Expected Return Calculation for Portfolio K and L

Case Study

The shares of two companies, K and L have the following expected returns: Prob Return K Return L 0.3 20% 6% 0.5 15% 10% 0.2 5% 12%

If I have a portfolio made up of 60% K and 40% L my expected return will be: Question 5Select one: a. 0.125 b. 0.1238 c. 0.132 d. 0.145

To calculate the expected return of the portfolio made up of 60% in Company K and 40% in Company L, we first need to calculate the expected return for each company based on the given probabilities and returns.

Step 1: Calculate the expected return for Company K

[ E(R_K) = (0.3 \times 20%) + (0.5 \times 15%) + (0.2 \times 5%) ]

Calculating each term:

• (0.3 \times 20% = 0.3 \times 0.20 = 0.06)
• (0.5 \times 15% = 0.5 \times 0.15 = 0.075)
• (0.2 \times 5% = 0.2 \times 0.05 = 0.01)

Now, summing these values:

[ E(R_K) = 0.06 + 0.075 + 0.01 = 0.145 \text{ or } 14.5% ]

Step 2: Calculate the expected return for Company L

[ E(R_L) = (0.3 \times 6%) + (0.5 \times 10%) + (0.2 \times 12%) ]

Calculating each term:

• (0.3 \times 6% = 0.3 \times 0.06 = 0.018)
• (0.5 \times 10% = 0.5 \times 0.10 = 0.05)
• (0.2 \times 12% = 0.2 \times 0.12 = 0.024)

Now, summing these values:

[ E(R_L) = 0.018 + 0.05 + 0.024 = 0.092 \text{ or } 9.2% ]

Step 3: Calculate the expected return of the portfolio

The expected return of the portfolio (E(R_P)) is calculated as follows:

[ E(R_P) = (w_K \times E(R_K)) + (w_L \times E(R_L)) ]

Where:

• (w_K = 0.6) (weight of Company K)
• (w_L = 0.4) (weight of Company L)

Substituting the values:

[ E(R_P) = (0.6 \times 0.145) + (0.4 \times 0.092) ]

Calculating each term:

• (0.6 \times 0.145 = 0.087)
• (0.4 \times 0.092 = 0.0368)

Now, summing these values:

[ E(R_P) = 0.087 + 0.0368 = 0.1238 \text{ or } 12.38% ]

Conclusion

The expected return of the portfolio is 0.1238 or 12.38%.

Thus, the correct answer is:

b. 0.1238