Answer:
a. Predicted Price = $1815.52
b. Predicted Price = $1,834.64
c. Predicted Price = $1425.4
Explanation:
The actual price of the bond as a function of yield to maturity is:
Yield to maturity --- Price
7% $1,620.45
8% $1,450.31
9% $1,308.21
a.
Using the Duration Rule, assuming yield to maturity falls to 6%:
Predicted price change = (-D/(1 + y)) * ∆y * Po
Where D = Duration = 12.88 years
y = YTM = 7%
∆y = 6% - 7% = -1%
Po = $1,620.45
So, Predicted Change = (-12.88/(1 + 0.07)) * -0.01 * 1,620.45
Predicted Change = 195.0597757009345
Predicted Change = $195.06 ----- Approximated
Therefore the new Predicted Price
= $1,620.46 + $195.06
= $1815.52
b.
Using Duration-with-Convexity Rule, assuming yield to maturity falls to 6%
Predicted price change
= [(-12.88/(1 + 0.07)) * (-0.01) + (½ * 235.95 * (-0.01²))] * 1,620.45
= 214.1770345759345
= $214.18 ------ Approximated
Therefore the new Predicted Price
= $1,620.46 + $214.18
= $1,834.64
c.
Using the Duration Rule, assuming yield to maturity rise to 8%:
Predicted price change = (-D/(1 + y)) * ∆y * Po
Where D = Duration = 12.88 years
y = YTM = 7%
∆y = 8% - 7% = 1%
Po = $1,620.45
So, Predicted Change = (-12.88/(1 + 0.07)) * 0.01 * 1,620.45
Predicted Change = -195.0597757009345
Predicted Change = -$195.06 ----- Approximated
Therefore the new Predicted Price
= $1,620.46 - $195.06
= $1425.4
