## EC Ultimate Guide To The Synthetic Long Stock Strategy

### Introduction

A synthetic long stock is a means of recreating the payoff profile of a long stock using options.

It is a combination of a long call and short put on the same underlying stock with identical strike price and expiration.

Simply put, a synthetic long stock position uses options to replicate the payoff of holding 100 shares of the stock without actually owning it.

This results in a leveraged position as the margin requirements for a synthetic long are much less than buying 100 shares.

It would be unfair if I just state the definition without providing an understanding of the building block of synthetic positions – known as the put-call parity.

Put-call parity shows the position equivalence of a portfolio of a call and risk-free bond with a portfolio of underlying stock and a put.

It defines the relationship between call prices and put prices with identical strike price and expiration.

In mathematical terms, put-call parity states:

C + X/(1+r)^t = S + P.

Where,

C = Call

X = Risk free bond

S = Stock

P = Put

Basically, it means that the price of call option has some information about the price of the corresponding put option, and vice versa.

I could spend an entire month talking about the derivation of put-call parity formula, but essentially the parity holds because any material divergence between put and call values will correct themselves as arbitrageurs take advantage of the mispricing.

It only holds for options that are held to expiration, but we don’t have to worry about that for now.

A simple understanding of the parity is enough to understand synthetic positions.

For the purposes of understanding synthetics, let’s assume interest rates are zero and the stock doesn’t pay a dividend.

Ok, so now that we have that out of the way. Let’s revisit the put-call parity and understand the synthetic positions formulaically and intuitively.

Formulaically if we rearrange the parity formula from above such that you have long stock on one side and the rest on the other side.

S = C – P – X(1+r)^t

We can ignore the risk-free bond (X) because all it means is that you have the money in your account to meet the strike price at expiration. Therefore, restated it is:

S = C – P (i.e. long stock equals long call and short put)

Formulas are fun but let’s understand the relationship intuitively.

Remember the payoff of a long stock. It states the value of your position increases as stock price rises above the purchase price and it decreases as stock price falls below the purchase price.

A synthetic strategy simply asks: How can we replicate the same payoff without buying the stock?

Disclaimer: The information above is for educational purposes only and should not be treated as investment advice. The strategy presented would not be suitable for investors who are ...

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