Portfolio Risk and Return: Part II

Portfolio Management. Worth 8 to 12 percent of the exam. One session: the lesson, the rules, the method, then the questions.

Portfolio ManagementPortfolio Risk and Return: Part II
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The lesson

The video lesson for this unit is recorded and waiting to be published. Until it is, the rules and the method below carry everything this session needs; watching is a way of hearing it, not the only way of getting it.

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.

What this unit turns on

Read these before the questions, not after them. Everything here traces to this module's own lesson and to the 2026 outline.

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.

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.

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.

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.

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.

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.

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.

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

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

The order to work a question of this type in, every time, before you touch the numbers.

  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."]]

Two worked examples, then you are on your own

The first is worked in full. The second gives you the setup and stops. After that the questions give you nothing, which is the point: the help fades on purpose, so the last thing you practise is the thing the exam actually asks of you.

Worked in full

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:

Answer 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%.

Your turn, setup given

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:

For a required-return question, compute the market risk premium first as its own line: expected market return minus the risk-free rate.

The practice run

Pick an answer, say how sure you are, then reveal. Being sure and wrong is the most useful thing that can happen in a session, so answer honestly: it sends the unit back to learning and puts it at the front of your revision queue.

Question 1Exam 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 2Exam 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 3Exam 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 4Exam 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 5Exam 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 6Exam 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 7Harder

Which of the following most accurately describes the relationship between the Capital Market Line (CML) and the Security Market Line (SML), most likely?

How sure are you?

Correct: B. The correct answer is The CML uses standard deviation as the risk measure; the SML uses beta.
A. The CML is the efficient frontier extension. You might think it covers all investments. The CML applies ONLY to efficient portfolios. The SML applies to ALL assets. This is reversed in option B.
C. The Sharpe ratio is a key metric and the CML slope is the Sharpe ratio. This answer is partially right. The SML slope is the market risk premium [E(Rm) - Rf], NOT the Sharpe ratio. Only the CML slope equals the Sharpe ratio. This is one of the highest-frequency exam traps.

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

Question 8Exam level

A stock has a beta of -0.3. The risk-free rate is 3% and the market risk premium is 6%. The CAPM required return is closest to:

How sure are you?

Correct: A. The correct answer is 1.2%.
B. You might may treat negative beta as beta = 0 (no market exposure) and return just Rf. Negative beta actively REDUCES required return below Rf. Beta = 0 gives Rf; beta = -0.3 gives less than Rf.
C. Using absolute value of beta: 3% + 0.3 x 6% = 4.8%. The negative sign matters. Negative beta means the asset provides negative systematic risk contribution. Its required return is below Rf.

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

Question 9Exam level

According to CAPM, which of the following would most likely cause the required return on ALL stocks to increase simultaneously?

How sure are you?

Correct: B. The correct answer is An increase in the risk-free rate.
A. Beta changes seem like they would affect required returns. Lower betas would DECREASE required returns for those specific stocks. Not increase returns for all stocks. Beta changes move stocks ALONG the SML, not shift the whole line.
C. More overall market risk sounds like it should increase required returns. Under CAPM, unsystematic risk is irrelevant to required returns. Only Rf and MRP shift the SML; only beta changes move a stock along the SML.

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

Question 10Harder

The risk-free rate is 2.0% and the expected market return is 8.0%. Stock A has a beta of 1.6 and an expected return of 12.0%. Stock B has a beta of 0.8 and an expected return of 6.4%. Which statement is most accurate?

How sure are you?

Correct: B. The correct answer is Stock A is undervalued; Stock B is overvalued.
A. You might calculate only one stock and apply the wrong direction to the other. A has positive alpha (+0.4%) = undervalued. B has negative alpha (-0.4%) = overvalued. A reverses both conclusions.
C. Both stocks seem to have reasonable returns relative to their betas at a glance. Must calculate both CAPM required returns precisely. Stock B's 6.4% < 6.8% required, then negative alpha, then overvalued.

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

Question 11Exam level

Portfolio A has a return of 12%, a standard deviation of 18%, and a beta of 0.9. Portfolio B has a return of 14%, a standard deviation of 22%, and a beta of 1.2. The risk-free rate is 3%. Which portfolio most likely has a higher Sharpe ratio?

How sure are you?

