Question
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
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?
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