Duración de Macaulay

Calculating Macaulay Duration of a Bond

Introduction to Macaulay Duration

• The session begins with an explanation of calculating the average duration of a bond, specifically focusing on the Macaulay duration formula.

• A nominal bond example is introduced, valued at 1000 with a coupon rate of 10%. The cash flows and payment dates are outlined for clarity.

Cash Flow Calculation

• Cash flows from the bond are structured over five years, starting from January 1, 2011. Each year will yield a coupon payment based on the stated interest rate.

• The total cash flow includes annual coupon payments and the return of principal at maturity, which is also noted in the calculations.

Yield to Maturity (YTM) Calculation

• The Yield to Maturity (YTM) for this standard bond is calculated as 10%, confirming that it aligns with the coupon rate. This step involves discounting each cash flow back to present value using YTM.

• A summation of discounted cash flows provides confirmation that the price equals 1000, validating initial assumptions about pricing and yields.

Duration Calculation Methods

Method One: Direct Formula Application

• To calculate duration using method one, the numerator consists of weighted cash flows divided by total price; this results in a duration expressed in years.

Method Two: Financial Function Assistant

• An alternative approach utilizes financial function assistants to compute duration directly by inputting relevant parameters such as purchase date, maturity date, coupon rate, YTM, and payment frequency. Both methods yield consistent results for verification purposes.

Modified Duration Calculation

Understanding Modified Duration

• Modified duration is derived by dividing Macaulay duration by (1 + YTM), providing insight into interest rate sensitivity without units tied to years anymore. This calculation can also be performed using financial functions for accuracy checks against manual calculations.

Conclusion on Bond Characteristics

• The final analysis reveals that while the bond matures in five years, its calculated Macaulay duration is slightly less than five due to earlier cash flow weights affecting overall averages—highlighting important characteristics regarding timing and risk assessment in fixed income investments.