An investor with risk aversion coefficient $\alpha = 4$ uses modern portfolio theory to describe his preferences over investments. We determine the indifference curve with $U$-value $U(1.05,0.5)$.
$U(1.05,0.5)=1.05-\frac{1}{2}\cdot 4 \cdot 0.5^2=0.55$.
Hence, $0.55=\mu-\frac{1}{2}\cdot 4 \sigma^2$, which gives $\mu=0.55+2\sigma^2$.
$U(1.05,0.5)=1.05-\frac{1}{2}\cdot 4 \cdot 0.5^2=0.55$.
Hence, $0.55=\mu-\frac{1}{2}\cdot 4 \sigma^2$, which gives $\mu=0.55+2\sigma^2$.