The question is about an investor who divides their investment between a risk-free asset and a risky portfolio $L$. The given information is:

• Expected return of portfolio $L$ ($E(R_L)$): 20%
• Standard deviation of portfolio $L$ ($\sigma_L$): 10%
• Risk-free rate ($R_f$): 5%
• Investment allocation: 40% in the risk-free asset and 60% in portfolio $L$.

Goal:

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

Step 1: Expected Return of the Portfolio

The formula for the expected return of a combined portfolio is:

$E(R_p) = w_f \cdot R_f + w_L \cdot E(R_L)$

Where:

• $w_f = 40\% = 0.4$ (weight in risk-free asset)
• $w_L = 60\% = 0.6$ (weight in portfolio $L$)
• $R_f = 5\% = 0.05$
• $E(R_L) = 20\% = 0.2$.

Substitute the values:

$E(R_p) = (0.4 \cdot 0.05) + (0.6 \cdot 0.2)$ $E(R_p) = 0.02 + 0.12 = 0.14 \, \text{or} \, 14\%$

Thus, the expected return of the portfolio is 14%.

Step 2: Standard Deviation of the Portfolio

The standard deviation of a portfolio with risk-free assets is proportional to the weight of the risky asset. The formula is:

$\sigma_p = w_L \cdot \sigma_L$

Where:

• $w_L = 60\% = 0.6$
• $\sigma_L = 10\% = 0.1$.

Substitute the values:

$\sigma_p = 0.6 \cdot 0.1$ $\sigma_p = 0.06 \, \text{or} \, 6\%$

Thus, the standard deviation of the portfolio is 6%.

Final Results:

1. Expected return: 14%
2. Standard deviation: 6%

Do you need further explanations or extensions on this solution?

Here are 5 related questions to deepen understanding:

1. How would the expected return and risk change if the investor allocated 100% to portfolio $L$?
2. What happens to the portfolio risk if the weight in the risk-free asset increases to 70%?
3. How do you calculate the Sharpe ratio of this combined portfolio?
4. What is the impact of increasing the standard deviation of portfolio $L$?
5. How can the capital allocation line (CAL) help determine the optimal allocation?

Tip: Remember, combining risk-free assets with risky portfolios reduces overall risk while achieving better risk-adjusted returns.