Question

The Macaulay convexity of a single cash flow is 64 at an annual effective interest rate of 10%. Calculate the modified duration of this single cash flow.
A 7.3
B 7.6
C 8.0
D 8.4
E. 8.8

Answer 1

Answer:

A 7.3

Explanation:

Macaulay Convexity = 64, as about a single cash flow

Since it is a single cash flows, convexity is square the Macaulay duration of the bond.

Convexity = √Macaulay duration.

So, Macaulay duration = Convexity^(1/2)

Macaulay duration = Convexity^(0.5)

Macaulay duration = 64^0.5

Macaulay duration = 8

So, the Macaulay duration = 8 years

Now, Modified duration = Macaulay duration/(1+yield)

Modified duration = 8/(1+0.1)

Modified duration = 8/1.1

Modified duration = 7.27273

Modified duration = 7.3 years