gen-define-duration-and-interest-rate-risk-and-give-one-short-wo-d0b0

Define duration and interest-rate risk and give one short worked example.

# Duration and Interest-Rate Risk ## Definitions **Duration** is a measure of the weighted average time it takes to receive all cash flows from a bond, measured in years. It indicates a bond's price sensitivity to interest rate changes. **Interest-Rate Risk** is the risk that a bond's value will decline due to rising interest rates. Since bond prices and interest rates move inversely, when rates rise, existing bond prices fall (and vice versa). ## Key Relationship The approximate percentage change in bond price is: **% Price Change ≈ -Duration × Change in Interest Rates** --- ## Worked Example **Given:** - A bond with a duration of 5 years - Current price: $1,000 - Interest rates increase from 4% to 5% (change of +1% or 0.01) **Calculate the approximate price change:** % Price Change ≈ -Duration × Δi % Price Change ≈ -5 × 0.01 % Price Change ≈ -0.05 or **-5%** **New bond price:** New Price = $1,000 × (1 - 0.05) = **$950** **Interpretation:** The bond with a 5-year duration loses approximately 5% of its value (or $50) when interest rates rise by 1%. The longer the duration, the greater the interest-rate risk, meaning the bond price is more sensitive to rate changes.