Chartered Financial Analyst Level 1

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Explanation:

The expected return of the portfolio, $E(R_p)$ , is calculated as:

$E(R_p) = W \times R_f + (1 - W) \times E(R_m)$

where:

$W$ is the proportion invested in the risk-free asset ( $R_f = 3%$ ),
$E(R_m)$ is the expected return on the market portfolio ( $15%$ ).

Given $E(R_p) = 18%$ , solving for $W$ :

$0.18 = W \times 0.03 + (1 - W) \times 0.15$

Simplifying:

$0.18 - 0.15 = W \times (0.03 - 0.15)$ $0.03 = W \times (-0.12)$ $W = \frac{0.03}{-0.12} = -0.25$

A negative $W$ indicates borrowing (a leveraged position) rather than lending. Thus, the portfolio is leveraged, not a lending portfolio (Option A) or the market portfolio (Option C).

Explanation:

The expected return of the portfolio, $E(R_p)$ , is calculated as:

$E(R_p) = W \times R_f + (1 - W) \times E(R_m)$

where:

$W$ is the proportion invested in the risk-free asset ( $R_f = 3%$ ),
$E(R_m)$ is the expected return on the market portfolio ( $15%$ ).

Given $E(R_p) = 18%$ , solving for $W$ :

$0.18 = W \times 0.03 + (1 - W) \times 0.15$

Simplifying:

$0.18 - 0.15 = W \times (0.03 - 0.15)$ $0.03 = W \times (-0.12)$ $W = \frac{0.03}{-0.12} = -0.25$

A negative $W$ indicates borrowing (a leveraged position) rather than lending. Thus, the portfolio is leveraged, not a lending portfolio (Option A) or the market portfolio (Option C).

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An investor constructs a portfolio by combining the risk-free asset and the market portfolio, with the ability to lend and borrow at the risk-free rate. Given a risk-free rate of 3% and an expected market return of 15%, if the investor's portfolio has an expected return of 18%, the portfolio is best described as:

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a portfolio with a positive investment in the risk-free asset.

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a portfolio with a negative investment in the risk-free asset.

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the market portfolio.

16.7%