415 Investment Company (415IC) owns a fixed income portfolio consisting of two US Treasury bonds, A and B, which are not very liquid. It is concerned about the interest rate risk of the portfolio and is considering using the liquid US Treasury bond C as a hedging instrument. Assume a flat term structure for interest rates; the current interest rate is 4%. Data on the portfolio and bond C are as follows:

Bond	Price	Duration (year)	Portfolio holdings in units of bonds (million)
A	100	2	2
B	101	9	3.5
C	98	6	0

(a) What is the total value of the portfolio?

(b) What is the modified duration of the portfolio?

(c) Suppose there is a parallel shift in interest rates by 0.5% (from 4% to 4.5%). By how much does the value of the portfolio change? Use the modified duration approximation.

(e) How many units of bond C should we go long/short to hedge parallel shifts in the interest rate? (use negative number if go short)

(f) What is the hedge ratio?