I don’t understand Chapter 30, Problem 1-4 of CAIA’s Workbook.
The current price of an equity index is $100. The trader buys one option contract for 100 shares. The delta of the option is 0.522.
The question is how to make the position delta hedged, and the solution given here is 0.522 x $100 = $52.2. However, since the contract is for 100 shares, shouldn’t you multiply the hedged position by 100 as well?
It also says that “the vega … of the position is 1.781. Note: The value of vega indicates that the position will change by $17.81 for each 1% change in implied volatility.” However, shouldn’t the position change by $1.781 instead?
Question 4 says, “the vega of the position will decline to 4.87.” But why going from 1.781 to 4.87 is a “decline” instead of an “increase”?