Collar Strategy Payoff Limits and Interim P&L

Summary

The document explains the expiration profit and loss bounds for a collar, consisting of long stock, a long put, and a short call at a higher strike. At expiration, the call caps the position’s upside, while the put limits its downside. The stated maximum profit is the call strike less the initial cost of the collar; the stated maximum loss is that cost less the put strike.

Before expiration, the position’s profit or loss does not necessarily sit at those bounds. How quickly it approaches them depends on time remaining and implied volatility. Dividends must also be included in the P&L calculation. The response notes that an expiration payoff cannot exceed the cap on the relevant side because the in-the-money option contributes only intrinsic value and the other option expires worthless. The discussion is brief and does not show a full valuation calculation; it also does not spell out discounting conventions for interim theoretical P&L, so those details depend on the pricing setup.

Key ideas

• A collar combines long stock, a protective put, and a short call.
• At expiration, the short call limits maximum profit and the long put limits maximum loss.
• The stated bounds depend on the initial cost and the option strikes.
• Before expiration, time remaining and implied volatility affect how P&L approaches its bounds.
• Dividends affect the position’s potential P&L and should be accounted for.

Tags

# Option strategy Collar


# Option strategy Collar












I've question regarding Collar strategy (long Put with strike $k_1$ and short Call strike $k_2$ and long stock), when calculating the theoretical P&L of the collar for large up movements of the underlying my theoretical P&L surpass maximum payoff or for large down movements of the underlying the opposite happens, I'm wondering if this actually makes sense ? Also do we need to discount the values theoretical P&L for collar ?

## Answer by Bob Baerker (score 1)

https://quant.stackexchange.com/a/59480

The maximum profit for a collar is the call strike less the collar's cost (at expiration).

The maximum loss is the collar's cost less the put strike (at expiration).

Prior to expiration, the speed at which the profit or loss approaches the maximum depends on the time remaining and is accelerated (or decelerated) by the implied volatility.

If there's a dividend, it must be accounted for but that merely changes the potential P&L.

It makes no sense that theoretical payoff exceeds the maximum payoff because the option on the side of the move can only attain intrinsic value (while the other side goes to zero).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.