Interest Rates and Bond Prices Sensitivity

Focus: The relationship between interest rates and bond prices.
Key Factors:
- Coupon rate
- Time to maturity
- Sensitivity of bonds to interest rate changes

Inverse relationship:
- When interest rates rise, bond prices fall.
- When interest rates fall, bond prices rise.
Interest rate risk:
- Definition: The risk that rising interest rates will negatively impact the value of a bond.
- Exists even in riskless treasury bonds, as they are still affected by market interest rate fluctuations.

Factors impacting sensitivity:
- Time to Maturity:
- Longer maturities lead to higher sensitivity to interest rate changes.
- Coupon Rate:
- Lower coupon rates correlate with greater interest rate risk.
- Yield to Maturity:
- Lower yield to maturity indicates higher sensitivity to interest rate changes.
Direct relationship between time to maturity and price sensitivity.
Inverse relationship between coupon rates, yield to maturity, and price sensitivity.

Bond A:
- Term: 8 years
Bond B:
- Term: 10 years
Market Scenario:
- Market yields increase by 50 basis points:
- Price of Bond B decreases by 3.54%
- Price of Bond A decreases by 3.01%
Conclusion: Bonds with longer maturities exhibit greater price sensitivity to interest rate changes.
Bonds A and C:
- Identical except for yield to maturity (C has lower yield).
- Market scenario:
- Increase in market interest rates by 50 basis points leads to a greater price impact on Bond C.
- Illustrates an indirect relationship between yield to maturity and interest rate sensitivity.
Bond D:
- Similar to Bond A but has a lower coupon rate of 6.5%.
- Demonstrates inverse relationship: Lower coupon rates increase price sensitivity.

Macaulay Duration:
- Definition: The weighted average time it takes to recoup the price paid for a bond.
- Lower values indicate less price sensitivity.
- Note: Difficult to calculate and communicate to non-experts; not covered in detail here.
Modified Duration:
- Definition: The expected price change of a bond in response to a 1% or 100 basis point change in interest rates.
- Example:
- For a bond with modified duration of 3.5:
  - Price decreases by 3.5% for a 1% rise in interest rates.
  - Price increases by 3.5% for a 1% drop in interest rates.
- Calculation:
- Modified duration = Macaulay duration / (1 + yield to maturity)
Price Change Calculation:
- If the CIO expects a rise in interest rates by 75 basis points:
- Expected price change = Negative modified duration (3.5) * 75 basis points = -2.63%.
Limitations:
- Duration is effective for assessing small interest rate changes but overestimates the impact of large increases and underestimates large decreases.

Definition: A measure that captures the curvature of the price-yield relationship in bond pricing.
Purpose: Adjust for the inaccuracies in duration assessment during interest rate shocks.
Calculation Example:
- Assume convexity of the bond = 15, with interest rates expected to rise by 200 basis points.
- Price change from duration prediction: -7% (based on duration of 3.5).
- Adjusted price change due to convexity:
- Convexity contribution = (1/2) * Convexity * (Change in yield)^2
- Change in yield = 0.02 (200 basis points)
- Calculation: 0.5 * 15 * (0.02)^2 = 0.3% (this reduces the estimated decline).
- Final adjusted price decline:
- From -7% to 6.7%, a key correction based on convexity.

Interest Rate Risk:
- Definition: The risk that increases in market interest rates will lead to a decrease in the value of bonds held.
Macaulay Duration:
- Definition: The average time to recoup the original investment in a bond, critical for flexibility in pricing.
Modified Duration:
- Definition: The expected change in bond price for a 1% shift in interest rates, the primary measure for small movements.
Convexity:
- Definition: Accounts for the non-linear relationship between bond prices and interest rate changes, particularly useful for larger shocks.