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Assume that all interest rates (i
Assume that all interest rates (i.e. discount rates) in the economy rise from 5% to 10%. Conduct a price sensitivity analysis to show which of the following bonds has the most price risk.
- An 8-year bond with 9% coupon rate
- A 5-year bond with 4% coupon rate
- A 10-year zero coupon bond
(Show your work neatly to get partial/full credits. A correct answer with NO work shown is worth ZERO point, but an incorrect or partial answer with some work shown may be worth partial credits.)
Expert Solution
In general, low coupon and longer maturity bonds will have higher price risk.
Use PV function in EXCEL to find the price of the bond
=PV(rate,nper,pmt,fv,type)
1. if rate=5%
nper=8 years
pmt=coupon rate*face value=9%*1000=90
fv=1000
=PV(5%,8,90,1000,0)=1258.53
==> if rate=10%
=PV(10%,8,90,1000,0)=946.65
The price change=(946.65-1258.53)/1258.53=-24.78%
2. if rate=5%
nper=5 years
pmt=coupon rate*face value=4%*1000=40
fv=1000
=PV(5%,5,40,1000,0)=956.71
==> if rate=10%
=PV(10%,5,40,1000,0)=772.55
The price change=(772.55-956.71)/956.71=-19.25%
3. if rate=5%
nper=10 years
pmt=0
fv=1000
=PV(5%,10,0,1000,0)=613.91
==> if rate=10%
=PV(10%,10,0,1000,0)=385.54
The price change=(385.54-613.91)/613.91=-37.20%
As I mentioned zero coupon bond has more risk and 8 year (long maturity) bond is more voltaile when compared to low maturity bonds (5 years)
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