The question discusses an investment scenario where the investor splits their funds between a risk-free asset and a portfolio L, which has the following properties:

1. Portfolio L:

   • Expected return ($R_L$) = 20%
   • Standard deviation ($\sigma_L$) = 10%

2. Risk-free asset:

   • Return ($R_f$) = 5%

3. Investment allocation:

   • 40% of funds in the risk-free asset.
   • 60% of funds in Portfolio L.

We aim to find the expected return and the standard deviation of the combined portfolio.

1. Expected Return of the Combined Portfolio

The formula for the expected return of a portfolio combining a risk-free asset and a risky asset is:

$R_p = w_f R_f + w_L R_L$

Where:

• $w_f = 0.4$ (weight in risk-free asset)
• $w_L = 0.6$ (weight in Portfolio L)
• $R_f = 5\% = 0.05$
• $R_L = 20\% = 0.20$

Substitute the values:

$R_p = (0.4 \cdot 0.05) + (0.6 \cdot 0.20)$

$R_p = 0.02 + 0.12 = 0.14 \quad \text{or } 14\%$

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

2. Standard Deviation of the Combined Portfolio

The risk (standard deviation) of a portfolio with a risk-free asset and a risky asset is calculated as:

$\sigma_p = w_L \cdot \sigma_L$

Where:

• $w_L = 0.6$
• $\sigma_L = 10\% = 0.10$

Substitute the values:

$\sigma_p = 0.6 \cdot 0.10 = 0.06 \quad \text{or } 6\%$

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

Final Answers

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

Do you want a more detailed explanation or further questions related to this problem?

Here are 5 related questions for further exploration:

1. How would the portfolio's return change if the risk-free rate increased to 8%?
2. If the investor allocated 50% to the risk-free asset and 50% to portfolio L, what would the new return and standard deviation be?
3. What is the Sharpe ratio of portfolio L given its return and standard deviation?
4. How does increasing the weight of portfolio L affect risk and return?
5. Can you derive the Capital Allocation Line (CAL) equation for this scenario?

Tip: Always consider the trade-off between risk and return when allocating funds between risky and risk-free assets.