Fundamentals of Corporate Finance

By applying the same formula for projects b and c, we get the portfolio return of 29.2%, higher than the combination of projects a and b. The portfolio standard deviation, on the other hand, is 0.119917-the higher risk accompanying the higher expected return for the portfolio.
Combinations of projects b and d have the highest return at 31.6%, with the highest risk of .120216 compared to the other two combinations. This higher return, when expected to have a drastic counterpart in the increase in risk is offset by the correlation of the two projects. This combination offers the lowest correlation at 0.3, which means that the projects’ returns are not strongly correlated to the movement of the other, although the positive sign of correlation suggests the same direction of the two stocks in terms of movement.
Recommendation
The four projects offer seven possible combinations. however, because these projects are indivisible, the only three possible combinations left which are possible within the 2,000,000 limits are the combinations a and b, b and c, and b and d. These three combinations are assessed according to their returns and risks, measuring the returns by getting the proportion and weighted return, and then getting the risk by getting the portfolio standard deviation. Because the investors require a minimum return of 25%, combination of projects a and b are already eliminated from the choices. When both the combination of projects b and c, and projects b and d offer returns higher than 25%, the combination of projects b and d should be chosen because such portfolio provides the highest returns. High returns definitely accompany higher risks, but as it is stated in the question that the investors are high-risk takers, they can opt for the combination which maximizes the value of their investment, which is the combination of projects b and d. This combination also offers the lowest correlation of all the seven combinations, which maximizes the effect of diversification.