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 4 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

Duration:-

Security A

YEAR (1)	CASH FLOW (2)	PRESENT VALUE FACTOR@ 8% (3)	PRESENT VALUE (PV) (4)	PROPORTION OF TOTAL PV (5)	DURATION = PROPORTION * TIME [(6) = (5) * (1)]
1	40	0.9259	37.036	0.3593	0.3593
2	40	0.8573	34.292	0.3327	0.6654
3	40	0.7938	31.752	0.3080	0.9240
		TOTAL	103.08	1.0000	1.9487

DURATION = 1.9487 YEARS

Security B

YEAR (1)	CASH FLOW (2)	PRESENT VALUE FACTOR@ 8% (3)	PRESENT VALUE (PV) (4)	PROPORTION OF TOTAL PV (5)	DURATION = PROPORTION * TIME [(6) = (5) * (1)]
1	20	0.9259	18.518	0.1414	0.1414
2	20	0.8573	17.146	0.1310	0.2620
3	120	0.7938	95.256	0.7276	2.1828
		TOTAL	130.92	1.0000	2.5862

DURATION = 2.5862 YEARS

Security C

YEAR (1)	CASH FLOW (2)	PRESENT VALUE FACTOR@ 8% (3)	PRESENT VALUE (PV) (4)	PROPORTION OF TOTAL PV (5)	DURATION = PROPORTION * TIME [(6) = (5) * (1)]
1	10	0.9259	9.259	0.0881	0.0881
2	10	0.8573	8.573	0.0815	0.1630
3	110	0.7938	87.318	0.8304	2.4912
		TOTAL	105.15	1.0000	2.7423

DURATION = 2.7423 YEARS

VOLATILITY :-

VOLATILITY = DURATION / (1+YIELD)

YIELD = 8%(GIVEN)

SECURITY A = 1.9487/1.08 = 1.80

SECURITY B = 2.5862/1.08 = 2.39

SECURITY C = 2.7423/1.08 = 2.54