traders and is a key Level II concept.

Construction (Bullish Risk Reversal):

1. Sell an OTM put at strike K_1 (below current price)
2. Buy an OTM call at strike K_2 (above current price)

Often structured as 'zero cost' — the put premium received funds the call purchase.

Directional Component:

The combination creates a synthetic long exposure between the two strikes:

• Below K_1: You're effectively long the stock (short put is exercised against you)
• Between K_1 and K_2: No obligation, both options expire worthless
• Above K_2: You profit from the long call

Volatility Skew Component:

This is the Level II insight. In equity markets, OTM puts typically trade at higher implied volatility than OTM calls (the 'skew' or 'smirk'). A risk reversal has exposure to this skew:

• Selling the OTM put: You're selling 'expensive' (high IV) volatility
• Buying the OTM call: You're buying 'cheap' (low IV) volatility
• Net effect: You profit if skew flattens (put IV falls relative to call IV)

Risk Reversal as a Skew Indicator:

Traders quote the 'risk reversal' as the IV difference between equidistant OTM calls and puts:

25-delta Risk Reversal = IV(25-delta call) - IV(25-delta put)

A negative value (typical for equities) means puts are more expensive than calls. A very negative value means extreme fear / high skew.

Worked Example:

Atlas Mining trades at $85. You're bullish and think put skew is excessive.

• Sell 1 $75 put (25-delta) at $3.40 (IV = 38%)
• Buy 1 $95 call (25-delta) at $3.20 (IV = 28%)
• Net credit: $0.20

Skew = 38% - 28% = 10 vol points. You're selling the expensive leg and buying the cheap leg.

If Atlas rises to $100:

• $75 put expires worthless (you keep $3.40)
• $95 call is worth $5.00
• Net profit: $5.00 + $0.20 = $5.20

If Atlas falls to $70:

• $75 put costs you ($75-$70) = $5.00, net of premium = $1.60 loss
• $95 call expires worthless
• Net loss: -$1.60

Exam Tip: Understand both the directional and skew dimensions. Know that equity risk reversals are typically quoted as call IV minus put IV, and that a more negative value implies greater investor fear. Be prepared to construct a risk reversal and calculate the payoff.

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