A portfolio of derivatives on a stock has a delta of 2400 and a gamma of 100. An option on the stock with a delta of 0.6 and a gamma of 0.04 can be traded.

a) What position in the option creates a portfolio that is gamma neutral? Give size of position and state whether it is long or short (10 points)

b) After this position has been taken what position in the stock is then necessary for delta neutrality? Give size of position and state whether it is long or short (10 points)