You decide to invest in a portfolio consisting of 30 percent Stock A, 30 percent Stock B, and the remainder in Stock C. Based on the following information, what is the expected return of your portfolio? State of Economy Probability of State Return if State Occurs of Economy Stock A Stock B Stock C Recession .17 - 18.8 % - 3.9 % - 22.8 % Normal .45 10.2 % 8.5 % 17.1 % Boom .38 28.6 % 15.8 % 31.7 %

The portfolio return is a function of the weighted average of the individual stocks returns' that form up the portfolio. The formula for portfolio return is,

Portfolio return = wA * rA + wB * rB + ... + wN * rN

Where,

w represents the weight of each stock
r represents the return of each stock

To calculate the expected return of portfolio, we first need to calculate the individual stock returns.

The expected rate of return of individual stocks can be calculated as follows,

r = pA * rA + pB * rB + ... + pN * rN

Where,

pA, pB and so on represents the probability of an event or return to occur

rA, rB and so on are the return in different events

For Stock A

rA = 0.17 * -0.188 + 0.45 * 0.102 + 0.38 * 0.286

rA = 0.12262 or 12.262%

For Stock B

rB = 0.17 * -0.039 + 0.45 * 0.085 + 0.38 * 0.158

rB = 0.09166 or 9.166%

For Stock C

rC = 0.17 * -0.228 + 0.45 * 0.171 + 0.38 * 0.317

rC = 0.15865 or 15.865%

Portfolio return = 0.3 * 0.12262 + 0.3 * 0.09166 + 0.4 * 0.15865

Portfolio return = 0.127744 or 12.7744% rounded off to 12.77%