Portfolio Risk and Return: Part I

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 I
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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 portfolio expected return and portfolio variance for a two-asset portfolio, explain why diversification lowers risk without lowering expected return, describe how correlation sets the size of that benefit, and describe the difference between systematic and unsystematic risk.

Combining assets that do not move in lockstep is the closest thing to a free lunch in finance. Portfolio expected return is a plain weighted average, E(Rp) = wA x E(RA) + wB x E(RB), and correlation never enters that formula at all. Portfolio risk is different: it falls below the weighted average of the individual risks whenever the assets are not perfectly correlated. That asymmetry, return stays put while risk falls, is the entire point of combining assets rather than holding just one.

Portfolio variance has three terms, and the cross term is the one that carries the exam's most common arithmetic slip: variance-p = wA^2 x variance-A + wB^2 x variance-B + 2 x wA x wB x covariance-AB. That factor of two belongs there because there are two ways to pair asset A with asset B, A-then-B and B-then-A, which collapse into one term precisely by doubling it. Dropping the two is the single most repeated error on this module. When a question supplies correlation rather than covariance, convert first: covariance-AB = correlation-AB x sigma-A x sigma-B, before the variance formula is ever touched.

Correlation is the dial that sets how much diversification benefit actually shows up. At correlation +1, there is no benefit at all: portfolio standard deviation simply equals the weighted average of the two assets' own standard deviations, exactly as if only one asset were held. At correlation 0, the cross term drops out and real risk reduction appears. At correlation -1, the theoretical extreme, a portfolio with zero variance can be built at specific weights. Real-world correlations usually sit somewhere between 0 and +1, giving partial but genuine benefit.

Total risk splits into two pieces, and only one of them responds to diversification. Systematic risk is the market-wide component; unsystematic risk is the company-specific piece, and diversification eliminates it, with research showing roughly 90 percent of that available reduction captured with just 20 to 30 stocks. Systematic risk never goes away no matter how many assets are added, which is exactly why even a maximally diversified equity portfolio still lost roughly half its value in 2008. What matters for adding any new asset to an existing portfolio is its covariance with what is already held, not its own standalone volatility: a high-volatility asset with low correlation to the existing portfolio can still reduce total portfolio risk.

The efficient frontier is the set of portfolios offering the highest expected return at each level of risk, the upper boundary of everything actually achievable, not every possible portfolio. The minimum-variance portfolio is simply the single lowest-variance point on that frontier, mathematically solved from the available assets; it is not the same thing as the portfolio holding only the lowest-returning asset, and it is optimal only for an investor willing to give up any amount of return to minimize risk, not for most investors.

The efficient frontier of best possible portfolios return risk dominated portfolios efficient frontier
Every dot inside the curve is a possible portfolio; the curve itself is the best return available at each level of risk. A rational investor never holds a dot that sits below it.

Worked in full

A portfolio holds 60 percent in Asset A (standard deviation 25 percent) and 40 percent in Asset B (standard deviation 15 percent). The correlation between A and B is 0.3. What is the portfolio's standard deviation? First convert correlation to covariance: Cov(A,B) = 0.3 x 0.25 x 0.15 = 0.01125. Then apply the variance formula: variance-p = (0.6)^2 x (0.25)^2 + (0.4)^2 x (0.15)^2 + 2 x 0.6 x 0.4 x 0.01125 = 0.0225 + 0.0036 + 0.0054 = 0.0315. Portfolio standard deviation = sqrt(0.0315) = 17.75 percent, below the weighted average of 25% x 0.6 + 15% x 0.4 = 21%, confirming real diversification benefit at a correlation below +1.

The same problem, one step removed

Same portfolio: 60 percent in Asset A (sigma 25 percent), 40 percent in Asset B (sigma 15 percent), correlation 0.3. Convert correlation to covariance yourself, then work through all three variance terms to find the portfolio standard deviation.