Correct: A. Sharpe A = (12% - 3%) / 18% = 9/18 = 0.50. Sharpe B = (14% - 3%) / 22% = 11/22 = 0.50. Both portfolios have identical Sharpe ratios of 0.50. However, if the question asks which portfolio has the higher Sharpe and they are equal, neither dominates on this measure. In a variant of this question the numbers differ. Always calculate both before eliminating. Option C is wrong because 0.56 would require Sharpe A = 9/16, which uses incorrect standard deviation.
B. You might round to the nearest sigma value or misread the given numbers. 0.56 requires sigma of 16, not 18 as given. Always label each portfolio's data before calculating.
C. Portfolio B has a higher return and candidates default to selecting the higher-return portfolio. Sharpe B = 11/22 = 0.50, not 0.55. The higher return is offset by the higher standard deviation.

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

Question 12Exam level

An investor is evaluating two fund managers. Manager X runs a diversified fund that closely tracks the S&P 500. Manager Y runs a concentrated fund of 15 stocks in the technology sector. Which performance measure is MOST appropriate for ranking Manager X, and which is MOST appropriate for ranking Manager Y?

How sure are you?

Correct: A. The Treynor ratio uses systematic risk (beta) as the denominator and is appropriate when the portfolio is a component of a larger diversified portfolio. Where only systematic risk is relevant. Manager X's diversified fund is held as part of a broader portfolio, so Treynor is appropriate. Manager Y's concentrated technology fund carries significant unsystematic risk that cannot be ignored; the investor must evaluate total risk via the Sharpe ratio. Option B inverts the logic. Option C introduces Jensen's alpha and IR, which are not the primary distinction tested here.
B. You might think 'diversified = Sharpe' because diversification is discussed alongside total risk. The decision is about the INVESTOR's portfolio context, not the fund's internal diversification. If the investor holds other assets, the fund is a sub-component and Treynor applies. B completely inverts the correct logic.
C. Both are sophisticated measures. Jensen's alpha is CAPM-based like Treynor, and IR applies to active managers. Jensen's alpha measures absolute skill vs CAPM expectations. It is not the primary ranking tool when comparing two funds in a diversification context. The exam tests Treynor vs Sharpe as the core decision.

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

Question 13Exam level

A portfolio manager generated a return of 16% last year. The CAPM expected return for this portfolio, given its beta of 1.1 and a risk-free rate of 4% with a market risk premium of 8%, is closest to:

How sure are you?

Correct: B. CAPM expected return = Rf + Beta x (Rm - Rf) = 4% + 1.1 x 8% = 4% + 8.8% = 12.8%. Jensen's alpha = Actual return - CAPM expected return = 16% - 12.8% = 3.2%. Option A incorrectly calculates 4% + 1.0 x 8% = 12% (ignores beta multiplier). 1 x 8.36% which is arithmetic error. This question is a prerequisite to Jensen's alpha. The exam often asks for alpha in the follow-on question.
A. You might forget to multiply by beta and uses 4% + 8% = 12%. CAPM multiplies the risk premium by beta. With beta 1.1, the premium contribution is 1.1 x 8% = 8.8%, not 8%.
C. You might multiply beta by market return (4% + 1.1 x 8.36%) due to arithmetic confusion. Market risk premium is the stated 8%. Do not recalculate it. Use it as given.

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

Question 14Exam level

Using the same data as the previous question (portfolio return 16%, CAPM expected return 12.8%), jensen's alpha for this portfolio is closest to:

How sure are you?

Correct: A. Jensen's alpha = Rp - [Rf + Beta x (Rm - Rf)] = 16% - 12.8% = 3.2%. A positive alpha indicates the manager generated excess return above what CAPM predicted given the portfolio's systematic risk. Option B (4%) is the raw excess return above the risk-free rate, not Jensen's alpha. Option C has no basis in the given data. The exam tests whether candidates know alpha is measured against CAPM expectation, not against the risk-free rate or market return.
B. You might subtract only the risk-free rate: 16% - 4% = 4% (confusing Sharpe's numerator with Jensen's alpha). Jensen's alpha subtracts the FULL CAPM expected return (12.8%), not just the risk-free rate (4%). The 4% result is the Sharpe numerator, not the alpha.
C. Option C has no basis in the given data.

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

Question 15Exam level

Portfolio X has a Treynor ratio of 0.08 and Portfolio Y has a Treynor ratio of 0.06. An investor holding a diversified market portfolio is considering adding one of these funds. Which fund should the investor most likely prefer, and why?

How sure are you?

