Question

A 6-year 5% bond is selling to yield 6%. The bond pays interest semi-annually. Using the approximate formula

1. What is the estimated bond price for 150 basis points decrease in the yield, using approximate duration formula to estimate the new price?

2. What would explain the difference between the estimated bond price and the actual bond price you find using the financial calculator?

3. How can you correct the mispricing? Please provide calculations for the correction.

Answer 1

1) Solution: Estimated bond price equals $1088.72

Working:

Face value is $1,000, thus the coupon payment: ($1000* 2.5%) = $25

As there is a fall in150 basis points in yield, thus:

100bps = 1%; which means

150 bps = 1% * 150/100 = 1.5% or 0.015

Thus yield have decreased to 4.5% (=6% -1.5%)

Estimated pond price: = [PV (Rate, Nper, PMT, FV)] = -PV (4.5%/2, 6*12, 25,1000) = $1,088.72

2) Actual bond price = [PV((Rate, Nper, PMT, FV)] = -PV(3%, 72,25,1000) = $950.23

The actual price of bond using 6% yield equals $950.23 while the above calculation gives the estimated price after fall of 150 basis points in yield as $1,088.72 arises as difference in price because of the change in the yield of bond; and price and yield have an inverse relation.

3) Mispricing can be corrected with the consideration of the original yield at 6%