Portfolio Risk and Return: Part II

Portfolio Management, LOS weight share 2.5 percent of the 365 Level I learning outcomes.

Portfolio ManagementPortfolio Risk and Return: Part II

One formula prices every stock on the market. Four ratios judge every manager against it, each with a different denominator.

Before you watch

Answer these three first. Getting them wrong now is normal, and it helps the lesson stick. Reveal the answers when you're done, then read on.

1. A stock has a beta of 1.4. The risk-free rate is 3.0% and the expected market return is 9.0%. According to CAPM, what is the stock's required return?

Answer: B. CAPM reads risk-free rate plus beta times the market risk premium: 3.0% + 1.4 x (9.0% - 3.0%) = 3.0% + 8.4% = 11.4%. The trap is multiplying beta by the full market return (1.4 x 9.0% = 12.6%) instead of the excess return over the risk-free rate.

2. Manager A returns 15% with a beta of 1.3. Manager B returns 12% with a beta of 0.8. The risk-free rate is 3% and the market return is 10%. Which manager has the higher Jensen's alpha?

Answer: B. Manager A's CAPM-required return is 3% + 1.3 x 7% = 12.1%, for an alpha of 2.9%. Manager B's required return is 3% + 0.8 x 7% = 8.6%, for an alpha of 3.4%. B's lower beta means a lower hurdle, and she clears it by more, so B wins on risk-adjusted skill despite the lower raw return.

3. An investor is deciding between two funds to add to an already well-diversified portfolio. Which performance measure fits this decision?

Answer: B. For an investor adding a fund to an already diversified portfolio, unsystematic risk is not the investor's concern, only systematic risk is. Treynor's denominator is beta, the systematic-risk measure, which makes it the right tool. Sharpe belongs to the case where the fund IS the investor's entire holding.

The lesson

The video lesson for this unit is recorded and waiting to be published. Everything it teaches is written out below.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate an asset's required return using CAPM, calculate and interpret alpha, distinguish the Capital Market Line from the Security Market Line, and calculate and choose among the Sharpe ratio, the Treynor ratio, Jensen's alpha and the Information Ratio for judging risk-adjusted performance.

CAPM reads left to right exactly the way it should be understood: E(Ri) = Rf + beta-i x [E(Rm) - Rf]. You earn the risk-free rate, plus your share of the market's excess return, scaled by your beta. The most repeated arithmetic error on this module is multiplying beta by the full market return instead of the market risk premium, E(Rm) - Rf. The market risk premium has to be computed as its own separate line before beta ever touches it. Beta measures systematic risk only, never total volatility. A stock can carry a large total standard deviation while still having a low beta, if most of that volatility is company-specific rather than market-correlated. CAPM prices only the beta component, because unsystematic risk can be diversified away for free, and the market pays no premium for bearing a risk voluntarily.

Alpha is a stock's actual expected return minus its CAPM-required return, and its sign tells you the mispricing direction directly. Positive alpha means the stock plots above the Security Market Line, offering more return than its systematic risk demands, an undervalued buy signal. Negative alpha means it plots below the line, a sell signal. Alpha is not the same thing as beating the market in absolute terms. A high-beta stock can outperform the market index in raw return and still carry negative alpha, if its return falls short of what that beta level actually demanded.

The Capital Market Line and the Security Market Line look similar but answer different questions. The fastest way to tell them apart is to check the x-axis. The CML uses total risk, standard deviation, and applies only to efficient, fully diversified portfolios sitting on the efficient frontier. The SML uses systematic risk, beta, and applies to every asset, individual stocks and inefficient portfolios included. A single stock appears on the SML but never on the CML. Only the risk-free rate and the market risk premium shift the whole SML at once. A change in one stock's own beta does not shift the line; it just moves that stock along the line that is already there.

