The mutual fund manager should aim for an average beta of 2.3636 for the new stocks added to the portfolio to achieve the desired required return of 14% on the entire portfolio.
To calculate the average beta of the new stocks that the mutual fund manager should add to the portfolio, we need to apply the concept of portfolio beta, which is a weighted average of the individual betas of the securities within the portfolio. Given the portfolio's current size and beta, as well as the risk-free rate and market risk premium, we can calculate the required average beta of the new investments necessary to achieve the desired required return on the entire portfolio.
The existing portfolio has a beta of 2.0 and a value of $80 million. With additional funds of $20 million to be invested, the total portfolio value will be $100 million. The desired required return on the entire portfolio is 14%, which we can relate to the Capital Asset Pricing Model (CAPM) to calculate the required average beta for the new investment.
The CAPM equation is: Required return = Risk-free rate + Beta x Market risk premium. We rearrange this equation to solve for the required beta. After the calculations, the average beta needed for the new stocks to achieve the overall required return of 14% is 2.3636, which is closest to option E.