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CMA Intermediate · Financial Management and Business Data Analytics

Risk and Return for CMA Intermediate Financial Management

Risk and return is the study of how much an investment is expected to earn and how much that outcome can vary. You solve problems by computing expected return, variance and standard deviation, then portfolio risk using weights and correlation, and finally required return using CAPM: Ke = Rf + β(Rm − Rf).

What this chapter covers

This chapter in Paper 11 explains how investors judge an investment on two things: the return they expect and the uncertainty around it. You start with the basic idea of risk, then split it into risk you can diversify away and risk you cannot. After that comes the numerical core: expected return, variance, standard deviation, and the same measures for a portfolio of two or more securities.

The second half moves from measuring risk to pricing it. CAPM links the required return on a security to its beta, which measures only market (systematic) risk. Arbitrage Pricing Theory and other multi-factor ideas then show that a single market factor is not the only possible explanation of returns.

The chapter connects directly to the rest of the paper. The required return from CAPM feeds the cost of equity in cost of capital. The risk ideas support capital budgeting, where you adjust discount rates or cash flows for risk. Portfolio thinking also helps in understanding financing and valuation choices.

Risk and Return is a scoring chapter because most of it is formula-driven. A single question can mix expected return, standard deviation, portfolio risk and CAPM, and each step earns marks if your working is shown. The same concepts also appear as standalone MCQs on beta, diversification and risk types, and CAPM gives you the cost of equity you need in other chapters, so the effort pays off more than once.

Risk and Return: topics in the order to study them

  1. 1Concept of Risk and ReturnStart here to fix the vocabulary of return, risk and the trade-off between them before any numbers.
  2. 2Types of Risk: Systematic and UnsystematicYou need this split to understand why diversification works and why beta counts only one kind of risk.
  3. 3Measuring Expected Return, Variance and Standard DeviationThese single-asset calculations are the base for every portfolio and CAPM question that follows.
  4. 4Portfolio Return and Risk, Correlation and DiversificationIt builds on single-asset measures by adding weights and correlation, the most calculation-heavy part of the chapter.
  5. 5Capital Asset Pricing Model (CAPM) and BetaOnce you know systematic risk and portfolio ideas, CAPM shows how the market prices that risk.
  6. 6Arbitrage Pricing Theory and Other ModelsStudy it last, as it extends CAPM to several factors and is mostly conceptual.

How to prepare Risk and Return

Treat this chapter as a mix of fixed formulas and short concept answers. Practise calculations until the layout is automatic, then add the theory.

  1. Write the key formulas on one page: expected return = Σ(p × R), variance = Σ p(R − expected R)², standard deviation = √variance, and CAPM.
  2. Solve single-asset problems in a table with columns for probability, return, p × R, deviation, squared deviation and p × squared deviation.
  3. Practise two-asset portfolios: portfolio return = w1R1 + w2R2, and portfolio variance = w1²σ1² + w2²σ2² + 2w1w2σ1σ2ρ12. Take the square root last.
  4. Try cases where correlation is +1, 0 and −1 so you see how risk falls as correlation falls.
  5. Solve CAPM questions step by step: list Rf, Rm and β, compute the market premium (Rm − Rf), then required return. Also practise finding beta from given data.
  6. Learn the types of risk, assumptions of CAPM and the idea behind APT as short bullet answers you can write in a few lines.
  7. Finish with timed MCQs on the concepts, then attempt two full written questions and check that every step and unit is shown.

Common mistakes in Risk and Return

  • Reporting variance when the question asks for standard deviation.

    Fix: Underline the required measure in the question and end your working with √variance whenever standard deviation is asked.

  • Taking portfolio standard deviation as the weighted average of individual standard deviations.

    Fix: Use the full variance formula with the correlation term, and apply the weighted average only to returns and beta.

  • Using percentages and decimals inconsistently in the variance formula.

    Fix: Choose one form at the start, either all percentages or all decimals, and state the unit in the final answer.

  • Using the market return instead of the market risk premium in CAPM.

    Fix: Write the premium on its own line first, then multiply by beta and add Rf.

  • Saying beta measures total risk.

    Fix: Remember that standard deviation measures total risk and beta measures only systematic risk.

  • Writing theory answers without linking them to the formula or an example.

    Fix: For each concept, add one line on why it matters, such as why unsystematic risk disappears in a diversified portfolio.

Last-day revision: Risk and Return

  • Risk is the variability of actual returns around the expected return.
  • Expected return = Σ(probability × return).
  • Variance = Σ p × (R − expected R)²; standard deviation = √variance.
  • Systematic risk comes from market-wide factors and cannot be removed by diversification.
  • Unsystematic risk is specific to a firm or industry and can be reduced by diversification.
  • Portfolio return is the weighted average of the individual expected returns.
  • Portfolio risk depends on weights, individual risks and correlation, so it is not a simple weighted average.
  • Correlation of +1 gives no diversification benefit; lower correlation gives more benefit.
  • Beta measures sensitivity of a security's return to market return; market beta is 1.
  • CAPM: Required return = Rf + β × (Rm − Rf).
  • Portfolio beta is the weighted average of the betas of its securities.
  • APT explains returns using several factors, with no single market factor assumed.

Risk and Return practice questions

Risk and Return in other exams

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

Risk and Return: frequently asked questions

Is Risk and Return mostly numerical or theory in CMA Inter?

It is a mix, with a strong numerical part. Expected return, standard deviation, portfolio risk and CAPM can all be asked as calculations, while risk types and APT suit short theory answers and MCQs. Prepare both sides.

Which formulas must I memorise for this chapter?

Learn expected return, variance, standard deviation, two-asset portfolio variance and CAPM. Also remember that portfolio beta is the weighted average of individual betas. Practise each one on questions until you can write it without looking.

Why does diversification reduce risk?

Returns of different securities do not move perfectly together, so losses in one are partly offset by gains in another. This removes unsystematic risk. Systematic risk remains because it affects the whole market.

How is this chapter linked to cost of capital?

CAPM gives the required return on equity, which is used as the cost of equity. If you can compute it accurately here, you can use it directly in cost of capital problems.