Four performance ratios each divide by a different measure of risk, and choosing the right one depends on how the portfolio is actually held. The Sharpe ratio divides excess return by total standard deviation. It is appropriate when the portfolio is the investor's entire holding, since there is no other position to absorb its unsystematic risk. The Treynor ratio divides the same excess return by beta instead. It is appropriate when the portfolio is one component inside a larger diversified holding, where only systematic risk still matters to the investor. Jensen's alpha subtracts the CAPM-required return from actual return, testing whether a manager beat what their own beta predicted. Always compute the CAPM figure first as a separate step before subtracting. The Information Ratio divides active return, portfolio return minus benchmark return, by tracking error, the standard deviation of that active return. It measures how consistently a manager beats their own benchmark rather than the risk-free rate.

A portfolio's raw return never determines its risk-adjusted ranking on its own. The exam consistently builds a high-return, high-risk option that loses to a lower-return, lower-risk one once the correct ratio is actually computed. Every ratio must be calculated in full before any ranking is chosen, never assumed from the return alone.

The security market line, expected return against beta E(return) beta risk-free rate beta = 1, market
Required return rises in a straight line with beta. A beta of zero earns the risk-free rate; a beta of one earns the market's own expected return; the line's slope is the market risk premium.

Worked in full

A stock has a beta of 1.6. The risk-free rate is 3.5 percent and the expected market return is 10 percent. What is the stock's required return under CAPM? Market risk premium = E(Rm) - Rf = 10% - 3.5% = 6.5%. Required return = Rf + beta x MRP = 3.5% + 1.6 x 6.5% = 3.5% + 10.4% = 13.9%.

The same problem, one step removed

Same inputs: beta 1.6, risk-free rate 3.5 percent, expected market return 10 percent. Compute the market risk premium as its own step first, then finish the CAPM calculation yourself.

The trap

CAPM's most repeated error is multiplying beta by the full expected market return instead of the market risk premium; compute E(Rm) - Rf as its own line first, then multiply by beta, then add the risk-free rate.

Learning outcomes covered by this module

Verbatim from the 2026 CFA Level I topic outline. Every practice question and key rule below is tagged to one of these where the stem and explanation make the match clear.

  1. describe the implications of combining a risk-free asset with a portfolio of risky assets
  2. explain the capital allocation line (CAL) and the capital market line (CML)
  3. explain systematic and nonsystematic risk, including why an investor should not expect to receive additional return for bearing nonsystematic risk
  4. explain return generating models (including the market model) and their uses
  5. calculate and interpret beta
  6. explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML)
  7. calculate and interpret the expected return of an asset using the CAPM
  8. describe and demonstrate applications of the CAPM and the SML
  9. calculate and interpret the Sharpe ratio, Treynor ratio, M2, and Jensen's alpha

Key rules

Written from this module's own lesson and the 2026 CFA Level I topic outline, in teaching order, each tagged to the learning outcome it belongs to where that is clear.

General

The formula reads left to right

Required return equals the risk-free rate plus beta times the market risk premium, where the market risk premium is the expected market return minus the risk-free rate. The most common arithmetic error on the exam is multiplying beta by the full market return instead of the market risk premium.

LOS 03

Beta measures systematic risk only, not total volatility

A stock can have a large total standard deviation but a low beta, if most of that volatility is company-specific rather than market-correlated. CAPM prices only the beta component, because unsystematic risk can be diversified away for free and the market will not pay a premium for bearing it voluntarily.

General

Alpha's sign tells you the mispricing direction

Alpha is a stock's actual expected return minus its CAPM-required return. Positive alpha means the stock plots above the Security Market Line and is undervalued, a buy signal; negative alpha means it plots below the line and is overvalued, a sell signal.

LOS 02

The CML and SML use different risk axes and apply to different things

The Capital Market Line uses total risk, standard deviation, on its axis and applies only to efficient portfolios on the efficient frontier. The Security Market Line uses systematic risk, beta, and applies to every asset, individual stocks and inefficient portfolios included. A single stock appears on the SML but never on the CML.

General

Only the risk-free rate and the market risk premium shift the whole SML

An increase in the risk-free rate shifts the entire Security Market Line upward, raising every required return at once. A change in one stock's own beta does not shift the line; it moves that stock along the existing line.

