You currently hold a portfolio worth $60,000. The portfolio comprises a 5-year zero-coupon bond worth $40,000 and a 6-year coupon bond worth $20,000 (coupons paid annually). The duration of this portfolio is 4.

If you can short an 8-year zero-coupon bond to immunize your portfolio against small changes in interest rates, how much of the 8-year zero-coupon bond should you sell?

You should re-invest the short sale proceeds into the 5-year zero-coupon and 6-year coupon bond while maintaining the relative weights of the long positions. (This is to say, 66.67% of your long position should be in the 5-year zero-coupon and 33.33% in the 6-year coupon bond after re-investing the proceeds from the short sale.)

Answer Choices:

10,000

60,000

11,250

120,000

30,000