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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?

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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.

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