# Time: Enemy Number One

It is a well know fact that time is the nemesis of the option buyer. This is doubly so for the straddle buyer as both a put and a call are purchased. Creating a straddle by buying puts and going long the stock does not circumvent this problem. You will note that in the example above we purchased 1000 shares and 20 put options, buying 2 options for each 100 shares held. So it is doubly important to be aware of the impact that the passage of time will have on a straddle.

The table below was constructed using the following theoretical example: the stock is trading at \$100 and we initially purchase a 100 straddle (the 100 call and the 100 put), paying \$4.46 for the call and \$4.19 for the put. These prices reflect a volatility of 35%, there are 5 weeks before option expiration, the stock does not pay a dividend and the risk-free rate is 3%.

Weeks to Expiration Call Value (Assumes Stock Remains at \$100) Put Value (Assumes Stock Remains at \$100) Straddle Value Straddle Value as % of Initial Value
5 4.46 4.19 8.65 100%
4 3.98 3.76 7.74 89.5
3 3.43 3.27 6.70 77.5
2 2.79 2.68 5.47 63.2
1 1.96 1.91 3.87 44.7
0 0 0 0 0

This table clearly illustrates options’ time decay. The important point to notice is that this decay is not linear. After 1 week, the straddle has lost just a little over 10% of its initial value. After 3 weeks, more than 60% of the initial value remains. The offshoot is that the cost of holding the straddle, as a percentage of the initial value, increases with every week. Plan accordingly.

One last point: if the stock in the example above does remain at \$100 for 5 weeks, the options’ implied volatility will more than likely decrease, and the value of the straddle will therefore be lower than that in the table above.