# Please can someone help me solve this?

#### broboss

##### New Member
We examine the effect of combining investments with positively corrected risks, negatively correlated risks, and uncorrelated risks. A firm is considering a portfolio of assets. The portfolio is composed of two assets which we call “A” and “B”. Let denote the annual rate of return from asset A in the following year, and denote the annual rate of return from asset B in the following year. Suppose that ()=0.15 and ()=0.20 , =0.05 and =0.05, and (,)=0.30.
a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the standard deviation of this return.
b) Replace (,)=0.30 by (,)=0.60 and answer the questions in part a). Do the same for (,)=−0.60,−0.3, and 0.0.
c) Use a spreadsheet to perform the following analysis. Suppose that the fraction of the portfolio that is invested in asset A is (1−). Letting vary from =0.0 to =1.0 in increments of 5% (that is =0.0,0.05,0.10,0.15,...) compute the mean and the standard deviation of the annual rate of return of the portfolio (using the original data for the problem). Notice that the expected return of the portfolio varies (linearly) from 0.15 to 0.20 and the standard deviation varies (non-linearly) from 0.05 to 0.06. Construct a chart plotting the standard deviation as a function of the expected return.
d) Perform the same analysis as in part c) with (,)=0.30 replaced by (,)=0.60,0.0,−0.30, and −0.60.