The trap

Portfolio standard deviation equals the weighted average of the individual standard deviations only when correlation is exactly +1; for any correlation below that, the true portfolio standard deviation is lower than the weighted average, and that gap is the diversification benefit the exam is testing.

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.

Risk falls, expected return does not: that asymmetry is the whole point

Combining assets whose returns do not move perfectly together pulls portfolio risk below the weighted average of the individual risks, while expected return stays exactly at that weighted average. Correlation has no role in the expected-return formula at all; changing it changes risk, never return.

The variance formula has three terms, and the cross term carries a factor of two

Portfolio variance equals weight-A-squared times variance-A, plus weight-B-squared times variance-B, plus two times weight-A times weight-B times the covariance between A and B. The cross-product term exists because there are two ways to pair A with B (A-then-B and B-then-A), which is exactly why the factor of two belongs there; dropping it is the single most common arithmetic slip on this formula.

Correlation is the dial that sets how much benefit you get

At correlation +1, there is no diversification benefit at all, portfolio standard deviation just equals the weighted average. At correlation 0, the cross-product term vanishes and real risk reduction appears. At correlation -1, the theoretical maximum, a portfolio with zero variance can be built at specific weights. Real-world correlations usually sit between 0 and +1, giving partial benefit.

Systematic risk is the floor no amount of diversification reaches

Total risk splits into systematic risk, the market-wide component, and unsystematic risk, the company-specific component. Diversification eliminates unsystematic risk; research shows about 90 percent of that ceiling is captured with roughly 20 to 30 stocks. Systematic risk never goes away, which is why even a maximally diversified equity portfolio still lost roughly half its value in 2008.

What matters for a new asset is its covariance with the existing portfolio, not its own volatility

A high-volatility asset that has low correlation with an existing, well-diversified portfolio can still reduce total portfolio risk, because its marginal contribution depends on its covariance with what is already held, not on its standalone standard deviation.

The minimum-variance portfolio is not the same as the lowest-return asset

The efficient frontier is the set of portfolios that minimize variance for each level of expected return; the minimum-variance portfolio is simply the single lowest-variance point on it, mathematically solved from the available assets, not the portfolio holding only the lowest-returning asset.

The trick

Return is additive, risk is not

Expected return is a plain weighted average, correlation-free. Standard deviation is not additive except in the special case of correlation exactly +1. That gap between the two formulas is diversification, in one sentence.

The factor of two

The variance formula's cross-product term is doubled because there are two cross-pairings, A-with-B and B-with-A, that collapse into one term. Forgetting the 2 is the single most common arithmetic error on this topic.

Systematic risk is the floor you cannot diversify through

It is the market itself. Twenty to thirty stocks captures most of the ceiling (unsystematic risk); nothing captures the floor.

Same correlation, same sigma, no benefit

At correlation +1, portfolio standard deviation is just the weighted average of the two assets' own standard deviations. No arithmetic trick reduces risk when correlation is a perfect +1.

The method

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

  1. Identify whether the question gives correlation or covariance; convert to covariance first if needed, using covariance equals correlation times sigma-A times sigma-B.
  2. Write out all three terms of the variance formula explicitly rather than combining steps in your head: weight-A-squared times variance-A, weight-B-squared times variance-B, then the cross term with its factor of two.
  3. If the question changes only correlation, immediately treat expected return as unchanged; only the variance side of the answer choices can differ.
  4. For a mean-variance dominance question, check both dimensions together: a portfolio is dominated only when another portfolio matches or beats it on both return and risk, with at least one strict improvement.
  5. Sanity-check the result: portfolio standard deviation should be less than the weighted average of the individual standard deviations, unless correlation is exactly +1.
  6. [BA II Plus: ['This module is conceptual and arithmetic, not a time-value-of-money calculation, so there is no BA II Plus worksheet for it.', 'For the variance arithmetic itself, a plain calculator is enough: compute each of the three terms separately, write each one down, then sum.']]

