INV2601 Assignment 2 (ANSWERS) Semester 1 2025

INV2601
ASSIGNMENT 2 SEMESTER 1 2025

UNIQUE NO.
DUE DATE: 2025

, Question 1: Effective Duration and Effective Convexity Calculation (20 Marks)

Given Data:

 Par Value: R100
 Coupon Rate: 6% per annum (R6 per year)
 Yield to Maturity (YTM): 8.5%
 Maturity: 6 years
 Interest Rate Change: ±100 basis points (±1%)

Step 1: Calculate the Initial Bond Price (P0P_0P0)

The bond price is the present value of future cash flows:

P0=t=1∑6(1+YTM)tC+(1+YTM)6F

Where:

 CCC = Annual coupon payment = 6% of R100 = R6
 FFF = Face value = R100
 YTMYTMYTM = 8.5% = 0.085

P0=(1.085)16+(1.085)26+(1.085)36+(1.085)46+(1.085)56+(1.085)66+(1.085)6100

Step 2: Compute Bond Price for Yield Changes

We calculate bond prices for two scenarios:

1. If YTM decreases by 1% (to 7.5%)
2. If YTM increases by 1% (to 9.5%)

Using the bond pricing formula:

When YTM = 7.5% (P−P_-P−)