Problem Analysis:

The question provides:

• Portfolio L offers an expected return $E(R_L) = 20\%$ with a standard deviation $\sigma_L = 10\%$.
• Risk-free asset has a return $R_f = 5\%$.
• An investor allocates 40% of their funds to the risk-free asset and 60% to Portfolio L.

We need to calculate the following for the combined portfolio:

1. Expected return $E(R_P)$
2. Standard deviation $\sigma_P$

Solution:

1. Expected Return: The expected return of the portfolio $E(R_P)$ is calculated as a weighted average of the returns from the risk-free asset and Portfolio L: $E(R_P) = w_f R_f + w_L E(R_L)$ where $w_f = 40\% = 0.4$ (risk-free) and $w_L = 60\% = 0.6$ (Portfolio L).

   Substituting the values: $E(R_P) = (0.4)(5\%) + (0.6)(20\%)$ $E(R_P) = 2\% + 12\% = 14\%$

2. Standard Deviation: Since the risk-free asset has zero risk (standard deviation $\sigma_f = 0$), the portfolio's standard deviation depends only on the risky portion (Portfolio L): $\sigma_P = w_L \cdot \sigma_L$ where $w_L = 0.6$ and $\sigma_L = 10\%$.

   Substituting the values: $\sigma_P = (0.6)(10\%) = 6\%$

Final Results:

• Expected Return: $E(R_P) = 14\%$
• Standard Deviation: $\sigma_P = 6\%$

Let me know if you need a step-by-step explanation or further clarifications!

Related Questions:

1. What happens to the expected return if the investor increases their allocation to Portfolio L?
2. How is the risk-return tradeoff shown graphically in this problem?
3. What would the portfolio standard deviation be if Portfolio L had a higher risk?
4. Can the Capital Market Line (CML) be used to analyze this allocation?
5. How would the investor’s risk preference impact their allocation between Portfolio L and the risk-free asset?

Tip:

When calculating portfolio standard deviation with a risk-free asset, the formula simplifies to the weight of the risky asset times its standard deviation. This helps save time and effort!