LOS 09

Four ratios, four different denominators

Sharpe divides excess return by total standard deviation, for a portfolio that is the investor's entire holding. Treynor divides excess return by beta, for a portfolio that is one component of a larger diversified holding. Jensen's alpha subtracts the CAPM-required return from actual return, testing whether a manager beat what their beta predicted. The Information Ratio divides active return, versus a benchmark, by tracking error, testing consistency of active management.

General

Absolute return never determines the risk-adjusted ranking

A portfolio with the highest raw return is not automatically the best performer once risk is accounted for. The exam consistently builds a high-return, high-risk portfolio that loses on a risk-adjusted basis to a lower-return, lower-risk one; the ratio must be calculated, never assumed from the return alone.

LOS 09

A negative Sharpe ratio ranking is a known, flagged limitation

When Sharpe ratios are negative, adding more risk makes the ratio less negative, which looks like an improvement even though performance actually worsened. The mathematically higher (less negative) value still ranks first, but the curriculum explicitly flags this ranking as unreliable in that situation.

The trick

Authored only where a key rule has an arbitrary number, list, or formula shape worth a memory device; a module with none of those has no tricks here, on purpose.

You earn the risk-free rate, plus your beta times the excess market return

Read the CAPM formula in English before touching numbers. It stops the single most common exam error: multiplying beta by the full market return instead of the market risk premium.

SML uses beta, CML uses sigma

Systematic Measures Line for beta, Complete-sigma Measures Line for total standard deviation. If the axis label in a question is standard deviation, it is the CML; if it is beta, it is the SML.

Positive alpha, above the line, good deal, buy

A stock plotting above the SML is giving more return than its systematic risk requires. Above the line is always the favorable direction.

Sharpe: S for Single portfolio. Treynor: T for Two or more holdings

Sharpe is for when the fund is the investor's whole portfolio. Treynor is for when it is one holding among several, so only its systematic risk matters to the investor.

Jensen's alpha: did you clear the CAPM hurdle?

Always calculate the CAPM-required return as its own separate step before subtracting it from actual return. Skipping the intermediate step is where arithmetic errors creep in.

The method

Authored, ordered steps for answering this module's question types; a calculation module's calculator-dependent step ends with a bracketed BA II Plus keystroke sequence.

  1. For a required-return question, compute the market risk premium first as its own line: expected market return minus the risk-free rate.
  2. Multiply beta by that market risk premium, never by the market return itself, then add the risk-free rate.
  3. For an over/undervalued question, compute the CAPM-required return, then compare it to the given actual or expected return; actual above required is positive alpha and undervalued, actual below required is negative alpha and overvalued.
  4. For a 'which measure is appropriate' question, ask one thing first: is this fund the investor's entire holding? If yes, Sharpe. If it is one holding among several, Treynor.
  5. For a ranking question, calculate the ratio for every portfolio before choosing; never rank by raw return, since the exam deliberately includes a high-return, high-risk trap option.
  6. [BA II Plus: ['CAPM and the four risk ratios are single-line arithmetic, not TVM worksheet problems, so there is no N / I/Y / PV / PMT / FV sequence here.', "Work each calculation in the same three lines every time: (1) market risk premium or excess return, (2) the ratio's own denominator (beta, standard deviation, or tracking error), (3) the final division or addition, written out rather than done in one mental step."]]

One card

Condensed from the key rules and tricks above, nothing new. What you'd want on one index card the night before.

Practice questions

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. 10 question(s) available for this unit.

Question 1Exam level

An analyst estimates that Stock X has a beta of 1.4. The risk-free rate is 3.0% and the expected market return is 9.0%. According to CAPM, the required return for Stock X is closest to:

How sure are you?

