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 expected return of the portfolio is 0.1256.

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.

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