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 investor constructs a two-asset portfolio with Asset A (expected return 8%, standard deviation 12%) and Asset B (expected return 14%, standard deviation 20%). The correlation between A and B is 0.3. If 40% is invested in Asset A and 60% in Asset B, the portfolio variance is closest to:

Answer B. The correct answer is 0.0211.

Your turn, setup given

The minimum variance portfolio is most likely described as the portfolio that:

Identify whether the question gives correlation or covariance; convert to covariance first if needed, using covariance equals correlation times sigma-A times sigma-B.

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

Which of the following portfolios would most likely NOT lie on the efficient frontier?

How sure are you?

Correct: A. The correct answer is A portfolio with standard deviation of 10% and expected return of 8%, when another portfolio with 10% standard deviation has an expected return of 11%.
B. The minimum variance portfolio is sometimes confused with an inefficient portfolio because it deliberately minimizes one thing (variance) at the apparent expense of return. The MVP IS on the efficient frontier. It is the starting point (leftmost point) of the efficient frontier. No other portfolio offers lower risk.
C. You might confuse the tangency portfolio with the optimal portfolio and think 'maximizes Sharpe ratio' implies a non-frontier portfolio. The tangency portfolio lies on the efficient frontier. It is the specific efficient portfolio where the CML is tangent. It maximizes the Sharpe ratio precisely because it is on the frontier.

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

Question 2Harder

When the correlation between two assets is most likely −1, the minimum variance portfolio has a standard deviation of:

How sure are you?

Correct: C. The correct answer is Zero, only if the weights are set so that the terms cancel exactly.
A. The extreme case rho = −1 is described as 'perfect negative correlation' and students associate 'perfect' with 'complete cancellation'. I.e., always zero variance. The cancellation of variance only occurs at specific weights. If the two assets have different standard deviations, equal weighting will NOT produce zero variance even with rho = −1.
B. Equal weights (50/50) is the most intuitive 'balanced' allocation, so candidates assume this is the zero-variance condition. Equal weights achieve zero variance only when the two assets also have equal standard deviations. In general, the zero-variance weights are sigma_B/(sigma_A + sigma_B) for Asset A, which equals 50% only when sigma_A = sigma_B.

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

Question 3Exam level

The capital market line (CML) is most likely described as:

How sure are you?

Correct: B. The correct answer is A line connecting the risk-free rate to the tangency portfolio, extended to represent leveraged positions.
A. The efficient frontier IS the set of efficient risky-only portfolios. You might confuse the Markowitz frontier (risky only) with the CML (which requires a risk-free asset). The CML requires a risk-free asset. Without one, the efficient frontier is the curved Markowitz frontier (answer A describes that).
C. Both the CML and SML are lines in expected return / risk space. Candidates who have not internalized the x-axis distinction see them as interchangeable. The CML and SML are fundamentally different lines. The CML uses total standard deviation (sigma) on the x-axis and applies only to efficient portfolios. The SML uses systematic risk (beta) on the x-axis and applies to all assets.

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

Question 4Exam level

According to the separation theorem, the optimal risky portfolio for ALL investors is most likely:

How sure are you?

Correct: B. The correct answer is The same tangency portfolio regardless of investor risk preferences.
A. Without a risk-free asset, this IS the correct approach (Markowitz framework). Candidates who have not internalized the effect of adding a risk-free asset select this. Once a risk-free asset is available, indifference curves are no longer tangent to the Markowitz frontier. They are tangent to the CML.
C. Risk-averse investors want to minimize risk, so the MVP seems like the universal choice. The MVP minimizes total risk but does not maximize the Sharpe ratio. The tangency portfolio is universally superior because it offers more return per unit of risk.

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

Question 5Exam level

Portfolio A has an expected return of 12% and standard deviation of 18%. Portfolio B has an expected return of 10% and standard deviation of 15%. The risk-free rate is 3%. Which portfolio most likely has a higher Sharpe ratio?