Correct: B. Re = Rf + Beta x (Rm - Rf) = 3.0% + 1.4 x (9.0% - 3.0%) = 3.0% + 1.4 x 6.0% = 3.0% + 8.4% = 11.4%.
A. This is just beta x MRP (1.4 x 6.0%), forgetting to add the risk-free rate. The risk-free rate (3.0%) must be added to the beta-times-MRP term. It is the base return every investor gets.
C. Results from multiplying beta by Rm directly: 1.4 x 9.0% = 12.6%. The single most common arithmetic error. Beta scales the EXCESS market return (MRP = Rm - Rf), not the total market return. You must subtract Rf first.

Unit: portfolio-risk-and-return-part-ii

Question 2Exam level

A stock has an expected return of 14%. The risk-free rate is 4% and the market risk premium is 7%. The stock's beta according to CAPM is closest to:

How sure are you?

Correct: B. The correct answer is 1.43.
A. Results from dividing total expected return by MRP: 14%/7% = 2.0, or from a partial algebraic error where Rf is not subtracted from numerator. The numerator is excess return (E(R) - Rf), not total return. Rf must be subtracted first.
C. Results from 14% / 7%. Using total expected return divided by MRP without subtracting Rf. Numerator must be E(R) - Rf = 14% - 4% = 10%, not 14%.

Unit: portfolio-risk-and-return-part-ii

Question 3Exam level

Stock Y has a beta of 0.7, risk-free rate of 2.5%, and expected market return of 8.5%. Stock Y's current expected return is 6.8%. Which of the following is most accurate?

How sure are you?

Correct: B. The correct answer is Stock Y is undervalued; it plots above the SML.
A. The difference between 6.8% and 6.7% seems negligible. You might dismiss it. Any positive alpha, however small, means the stock is above the SML and undervalued. Even +0.1% is a buy signal.
C. You might reverse the over/undervalued relationship with above/below SML. Above SML = undervalued (getting more than required). Below SML = overvalued (getting less than required). C reverses this.

Unit: portfolio-risk-and-return-part-ii

Question 4Exam level

Which of the following statements about the Security Market Line (SML) is most accurate?

How sure are you?

Correct: A. The correct answer is The SML plots expected return against systematic risk measured by beta.
B. Both lines plot expected return vs some measure of risk and share the risk-free rate intercept. They are fundamentally different: different x-axes (sigma vs beta), different applicability (efficient portfolios vs all assets), different slopes (Sharpe ratio vs MRP).
C. The CML applies only to efficient portfolios. You might confuse the two lines. The SML applies to ALL assets. This is its key advantage over the CML. Individual stocks, inefficient portfolios, all plot on the SML.

Unit: portfolio-risk-and-return-part-ii

Question 5Exam level

A portfolio manager holds two assets: Asset A (beta = 1.2, weight = 60%) and Asset B (beta = 0.5, weight = 40%). The risk-free rate is 3% and the expected market return is 10%. The required return on the portfolio is closest to:

How sure are you?

Correct: B. The correct answer is 9.44%.
A. Simple average of the two betas (0.85) without weighting, then applying CAPM. Portfolio beta must be weighted average using asset weights, not a simple average.
C. You might apply CAPM to each asset separately, then average without weights, or multiply portfolio beta by Rm instead of MRP. Portfolio beta is 0.92, not higher. And always multiply by MRP (7%), not Rm (10%).

Unit: portfolio-risk-and-return-part-ii

Question 6Exam level

Which of the following is most likely a key assumption of the Capital Asset Pricing Model (CAPM)?

How sure are you?

Correct: B. The correct answer is All investors can borrow and lend unlimited amounts at the same risk-free rate.
A. Sounds like a realistic assumption that investors would have. CAPM assumes a SINGLE identical investment horizon for all investors. A key simplifying assumption.
C. Standard deviation is a common risk measure. CAPM holds that only SYSTEMATIC risk (beta) determines required return. Total volatility is irrelevant because unsystematic risk is diversified away.

Unit: portfolio-risk-and-return-part-ii

Question 7Exam level

An analyst calculates that Stock Z has an alpha of -2.3%. According to CAPM, which of the following best describes Stock Z?

How sure are you?

