Question

You are concerned about potential volatility in market interest rates in the coming years that could drive YTM up or down suddenly. Since you are managing a bond portfolio, you want to be able to say how much your bond values will change in the face of a changing YTM. Irn particular, you are looking at a $1,000 face value bond by Pik-U-Up, Inc. The bond has 4 years until maturity, has a coupon of 4 (4.875%) paid semiannually, and an initial 6.75% YTM A. What is the current price of the bond? O A. O B O C O D $856.03 880.27 900.11 908.05 935.22 B. What is the modified duration of the bond? O A. O B O C O D 3.35 years 3.55 vears 3.61 years 3.79 vears 4.08 years

Answer 1

Par value of Bond = $1,000

Period = 4 years

Coupon = 4.875% per annum paid semi-annually

Initial YTM = 6.75%

Using Bond calculation,

$PV of Bond = \sum_{t=1}^{t} C_{t}/(1+r)^t + Par value/(1+r)^t$

PV = $935.22

Option E is correct.

b.

$Macaulay Duration = \sum_{i}^{n} t_{i} * PV_{i}/P$

PV = present value of cash flow in particular year, P = PV of bond

Macaulay Duration = 3.67 years

Modified Duration = Macaulay Duration/(1+r)

Duration = 3.55 years

Option B is correct.