Question

The returns of United Railroad Inc. (URI) are listed below, along with the returns on Major Application of Technology (MAT). Economy 1 (with probability .15) gives a return of -14% for URI and -9% for MAT. Economy 2 (with probability .25) gives a return of 16% for URI and 11% for MAT. Economy 3 (with probability .30) gives a return of 22% for URI and 15% for MAT. Economy 4 (with probability .20) gives a return of 7% for URI and 5% for MAT. Economy 5 (with probability .10) gives are return of -2% for URI and -1% for MAT. What is the expected return and standard deviation on a portfolio that is 50% URI and 50% MAT?

Answer 1

State of economy	Probability	Return on URI	Return on MAT	Return on portfolio (0.5 * Return on URI + 0.5 * Return on MAT)
1	0.15	-14%	-9%	-11.50%
2	0.25	16%	11%	13.50%
3	0.3	22%	15%	18.50%
4	0.2	7%	5%	6.00%
5	0.1	-2%	-1%	-1.50%

Therefore, expected return on the portfolio= 0.15*(-11.50%) + 0.25*13.50% + 0.3*18.50% + 0.2*6% + 0.1*(-1.50%) = 8.25%.

The variance of the portfolio is calculated as follows:

0.15*(-11.50%-8.25%)^2 + 0.25*(13.50%-8.25%)^2 + 0.3*(18.50%-8.25%)^2 + 0.2*(6%-8.25%)^2 + 0.1*(-1.50%-8.25%)^2= 0.0107

Therefore, standard deviation of the portfolio= (0.0107)^0.5= 0.1037 = 10.37%.