Weight for a riskless mix of two opposite assets

Asset 1 has expected return $4\%$ and variance $0.15$; asset 2 has expected return $2\%$ and variance $0.04$; their returns have correlation $-1$. You form a portfolio with weights $w_1$ and $w_2$, $w_1+w_2=1$, so that it has zero variance. Find $w_1$ to two decimals.

$w_1\approx0.34$. With $\rho=-1$ the portfolio volatility is $|w_1\sigma_1-w_2\sigma_2|$, which vanishes when $w_1=\frac{\sigma_2}{\sigma_1+\sigma_2}=\frac{0.2}{0.387+0.2}\approx0.34$. Expected returns play no role.