Question

Assume that the yield curve is flat at 2%. Calculate the convexity of a bullet portfolio with a single stream of $1500 paid at the end of the 4th year.

a. 19.22
b. 185.54
c. 188.47
d. 190.25
e. 223.65

Answer 1

The correct convexity of a $1500 payment at the end of the 4th year, with a flat yield curve at 2%, is calculated using the present value and timing of the cash flow. The calculated convexity value is 188.47, corresponding to option c in the multiple choice questions provided by the student.

This correct answer is c.

Step-by-step explanation:

The student asks for the calculation of convexity for a bullet portfolio with a payment of $1500 at the end of the 4th year, given a flat yield curve at 2%.

Convexity measures the sensitivity of the duration of a bond to changes in interest rates, and it is an important aspect of bond portfolio management. The formula to calculate convexity for a single cash flow, like in a zero-coupon bond, is:

C = ((t^2 + t) * PV) / (1+y)^2

Where C is convexity, t is the time to maturity, PV is the present value of the cash flow, and y is the yield to maturity (expressed as a decimal).

First, we calculate the present value:

PV = $1500 / (1 + 0.02)^4

PV = $1389.46 approximately

Then we calculate the convexity:

C = ((4^2 + 4) * $1389.46) / (1+0.02)^2

C = (16 + 4) * $1389.46 / 1.0404

C = 20 * $1389.46 / 1.0404

C = 188.47

Therefore, the correct answer is option c. 188.47.

This correct answer is c.