Question

A hedge fund is holding a three-year, $10 million face value 6 percent annual coupon bond selling at par.

1. What is the impact of a 75-basis point increase in interest rates on the net asset value of an open-end bond mutual fund holding a seven-year, $100 million face value 7 percent annual bond outstanding?   

Answer 1

For the 3-year bond, YTM = coupon rate since the bond is selling at par. That means the current market interest rate is 6%

(a)

If the interest rates increase by 75 basis points, the new market interest rate is 6.75%

For a $100 million face value bond :

price before increase in interest rate is calculated in Excel using PV function with these inputs :

rate = 6%

nper = 7 (years left to maturity)

pmt = 7 million (annual coupon payment)

fv = 100 million (face value)

PV (or price) = $105,582,381.44

price after increase in interest rate is calculated in Excel using PV function with these inputs :

rate = 6.75%

nper = 7 (years left to maturity)

pmt = 7 million (annual coupon payment)

fv = 100 million (face value)

PV (or price) = $101,359,145.33

Impact of increase in interest rates = new price - old price

Impact of increase in interest rates = $101,359,145.33 - $105,582,381.44 ==> -$4,223,236.11

The impact is a fall in asset value by $4,223,236.11