You are responsible for managing the risk of a portfolio of assets whose value is sensitive to changes in the value of gold. Your portfolio is currently delta neutral. However, your portfolio currently has a gamma of -20 and a vega (per %) of -20,000.

There are put and call options written on gold. For simplicity, assume that the options are for cash settlement on the expiration date, where each contract is for $100 times the amount the value of gold is in the money relative to the exercise price at expiration; that is, each contract is like you have 100 options written on 1 share (i.e., ounce) of gold. The current value of gold is $1300 per ounce. The annual volatility of gold is currently estimated to be = .21 (i.e., 21 percent). The current annualized risk-free rate of interest is 2.0 percent at all maturities over the next year.

Below is some data on a few of the options available in the market currently. The values are per share; the values per contract are 100 times the values shown below. All values are for European call options.

Exercise Expiration

Price Time Delta Gamma Vega (per %) Price

1275 1 year .61512 .0014000 4.96877 $133.60

1275 6 months _______ ________ _______ _______

Questions:

1. Fill in the blanks in the table above. Show your work below. (6 points total)

2. Given the data above (and the data you provided in the blanks if necessary), what strategy can you implement now that will allow you to hedge your firms exposure to changes in the value of gold and create a delta, gamma, and vega neutral portfolio? Tell me exactly how many units of each security you will need to buy or sell in order to implement this strategy. (9 points total)