The question describes a portfolio allocation problem where the investor combines a risk-free asset and a risky portfolio. Here's the breakdown of the information provided:

Given:

1. Expected Return of Portfolio L: $E(R_L) = 20\% = 0.20$
2. Standard Deviation of Portfolio L: $\sigma_L = 10\% = 0.10$
3. Risk-Free Rate: $R_f = 5\% = 0.05$
4. Investment Allocation:
   • 40% in risk-free asset: $w_f = 0.40$
   • 60% in portfolio L: $w_L = 0.60$

We are to calculate the expected return and the standard deviation of the combined portfolio.

1. Expected Return of the Portfolio

The expected return of a combined portfolio is given by: $E(R_P) = w_f R_f + w_L E(R_L)$

Substitute the values: $E(R_P) = (0.40)(0.05) + (0.60)(0.20)$

$E(R_P) = 0.02 + 0.12 = 0.14 \, \text{or} \, 14\%$

2. Standard Deviation of the Portfolio

The risk-free asset has no standard deviation (zero risk). Therefore, the standard deviation of the combined portfolio depends only on the risky portion $w_L \sigma_L$, calculated as: $\sigma_P = w_L \sigma_L$

Substitute the values: $\sigma_P = (0.60)(0.10)$

$\sigma_P = 0.06 \, \text{or} \, 6\%$

Final Answer:

1. Expected Return: $14\%$
2. Standard Deviation: $6\%$

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Here are 5 related questions you might find useful:

1. How would the expected return change if the allocation to the risky portfolio was increased to 80%?
2. What happens to the portfolio's standard deviation if the risk-free rate changes?
3. How do we calculate the Sharpe ratio for this combined portfolio?
4. What is the role of the capital allocation line (CAL) in determining the optimal allocation?
5. How does the portfolio’s risk and return change if the standard deviation of Portfolio L increases?

Tip: Combining a risk-free asset with a risky portfolio helps investors balance risk and return based on their risk tolerance.