Oct

2

Looking at Leverage

Filed Under Option Trading Articles 

In order to truly understand the leverage of an option, we must compare “dollar equivalent” exposure. For example, let’s assume the $75 call trading for $8.30 has a delta of 0.60. For the next one-dollar move, this option’s price will rise by the delta, or 60 cents, from $8.30 to $8.90. This 60-cent move is equivalent to $60 per contract. Now let’s see what a stock investor must spend to get this same $60 gain from a one-dollar move in the stock. A stock buyer must buy the delta equivalent number of shares, which is 60 shares of stock that would cost 60 * $79.46 = $4,767.60. So if an option trader buys the $75 call and a stock trader buys 60 shares of stock, then both will capture a $60 profit on the next one-dollar move in the stock. Now we just need to compare the costs of these dollar equivalent exposures. The stock trader spends $4,767.60 while the option trader spends $830, which means there is $4,767.60/$830 = 5.7 times as much leverage in the option as compared to the stock. (But keep in mind that this number will change as the delta of the option changes. We’re just saying this is how you’d need to calculate the leverage in the option at this point in time.)

Other Views of Leverage
Although the above calculation is probably best for comparing the true leverage of an option there are other views we could take.

For example, say a stock is trading for $100 and a $100 call is trading for $5. One way to view the leverage is to realize that the option trader, in this example, has leveraged the returns by a factor of 20. That is, for every 100 shares the stock investor buys ($10,000 worth), the option buyer can buy 20 contracts ($10,000/$500 per option = 20).

Let’s assume that the stock now rises from $100 to $115. If the stock trader buys 100 shares then the total value would be 100 * $115 = $11,500, which leaves a profit of $1,500. With the stock at $115, the $100 call would be worth $15, or $15 * 2,000 = $30,000 for the 20 contracts.

If we multiply the $1,500 profit of the stock trader by 20 we end up with $30,000, which is the value of the option trader’s total position. In this example, the option trader’s total value will always be worth 20 times the stock trader’s profit, assuming the $100 call option has intrinsic value. This is a somewhat awkward view of leverage since we’re comparing the profit of the stock trader to the total value of the option trader. Still, it is a very common use that you will encounter.

It’s important to understand that this method only works in such a straightforward way if we compare at-the-money options. Using our IBM example, the stock is $79.46 and the $75 call is trading for $8.30, which means the option trader has leveraged the returns by a factor of $79.46/$8.30 = 9.5 times. Once again, this means that for every 100 shares the stock investor buys ($7,946 worth of stock) the option buyer can control 950 shares since $7,946/$830 = 9.5 contracts, or 950 shares. (You cannot buy fractional contracts but we must assume this to make the comparisons.) Now we should expect that for any given gain in the stock’s price, the option’s total value would be 9.5 times as great as the stock trader’s profits.

Let’s see if it works. Assume the stock rises from $79.46 to $85 by expiration. The stock trader invested $7,946 and can sell for $8,500 for a total profit of $554. With the stock at $85, the $75 call would be worth $10, or a total value of 950 shares * $10 = $9,500. However, we see that $9,500/$554 = 17 times. Why does it not equal 9.5 times? The reason is that this option is not at-the-money. The stock is $79.46, which means this $75 call has $4.46 worth of intrinsic value that we must take back out. The value that must be subtracted from the $9,500 total option value is then 950 shares * $4.46 = $4,237, which leaves us $5,263. If we take $5,263/$554 we get leverage of 9.5!

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