The Capital Market Line (CML) represents the set of efficient portfolios in the market, offering the highest expected return for a given level of risk. It is derived from the combination of the risk-free asset and the market portfolio. To calculate the CML, we need to find the optimal combination of the risk-free asset and the market portfolio.
Given the information:
- Weight of Security A in the market portfolio (WA) = 40%
- Weight of Security B in the market portfolio (WB) = 60%
- Expected return of Security A (RA) = 10%
- Expected return of Security B (RB) = 15%
- Standard deviation of Security A (σA) = 20%
- Standard deviation of Security B (σB) = 28%
- Correlation between the assets (ρ) = 0.3
- Risk-free rate (RF) = 5%
The expected return of the market portfolio (RM) can be calculated as the weighted average of the expected returns of the individual securities in the portfolio:
RM = WA * RA + WB * RB
RM = 0.4 * 10% + 0.6 * 15%
RM = 4% + 9%
RM = 13%
Next, we calculate the standard deviation of the market portfolio (σM) using the formula:
σM = √(WA^2 * σA^2 + WB^2 * σB^2 + 2 * WA * WB * ρ * σA * σB)
σM = √(0.4^2 * 0.2^2 + 0.6^2 * 0.28^2 + 2 * 0.4 * 0.6 * 0.3 * 0.2 * 0.28)
σM = √(0.016 + 0.062208 + 0.02016)
σM = √0.098368
σM ≈ 0.3138 or 31.38%
Now, we can calculate the expected excess return of the market portfolio (RM - RF):
Expected excess return = RM - RF = 13% - 5% = 8%
The slope of the CML, which represents the risk premium, is given by the formula:
Slope of CML = (RM - RF) / σM
Slope of CML = 8% / 0.3138 ≈ 0.2549
The y-intercept of the CML is the risk-free rate, so the equation of the CML is:
Expected return (E) = RF + Slope of CML * σ
E = 0.05 + 0.2549 * σ
Thus, the Capital Market Line for the given portfolio is E = 0.05 + 0.2549 * σ. This line represents the efficient portfolios that offer the highest expected return for each level of risk, and any portfolio lying above the CML is considered inefficient. Investors can use the CML to make informed decisions about their investment choices based on their risk tolerance and return objectives.