Let us consider a bond with face value \(\$ 10,000\), maturing in three years, and paying an annual coupon at rate \(6 \%\). If annual yield is \(4 \%\), the bond price is

and its Macauley duration is

If yield does not change, we reinvest coupons at \(4 \%\), and sell the bond at time \(H=284\), wealth will be

To understand this expression, note that the first two cash flows are reinvested up to time \(t=2.84\), whereas the third cash flow is discounted from time \(t=3\) to \(t=2.84\). If yield is increased by 50 basis points, wealth will be

Indeed, up to an approximation error, future wealth at the right time horizon is insensitive to small changes in yield.

Transcribed Image Text:

600 Pc(4%) 600 10,600 + + 1.04 1.042 1.043 = $10,555.02,