FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A portfolio manager has a delta-neutral portfolio with gamma of -3,000. A traded option has delta 0.50 and gamma 1.50. To make the portfolio both gamma-neutral and delta-neutral, what trades are needed, in this order of the option position and then the underlying?
Buy 2,000 options to offset the -3,000 gamma (3,000/1.5), which adds 1,000 of delta. Then sell 1,000 shares of the underlying to return the portfolio to delta neutrality.
- ABuy 2,000 options, then sell 1,000 sharesCorrect
- BBuy 2,000 options, then buy 1,000 shares
- CSell 2,000 options, then buy 1,000 shares
- DBuy 3,000 options, then sell 1,500 shares
Explanation
Options needed: 3,000 / 1.5 = 2,000 bought to bring gamma to zero. This adds delta of 2,000 x 0.5 = 1,000, so sell 1,000 shares to restore delta neutrality. Buying shares would double the delta exposure.
Did you get it right without looking?
One question tells you little. A timed set on Option Sensitivity Measures: The "Greeks" shows your real accuracy, how long you take and where you lose marks.
More Option Sensitivity Measures: The "Greeks" questions
- For European options on a non-dividend-paying stock, all else equal, which statement about the signs of rho under the Black-Scholes-Merton m…
- A call option is initially at-the-money with delta near 0.5. Holding other inputs constant, as the option moves deep in-the-money close to e…
- A delta-neutral, long-gamma option position is held for one day with no rebalancing. Ignoring theta, which statement best describes the expe…
- A European call on a non-dividend-paying stock has delta N(d1) = 0.62. What is the delta of a European put with the same strike, maturity an…
- A trader is short 10,000 European call options on a non-dividend-paying stock. Each option has a delta of 0.55. To make the position delta-n…
- A trader holds a long position in a European call option on a non-dividend-paying stock. Holding all else constant, which statement about th…