Correct: B. For a fully diversified investor, systematic risk (beta) is the only relevant risk measure. Unsystematic risk has been eliminated. The Treynor ratio measures (Rp - Rf) / Beta, i.e., excess return per unit of systematic risk. A higher Treynor ratio is better. Portfolio X at 0.08 outperforms Portfolio Y at 0.06 on this basis. Option A describes the Sharpe ratio (total risk).
A. The conclusion (Portfolio X) is correct but the reasoning describes Sharpe, not Treynor. Treynor uses SYSTEMATIC risk (beta), not total risk (sigma). An answer with correct conclusion but wrong reasoning is wrong on the CFA exam.
C. Students who confuse the Sharpe/Treynor decision rule may invert it. This completely reverses the correct rule. Treynor IS appropriate for diversified investors (because they have eliminated unsystematic risk). Sharpe is appropriate for undiversified standalone portfolios.

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

Question 16Exam level

An active equity manager has an information ratio of 0.65 and a tracking error of 5.0%. The manager's annual active return (alpha) relative to the benchmark is closest to:

How sure are you?

Correct: B. Information Ratio = Active Return / Tracking Error. Therefore Active Return = IR x Tracking Error = 0.65 x 5.0% = 3.25%. The information ratio measures the consistency of active returns relative to active risk taken. Option A divides tracking error by IR (inverted). The exam tests the formula rearrangement: given IR and TE, solve for active return.
A. You might divide 0.65 by 5.0 (inverts the formula). IR = Active Return / TE. Rearranging: Active Return = IR x TE = 0.65 x 5% = 3.25%. Dividing gives the inverse.
C. You might be tempted to choose 7.69% if you incorrectly multiplied the information ratio by 10 instead of the tracking error percentage, confusing the scale of the inputs; this choice violates the correct formula application by using an incorrect multiplier, leading to an inflated active return figure.

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

Question 17Exam level

Three portfolios have the following characteristics. Risk-free rate is 2%. Portfolio P: Return 10%, Std Dev 15%, Beta 0.8. Portfolio Q: Return 13%, Std Dev 20%, Beta 1.1. Portfolio R: Return 9%, Std Dev 12%, Beta 0.7. Rank these portfolios from best to worst using the Sharpe ratio, most likely.

How sure are you?

Correct: B. Sharpe P = (10-2)/15 = 8/15 = 0.533. Sharpe Q = (13-2)/20 = 11/20 = 0.550. Sharpe R = (9-2)/12 = 7/12 = 0.583. Ranking: R = 0.583 > Q = 0.550 > P = 0.533. Portfolio R has the LOWEST absolute return but the BEST Sharpe ratio because its risk (sigma = 12) is lowest. Portfolio Q has the highest return but middle Sharpe because of high volatility. The exam tests whether candidates realize that absolute return ranking (Q > P > R) is NOT performance ranking.
A. Q has the highest absolute return. You might default to raw return ranking. Q's high sigma (20) penalises its Sharpe ratio despite the high return. Calculate before ranking.
C. P has the middle return and middle sigma. This seems 'balanced' and candidates place it first. R's lower sigma (12 vs 15) gives it a superior ratio even with lower return. Arithmetic must be done, not estimated.

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

Question 18Exam level

Portfolio Z has a Sharpe ratio of -0.15. Portfolio W has a Sharpe ratio of -0.30. Which portfolio performed better on a risk-adjusted basis, most likely?

How sure are you?

Correct: B. When the Sharpe ratio is negative (portfolio return below the risk-free rate), the standard interpretation still holds mathematically: a higher (less negative) ratio is better. Portfolio Z at -0.15 lost less per unit of risk than Portfolio W at -0.30. However, the deeper CFA exam point is this: when comparing two portfolios with NEGATIVE Sharpe ratios, adding more risk can paradoxically make the Sharpe 'look better' (less negative) even though more risk was taken. This is the known breakdown of Sharpe ratio ranking when returns are below the risk-free rate. Option C is true but does not answer the ranking question.
A. You might assume more negative = smaller denominator = less risk taken. The negative sign reflects the numerator (return below Rf), not the denominator. A more negative Sharpe means MORE underperformance per unit of risk, not less risk taken.
C. True statement. But it does not answer 'which performed better'. Both underperformed the risk-free rate is correct (negative Sharpe confirms this) but the question asks for a relative ranking, not whether either beat the hurdle.

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

Question 19Exam level

Which of the following statements about the Information Ratio is MOST accurate?

How sure are you?

