Question

You have a portfolio which is comprised of 70% of Stock A and 30% of Stock B. What is the expected rate of return on this portfolio?

Rate of Return if State Occurs State of the Economy Probability of State of Economy Stock A Stock B Boom .25 24 % 15 % Normal .65 12 % 12 % Recession .10 -36 % 8 %

Answer 1

What is the expected rate of return on this portfolio?

Answer: 10.85%

Workings

Formula for calculating expected return of the portfolio is as follows;

Expected Return on portfolio = (Px * ERx) + (Py * ERy)                                                                                                             

= (70% * 10.20%) + (30% * 12.35%)

                                                              = 7.14% + 3.705%

                                                              = 10.845%

                                                              = 10.85%

                                               

Where,

Px = Proportion of stock A in the portfolio =70%

Py = Proportion of stock B in the portfolio = 30%

ERx = Expected Return on stock A = 10.20% (see note 1)

ERy = Expected Return on stock B = 12.35% (see not 2)

Note 1 - Expected Return on stock A

Formula for calculating expected return of a stock is provided below;

Expected Return on stock       = Total of (probability * return)

                                                = (.25 * 24%) + (.65 * 12%) + (.10 * -36%)

                                                = .06 + .078 - .036

                                                = .102

                                                = 10.20%

Note 1 - Expected Return on stock B

Formula for calculating expected return of a stock is provided below;

Expected Return on stock       = Total of (probability * return)

                                                = (.25 * 15%) + (.65 * 12%) + (.10 * 8%)

                                                = .0375 + .078 + .008

                                                = .1235

                                                = 12.35%