Question

QUESTION 57

1. What is the duration of a 7-year zero coupon bond priced to yield 10%?

   		a. 5.55.
   		b. 5.93.
   		c. 6.34.
   		d. 7.00.

QUESTION 58

1. Which of the following statements is correct about duration?

   		a. Duration will always be less than the maturity for a bond.
   		b. The duration of a bond increases as YTM increases.
   		c. Modified duration is a precise measure of the change in the price of a bond based on a change in interest rates.
   		d. The duration of a portfolio equals the sum of the weighting of each portfolio component multiplied by its duration.

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =7

Bond Price =∑ [(0*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^7

k=1

Bond Price = 513.16

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($513.16)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	-	1.10	-	-
2	-	1.21	-	-
3	-	1.33	-	-
4	-	1.46	-	-
5	-	1.61	-	-
6	-	1.77	-	-
7	1,000.00	1.95	513.16	3,592.11
			Total	3,592.11

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3592.11/(513.16*1)

=7

Please ask remaining parts seperately