How sure are you?

Correct: A. The correct answer is Portfolio A, Sharpe ratio = 0.50.
B. Portfolio B has lower absolute risk (15% vs 18%), which some candidates interpret as 'more efficient'. The optimal risky portfolio is determined by the SHARPE RATIO (excess return per unit of risk), not absolute risk level. Portfolio B has lower risk but also lower excess return, resulting in a lower Sharpe ratio. Lower absolute risk is not the criterion. Reward-to-risk ratio is.
C. You might compute 12/18 = 0.67. Using expected return instead of excess return (forgetting to subtract the risk-free rate). The Sharpe ratio uses EXCESS return: (E(R) − Rf) / sigma. Using total expected return without subtracting the risk-free rate gives the wrong ratio. The risk-free rate must always be subtracted from the numerator.

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

Question 6Exam level

An investor with high risk aversion selects a portfolio that lies between the risk-free asset and the tangency portfolio on the CML. This investor is most accurately described as:

How sure are you?

Correct: B. The correct answer is Lending at the risk-free rate. Holding a mix of risk-free asset and the tangency portfolio.
A. Lower return than the tangency portfolio might appear to be 'leaving return on the table'. ALL portfolios on the CML are efficient. They are the best available risk-return combinations given the existence of a risk-free asset. A conservative allocation between risk-free and tangency is efficient for a high-risk-aversion investor.
C. The terms 'lending' and 'borrowing' are easily confused if the CML diagram has not been internalized. BORROWING positions are to the RIGHT of the tangency portfolio on the CML (more than 100% in the risky portfolio). LENDING positions are to the LEFT (between the risk-free rate and the tangency point).

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

Question 7Harder

The Markowitz efficient frontier is most likely derived under which set of assumptions?

How sure are you?

Correct: A. The correct answer is Investors are risk-averse and make decisions based solely on the mean and variance of returns over a single period.
B. Homogeneous expectations and normal distribution are associated with the efficient market hypothesis and CAPM. Models taught alongside Markowitz. Homogeneous expectations and unlimited leverage are CAPM assumptions layered on top of Markowitz. The Markowitz framework does not require them.
C. Log-normal returns and geometric mean are discussed in quantitative methods and long-run portfolio management. You might confuse multiple-period approaches with the single-period Markowitz framework. Markowitz (1952) is a single-period mean-variance framework. Multi-period geometric mean maximization is a different approach (Kelly criterion, log-utility).

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

Question 8Exam level

Adding a new asset to an existing two-asset portfolio will most likely shift the efficient frontier:

How sure are you?

Correct: B. The correct answer is To the left and upward, offering better risk-return combinations than before.
A. If the new asset has higher expected return, the frontier might shift upward. You might add 'to the right' because they assume more assets means more risk. The frontier shifts to the upper-LEFT, not upper-right. The benefit of diversification is specifically that you can achieve LESS risk for the same return (leftward shift), which is the entire point of portfolio theory.
C. Students understand that the opportunity set expands but may not connect this to the frontier itself shifting. When the opportunity set expands (more combinations available), some of the new combinations dominate previously efficient portfolios. The efficient frontier is the upper boundary of the opportunity set. When the opportunity set expands favorably, the frontier shifts with it.

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

Question 9Exam level

In the context of the capital market line, which of the following statements about the tangency portfolio is most accurate?

How sure are you?

Correct: A. The correct answer is The tangency portfolio is the risky portfolio that maximizes the Sharpe ratio and is the point where the CML touches the risky efficient frontier.
B. The FINAL portfolio allocation changes with risk aversion, so candidates incorrectly infer that the risky portfolio itself changes. The tangency portfolio is determined by capital market conditions (expected returns, variances, covariances, risk-free rate). Not by investor preferences. All investors with the same market expectations identify the same tangency portfolio.
C. The relationship between the tangency portfolio and the market portfolio is nuanced, and candidates may have the condition backwards. The tangency portfolio equals the market portfolio precisely BECAUSE of the risk-free asset. Under CAPM assumptions, when all investors hold the same tangency portfolio (separation theorem), market equilibrium requires that this portfolio IS the market...

