Why Equal DV01 Does Not Mean Equal Bond Risk

Summary

The document explains why two bonds with the same DV01, such as short and long tenor bonds, may still carry different risk. DV01 measures the approximate price change for a small change in yield, but translating that sensitivity into risk also requires an estimate of rate volatility. Under a first-order approximation with normally distributed rate changes, the variance of value changes depends on DV01 squared multiplied by yield-change variance.

If the yield curve moves in parallel and the relevant yield volatilities are alike, equal DV01s can imply similar risk. In practice, short and long rates may have different volatilities, so the bonds can have different risks despite equal DV01. This explanation is limited to a linear approximation and does not account for nonparallel curve moves or higher-order effects such as convexity. The answer gives a conceptual relationship rather than empirical evidence or a complete portfolio risk model.

Key ideas

• DV01 measures first-order price sensitivity to a small yield change.
• Equal DV01 implies similar risk only under assumptions about the rate shifts affecting each bond.
• Under a linear model, value-change variance scales with DV01 squared and yield-change variance.
• Short and long rates can have different volatilities, producing different risks for bonds with equal DV01.
• Nonparallel curve shifts and higher-order price effects are outside the simple approximation.

Tags

# Is the risk the same for two different tenor bonds with the same DV01?


# Is the risk the same for two different tenor bonds with the same DV01?












I have two different bonds (for e.g. 1yr and 10yr) that have the same DV01. The notional for 1yr bond is definitely more than the 10yr bond. Is the risk same for the bonds the same because DV01 for both the bonds is the same?

## Answer by Kermittfrog (score 4, accepted)

https://quant.stackexchange.com/a/58547

To a first order of approximation, $dV=\frac{\partial V}{\partial r}dr$, and assuming normally distributed rate shifts, $dr\sim N(0,\sigma_r^2)$, then your risk is -- again to a first oder of approximation -- $\sigma_V^2=DV01^2\sigma_r^2$. Hence, your two risks may be the same if the curve shifts are parallel along the curve.

What is more likely, though, is that you see different rate volatilities at the long and at the short end, $\sigma_{r_1}^2\neq\sigma_{r_{10}}^2$, and hence different risks -- even to a first order of approximation.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.