For a species to undergo disproportionation, the standard reduction potential of the reaction to its right (reduction) must be greater than the standard reduction potential of the reaction to its left (from which it was formed by reduction). In other words, $E^\circ_{\text{right}} > E^\circ_{\text{left}}$. Based on standard Latimer diagram values for bromine in acidic medium, the reduction potential of $\text{HBrO}$ to $\text{Br}_2$ is $+1.59 \text{ V}$, which is greater than the reduction potential of $\text{BrO}_3^-$ to $\text{HBrO}$ ($+1.50 \text{ V}$). Therefore, $\text{HBrO}$ is thermodynamically unstable and spontaneously disproportionates into $\text{BrO}_3^-$ and $\text{Br}_2$.