Price Risk
Price risk (also called interest rate risk) is the risk that the market value of a bond or fixed-income portfolio falls due to a rise in interest rates. Its sensitivity to a yield change \Delta j is quantified by Modified Duration D_{Mod}.
\frac{\Delta P}{P} \approx -D_{Mod} \cdot \Delta j
- Bond prices and yields move in opposite directions, so an unexpected yield increase causes an immediate capital loss for an investor who must sell before maturity.
- Bonds with longer Macaulay Duration carry more price risk: a 1% yield rise causes a much larger percentage price drop for a 20-year bond than for a 2-year bond.
- Price risk is the complement of Reinvestment Risk — strategies that reduce one typically increase the other.
- Redington Immunization and Cash Flow Matching manage price risk (and reinvestment risk) for institutions with known future liabilities.
Price Risk and Duration Portfolio A has modified duration 10 years; Portfolio B has modified duration 2 years. Both are worth $
1{,}000{,}000. Yields rise by 0.5% (\Delta j = 0.005). Estimate the loss in value for each portfolio.Answer
\Delta P_A \approx -(10)(1{,}000{,}000)(0.005) = -\$50{,}000\Delta P_B \approx -(2)(1{,}000{,}000)(0.005) = -\$10{,}000Portfolio A loses five times as much value as Portfolio B for the same rate move, illustrating that longer-duration portfolios bear substantially more price risk. An investor with a 2-year horizon should prefer Portfolio B.