Calculate the durations and volatilities of securities A B a

Calculate the durations and volatilities of securities A, B, and C. Their cash flows are shown below. The interest rate is 10%. (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 50 50 60 years B 30 30 140 years C 20 20 130 years

Solution

Duration = Present value of a bond\'s cash flows, weighted by length of time to receipt and divided by the bond\'s current market value.

Duration of Bond A

Period Cash Flow Period X Cash Flow Discounting Factor @ 10% PV of Cash Flows

1 50 50 0.909 45.45

2 50 100 0.8264 82.64

3 60 180 0.751 135.24

Total 263.33

Assuming Bond\'s Current Market Value to be $100 Duration of Bond A = 263.33/100 = 2.63 yrs

Similarly Duration of Bond B & C can also be calculated

Duration of Bond B= 392.41/100 = 3.92yrs

Duration of Bond C= 344.25/100 = 3.44yrs