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fundementals of finance - Math Problem Example
1. Top Choice Investments have given you '2,000,000 to invest for them. The funds can be invested in one or more projects. These projects are all indivisible. The investors require a minimum return of 25% and they are high risk takers.
Portfolio theory suggests that the decision for the combination of stocks in order to maximize the return to the investors should incorporate two measures: the portfolio return of the combination, as well as the portfolio risk which is measured by the standard deviation of the portfolio.
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. ...