The same goes for stock b. By adding the product of the proportion and the return of these two stocks that form the combination, we get the portfolio return of 24.4%
In order to get the risk of the combination of projects a and b, we use the formula for 'p=sqrt (wa2'a2 + wb2'b2 + 2wawb'ab'a'b), where we get the products of the variances of the proportions and the individual risks, adding them and adding them to the last figure which incorporates their correlation. With projects a and b's correlation of 0.7, we get a risk of .081191.
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.
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 limit 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 is already eliminated from the choices.