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:
Yield volatility varies across the curve:
Yield volatility is a critical input for:
The Salomon Brothers primer "Understanding Duration and Volatility" provides the foundational framework for combining duration and yield volatility to estimate return volatility.
The choice between basis point volatility and percentage volatility is not cosmetic. The two can tell opposite stories about the same market.
Basis point volatility, sometimes called normal volatility, assumes a yield is as likely to move 10 bps at 1% as at 6%. Percentage volatility, sometimes called lognormal volatility, assumes the size of a move scales with the level of the yield.
The difference shows up hardest at low yields. A yield falling from 0.50% to 0.40% is a 10 bp move and a 20% move. Measured in basis points the market looks calm. Measured in percentage terms it looks violent. Neither reading is wrong, and reporting only one of them at low yield levels is misleading.
The market's own preference is settled. Rate options are quoted in basis point volatility, and the convention became near universal after yields approached and then crossed zero in several currencies, since a percentage change is undefined at a yield of zero and meaningless below it.
The practical rule is to use basis point volatility for anything touching risk or option pricing, and to state which convention is in use whenever the number is published.
The page above describes realized volatility, which is calculated from yield changes that have already happened. The other kind is implied volatility, which is extracted from the price of an option.
The two answer different questions. Realized volatility says how much yields moved. Implied volatility says how much the market is charging to insure against future movement.
They diverge in a systematic way. Implied volatility usually sits above subsequent realized volatility, because an option seller demands compensation for taking the risk. The gap widens before events with known dates, such as an FOMC meeting or a major data release, and collapses once the event passes.
That collapse is worth understanding for anyone reading a volatility chart. A sharp fall in implied volatility on the day after a meeting is not a sign that the market calmed down. It is the removal of an event premium that was scheduled to expire.
The MOVE index is the most cited measure of implied Treasury volatility. It combines options on several tenors into a single number, weighted toward the 10 Yr, and is quoted in annualized basis points.
Volatility is not uniform along the curve, and where it concentrates says something about what is driving the market.
When policy is the dominant force, volatility concentrates in the front end and the belly. Those tenors carry the expected path, so every revision to the policy outlook reprices them. The long end moves less, because a change to the next two years is a small part of a thirty year average.
When inflation or fiscal supply dominates, the pattern reverses. Volatility concentrates at the long end, where the term premium sits, and the front end stays anchored to a policy rate that is not in question.
Reading the shape of volatility across tenors is therefore a diagnostic. A market that has become volatile at the back and quiet at the front has stopped arguing about the Federal Reserve and started arguing about something else.
For position sizing, the relevant number is not yield volatility alone but its product with DV01. A long bond with modest yield volatility can carry more dollar risk than a short note with high yield volatility, because its price responds so much more to each basis point.
Because basis point quoting stays well behaved at any yield level, including zero and below. Percentage volatility requires dividing by the yield, which produces enormous values as the yield approaches zero and breaks entirely at negative yields. The rates options market standardized on basis point quoting for this reason.
Not by itself. Portfolio risk is roughly the product of yield volatility and dollar duration, so a portfolio can reduce risk in a volatile market by shortening duration. Volatility also cuts both ways for a holder of positive convexity, since a convex position gains more from large moves down in yield than it loses from equally large moves up.
Convexity is more valuable when volatility is high, because its benefit comes from large yield moves in either direction. That is why convexity is not free. In a high volatility environment investors bid up convex bonds and accept lower yields on them, and the size of that concession tracks implied volatility.