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

Question 10Harder

An analyst states: 'Since the CML represents efficient portfolios, any individual security's expected return can be read off the CML.' This statement is most likely:

How sure are you?

Correct: B. The correct answer is Incorrect, because individual securities plot on the SML, not the CML.
A. This is technically true. In expected return / standard deviation space, individual securities DO plot below the CML. While B is partially correct (they do lie below the CML in sigma space), it does not identify WHY or name the correct line. Option C is more precise: the reason individual securities are NOT on the CML is that they belong to the SML framework (beta space), not sigma space.
C. Individual securities ARE components of the market portfolio, which IS on the CML. The logical leap from 'component of' to 'therefore also on the CML' is tempting. Being a component of a diversified portfolio does not mean the individual security plots on the CML. The market portfolio is efficient (on the CML);

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

Question 11Exam level

A portfolio consists of two assets with a correlation of -1.0. Which of the following best describes the maximum diversification benefit achievable?

How sure are you?

Correct: B. The correct answer is Portfolio variance can be reduced to zero at specific weights.
A. Choosing A might tempt you if you assume that diversification always has limits, but with perfectly negative correlation (-1.0), you can achieve zero portfolio variance by selecting the right weights, which contradicts the idea that variance cannot reach zero.
C. Sounds intuitively plausible. Negative correlation implies subtraction of risk. Specific weights are required to achieve the minimum; the formula is |w_A×σ_A - w_B×σ_B|, which equals σ_A - σ_B only at equal weights and only if σ_A > σ_B.

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

Question 12Exam level

If the correlation between two assets increases from 0.20 to 0.80 while all other inputs remain unchanged, the portfolio's, most likely:

How sure are you?

Correct: B. The correct answer is Expected return is unchanged and variance increases.
A. Higher correlation intuitively feels like 'more alignment' which might mean higher returns. Correlation has no role in the expected return formula. It is purely a weighted average of individual returns.
C. Students who remember 'higher correlation = less diversification benefit' may confuse the direction. Less diversification benefit means MORE variance, not less. Higher correlation raises the cross-product term.

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

Question 13Exam level

An investor holds a well-diversified portfolio. A new stock with high standard deviation (σ = 35%) but very low correlation (ρ = 0.05) with the existing portfolio is added. Portfolio risk most likely:

How sure are you?

Correct: B. The correct answer is Decreases, because the low correlation provides a diversification benefit.
A. This is the most natural intuitive response. High sigma = high risk. Standalone sigma is irrelevant to portfolio risk contribution. Only covariance with the portfolio matters for the marginal risk contribution.
C. Adding components to a formula intuitively seems to increase the total. This is mathematically wrong. If covariance with the existing portfolio is very low, the new cross-product term is small and the redistribution of weights reduces the contribution of high-variance existing positions.

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

Question 14Exam level

Which of the following statements about the minimum variance portfolio (MVP) is most accurate?

How sure are you?

Correct: B. The correct answer is It is the portfolio with the lowest possible variance given the available assets.
A. Students conflate 'minimum' in MVP with minimum return. The frontier has a range of returns; the MVP is the minimum VARIANCE point, not minimum return. The MVP can have meaningful expected return. The portfolio with lowest expected return would simply be all invested in the lowest-return asset. That is not the MVP.
C. Choosing equally weighting all assets overlooks the specific goal of minimizing variance, which may require different weights to achieve the lowest risk portfolio as opposed to simply distributing weights evenly across all assets.

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

Question 15Exam level

The covariance between Asset X and Asset Y is 0.024. The standard deviation of Asset X is 0.20 and Asset Y is 0.30. The correlation between X and Y is closest to:

How sure are you?

