When using antithetic variables, the variance of the estimator with $N$ total samples (which forms $N/2$ pairs) becomes $\frac{\sigma^2}{N} (1 + \rho)$, where $\rho$ is the correlation between the antithetic pairs. The new standard error is proportional to $\sqrt{1 + \rho}$. Given $\rho = -0.65$, the ratio of the new standard error to the original is: $\sqrt{1 - 0.65} = \sqrt{0.35} \approx 0.5916$. The percentage change is therefore $(0.5916 - 1) \times 100\% = -40.84\%$.