CFA CFA Level 1 Question of the Week – Standard Deviation

# Question of the Week – Standard Deviation

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• 1

A portfolio has a risk-adjusted expected rate of return of 18% over the course of the next year, in an environment with a risk free rate of 6%, and an expected market return of 12%. If the markets are expected to have a standard deviation of returns of 4.5%, what is the expected standard deviation of the actual portfolio?

• 6.75%
• 9%
• Covariance is required to solve this problem
• 5

This problem is solved by multiplying the portfolio CML equation by the ratio of the portfolio standard deviation to market standard deviation. The equation is then rearranged and solved for the portfolio standard deviation. The trick is to remember that this market portfolio will have a beta of one, and that a market portfolio is solved for non-systemic risk instead of beta. Similarly, covariance would only be required if we were solving for systemic risk, as would be accomplished for the SML equation rather than the CML.

• 5

this may be a stupid question, but do we multiply by the ratio of the portfolio st.dev to market st.dev because that’s what beta is (correlation of risk between market and stock/portfolio)?

• 4

thanks! for some reason i read CAPM in the explanation instead of CML….sign i need a study break

• 2

Not exactly. The way I think about it is that the portfolio is risk-adjusted, meaning that (returns excess of risk free rate) / (std dev) of the market must equal that of the portfolio.

Hence to use @exam_whiz‌’s convention,

(ERp – Rf) / sdp = (ERm – rfr) / sdm

Which you can rearrange into what @exam_whiz‌ shows in their answer.