ABC is currently trading at $77 per share. Your previous calculation of the historical volatility for ABC indicated an annual standard deviation of return of 20 percent; but examining the implied volatility of several ABC options reveals an increase in annual volatility to 30 percent.

There are two traded options series that expire in 360 days as show in the following table:

X = 75 X = 80

Call Put Call Put

DELTA 0.6674 -0.3326 0.574 -0.426

GAMMA 0.0176 0.0176 0.019 0.019

The options have $75 and $80 strike prices respectively. The current risk-free interest rate is 3 percent per annum, and you hold 5,000 shares of ABC.

Construct a portfolio that is DELTA - and GAMMA - neutral using the call options written on ABC. Show all calculations.