BOND VALUATION
Chapter 6
Bond Valuation
6.5 Duration and Convexity
Problem
Given a 4-yr treasury bond with a face value of $1,000, an annual coupon rate of 3.20%, which had a yield to maturity of 2.53%, this bond makes 2 semi-annual coupon payments. Thus has 8 periods until maturity and we are required to determine what the duration, modified duration, and convexity of this bond is, based on the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR). Also, we are asked to explain an intuitive interpretation of duration.
Methodology
First, I entered the coupon rate for all bonds 1 through 8 and calculated the discount rate/period(r). Then, I used the present value formula (yr-8 cash flow/(1+discount rate/period)^8) to find the bond price. I copied the formulas for present value and duration from the duration and convexity spreadsheet into the corresponding cells. Next, to find the duration I was able to calculate the weight and convexity of liabilities by taking (sum of weight * (time ^2 + time)) / ((1+yield to maturity / # of payments)^2). Finally, I was able to calculate the total assets minus liabilities, the present value of assets minus present value of liabilities, the duration of assets minus duration of liabilities and the convexity of assets minus the convexity of liabilities.
Assumptions
I assumed that this 4-yr Treasury bond had a face value of $1,000 and an annual coupon rate of 3.20%, which had a yield to maturity of 2.53%. The assumption that this bond makes 2 payments per year was a large factor in my calculations and when I accidently entered the wrong number for periods I noticed drastic changes.
Results
The results revealed that for the APR convention, the duration equaled 3.79, the modified duration equaled 3.74, and the convexity resulted in 18.17.
The results revealed that for the EAR convention, the duration equaled 3.79, the modified duration equaled 3.74, but the convexity resulted in 18.18.
Conclusions
I was able to calculate the
Bond Valuation
6.5 Duration and Convexity
Problem
Given a 4-yr treasury bond with a face value of $1,000, an annual coupon rate of 3.20%, which had a yield to maturity of 2.53%, this bond makes 2 semi-annual coupon payments. Thus has 8 periods until maturity and we are required to determine what the duration, modified duration, and convexity of this bond is, based on the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR). Also, we are asked to explain an intuitive interpretation of duration.
Methodology
First, I entered the coupon rate for all bonds 1 through 8 and calculated the discount rate/period(r). Then, I used the present value formula (yr-8 cash flow/(1+discount rate/period)^8) to find the bond price. I copied the formulas for present value and duration from the duration and convexity spreadsheet into the corresponding cells. Next, to find the duration I was able to calculate the weight and convexity of liabilities by taking (sum of weight * (time ^2 + time)) / ((1+yield to maturity / # of payments)^2). Finally, I was able to calculate the total assets minus liabilities, the present value of assets minus present value of liabilities, the duration of assets minus duration of liabilities and the convexity of assets minus the convexity of liabilities.
Assumptions
I assumed that this 4-yr Treasury bond had a face value of $1,000 and an annual coupon rate of 3.20%, which had a yield to maturity of 2.53%. The assumption that this bond makes 2 payments per year was a large factor in my calculations and when I accidently entered the wrong number for periods I noticed drastic changes.
Results
The results revealed that for the APR convention, the duration equaled 3.79, the modified duration equaled 3.74, and the convexity resulted in 18.17.
The results revealed that for the EAR convention, the duration equaled 3.79, the modified duration equaled 3.74, but the convexity resulted in 18.18.
Conclusions
I was able to calculate the