What does it mean for an option strategy to be leveraged

Probably a newbie question, but what do traders mean when they say that an option strategy is leveraged ? And when can we say that it is the case ?

• A strategy is 'leveraged' when a small change in the underlying results in a larger change in the portfolio. For example, if a stock goes from 100 to 101.5, it increases by 1.5%. If the at the money option jumps from 2 to 3, it's increases by 150%, a lot more.
– user59
May 1 '16 at 21:18

In general any investment position is said to be leveraged, if it is financed by a debt position. This is with regards to options, stocks or any other security.

Say you buy an option with maturity in one year at a premium of 100 USD, hold it to maturity and get a payoff of 120. You will have a profit of 20 USD, or 20% of your invested capital.

Instead you borrow 50 USD at 2%, and provide the other 50 USD from your own pocket, and buy the option. At a payoff of 120 USD, you will have a profit of 70 - 1 interest = 69 USD. Since you only invested 50 USD of your own capital, you have an effective return of 138% from the geared position, compared to 20% in the case of pure equity.

There is a little known Greek called "lambda" or leverage which equals Delta times Stock price divided by option price $\lambda=\frac{\Delta . S}{c}$. So if $\lambda>1$ the option could be said to be leveraged, meaning the dollar value of a delta equivalent amount of stock is greater than the market value of the option.

• $\lambda>1$ for a European call.
– Hans
Jan 30 '18 at 8:43
• Can 𝜆 be aggregated together for a portfolio measure assuming all trades have the same underlying? Dec 31 '20 at 19:18

Let's say you have 100k USD account and trade some futures, which monetary volume is about 100+/-10k. To trade it you actually need only a ~10 000 for maintenance margin. So on your 100k you can open 10 contracts, it means the leverage will be 10.

The same is for options. Options on futures require maintenance margin and it maight be compared to the monetary volume of a position.