Calculate the volatilities for two assets

Question

Problem:

You believe that the expected return of the market is E(rm) = 10% p.a., its volatility is σ_m = 20% p.a. and the risk-free rate of return for both borrowing and lending is r_f = 5%. There exists also two risky assets in the market, namely A and B. You believe that the relation between the returns for these two assets and the market porfolio can be presented by following characteristic line regresión:

(r_i – r_f ) = α_i + β_i(r_m – r_f) + ε_i     i = A,B

In which the coefficient of determination (i.e. R²) is 0.95 for both A and B. The error terms εi’s are uncorrelated. The betas of the two risky assets are β_a = 0.5 and β_b = 1.5. You have also calculated the alphas for these two assets α_a = +1.5% and α_b = -1.5%.

Calculate the volatilities σa and σb for these two assets A and B.