Fixed Income Volatility: Convexity

Excel User Guide: Applying Convexity in Bond Investing

Introduction to Using Excel for Convexity

In this guide, we'll explore how to leverage Microsoft Excel to calculate and apply convexity in bond investing. Convexity is a crucial tool that helps us understand the risks associated with changes in interest rates and optimize our bond investments accordingly. Let's dive into a practical example to demonstrate how you can use Excel for effective convexity analysis.

Step 1: Set Up Your Excel Sheet

Assuming the following cell references and sample values:

• Cash Flow: Cell A2 to A5

  • A2: $50
  • A3: $50
  • A4: $50
  • A5: $50

• Time Until Receipt of Cash Flow: Cell B2 to B5

  • B2: 1
  • B3: 2
  • B4: 3
  • B5: 4

• Bond Price: Cell C2

  • C2: $1000

• Yield: Cell D2

  • D2: 0.05 (5%)

Step 2: Calculate Convexity Using Excel Formulas

Now, let's use these cell references in the formula:

=SUMPRODUCT(A2:A5*(B2:B5^2))/C2*(1+D2)^2

Step 1: Set Up Your Excel Sheet

Assuming the following cell references and sample values:

• Cash Flow: Cell A2 to A5

  • A2: $50
  • A3: $50
  • A4: $50
  • A5: $50

• Time Until Receipt of Cash Flow: Cell B2 to B5

  • B2: 1
  • B3: 2
  • B4: 3
  • B5: 4

• Bond Price: Cell C2

  • C2: $1000

• Yield: Cell D2

  • D2: 0.05 (5%)

Step 2: Calculate Convexity Using Excel Formulas

Now, let's use these cell references in the formula:

=SUMPRODUCT(A2:A5*(B2:B5^2))/C2*(1+D2)^2

This formula calculates the convexity based on the example. Adjust the cell references and values according to your bond's specific data.

Step 3: Understand the Convexity Result

The calculated convexity value represents the bond's sensitivity to changes in interest rates, considering the curvature in the price-yield relationship. A higher convexity indicates greater sensitivity.

Step 4: Analyze Positive and Negative Convexity

Divide your analysis into two sections:

Positive Convexity Analysis

• If convexity is positive, your bond benefits from a decreasing interest rate environment.
• Consider holding onto or investing in such bonds during periods of falling interest rates for potential capital gains.

Negative Convexity Analysis

• If convexity is negative, your bond is more vulnerable to rising interest rates.
• Evaluate whether the potential risks outweigh the benefits, especially during periods of increasing interest rates.

Step 5: Incorporate Convexity into Investment Decisions

Enhanced Risk Assessment

• Use convexity to complement duration in assessing interest rate risk.
• Bonds with positive convexity can act as a hedge during falling interest rates, providing a cushion against potential losses.

Portfolio Optimization

• Optimize your portfolio by balancing positive and negative convexity exposures.
• Consider the overall convexity profile when constructing a diversified bond portfolio.

Step 6: Monitor Changing Market Conditions

Be aware that convexity calculations assume a stable relationship between yields and prices. Regularly update your Excel sheet to reflect changing market conditions, shifts in interest rate expectations, or increased market volatility.

Conclusion

This Excel user guide illustrates a practical approach to calculating and using convexity for informed bond investing decisions. By incorporating convexity into your Excel analysis, you gain a deeper understanding of interest rate risk, enhance risk assessment, and optimize your bond portfolio for varying market conditions. Remember to adapt your strategy based on the calculated convexity, and regularly update your Excel sheet to stay informed about changing market dynamics.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.