Question

Calculate the durations and volatilities of securities A, B, and C. Their cash flows are shown below. The interest rate is 8%. (Do not round intermediate calculations. Round "Duration" to 3 decimal places and "Volatility" to 2 decimal places.)

	Period 1	Period 2	Period 3	Duration	Volatility
A	40	40	40	years
B	20	20	120	years
C	10	10	110	years

Answer 1

Lets take the periods row vertically for our convenience

present value of price of A at year 1

= price at year 1/(1+r)^t

r = 8%

= 40/1.08 = 37.04

present value of price of A at year 2

= 40/(1.08)^2 = 34.292

present value of price of A at year 3

= 40/(1.08)^3 = 31.75

Similarily for present value of securities B and C

Propotion of total value for A

Propotion of total value for A at year 1

= (present value of price A at year 1) / (present value of price A at year 1 + present value of price A at year 2 + present value of price A at year 3)

= 37.04/103.082 = 0.3593

Propotion of total value for A at year 2

= (present value of price A at year 2) / (present value of price A at year 1 + present value of price A at year 2 + present value of price A at year 3)

= 34.292/103.082 = 0.3327

Propotion of total value for A at year 3

= (present value of price A at year 3) / (present value of price A at year 1 + present value of price A at year 2 + present value of price A at year 3)

= 31.75/103.082 = 0.308

Similarily for securities B and C

Duration = propotion * time = propotion of total value * year

propotion * time for year 1 for security A = 0.3593 * 1 = 0.3593

propotion * time for year 2 for security A = 0.3327 * 2 = 0.6654

propotion * time for year 3 for security A = 0.308 * 3 = 0.9241

Similarily for security B and C

Total duration for A

= 0.3593 + 0.6654 + 0.9241 = 1.9488

Similarily calculate the total duartion for B and C

Volatility for security A = (Total Duration) / ( 1+ r) = 1.9488/1.08 = 1.81

Similarily for security B and C

Kindly take a look at the below snapshot for the complete table