Assume that the market rate of interest rises from 6% to 12%. Which one of the...

Assume that the market rate of interest rises from 6% to 12%. Which one of the following two bonds would have higher price risk? Show your work.

An 8-year 9% annual coupon rate bond
A 10-year zero coupon bond

Expert Solution

Coupon bond

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = (YTM of bond = market interest rate)

nper = (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 9% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1. Alternatively, pmt and fv could be inputted with a negative sign.

Zero coupon bond

Price = face value / (1 + YTM)^{years to maturity}

The price of each bond, before and after the interest rate change, are calculated below ;

The zero-coupon bond has much higher interest rate risk, since the % change in price is much higher for the zero-coupon bond

jeff jeffy answered 2 years ago

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