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Understanding Option Leverage

"Give me a lever long enough and I'll move the world."
-Archimedes


Options are a very popular tool for the purposes of hedging and speculating because of their exponential return profile... relatively small cash outlays have the potential of delivering very large profits.

Above, we see a chart of the April 22nd ATM put option on the SPY (currently trading just above $203).  The contract is priced at $2.85 and in the case of an immediate move in the price of the ETF, the price of the option will follow the blue curve... exponentially higher in the case of lower SPY prices and lower at a decreasing velocity in the case of higher a higher SPY price.  At 4pm EST on April 22nd, the price of the contract will lie directly on the orange line as the time value associated with the contract will have completely decayed.

The line and curve in the chart above represent the leverage benefits of options investing.  If, at expiration, the price of the SPY has fallen to $190, the value of the $203 put option would be $13... that represents a 256% return on the $2.85 contract.

One way to easily understand the return potential of an option is to measure its leverage.  By leverage, we mean how much it would cost to achieve the same nominal return using linear, cash products.  Going back to our example, in order to generate a profit of  $1,015 on a ($13) move in the SPY, we would have had to of shorted 77 shares of the ETF at an exposure cost of more than $15,500.  Instead, the put option was purchased for a mere $285... that represents a leverage factor of over 55 times.


THE LEVERAGE FORMULA


In looking at the leverage formula, the first thing that stands out is that delta is one of the factors.  Delta is the first derivative of the options pricing formula and, therefore, represents the linear relationship of the price of the underlying relative to the strike price of the option.  However, we know that options are not linear instruments and so we can conclude that our leverage calculation will only apply to small changes in the price of the underlying asset.

Going back to our earlier example of the SPY April 22nd put option priced at $2.85, we generate a leverage calculation of 36.7x... but we saw that a large move in the SPY would generate more than 55x leverage.

Another factor that stands out in our leverage calculation is the inverse relationship of option price to leverage... it's a negative factor in the numerator and a positive factor in the denominator.  Therefore, as prices get lower leverage gets higher. 

Here's a chart that shows how option the leverage on our SPY put would change over the course of a year... as options get closer to expiration, prices get smaller and leverage increases at drastic rates.


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