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CFA Level I · CFA Level I Exam

Portfolio Risk and Return: Part I for CFA Level 1

Portfolio Risk and Return: Part I shows how to measure return and risk for single assets and for portfolios. You compute returns, variance, covariance and correlation, combine assets into a portfolio, see how diversification cuts risk, and pick the best mix on the capital allocation line. Solve by formula first, then check the logic.

What this chapter covers

This chapter builds the maths and logic of modern portfolio theory. You start with return measures such as holding period return, arithmetic mean, geometric mean and money-weighted return. Then you look at how returns are distributed and how investors feel about risk. Next come the statistics that describe risk: variance, standard deviation, covariance and correlation.

The second half puts these pieces together. You calculate the expected return and risk of a portfolio of two or more assets, and you see why combining assets with correlation below +1 lowers risk. This leads to the efficient frontier, the risk-free asset, the capital allocation line and the optimal portfolio for a given investor.

The chapter links to several other parts of the paper. Quantitative Methods supplies the statistics. Equities and Fixed Income use the return measures. Portfolio Construction builds directly on the efficient frontier and the CAL, and later ideas such as CAPM rest on this foundation. Learn it well once and it pays off across the paper.

Portfolio Construction carries an 8-12% topic weight in the 2027 curriculum, and this chapter is its numerical core. Questions are standalone three-option MCQs, so a clean formula and a quick sense check win marks fast. Portfolio variance, correlation and expected return are testable as short calculations, and diversification and risk aversion are testable as concept checks. With no penalty for wrong answers, you should attempt every question, and a solid grasp here lets you eliminate two options with confidence.

Portfolio Risk and Return: Part I: topics in the order to study them

  1. 1Holding Period Return and Return MeasuresEvery later topic uses returns, so you need the definitions and the differences between the mean types first.
  2. 2Return Distributions and Investor Risk PreferencesIt sets out what risk means and how risk-averse investors judge it, which gives the reason for the maths that follows.
  3. 3Variance, Standard Deviation, Covariance and CorrelationThese are the building blocks of portfolio risk, so you must be fluent before combining assets.
  4. 4Portfolio Expected Return and RiskYou apply the statistics to a portfolio and see why correlation drives portfolio risk.
  5. 5Diversification and Efficient FrontierIt explains the result of the two-asset maths and extends it to the full set of efficient portfolios.
  6. 6Capital Allocation Line and Optimal PortfolioIt comes last because it adds a risk-free asset to the frontier and links the investor's preferences to the final choice.

How to prepare Portfolio Risk and Return: Part I

Work from definitions to calculations to concepts. Keep the calculator in your hand for every numerical topic.

  1. Read each topic once for the idea, then write the formula in your own words with the meaning of every symbol.
  2. Practise the return measures until HPR, arithmetic mean, geometric mean and money-weighted return feel routine, and learn when each one is the right choice.
  3. Drill variance, covariance and correlation using small data sets. Use the statistics mode on your TI BA II Plus or HP 12C where it saves time, and learn the keystrokes.
  4. Do portfolio variance for two assets many times, including cases with correlation of +1, 0 and -1, until you can do it in under two minutes.
  5. Sketch the efficient frontier and the CAL by hand, label axes and the tangency point, and explain each in one sentence.
  6. Finish with timed sets of standalone MCQs at about 90 seconds each. For every miss, note whether it was a formula slip, a unit slip or a concept gap.

Common mistakes in Portfolio Risk and Return: Part I

  • Averaging standard deviations to get portfolio risk

    Fix: Use the full variance formula with the covariance term, and take the square root at the end.

  • Forgetting to take the square root, or forgetting the 2 in the covariance term

    Fix: Write the three terms separately, add them, then take the square root. Check that the answer is a sensible size.

  • Using the arithmetic mean when the question needs the geometric mean

    Fix: Use the geometric mean for compound growth over several periods, and the arithmetic mean for a single-period expected return.

  • Mixing up covariance and correlation

    Fix: Remember that correlation is bounded between −1 and +1 and covariance has no fixed bounds. Convert between them using the standard deviations.

  • Entering percentages and decimals inconsistently

    Fix: Convert everything to decimals before squaring or multiplying, then convert the answer back.

  • Choosing a point on the risky-asset efficient frontier as the optimal portfolio once a risk-free asset exists

    Fix: With a risk-free asset, if investors share the same expectations (homogeneous expectations), every investor holds the same tangency risky portfolio and adjusts risk by mixing it with the risk-free asset.

Last-day revision: Portfolio Risk and Return: Part I

  • HPR = (ending value − beginning value + income) ÷ beginning value.
  • The geometric mean is never above the arithmetic mean, and they are equal only when all returns are identical.
  • Variance is the average squared deviation. Standard deviation is its square root.
  • Covariance shows the direction of co-movement. Correlation = Cov(A,B) ÷ (σA × σB) and lies between −1 and +1.
  • Portfolio expected return is the weighted average of asset expected returns.
  • Two-asset variance = wA²σA² + wB²σB² + 2wAwB·Cov(A,B).
  • Portfolio risk is not a weighted average of standard deviations unless correlation is +1.
  • Lower correlation gives more diversification benefit, and perfect −1 can bring risk to zero at some weights.
  • Risk-averse investors want more return for more risk and prefer less risk at equal return.
  • The efficient frontier holds portfolios with the highest return for each level of risk.
  • The CAL joins the risk-free asset and the optimal risky portfolio, and its slope is the Sharpe ratio. If investors share the same expectations (homogeneous expectations), every investor holds the same tangency risky portfolio.
  • The optimal portfolio is where the investor's highest indifference curve touches the CAL.

Portfolio Risk and Return: Part I practice questions

Portfolio Risk and Return: Part I in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Portfolio Risk and Return: Part I: frequently asked questions

Which calculations should I practise most in this chapter?

Practise two-asset portfolio variance and standard deviation, and finding correlation from covariance. These are testable as short calculations, so practise them until you can do them quickly and accurately on your calculator.

Do I need to memorise the derivation of the efficient frontier?

No. You need to understand what the frontier shows, which portfolios are on it, and how it changes with correlation. Questions test interpretation more than derivation.

How does this chapter connect to Portfolio Construction?

It supplies the base ideas: risk aversion, diversification, the efficient frontier and the CAL. Later material builds on these, so weak understanding here will cost you marks again.

Can I use my calculator's statistics mode here?

Yes. The TI BA II Plus and HP 12C both let you enter data and get means and standard deviations. Check whether the result is a sample or population figure, and use the one the question needs.