Bond Duration and Convexity Concepts

Macaulay Duration

• Measures the weighted average time until bond cash flows are received.
• Expressed in years.
• Indicates the time for an investor to recover the bond's price.
• Gauges the bond's sensitivity to interest rate changes.

Modified Duration

• Adjusts Macaulay duration to estimate the percentage change in a bond's price given a 1% change in interest rates.
• A practical measure of interest rate risk.
• Shows how sensitive a bond's price is to interest rate fluctuations.

Convexity

• Measures the curvature or non-linear relationship between bond prices and changes in interest rates.
• Accounts for changes in a bond's duration as interest rates change.
• Bonds with higher convexity are less affected by interest rate volatility, providing more accurate duration estimates for larger rate changes.

Primary Capital Market

• Market where new securities (stocks, bonds) are issued and sold to investors.
• Issuers raise new capital.
• Transactions result in a capital inflow for the issuer.

Secondary Capital Market

• Market where existing securities are traded between investors.
• Provides liquidity and marketability.
• Transactions do not directly affect the issuer’s capital.
• Examples include stock exchanges and over-the-counter (OTC) markets.

Macaulay vs. Modified Duration

• Macaulay Duration: Expressed in years, reflects the weighted average time until bond cash flows are received, primarily a theoretical measure.
• Modified Duration: Adjusted from Macaulay duration to reflect price sensitivity, estimates the percentage price change of a bond in response to a 1% change in interest rates, making it more practical for assessing interest rate risk.

How Weather Derivatives Work

• Financial instruments used to hedge against or speculate on weather-related risks.
• Impacts sectors like agriculture and energy.
• Buyer of a weather derivative sets terms based on a weather index (e.g., CDDs, HDDs, or precipitation levels) for a specific period.
• If the weather outcome differs from the index by a predetermined margin, the seller compensates the buyer.
• They provide a flexible way to manage weather exposure in climates with variable conditions.