D) Following is forecast for economic situation and Rachel's portfolio returns next year, calculate the

expected return, variance and standard deviation of the portfolio. (4 marks)

State of economy Probability Rate of returns

Mild Recession 0.35 - 5%

Growth 0.45 15%

Strong Growth 0.20 30%

Expected return = 15.25%

Variance = 80.31

Standard deviation = 8.961

Explanation:

Expected value of return (Er) =

(0.35 * 5%) + (0.45 * 15%) + (0.20 * 30%) = 15.25 %

Variance and standard deviation

Outcome Rate Deviation Variance

r - Er (r-Er) ^2. P

Mild 5 - 10.25 36.771875

Growth 15 - 0.25 0.028125

Strong 30 14.75 43.5125

Total 80.3125

Variance = 80.3125

Standard deviation = √variance = √80.3125

= 8.96

Expected return = 15.25%

Variance = 80.31

Standard deviation = 8.961