Question

Consider the following information:

State Probability Stock A Stock B Stock C

Boom 0.65 -0.11 0.23 0.26

Bust 0.35 0.16 0.03 -0.08

What is the expected return on an equally weighted portfolio of these three stocks? (Hint: Equally means that each stock has the same weight. Given that there are only 3 stocks, each has a weight of 1/3) Enter the answer with 4 decimals (e.g. 0.1234).

Answer 1

Calculate the return of portfolio each state of economy

return of portfolio = return of each Assets / number of Assets

Return of portfolio Boom = - 0.11 + 0.23 + 0.26 /3= 0.38/3

Return of portfolio Boom=12.67%

Alternative :

Weights: = 1/3= 0.33333

0.33333× -0.11 + 0.33333 × 0.23 + 0.33333 × 0.26= (- 0.03667 + 0.07667 + 0.08667= 12.67% or 0.1267

Return of portfolio Bust = 0.16 + 0.03 + (-0.08)= 0.11/3

Return of portfolio Bust = 3.67% or 0.0367

Alternative = 0.33333 × 0.16 + 0.3333× 0.03 + 0.33333 × -0.08= 0.05333 + 0.00999 + (0.02667)= 3.67%

Expected return of portfolio = probability of Boom × return of Boom + probability of Bust × return of Bust

Expected return of portfolio = 0.65 × 0.1267 + 0.35 × 0.0367 =0.082355 + 0.012845

Expected return of portfolio = 0.0952 or 9.52%