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CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio

An investor combines a risk-free asset with a risky portfolio on the capital allocation line (CAL). The investor chooses to borrow at the risk-free rate and invest more than 100% of her wealth in the risky portfolio. The resulting portfolio's expected return and standard deviation are most likely:

Leveraging a position in the risky portfolio moves the investor along the CAL beyond the risky portfolio, so both expected return and standard deviation are higher than those of the risky portfolio. Borrowing adds exposure to risky returns, increasing risk and, given a positive risk premium, expected return.

  1. ALower than the risky portfolio's expected return and standard deviation
  2. BEqual to the risky portfolio's expected return with a lower standard deviation
  3. CHigher than the risky portfolio's expected return and standard deviationCorrect

Explanation

Borrowing at the risk-free rate to invest more than 100% in the risky portfolio is a leveraged position, which lies on the CAL beyond the risky portfolio. Both expected return and standard deviation rise, assuming the risky portfolio's expected return exceeds the risk-free rate. Expected return cannot stay equal while risk rises or falls.

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