Question

If a three-month Treasury bill sells for $98 and a six-month Treasury bill sells for $96, do they have the same annual yield? Explain.

Consider two bonds with $1000 face values, coupon rate of 8%, making annual coupon payments, and exhibiting similar risk characteristics. However, the first bond has five years to maturity whereas the second has 10 years to maturity. The appropriate discount rate for bonds of similar risk is 8%. If the discount rate rises by 200 basis points, what will be the respective price changes of the two bonds?

Answer 1

Annual yield for 3 month T-bill = 3 month yield * 4 = 2/98*4= 8/98%

Annual yield for 6 month T-bill = 6 month yield * 2 = 4/96*2= 8/96%

So, the yield are not same for both the T bills

Both the 5 year and 10 year bonds are trading at par as the coupon rate is same as the discount rate

After increase in interest rates, i =8%+200 basis point = 10% =0.1

Price of 5 year bond = 80/0.1*(1-1/1.1^5)+1000/1.1^5 = $924.18

Price of 5 year bond = 80/0.1*(1-1/1.1^10)+1000/1.1^10 = $877.11

So, 5 year bond price will decrease by (1000-924.18)/1000 = 7.58% or price change is -7.58%

and 10 year bond price will decrease by (1000-877.11)/1000 = 12.29% or price change is -12.29%