An investor has a portfolio with 30% invested in gold stocks, and 70% in industrial stocks. It is expected that gold stocks will provide a 4% return in a good economy and 18% in a poor economy. Industrial stocks are expected to provide 9% return in a good economy and -9% in a poor economy. The probability of a good economy is 40% and 60% in a poor economy. Given this information, calculate the expected return on the portfolio.
A) 1.46%
B) 2.46%
C) 3.46%
D) 4.46%
E) 5.46%

Question

Quizplus · Accepted Answer

The expected return on the portfolio can be calculated by taking the weighted average of the expected returns of gold and industrial stocks in both economic scenarios, multiplied by the probability of each scenario. For a good economy, the expected return is: $$ (0.30 \times 4\%) + (0.70 \times 9\%) = 1.2\% + 6.3\% = 7.5\% $$For a poor economy, the expected return is: $$ (0.30 \times 18\%) + (0.70 \times -9\%) = 5.4\% - 6.3\% = -0.9\% $$The overall expected return is: $$ (40\% \times 7.5\%) + (60\% \times -0.9\%) = 3\% - 0.54\% = 2.46\% $$

An Investor Has a Portfolio with 30% Invested in Gold