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CFA Level I · CFA Level I Exam

The Return and Risk of a Financial Portfolio for CFA Level I

This chapter shows how to measure the return of a portfolio and the risk that comes with it. You compute holding period returns, then portfolio expected return and variance using weights, covariance and correlation. Then you see how diversification, investor risk aversion and the capital allocation line lead to an optimal portfolio.

What this chapter covers

This chapter builds the core toolkit of portfolio theory. It starts with return measures such as holding period return, arithmetic mean and geometric mean. It then moves to portfolio expected return and variance, and to covariance and correlation, which explain why a portfolio's risk is not simply the average of its parts.

The second half uses those tools to answer a practical question: how should an investor choose a portfolio? You study diversification and the efficient frontier, then utility theory, which describes how risk-averse investors trade risk for return. The chapter ends with the capital allocation line, which combines a risk-free asset with a risky portfolio to find the best mix for a given investor.

The chapter links to other topics. Quantitative Methods supplies the statistics behind variance, covariance and correlation. Portfolio Construction and Equities use these ideas when you assess risk and return.

Portfolio Construction, the topic that contains this material, carries an 8-12% weight in the 2027 curriculum. That weight covers the whole topic, not this chapter alone. The ideas here also support other topics, so the effort pays off across the paper. The questions are often numerical and short, which suits the 90-second pace per question. With three options and no penalty for wrong answers, a candidate who knows the formulas can eliminate two options fast and avoid losing easy marks. The chapter also builds concepts that later portfolio and risk questions assume you already know.

The Return and Risk of a Financial Portfolio: topics in the order to study them

  1. 1Holding Period Return and Return MeasuresReturn is the base of everything else, and you need to tell apart the different ways of averaging it before you build portfolios.
  2. 2Expected Return and Variance of a PortfolioThis introduces weights and the two-asset formulas, the main calculation tool for the rest of the chapter.
  3. 3Covariance and Correlation of Asset ReturnsCovariance and correlation feed directly into portfolio variance, so you need them before you can explain diversification.
  4. 4Diversification and the Efficient FrontierOnce you know how correlation drives portfolio risk, you can see why combining assets lowers risk and how the efficient set is formed.
  5. 5Risk-Averse Investors and Utility TheoryThe efficient frontier shows what is available. Utility theory explains which portfolio a given investor prefers.
  6. 6Capital Allocation Line and Optimal PortfolioThis brings the risk-free asset, the frontier and investor preferences together, so it comes last.

How to prepare The Return and Risk of a Financial Portfolio

Treat this chapter as a chain. Each topic uses the one before it, so build the chain in order and practise calculations until they are quick.

  1. Read each topic once for the idea, then write the key formulas from memory: holding period return, portfolio expected return, portfolio variance and correlation.
  2. Practise the two-asset portfolio variance formula with at least five different sets of numbers: σp² = w1²σ1² + w2²σ2² + 2w1w2Cov(1,2). Do the same with Cov(1,2) = ρ × σ1 × σ2.
  3. Use your calculator for the arithmetic. On the TI BA II Plus, store the weights and variances in memory, and use the statistics worksheet for means and standard deviations. Check your answer by estimating it first.
  4. Draw the efficient frontier and the capital allocation line by hand. Mark the minimum-variance portfolio, the optimal risky portfolio and where an investor's indifference curve touches.
  5. Do timed sets of standalone three-option questions at about 90 seconds each. For each one, say why the two wrong options are wrong.
  6. Keep a short error log. Revisit it two days later and again just before the exam.

Common mistakes in The Return and Risk of a Financial Portfolio

  • Averaging the standard deviations of the assets to get portfolio risk.

    Fix: Always use the full variance formula with the covariance term, then take the square root at the end.

  • Forgetting to square the weights or leaving out the 2 in the covariance term.

    Fix: Write the formula down first, then substitute. Check that the three terms are w1²σ1², w2²σ2² and 2w1w2Cov.

  • Mixing up covariance and correlation, or using a percentage where a decimal is needed.

    Fix: Remember that covariance has units of squared returns and correlation is unit-free. Convert percentages to decimals before calculating.

  • Using the arithmetic mean when the question asks about compound growth over several periods.

    Fix: Use the geometric mean for multi-period growth. Use the arithmetic mean for a one-period expected return estimate.

  • Saying diversification removes all risk.

    Fix: Remember that risk reaches zero only in special cases such as perfect negative correlation with the right weights. Otherwise, some risk remains.

  • Confusing the efficient frontier with the capital allocation line, or the optimal risky portfolio with the investor's chosen portfolio.

    Fix: The frontier lists risky portfolios. The line adds the risk-free asset. The investor's own risk aversion decides where on the line they end up.

Last-day revision: The Return and Risk of a Financial Portfolio

  • Holding period return = (ending value − beginning value + income) ÷ beginning value.
  • The geometric mean is never above the arithmetic mean, and it is the better measure of compound growth.
  • Portfolio expected return is the weighted average of asset expected returns.
  • Portfolio variance is not a weighted average of variances. Covariance terms matter.
  • Correlation = Cov(1,2) ÷ (σ1 × σ2), and it always lies between −1 and +1.
  • Lower correlation means more diversification benefit. At a correlation of +1 there is no risk reduction beyond averaging.
  • Standard deviation is the square root of variance. Use decimals, and do not average standard deviations to get portfolio risk unless correlation is +1.
  • The efficient frontier is the set of risky portfolios offering the highest expected return for a given level of risk, or equivalently the lowest risk for a given expected return. It starts at the minimum-variance portfolio and runs upward from there.
  • A risk-averse investor needs more expected return to accept more risk. The investor's indifference curves slope upward and are convex, and curves further up and to the left are preferred.
  • The capital allocation line runs from the risk-free rate through the optimal risky portfolio.
  • On the capital allocation line, the slope is the Sharpe ratio: (expected return − risk-free rate) ÷ standard deviation.
  • Combining the risky portfolio with the risk-free asset gives portfolio risk = |weight in risky portfolio| × risky portfolio standard deviation. With a non-negative weight (no short selling of the risky portfolio), this is simply weight × standard deviation.

The Return and Risk of a Financial Portfolio practice questions

The Return and Risk of a Financial Portfolio in other exams

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

The Return and Risk of a Financial Portfolio: frequently asked questions

How should I use my calculator for portfolio variance questions?

Convert percentages to decimals, then compute each of the three terms and add them. The TI BA II Plus and HP 12C both let you store values in memory, which cuts keying errors. Take the square root last if the question asks for standard deviation.

Do I need to memorise the formulas, or are they given?

Plan to know them well. You should be able to recall each formula and apply it quickly, because you have only about 90 seconds per question. Practise until you can write each one from memory without hesitation.

Is the geometric mean always lower than the arithmetic mean?

The geometric mean is less than or equal to the arithmetic mean. They are equal only when all returns are identical. The more the returns vary, the larger the gap.

How do I eliminate options in a numerical question here?

Estimate first. For example, portfolio standard deviation must be at or below the weighted average of the asset standard deviations when correlation is at most +1. This often removes the largest option straight away.