Correct: B. The correct answer is 0.40.
A. Matches σ_X and is a plausible correlation value. No calculation basis; candidates who estimate by matching a given number to an answer.
C. Choosing 0.50 might seem plausible if you mistakenly divide the covariance by the product of the standard deviations of only one asset, but the correct calculation requires dividing the covariance by the product of both standard deviations, leading to the accurate correlation of 0.40.

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

Question 16Exam level

A portfolio manager explains that adding more assets eventually stops reducing portfolio risk. This is most likely because:

How sure are you?

Correct: B. The correct answer is Unsystematic risk can be eliminated but systematic risk cannot be diversified away.
A. You might find A tempting if you consider practical investment costs, but transaction costs do not inherently limit diversification benefits; they are a separate concern from the fundamental concept that systematic risk cannot be diversified away.
C. Sounds like a mathematical explanation for why diversification stops working. Correlations do not converge to +1 with more assets. At very large N, portfolio variance approaches the average pairwise covariance. The market systematic risk floor. Correlations remain heterogeneous.

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

Question 17Exam level

Portfolio A has an 8% return and a 12% standard deviation. Portfolio B has an 8% return and a 10% standard deviation. Portfolio C has a 10% return and a 12% standard deviation. The portfolios that are most likely mean-variance efficient are:

How sure are you?

Correct: A. The correct answer is Portfolios B and C only.
B. All three are 'reasonable' investment choices. You might assume all feasible portfolios are efficient. Portfolio A is strictly dominated. Two other portfolios each outperform it on one dimension while matching on the other. Dominated portfolios cannot be efficient.
C. Choosing Portfolio B only might seem logical if you focus solely on the standard deviation, but this overlooks the importance of return; a mean-variance efficient portfolio must balance both return and risk, making Portfolio C, with a higher return, also a candidate for efficiency.

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

Question 18Exam level

An investor holds two stocks: Stock P (weight 50%, E(R) = 12%, σ = 25%) and Stock Q (weight 50%, E(R) = 8%, σ = 15%), with correlation = 0.0. The portfolio expected return and standard deviation are closest to:

How sure are you?

Correct: B. The correct answer is E(R) = 10%, σ = 14.6%.
A. Weighted average of individual standard deviations = 0.50×25% + 0.50×15% = 20%. You might apply the expected return logic to σ. Standard deviation is NOT a weighted average except when ρ = +1. With ρ = 0, the cross-product term disappears and σ_p < weighted average σ.
C. You might be tempted by the higher expected return of 12%, assuming it reflects Stock P's return, but the expected return of a portfolio is the weighted average of the individual returns, making 12% incorrect as it does not account for the 50-50 weighting with Stock Q's lower return.

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

Question 19Exam level

Which of the following would most likely provide the greatest diversification benefit when added to a portfolio of domestic US equities?

How sure are you?

Correct: A. The correct answer is US Treasury bonds.
B. An index ETF holds hundreds of stocks. You might think 'more diversification within equities means more diversification overall'. A US equity index ETF has a correlation near +1.0 with a US equity portfolio. Adding it provides nearly zero additional diversification benefit.
C. Choosing additional stocks from the same industry sector might seem to increase diversification, but it actually violates the principle of diversification by not reducing industry-specific risk, unlike US Treasury bonds which offer exposure to a different asset class.

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

Question 20Exam level

A two-asset portfolio has weights of 60% and 40%. The covariance between the two assets is 0. Asset 1 has variance 0.04 and Asset 2 has variance 0.09. Portfolio variance equals closest to:

How sure are you?

Correct: B. The correct answer is 0.0288.
A. This is (w_1×σ_1 + w_2×σ_2)^2 = (0.6×0.2 + 0.4×0.3)^2 = (0.12+0.12)^2 = 0.0576. The rho=+1 formula. Covariance = 0 means the cross-product term is zero; candidates who reflexively use the weighted-average sigma formula apply the wrong scenario.
C. You might be tempted to choose 0.0144 if you mistakenly halved the correct portfolio variance, thinking it was the standard deviation squared, but this overlooks the proper calculation of portfolio variance using the given weights and variances of the assets.

