The expected returns on securities A and B are $25\%$ and $50\%$ per year respectively. The standard deviations of their returns are $20\%$ and $40\%$ per year respectively. The risk$-$free rate of return is expected to be $10\%$ per year. The covariance between the returns of the two securities has been zero. Required: a$.$ Find out the proportion of security A and B that a risk$-$averse investor should hold in the risky part of his investment portfolio. b$.$ Also, find the expected return and standard deviation of return on the risky part of his portfolio.