How to calculate options leverage?

Financial leverage allows a smaller amount of money to participate in and own profits usually assessable only to a larger amount of money. Leverage is a major benefit of options investing, and when used carefully it can provide significant profits.

Options leverage – also called Lambda in options terminology - is the cash equivalent multiple of one's options position relative to the actual cash (spot) price of the underlying asset.

Stock options produce options leverage as every contract represents 100 shares of the underlying stock while costing only a fraction of the price. This allows option traders to control the profits on the same number of shares at a much lower cost.

To explain how options leverage is calculated, here is an introducing example. Assuming you have $1000 and wish to invest in shares of a certain company, which is currently trading at $20, you can only buy 50 shares. That's further imagine that it's $20 strike price call options are trading at $2.00, which means a single contract costs $200.

Instead of buying the shares you can buy 5 contracts of $20 strike call options to control 500 shares! With the same amount of money, you can control 10 times more shares than you normally can do by buying shares. This gives you a first impression about options leverage in option trading but not unveils the complete story.

The problem with the illustration above is that even though 5 contracts of the $20 strike price call options represents 500 shares, but the option price does not move in exactly the same magnitude as the shares of the company. Stock options move only a fraction of the price of its underlying stock, governed by its “Delta” value. An "at-the-money" option, typically
has a delta value of 0.5. This means that each contract of $20 strike call options moves only $0.50 for every $1 move in the underlying stock. The delta is sometimes also used to describe the probability of the option to end “in-the-money”. The delta of “out-of-the-money” call options is typically between 0 to 0.5, whereas the delta of “in-the-money” call options is above 0.5.

If the stock, in our example, rallies to $24, the $20 strike call options rise $2.00 to $4.00 due to their intrinsic value. In this case the rise in stock price is 20%, whereas the increase in the option price is 100%. This ratio (100% / 20%) is the options leverage.

The formula to calculate options leverage is defined as:

Options Leverage (or Lambda) = Delta x Stock price (S) / Option price (V)

with

Delta = dV / dS = Change of option price / Change of stock price

In our example:

Options Leverage = 0.5 x $20 / $2.0 = 5

As you can see, the calculation of options leverage is quite easy if you know the Delta value, but it is hard business, if Delta is not yet available. Especially, if the option is far “out-of-the-money” or deep “in-the-money”. Several financial models - like the Black-Scholes model - provide equations to calculate Delta and other options related numbers approximately, but due to their complex mathematical expressions they are not feasible by the usual options investor.

Usually, your brokerage system should provide option parameters like the Delta. If not, we have developed a proprietary approach to determine Delta from option prices. If you want to determine the Delta parameter of a particular call option, you can do so by exercising the following formula:

Delta = (price of next expensive option – price of target option) / (strike of target option – strike of next expensive option)

Example with call options:
Spot price of underlying security: $41.00
Price of target option: $2.30, strike price: $46.00
Price of next expensive option: $2.63, strike price: $45.00

Delta = ($2.63 - $2.30) / ($46.00 - $45.00) = $0.33 / $1.00 = 0.33

Please, be aware that the result of this calculation is not precise and contains certain amount of inaccuracy. But nevertheless, it’s a feasible approach to calculate Delta in line with the mathematical definition.