Answer:
The expected return of the portfolio is 0.1256.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
State Probability Stock A Return Stock B Return Stock C Return
Boom 0.32 0.22 0 -0.07
Bust 0.68 0.02 0.21 0.24
What is the expected return of a portfolio that has invested $9,805 in Stock A, $18,289 in Stock B, and $6,201 in Stock C? (Hint: calculate weights of each stock first). Enter the answer with 4 decimals (e.g. 0.1234).
The explanation of the answer is now given as follows:
Step 1. Calculation of weights of each stock
Total investment = Amount invested in A + Amount invested in B + Amount invested in C = $9,805 + $18,289 + $6,201 = $34,295
Weight of stock A = Amount invested in A / Total investment = $9,805 / $34,295 = 0.2859
Weight of stock B = Amount invested in B / Total investment = $18,289 / $34,295 = 0.5333
Weight of stock C = Amount invested in C / Total investment = $6,201 / $34,295 = 0.1808
Step 2. Calculation of expected return of stock
Expected return of a stock = (Probability during Boom * Stock return during Boom) + (Probability during Bust * Stock return during Bust)
Expected return of stock A = (0.32 * 0.22) + (0.68 * 0.02) = 0.0840
Expected return of stock B = (0.32 * 0) + (0.68 * 0.21) = 0.1428
Expected return of stock C = (0.32 * (-0.07)) + (0.68 * 0.24) = 0.1408
Step 3. Calculation of expected return of the portfolio
Expected return of the portfolio = (Weight of stock A * Expected return of stock A) + (Weight of stock B * Expected return of stock B) + (Weight of stock C * Expected return of stock C) = (0.2859 * 0.0840) + (0.5333 * 0.1428) + (0.1808 * 0.1408) = 0.1256
Therefore, the expected return of the portfolio is 0.1256.