Financial Risk Manager Part 1

Explanation

This question uses the Capital Market Line (CML) formula to calculate the expected return of a portfolio consisting of a risk-free asset and the market portfolio.

CML Formula:

$R_p = R_f + \left( \frac{R_m - R_f}{\sigma_m} \right) \sigma_p$

Where:

• $R_p$ = Expected portfolio return
• $R_f$ = Risk-free rate = 5%
• $R_m$ = Expected market return = 25%
• $\sigma_m$ = Standard deviation of market portfolio = 10%
• $\sigma_p$ = Standard deviation of portfolio = 5%

Calculation:

$E(R_p) = 5 + \frac{(25 - 5)}{10} \times 5$ $E(R_p) = 5 + \frac{20}{10} \times 5$ $E(R_p) = 5 + 2 \times 5$ $E(R_p) = 5 + 10 = 15\%$

Key Points:

• The portfolio is on the CML, which represents efficient portfolios combining the risk-free asset and the market portfolio
• The slope $\frac{R_m - R_f}{\sigma_m} = \frac{20}{10} = 2$ represents the market price of risk
• The portfolio's standard deviation (5%) is less than the market's (10%) because it includes the risk-free asset
• The expected return of 15% is appropriately between the risk-free rate (5%) and market return (25%)