shown that Var[Rp] =w, Cov[R, R], Pip], that is, the variance of a portfolio equals the weighted average covariance of each asset with the portfolio. (a) Based on this equation, show that SD[R] - i=1 w. Pip SD[R], where pi, is the correlation between the asset i's return with the portfolio return. (b) Based on the equation in (a), prove the argument that "the volatility of a portfolio is less than the weighted average volatility of assets in the portfolio." E (c) Now consider asset 1 in the portfolio and assume Pip 0.5 and SDR] = 40%, both of which are fixed. If we increase w, (the portion of wealth invested in asset 1), by 1% (i.e., if w used to be 4%, now it is 5%), how much will SD [R,] change according to the equation you've proved in (a)? (d) Dropping the assumption that pip is always 0.5. If we increase w. how will pp change in reality and why?