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Teacherbot 04 Jul, 16:42:56

Per calcolare la duration del titolo, dobbiamo prima calcolare il valore attuale di ogni flusso di cassa utilizzando il tasso di rendimento del 2%.

Il valore attuale del primo flusso di cassa (-P) al tempo 0 è semplicemente -P.

Il valore attuale del secondo flusso di cassa (1000) al tempo 2 è dato da 1000 / (1 + 0.02)^2 = 961.17.

Il valore attuale del terzo flusso di cassa (150.28) al tempo 4 è dato da 150.28 / (1 + 0.02)^4 = 135.92.

Ora possiamo calcolare la duration utilizzando la formula:

D = (2 * 961.17 * 2 + 4 * 135.92) / (961.17 + 961.17 + 135.92)

D = (1922.34 + 543.68) / 2058.26

D = 2466.02 / 2058.26

D = 1.20

Quindi, la duration del titolo è 1.20.

You 04 Jul, 16:43:11

Make this more complex

Teacherbot 04 Jul, 16:43:11

To calculate the duration of the bond, we need to consider the present value of each cash flow at the given yield rate of 2%.

The present value of the first cash flow (-P) at time 0 is simply -P.

The present value of the second cash flow (1000) at time 2 is given by 1000 / (1 + 0.02)^2 = 961.17.

The present value of the third cash flow (150.28) at time 4 is given by 150.28 / (1 + 0.02)^4 = 135.92.

Now, let’s calculate the weighted average of the present values to determine the duration.

The weighted average of the present values is calculated as follows:

Weighted average = (Present value of cash flow 1 * Time of cash flow 1 + Present value of cash flow 2 * Time of cash flow 2 + Present value of cash flow 3 * Time of cash flow 3) / (Present value of cash flow 1 + Present value of cash flow 2 + Present value of cash flow 3)

Weighted average = (-P * 0 + 961.17 * 2 + 135.92 * 4) / (-P + 961.17 + 135.92)

Now, let’s assume P = 100. Substituting this value into the equation:

Weighted average = (-100 * 0 + 961.17 * 2 + 135.92 * 4) / (-100 + 961.17 + 135.92)

Weighted average = (1922.34 + 543.68) / 997.09

Weighted average = 2466.02 / 997.09

Weighted average = 2.47

Therefore, the duration of the bond is 2.47.