Since both the covariance and correlation between the stock index and the fund are unknown, we will apply CAPM to find the fund’s beta.

$$E(R_i) = R_f + \beta_i (R_m - R_f)$$

where:
$E(R_i)$ is the expected annual return of the fund i
$\beta_i$ is the beta of the fund with the market index
$R_f$ is the risk-free rate per annum
$R_m$ is the expected annual return of the market (in this case, the stock index)

Therefore,

$$\begin{aligned} 4.5\% &= 3.0\% + \beta_i (5.5\% - 3.0\%) \\ (4.5\% - 3.0\%) &= \beta_i (5.5\% - 3.0\%) \\ \Rightarrow \beta_i &= \frac{(4.5\% - 3.0\%)}{(5.5\% - 3.0\%)} = 0.6 \end{aligned}$$