Correct: A. IR = (Rp - Rb) / Tracking Error, where Rb is the benchmark return and tracking error is the standard deviation of (Rp - Rb). It measures whether the active return generated per unit of active risk is consistent and positive. I.e., the manager's skill in generating alpha relative to the volatility of that alpha. Option A is wrong. Higher IR means BETTER risk-adjusted active returns, not more risk taken. Option C describes the Treynor ratio.
B. Beta appears in Treynor ratio; candidates conflate the two measures. The IR denominator is tracking error (std dev of active returns), not beta. Beta is the Treynor denominator.
C. Zero IR suggests no performance difference from the benchmark, which sounds like 'matched benchmark'. IR of zero means active return = zero (numerator is zero). It says nothing about tracking error (denominator). A manager could have zero active return with significant tracking error. Still IR = 0, but high active risk.

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

Question 20Exam level

A portfolio manager's fund returned 11.5% over the past year. The benchmark returned 9.0%. The fund's tracking error was 4.0%. The Information Ratio is closest to:

How sure are you?

Correct: A. Active return = Portfolio return - Benchmark return = 11.5% - 9.0% = 2.5%. Information Ratio = Active Return / Tracking Error = 2.5% / 4.0% = 0.625. An IR above 0.5 is generally considered a good active management result. Option B divides 11.5 by 4.0 (uses portfolio return, not active return). Option C divides 4.0 by 2.5 (inverted).
B. You might use portfolio return (11.5%) in the numerator instead of active return (2.5%): 11.5/4.0 = 2.875. The IR numerator is ACTIVE return = Rp - Rb = 11.5% - 9.0% = 2.5%. Using total portfolio return is the most common IR calculation error.
C. You might invert the formula: tracking error / active return = 4.0/2.5 = 1.6... then divides again. IR = active return divided by tracking error, not tracking error divided by active return.

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

Question 21Harder

Which performance measure would be MOST appropriate when comparing the performance of mutual fund managers who each manage a single fund that represents the investor's ENTIRE portfolio?

How sure are you?

Correct: C. When the fund IS the investor's entire portfolio. I.e., there is no broader diversified portfolio in which this fund is just one component. Total risk (standard deviation) is the relevant risk measure. The investor bears ALL the risk of the fund, including its unsystematic risk. Therefore the Sharpe ratio, which uses total standard deviation in the denominator, is the appropriate measure. Treynor (Option A) is only appropriate when the fund is a sub-component of a larger diversified portfolio where unsystematic risk has been eliminated. Jensen's alpha (Option B) measures raw skill but not risk per unit. It does not account for how much total risk was taken.
A. The phrase 'mutual fund manager' triggers 'professional = diversified = Treynor' pattern matching. The question specifies this fund IS the entire portfolio. The diversification assumption breaks down. Treynor ignores unsystematic risk, which the investor fully bears when this is their only holding.
B. Jensen's alpha seems 'most rigorous' and candidates prefer it as a catch-all measure. Jensen's alpha measures whether a manager beat CAPM expectations. It does not rank managers on how much total risk they took per unit of return. Sharpe does that.

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

Question 22Exam level

Portfolio A: Return 15%, Beta 1.3, Std Dev 20%. Portfolio B: Return 12%, Beta 0.8, Std Dev 14%. Risk-free rate 3%, Market return 10%. Calculate Jensen's alpha for both portfolios and identify which manager added more value relative to market expectations, most likely.

How sure are you?

Correct: A. CAPM expected return A = 3% + 1.3 x (10% - 3%) = 3% + 9.1% = 12.1%. Alpha A = 15% - 12.1% = 2.9%. CAPM expected return B = 3% + 0.8 x 7% = 3% + 5.6% = 8.6%. Alpha B = 12% - 8.6% = 3.4%. Despite Manager A achieving a higher absolute return (15% vs 12%), Manager B's Jensen's alpha is higher (3.4% vs 2.9%) because Manager B took on less systematic risk. Manager B generated more return per unit of CAPM-predicted risk. This is the core insight Jensen's alpha provides over raw returns.
B. You might subtract only the risk-free rate from each portfolio's return instead of computing the full CAPM expected return. Using the market return directly instead of the risk premium (market return minus the risk-free rate) in the CAPM formula produces inflated expected returns and the wrong alphas.
C. Alpha A (2.9%) is correct, but candidate calculates Alpha B wrong: 12% - [3% + 0.8 x 8.5%] using wrong risk premium. Market risk premium = 10% - 3% = 7%, not 8.5%. CAPM B = 3% + 0.8 x 7% = 8.6%, giving Alpha B = 3.4%.

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

Question 23Above 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 24Above 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