The investment manager wishes to hedge interest rate uncertainty. Suppose that the portfolio manager has a $10 million bond portfolio with a modified duration of 9 years. If as feared, market interest rates increase and the bond portfolios yield also rises, say by 10 basis points (.1%), the fund will suffer a capital loss. Suppose the bond portfolio is twice as large, $20 million, but that its modified duration is only 4.5 years. Show that the proper hedge position in T-bond futures is the same as the value 100 contracts. (one T-bond contract is equivalent $100,000).