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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 of stocks and plots all feasible combinations in expected return–standard deviation space. The resulting capital allocation line (CAL) is most likely:

The CAL is a straight line because the risk-free asset has zero risk and zero correlation with the risky portfolio. Its slope equals the risky portfolio's Sharpe ratio, the excess return per unit of standard deviation. Beta is the slope concept for the security market line, not the CAL.

  1. Aa straight line whose slope is the Sharpe ratio of the risky portfolioCorrect
  2. Ba concave curve that bends toward the expected return axis
  3. Ca straight line whose slope is the beta of the risky portfolio

Explanation

Because the risk-free asset has zero variance and zero covariance with the risky portfolio, portfolio risk is linear in the weight in the risky asset. Expected return is also linear in that weight, so the CAL is a straight line. Its slope is (E(Rp) - Rf)/σp, the Sharpe ratio. Beta is the slope of the security market line, not the CAL.

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