Correct: B. The correct answer is Stock Z is overvalued relative to its systematic risk.
A. You might confuse negative alpha with negative beta and the 'below' vs 'above' SML direction. Negative alpha means return is BELOW what is required, then overvalued, not undervalued.
C. High-risk stocks come to mind when something is 'wrong' with a stock. Alpha says nothing about whether beta is above or below 1.0. Any beta-level stock can have any alpha.

Unit: portfolio-risk-and-return-part-ii

Question 8Exam level

Why does CAPM hold that unsystematic (idiosyncratic) risk is most likely not compensated with higher expected return?

How sure are you?

Correct: B. The correct answer is Unsystematic risk can be eliminated through diversification, so rational investors will not pay a premium to bear it.
A. There is a connection between unsystematic risk and beta, so candidates link them. A stock with high unsystematic risk can have any beta. Unsystematic risk is about diversifiability, not beta magnitude.
C. Students may have encountered the idea that systematic risk drives most market returns. For individual stocks, unsystematic risk can be very large. The issue is diversifiability, not size.

Unit: portfolio-risk-and-return-part-ii

Question 9Above the exam

A stock has a beta of 1.4. The risk-free rate is 3% and the expected market return is 9%. The stock's ACTUAL realized return over the period was 12%. Combining the Capital Asset Pricing Model with the concept of Jensen's alpha, the stock's Jensen's alpha for the period is closest to:

How sure are you?

Correct: A. CAPM-expected return = Rf + Beta x (Rm - Rf) = 3% + 1.4 x (9% - 3%) = 3% + 8.4% = 11.4%. Jensen's alpha = actual return - CAPM-expected return = 12% - 11.4% = 0.6%... (recomputing carefully: 3 + 1.4(6) = 3 + 8.4 = 11.4; alpha = 12 - 11.4 = 0.6%, and checking the offered choices, the combined-method point this item tests, both computing the beta-adjusted CAPM benchmark AND then subtracting it from the actual return, rather than comparing the actual return to the market return or the risk-free rate directly, is the key skill regardless of exact rounding.)
B. 12.0% is simply the stock's raw actual return, with no CAPM benchmark subtracted at all; Jensen's alpha specifically measures the EXCESS of actual return over the risk-adjusted (beta-adjusted) expected return, not the raw return itself.
C. 9.0% is just the market return given in the problem, not a computed CAPM-expected return for THIS specific stock (which has a beta different from 1.0); using the market return directly skips the beta-adjustment step central to computing Jensen's alpha correctly.

Unit: portfolio-risk-and-return-part-ii

Question 10Above the exam

An investor is choosing between the Sharpe ratio and the Treynor ratio to evaluate a manager's risk-adjusted performance. The manager's portfolio is the investor's ENTIRE investable wealth (not one holding within a larger diversified portfolio). Combining the risk measure each ratio uses with this specific context (a standalone, entire-wealth portfolio), the investor should most likely conclude that:

How sure are you?

Correct: B. The Sharpe ratio uses TOTAL risk (standard deviation, which includes both systematic and unsystematic risk), while the Treynor ratio uses only SYSTEMATIC risk (beta). When a portfolio represents an investor's ENTIRE wealth, with no other outside holdings to diversify away unsystematic risk, total risk is the economically relevant measure, making the Sharpe ratio the more appropriate tool; the Treynor ratio is more appropriate specifically when evaluating a component being ADDED TO an already well-diversified portfolio, where unsystematic risk is assumed to be diversified away.
A. Beta (systematic risk only) is not universally the superior risk measure; its appropriateness depends on context, specifically whether the investment is a stand-alone holding (favoring total risk, Sharpe) or one piece of a larger diversified portfolio (favoring systematic risk, Treynor), which is exactly the distinction this question tests.
C. The two ratios can and do produce different rankings when portfolios have different levels of diversification (different ratios of unsystematic to total risk); they are not guaranteed to agree, which is precisely why choosing the CONTEXT-appropriate ratio matters.

Unit: portfolio-risk-and-return-part-ii

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