Am I doing the math for this long straddle strategy correctly?

Question

I'm looking at making a long straddle trade, and I'm trying to make sure I have the math correct before making the trade. Here are the details in the example I want to work out:

1. I'm using options on the SPY, specifically this call and this put that expire in March 2014. The price of the call is 23.50 and the price of the put is 3.36.

2. The current share price of SPY is 175.50, and I pay $7.95 in commissions per trade and $0.75 per options contract. I want to buy 10 call contracts and 10 put contracts.

Here's the math I'm using:

1. First, I long the options contracts. I buy 10 of each contract, so the cost is

   [10*(23.50 + 0.75)+7.95] + [10*(3.36 + 0.75) + 7.95] = $299.50
   

2. If the share price is unchanged at expiration, the options expire worthless and I lose $299.50 (the cost of my position). This is my maximum downside.

3. If the share price increases 1% to $177.255 at expiration (as an example), the put options expire worthless, and I exercise the call options like this:

   10 * 100 * (177.255 - 175.50) - 10 * 0.75 - 7.95 = $1,739.55
   

for a profit of $1,739.55 - $299.50 = $1,440.05.

1. If the share price decreases 1% to $173.745 at expiration, the call options expire worthless, and I exercise the put options like this:

   10 * 100 * (175.50 - 173.745) - 10 * 0.75 - 7.95 = $1,739.55
   

for a profit of $1,739.55 - $299.50 = $1,440.05.

Is this math correct?

Answer 1

The math is not correct. Your option prices are off by a factor of 100.

Option contracts typically represent 100 underlying shares, but the prices quoted are per underlying share. In purchasing an options position, you need to multiply the quoted price by 100, and also by the number of contracts desired.

If you re-do your calculations, you'll find the percentage price increase or decrease required to make the position profitable is substantially more than a 1% swing. Your maximum downside is also understated as a result of the price error.