## Definition

The term equivalent strategy refers to two positions that share the same risk and reward profile. When two traders assume different, but equivalent strategies, they will share the same payoff.

### Explanation

Also known as equivalent positions, equivalent strategies are two different sets of trades that result in the same outcome. While the positions don't have to be identical, each of the positions will provide the investor with the same gain or loss at any price for the underlying asset. Investors can use knowledge of equivalent strategies to their advantage, potentially saving on commissions and / or premiums.

Perhaps the best-known example of an equivalent strategy is writing a covered call versus selling a naked put. If these two options are priced efficiently, then the trader will be indifferent to each strategy. However, if the options are priced inefficiently, it's possible for arbitrageurs to profit from the discrepancy. Fortunately, it's also possible to determine if a position is equivalent by using one very simple formula:

Stock = Call - Put

Where:

- Stock = ownership of the underlying asset
- Call / Put = the buying (+) or selling (-) of the option

The above formula tells us that owning 100 shares of stock (being long) is equivalent to buying one call option and selling one put option. In all of these equivalent strategies, each position involves the same underlying asset, strike price, and expiration date.

If we rearrange the above formula, we can also get:

Call = Stock + Put

This tells us that buying one call option is equivalent to buying one put option and owning 100 shares of stock. Another variation of this formula includes:

- Put = Stock - Call

This tells us that selling one put is equivalent to owning 100 shares of stock and selling one call. This example was mentioned earlier, since it's a naked put versus a covered call.

### Related Terms

equity option, early exercise, diagonal spread, derivative