Given:

• Portfolio return $R_p = 17\%$
• Risk-free rate $R_f = 8\%$
• Investor allocation: 115% in the risky portfolio ⇒ investor borrows 15% at the risk-free rate.

This means the investor borrows 15% at the risk-free rate to invest 115% in the portfolio.

Formula for Leveraged Portfolio Return:

$$\text{Expected Return}_{\text{leveraged}} = w \cdot R_p + (1 - w) \cdot R_f$$

Where:

• $w = 1.15$ (the proportion invested in the risky portfolio)
• $1 - w = -0.15$ (borrowed at the risk-free rate)

Calculation:

$$\begin{aligned} \text{Expected Return} &= (1.15)(0.17) + (-0.15)(0.08) \\ &= 0.1955 - 0.012 \\ &= 0.1835 \\ &= 18.35\% \end{aligned}$$

Things to Remember

• Portfolio Beta: The beta of a portfolio is the weighted sum of the betas of the individual assets in the portfolio, where the weights are the proportions of the total portfolio value invested in each asset.
• Portfolio Standard Deviation: The standard deviation of a portfolio is a measure of the portfolio's volatility, taking into account the individual asset volatilities and their correlations.
• Capital Asset Pricing Model (CAPM): CAPM is a model that describes the relationship between risk and expected return, helping investors calculate the expected return on an investment based on its beta and the risk-free rate.