Question

When interest rates shift, the price of zero coupon bonds are volatile Multiple Choice more; if they have a short maturity rather than a long maturity not; because their duration always matches their maturity equally; regardless of their maturity. less; than coupon bonds of the same maturity. more; than coupon bonds of the same maturity.

Answer 1

1. more,than coupon bonds of the same maturity.

Duration is the measure of bond's volatility due to change in interest rate. Duration of Zero coupon bonds always to its maturity and Duration of Coupon Bonds always less than its maturity which means Zero coupon bonds would have higher duration (volatility) than coupon bonds if both bonds have same maturity.

2.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

В C E F G 1 Par value of Bond Coupon rate Years to maturity Currently selling at $1,000.00 2 9.50% 4 $1,000.00 6 YTM 9.50% 7 Year (t) PVF(9.50%) t*PV CF 8 Cash Flow PV CF $95.00 $86.76 $86.76 9 1 0.91324 $95.00 $79.23 $158.46 10 2 0.83401 $95.00 $72.36 $217.07 11 0.76165 $1,095.00 $761.65 $3,046.62 $3,508.91 12 4 0.69557 $1,000.00 13 14 3.50891 15 Duration 16

Cell reference -

A C D E F 1 Par value of Bond 1000 0.095 2 3 Coupon rate Years to maturity 4 Currently selling at 1000 6 YTM - C3 7 PVF(9.50%) - 1 / (1+$C$6)^B9 =1/(1+$C$6)^B10 = 1/(1+$C$6)^B11 -1/(1+$C$6)AB12 Year (t) t*PV CF Cash Flow PV CF -C9* D9 -$C$3*$C$2 9 B9*E9 1 C10* D10 -B10*E10 $C$3*$C$2 10 2 -$C$3*$C$2 =$C$3*$C$2+C2 11 C11*D11 =B11*E11 B12*E12 12 -C12*D12 =SUM(E9:E12) 13 SUM(F9:F12) 14 =F13/E13 15 Duration 16 17

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.