Use the information below to answer questions 28 to 30. Bond C is a 2-year semi-annual bond with a par value of R1000. It has a yield to maturity of 14% and a coupon rate of 10%. Bond C has a convexity of 19.303. Calculate the total effect of Bond C, if the yield to maturity increases by 1%.Select one:a.-1.54%b.1.94%c.-1.94%d.1.54%
Question
Use the information below to answer questions 28 to 30. Bond C is a 2-year semi-annual bond with a par value of R1000. It has a yield to maturity of 14% and a coupon rate of 10%. Bond C has a convexity of 19.303. Calculate the total effect of Bond C, if the yield to maturity increases by 1%.Select one:a.-1.54%b.1.94%c.-1.94%d.1.54%
Solution
To calculate the total effect of Bond C if the yield to maturity increases by 1%, we need to consider both the duration effect and the convexity effect.
First, let's calculate the duration effect. The formula for the duration effect is:
- (Duration * Change in Yield)
Given that the bond is a 2-year semi-annual bond, the duration is 2 years. The change in yield is an increase of 1%, or 0.01. So, the duration effect is:
- (2 * 0.01) = -0.02 or -2%
Next, let's calculate the convexity effect. The formula for the convexity effect is:
- 0.5 * Convexity * (Change in Yield)^2
Given that the convexity of Bond C is 19.303, and the change in yield is 0.01, the convexity effect is:
- 0.5 * 19.303 * (0.01)^2 = +0.0096515 or +0.96515%
Finally, let's calculate the total effect, which is the sum of the duration effect and the convexity effect:
Total Effect = Duration Effect + Convexity Effect
Total Effect = -2% + 0.96515% = -1.03485%
So, the total effect of Bond C if the yield to maturity increases by 1% is approximately -1.03%. However, this option is not available in the choices. The closest option is -1.54%, but this is not the correct answer based on the calculations. There might be a mistake in the question or the provided options.
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