Question

A semi-annual coupon bond has a coupon of 6% and its duration is 5.78 years. It trades at a yield of 7%, or a price of $94.54 per $100 face. The comparable Treasury rate is 5%. If the yield curve shifts up across the board by 50 bp and the spread increases to 280 bp, what is the new price of the bond

Answer 1

$ 101.39

Step-by-step explanation:

The new coupon rate would be the treasury rate plus 280bp which is 5%+2.8%=7.8%

The new yield to maturity would be 7%+0.5%=7.5%

Note that 100 basis point is 1%

The new price can be computed using excel pv formula

new price=-pv(rate,nper,pmt,fv)

rate is the semiannual yield i.e 7.5%*6/12=3.75%

nper is the number of semiannual coupons of the bond i.e 5.78*2=11.56

pmt is the semiannual coupon =$100*7.8%*6/12=$3.9

face value is $100

=-pv(3.75%,11.56,3.9,100)=$101.39