Final answer:
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.