The Value Line Daily Options Survey

Leveraging with Options

One attractive feature of options is the leverage that they offer. By this, we mean that options can produce large profits on relatively small outlays of capital. By way of example, the average at-the-the-money call these days is leveraged about 9 to 1 to the stock. In this week’s report, we show you a “quick and dirty” way to calculate the leverage of an option. We will also show you how to use the leverage numbers that we provide in our service.

Lambda – Another “Greek”

In addition to the other well-known option risk measures (Delta, Gamma, Theta and Vega), there is Lambda. What Lambda measures is the expected percentage move of the option given a 1% move in the stock. You can easily calculate Lambda using the current premium and the current Delta.

Lambda = Stock Price x Delta (as a decimal)/Premium.

For instance, on April 21st, the near-the-money IBM July $125 call was offered at $4.80 with the stock at $123.54 and the Delta at 49. The Lambda calculation is ($123.54 x .49)/$4.80. This number works out to be 12.61.

Let us go through what we have done with this calculation. If the stock moves by 1% then the change in the stock has been $1.2354 in dollar terms (.01 times $123.54). Using the Delta calculation, we see that the option will move by $0.6053 (or by .49 times $1.2354). This works out to be a 12.61% move in the option premium ($0.6053 divided by $4.80). Thus, one can say that the call is leveraged 12.61 to 1 for a small move in the stock.

Our Leverage Numbers

While Lambda calculations are not included in our service, we do provide similar numbers that are useful.

One such set of numbers is our “Buyer’s Leverage” numbers. These show the expected change in the premium given a 10% rise and a 10% decline in the stock. For instance, the IBM July $125 call is expected to rise by 174% if the stock were to go up 10% right away and to decline by 81% if the stock were drop by 10%.

A Bull Call Spread

Notice that these numbers suggest that the call is leveraged by 17.4 to 1 on the upside (174% divided by 10%) and by 8.1 on the downside (81% divided by 10%) and that the average of these two leverage numbers is 12.75, which in turn is close to our original Lambda calculation of 12.61

You will find these leverage numbers in our Options Profiles online and in columns AA (+10%) and AB (-10%) in our spreadsheet files. (See Figure 1 on page 1 and Figure 2 on page 3.) You will also find these numbers our Options Screener criteria. (Note: We calculate “Buyer’s Leverage” numbers with a Black-Scholes model using the current mid-point implied volatility and the stock price level given a 10% rise and a 10% decline in the stock.)

Another leverage number that we provide is our Percent to Double numbers. We do not include these in our Options Profiles, but include them in our spreadsheet data (column AQ in Figure 2) and in our screener. These numbers tell you, if you are a buyer, how much the stock needs to move in the direction you want it to (up for calls, down for puts) for you to double your premium. Notice that for the July $125 call on IBM, if the stock rises by 5% right away, your premium should approximately double.

Reality Check

If some of these leverage numbers look “too good to be true,” it may be because they do not indicate the effects of the bid/ask spread - and of the passage of time. Let us examine the IBM July $135 call, priced at $1.35 bid and $1.40 ask. According to our “buyer’s leverage” numbers this call offers a 340% gain if the stock goes up 10% right away versus only a 90% decline if the stack falls 10%. This call has a “percent to double” number of only 4% based its very high upside leverage.

In Graph 1 on page 3, we have used our Whatifi3.Xls template to chart the course of this call on the day we put it on (April 22, 2008), in one month’s time (May 22, 2008) and at its expiration (July 19, 2008). This template marks your position to the other side of the market. Thus, in this example, we are assuming at loss of $5 the moment you establish the position based on the $0.05 spread between the bid and ask prices. Notice that because of this bid/ ask spread, the stock will have had to move by more like 4.5% rather than by 4% for us to double our money on the day we establish it.

Looking ahead to May 22, 2008, the stock will have to rise by about 2.5% to 3.0% just for us to break even and by about 9% for us to double our money. At expiration, the stock needs to go up by a little less than 10.5% for the call to break even and by 11.5% to $137.80 for the investor to double his or her money.

Summary

Prepared by Lawrence D. Cavanagh
vloptions@valueline.com