Question

Questions 1-4 show excel formulas

The coupon rate and market price for the 10-year US Treasury bond are 2.50% and 96.3828 respectively. Note, the price is expressed as a percentage of par (like other bonds). If par is $1000, then this bond is selling for $963.828.

1. Assume that this bond will mature in precisely 10 years, pay coupons semi-annually, and has a par value of $1000. Determine the yield to maturity for this bond.

2. Compute the duration of this bond and use it to estimate the new value of the bond if rates were to suddenly decline by 0.80%.

3. Calculate the bond's value directly (using the present value approach) assuming that rates declined 0.80% from the yield to maturity you estimated in the first question.

4. Compare your answers to Questions 2 and 3. Explain the source of any difference. Which is more correct

Answer 1

1.
=RATE(10*2,2.5%*1000/2,-963.828,1000)*2=2.920%

2.
Macaulay Duration:
=DURATION(DATE(2016,1,1),DATE(2026,1,1),2.5%,2.92%,2)=8.884352504
Modified Duration=8.884352504/(1+2.92%/2)=8.756507495

New value=963.828*(1+0.80%*8.756507495)=1031.346137

3.
=PV((2.920%-0.8%)/2,2*10,-2.5%*1000/2,-1000)=$1,034.08

4.
Question 3 is more correct because Question 2 ignores the convexity and assumes linear relationship