Why is small actual volatitlity profitable for a long call option?

[Liming]

Dear David,

Appreciate your enlightenment on the FRM handbook question (page 335 Example 13.3 5th edition) below. The book's explanation is that the long call position is profitable when the actual volatility is small but this statement seems contradictory to what I've learned about long options that long a option is long implied volatility therefore it benefits from increasing volatility?

Example 13.3
A trader buys an at-the-money call option with the intention of delta-hedging it to maturity. Which one of the following is likely to be the most profitable over the life of the option?
A. An increase in implied volatility
B. The underlying price steadily rising over the life of the option
C. The underlying price steadily decreasing over the life of the option
D. The underlying price drifting back and forth around the strike over the life of the option
Answer Provided: D

Thanks
Liming
19/11/09

 

[hsuwang]

Hello Liming,

this here might help: http://forum.bionicturtle.com/viewthread/1870/#3812

 

[David Harper CFA FRM]

Thanks for the help Jack! Your instincts are fine Liming, the last sentence in the answer is wrong: Just like a naked long option position, the long option delta-hedger is long volatilty (vega) and long gamma, so he/she profits when realized volatility > implied volatilty at the time the option was purchased, b/c at that point, the option premium has been paid for...David