2.4 A trader's portfolio is delta neutral and has a gamma of -4,250. The delta and gamma of a particular traded call option are 0.62 and 1.52, respectively. The trader wants to make

the portfolio gamma neutral as well as delta neutral. What position should the trader take.

Explain to the trader what protection delta and gamma neutrality can provide to his

portfolio.

2.5 Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum (continuously compounded).

(a) Show that both portfolios have the same duration.

(b) Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.

(c) What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?