Question

Consider the following information

State       Probability   X       Z

Boom       .25       15%       10%

Normal      .60       10%       9%

Recession   .15       5%       10%

What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Y?  

Answer 1

Return of stock X = 0.25(0.15) + 0.6(0.1) + 0.15(0.05) = 0.105

Return of stock Z = 0.25(0.1) + 0.6(0.09) + 0.15(0.1) = 0.094

Weight of asset X = 6000 / 10000 = 0.6

weight of asser Z = 4000 / 10000 = 0.4

Expected return = 0.6 * 0.105 + 0.4 * 0.094

Expected return = 0.063 + 0.0376

Expected return = 0.1006 or 10.6%

Variance of the portfolio = 0.6 ( 0.105 - 0.1006)² + 0.4(0.094 - 0.1006)²

Variance of the portfolio = 0.000012 + 0.000017

Variance of the portfolio = 0.000029

Standard deviation is square root of variance

Sqaure root od 0.000029 is 0.005424 or 0.5424%

Standard deviation is 0.5424%