Let the market risk be $\sigma_m=28\%$. A portfolio consists of four stocks, all with the same weight ($w_i=0.25$ for all $i$). We also know that $\sigma_a=18\%,\sigma_b=36\%,\sigma_c=22\%,\sigma_d=17\%$ where $\sigma_i$ is the standard deviation of stock $i$ and the portfolio's risk is $\sigma_p=24\%$
Calculate the portfolio beta ?
This is a multiple choice question with choices:(A) 0.71 (B) 0.74 (C) 0.77 (D) 0.79 (E) 0.82
I tried using the formulas $\sigma_p^2=\beta_p^2\sigma_m^2+\sum_{i=1}^n{w_i^2\sigma_{\epsilon,i}^2}$ and $\sigma_i^2=\beta_i^2\sigma_m^2+\sigma_{\epsilon,i}^2$ but i get stuck because I know neither the individual betas nor the error terms' variances.
Am I missing something or is the given data insufficient? Any tips?