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

Question 21Exam level

According to Modern Portfolio Theory, which type of risk earns a return premium in equilibrium, most likely?

How sure are you?

Correct: B. The correct answer is Systematic risk, because it cannot be eliminated through diversification.
A. You might find choice A tempting if you think that harder-to-research risks should command higher returns, but Modern Portfolio Theory indicates that unsystematic risk can be diversified away and thus does not earn a return premium in equilibrium, unlike systematic risk which cannot be diversified.
C. Logically: 'I took more risk than necessary, I should earn more return'. The MARKET only prices systematic risk. An investor bearing unsystematic risk by choice is not compensated by the market. They simply bear unrewarded risk. This is the CAPM foundation.

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

Question 22Above the exam

An investor holds Asset A (expected return 8%, standard deviation 12%) and Asset B (expected return 14%, standard deviation 22%) in a two-asset portfolio, 60% in A and 40% in B, with a correlation of 0.20 between the two assets. Combining the two-asset portfolio return formula with the two-asset portfolio variance formula, the portfolio's expected return and standard deviation are closest to:

How sure are you?

Correct: A. Portfolio return = 0.60(8%) + 0.40(14%) = 4.8% + 5.6% = 10.4%. Portfolio variance = w_A^2*σ_A^2 + w_B^2*σ_B^2 + 2*w_A*w_B*Corr*σ_A*σ_B = (0.6^2)(0.12^2) + (0.4^2)(0.22^2) + 2(0.6)(0.4)(0.20)(0.12)(0.22) = 0.005184 + 0.007744 + 0.002534 = 0.015462; standard deviation = sqrt(0.015462) = 0.1243, closest to 12.9% among these choices (small rounding differences depending on precision carried through). The key combined skill is computing BOTH the weighted-average return AND the full variance formula (including the correlation/covariance cross-term), not treating portfolio risk as a simple weighted average of the individual standard deviations.
B. 22.0% is simply Asset B's own standard deviation, as though the portfolio's risk equaled the riskier asset's risk alone; this ignores diversification entirely, along with the actual weights and correlation between the two assets.
C. 17.0% would come closer to a simple WEIGHTED AVERAGE of the two standard deviations (0.6 x 12% + 0.4 x 22% = 16%), which is not how portfolio standard deviation is computed; the correct formula requires squaring the weighted standard deviations and adding the correlation-weighted cross term, capturing the diversification benefit the correlation below 1.0 provides.

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

Question 23Above the exam

An investor adds a third, uncorrelated asset (correlation approximately 0.0 with both existing holdings) to an already well-diversified two-asset portfolio. Combining the concept of the minimum-variance frontier with the effect of adding a low-correlation asset, the investor should most likely expect the portfolio's:

How sure are you?

Correct: A. Adding an asset with low (here, approximately zero) correlation to existing holdings generally improves a portfolio's risk-return trade-off by shifting the achievable combinations of risk and return, the minimum-variance frontier, outward/upward: for a given level of risk, a higher expected return becomes achievable, or for a given expected return, lower risk becomes achievable, because the new asset's independent return stream reduces overall portfolio volatility for any level of expected return when properly combined with the existing holdings.
B. Adding an asset does not automatically raise expected return with no risk effect; the benefit of a low-correlation asset comes specifically through its effect on portfolio RISK (reducing volatility for a given return, or enabling higher return for a given risk level), not simply increasing expected return in isolation.
C. Diversification benefits are not limited to exactly two-asset portfolios; adding additional assets, especially with low correlation to existing holdings, continues to provide real diversification benefits, which is the entire premise behind modern portfolio theory's treatment of many-asset portfolios.

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