Straddles and Strangles

Sometimes you don't know which way a stock will go, but you're sure it's about to move a lot. Earnings tonight, a court ruling tomorrow, a Fed decision at 2pm. Betting on direction is a coin flip, but betting on magnitude is a real view, and that is exactly what a straddle buys you.

A straddle is a call and a put bought at the same strike and expiry. Whichever way the price breaks, one of the two legs pays. You've bought both lottery tickets, so you don't care about direction anymore, only about whether the move is big enough to cover what both tickets cost. A strangle is the budget version: same idea, but the call and put sit at different, out-of-the-money strikes, so it's cheaper to put on but needs a larger move to pay.

The payoff

Because a long call pays $\max(S-K, 0)$ and a long put pays $\max(K-S, 0)$, holding both at the same strike $K$ gives a payoff that is just the distance from the strike:

$$\text{straddle payoff} = \max(S-K,\,0) + \max(K-S,\,0) = |S - K|.$$

Here $S$ is the underlying's price at expiry and $K$ is the shared strike. The absolute-value shape is a V: worth nothing if the price finishes exactly at the strike, and worth more the farther it lands on either side. Your cost is the two premiums added together, so your profit is that V slid down by the total premium. The two breakevens are the strike plus and minus the total premium.

A strangle looks like the same picture with a flat bottom. Between the lower put strike and the higher call strike neither leg is worth exercising, so you sit at the maximum loss across that whole middle band, then the wings climb once the price escapes it.

Worked example

A stock trades at $100 the day before earnings. The at-the-money call costs $4 and the at-the-money put costs $4, so the straddle costs $8. Breakevens are $100 \pm 8$, meaning $92 and $108.

• The stock gaps to $115. The call is worth $\max(115-100,0)=15$, the put expires at $0. Payoff $15, minus the $8 you paid, is a $7 profit.
• The stock craters to $85. Now the put pays $\max(100-85,0)=15$ and the call is worthless. Same $7 profit — the direction didn't matter.
• The stock closes at $100. Both legs expire worthless and you lose the whole $8. Even a move to $105 leaves you down $3, because the $5 the call is worth doesn't cover the $8 you spent.

The strangle version: buy the $95 put for $2 and the $105 call for $2, total $4. It costs half as much, but the breakevens widen to $91 and $109, so the stock has to move even harder before you make a cent.

Where it misleads

Buying a straddle feels like a free bet on chaos. It isn't — you paid a fat premium for it, and two forces work against you.

• Time decay eats you alive. You own two options, so you're paying two premiums that bleed value every day the big move doesn't arrive. This is theta working double against you.
• The vol crush. Options are most expensive right before a known event, because everyone is bidding up implied volatility. The instant the news is out, that uncertainty collapses and implied vol drops. A stock can move exactly as much as you hoped and you still lose, because the premium you overpaid for deflated. This is the buyer's side of the variance risk premium.
• You need a move bigger than the market already expects. The breakevens are set by the premium, which already prices in the anticipated move. You don't profit from a big move, you profit from a bigger-than-priced move.

Selling these structures flips the trade entirely: a short straddle or strangle collects both premiums and profits when the underlying stays calm, which is precisely how traders harvest the variance risk premium — small, steady income in exchange for a dangerous tail. If you want a directional bet with capped cost instead, look at Vertical Spreads.