Yield volatility measures the dispersion of yield changes over time, typically expressed as an annualized standard deviation of daily basis-point changes or percentage changes.
Two conventions are used:
- Basis-point volatility: standard deviation of daily yield changes in bps, annualized by multiplying by sqrt(252). For example, if daily 10Y yield changes have a standard deviation of 5 bps, annualized bp vol is approximately 79 bps.
- Percentage volatility: standard deviation of percentage changes in yield (yield change / yield level). This normalizes for the yield level.
Yield volatility varies across the curve:
- Short-term rates have high basis-point volatility when the Fed is active (rate hikes or cuts) but low volatility between meetings
- Long-term rates have more persistent, moderate volatility driven by term premium shifts, inflation expectations, and supply/demand dynamics
- The belly (5-7Y) often has the highest basis-point volatility due to its sensitivity to both policy expectations and term premium
Yield volatility is a critical input for:
- Duration risk: price volatility = duration x yield volatility. A bond with higher duration but lower yield volatility can be less risky than a shorter-duration bond in a volatile sector.
- Option pricing: Treasury options and swaptions are priced using implied yield volatility
- Trade sizing: position size should be scaled inversely with yield volatility to maintain consistent risk
The Salomon Brothers primer "Understanding Duration and Volatility" provides the foundational framework for combining duration and yield volatility to estimate return volatility.