Now suppose a financial institution has a duration gap of -4 years and $5 million in assets. The cheapest to deliver bond for Treasury futures contracts has a duration of 3 years. How will the manager hedge this interest rate risk? Assume the cheapest to deliver bond is trading at par.

EBK CONTEMPORARY FINANCIAL MANAGEMENT
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Chapter12: The Cost Of Capital
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  1. Now suppose a financial institution has a duration gap of -4 years and $5 million in assets. The cheapest to deliver bond for Treasury futures contracts has a duration of 3 years. How will the manager hedge this interest rate risk? Assume the cheapest to deliver bond is trading at par.
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Introduction

Bond's market value has a negative relationship with market interest rates. When interest rate increases, bond' market value decreases. This is so because, investor's expected rate of return increases whereas bond is providing a lower rate.

Duration measures the decrease in the value of the bond when interest rate increases. In case, a bond has 4 year duration then every 1% increase in the market interest rate would reduce the bond's value by 4%.

Negative duration refers when increase in interest rates would increase the value of security. 

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