26 cards · Stock Market & Investing · answer each one, then read the explanation. Your score tallies below. Looking for Two-asset portfolio variance & minimum-variance weights, worked example? Read the explainer.
An investor holds a portfolio of 30 stocks, all in the oil and gas sector. They believe this is well diversified because it contains many individual positions. What is the main flaw in this reasoning?
AHolding 30 stocks is too many — optimal diversification is achieved with exactly 10 to 15 stocks regardless of sector
BThe portfolio is actually well diversified because academic research shows that any 30 randomly selected stocks eliminate virtually all risk, sector concentration included
CDiversification requires exposure across sectors and asset classes, not just a large number of holdings — stocks in the same sector tend to be driven by the same risk factors (oil prices, regulation, geopolitical supply shocks), so a 30-stock single-sector portfolio still carries concentrated sector risk
DDiversification only matters for bond portfolios; equity portfolios benefit from concentration because it allows the investor to develop deep sector expertise
Correct answer: .
Diversification reduces unsystematic (company-specific) risk, but sector concentration leaves the portfolio exposed to systematic risks shared across the entire sector. Thirty oil-and-gas stocks will all suffer when oil prices crash, regardless of how many individual companies are held. True diversification requires spreading risk across uncorrelated or weakly correlated sectors and, ideally, asset classes. The option claiming 10-15 is optimal cites a number often quoted for eliminating most stock-specific risk within a diversified universe, but that finding assumes stocks are drawn from different industries. The option claiming 30 stocks always eliminate all risk misapplies the research — the studies assume random selection from the entire market, not from a single sector. The option limiting diversification to bonds is baseless; diversification is a universal principle of portfolio construction.
Source: CFA Institute, Portfolio Management: An Overview; Markowitz, 'Portfolio Selection' (1952)
According to Modern Portfolio Theory, what does the 'efficient frontier' represent?
AThe line connecting the risk-free rate to the highest-returning asset in the investable universe, representing the only rational investment strategy
BThe set of portfolios that offer the highest expected return for each level of risk (standard deviation), meaning no portfolio on the frontier can increase its expected return without also increasing its risk
CA single optimal portfolio that every investor should hold, regardless of their individual risk preferences or investment horizon
DThe boundary below which all portfolios are considered too risky for any rational investor, regardless of their risk tolerance
Correct answer: .
The efficient frontier, introduced by Harry Markowitz in 1952, is the set of optimal portfolios that offer the maximum expected return for a given level of risk (measured by standard deviation of returns). Portfolios below the frontier are sub-optimal because they deliver less return for the same risk or more risk for the same return. The option describing a floor below which all portfolios are too risky misunderstands the concept — different investors choose different points on the frontier based on their risk tolerance. The option describing a single portfolio confuses the frontier with the tangency portfolio (relevant when a risk-free asset is introduced). The option describing the Capital Market Line conflates it with the efficient frontier; the CML extends from the risk-free rate through the market portfolio but is a different concept.
Source: Markowitz, H. (1952), 'Portfolio Selection', Journal of Finance; CFA Institute, Portfolio Management curriculum
Two assets have expected returns of 8% and 12% respectively. If their returns are perfectly negatively correlated (correlation coefficient of −1), what is theoretically possible when combining them in a portfolio?
ANegative correlation has no effect on portfolio risk; only the individual standard deviations of each asset determine the portfolio's total risk regardless of how the assets co-move
BThe portfolio's expected return can exceed 12%, because negative correlation creates a synergy bonus that amplifies returns beyond either individual asset
CA correlation of −1 means one asset always gains exactly what the other loses, so combining them always produces a return of zero — the assets cancel each other out entirely
DThe portfolio's risk (standard deviation) can be reduced to zero at a specific weighting, while the expected return falls between 8% and 12% depending on the allocation chosen
Correct answer: .
When two assets are perfectly negatively correlated (correlation equals −1), there exists a specific combination of weights that reduces portfolio standard deviation to exactly zero — a risk-free portfolio — while the expected return is the weighted average of the two individual returns, falling between 8% and 12%. The option claiming returns can exceed 12% is wrong because portfolio expected return is always a weighted average of component returns, never exceeding the highest component. The option claiming zero total return confuses the variability of returns with their level; negative correlation means the assets move in opposite directions relative to their own means, not that one's gain literally equals the other's loss in absolute terms. The option denying any effect of correlation on portfolio risk contradicts the portfolio variance formula, where the covariance term directly reduces or increases total risk.
Source: CFA Institute, Portfolio Risk and Return: Part I; Markowitz portfolio variance formula
An investment analyst explains that a stock's total risk can be split into two components: risk from broad market-wide factors affecting nearly all securities, and risk specific to the individual company or its industry. Which statement correctly distinguishes these two components and how diversification affects each?
ABoth components can be eliminated entirely by holding enough different asset classes, since diversification removes all forms of risk given a large enough portfolio
BThe company-specific component (unsystematic risk) cannot be reduced by diversification, while the market-wide component (systematic risk) can be fully eliminated by holding 20-30 stocks
CThe company-specific component (unsystematic risk) can be reduced or eliminated by holding a diversified portfolio, while the market-wide component (systematic risk) reflects factors like interest rates, inflation, and economic cycles that affect all securities and cannot be diversified away
DSystematic risk only applies to bonds and other fixed-income securities, while unsystematic risk only applies to equities, so investors holding both asset classes automatically eliminate all risk
Correct answer: .
Total risk decomposes into systematic risk, driven by economy-wide factors like interest rates, inflation, and business cycles that affect virtually every security, and unsystematic risk, arising from factors specific to one company or industry, such as a product recall or a management scandal. Because unsystematic events are largely independent across companies, combining many different holdings causes their idiosyncratic swings to average out, reducing that portion of total risk. Systematic risk cannot be diversified away because it stems from forces that hit the entire market simultaneously, no matter how many securities are held. The option promising complete elimination of all risk misstates the limits of diversification. The option reversing which type is diversifiable inverts the correct relationship. The option restricting each risk type to a single asset class is incorrect: both stocks and bonds carry their own systematic and unsystematic components.
Source: CFA Institute, Portfolio Risk and Return: Part I; Markowitz, H. (1952), 'Portfolio Selection', Journal of Finance
Two assets, X and Y, have a correlation coefficient of exactly +1 (perfect positive correlation). If an investor combines them in a portfolio, what is true about the diversification benefit?
AThere is no diversification benefit: the portfolio's standard deviation is simply the weighted average of the two assets' individual standard deviations, because the assets always move in the same direction by the same proportional amount
BThe diversification benefit is maximized, since perfectly positively correlated assets naturally offset each other's price movements over time
CThe portfolio's risk drops to zero regardless of the weights chosen, just as it would with a correlation of -1
DPerfect positive correlation means the two assets have identical expected returns, so combining them changes nothing about the portfolio's return or risk
Correct answer: .
When two assets are perfectly positively correlated, they move in the same direction by the same proportional amount relative to their own means, so the portfolio's standard deviation reduces mathematically to the simple weighted average of the two individual standard deviations — the covariance term contributes no offsetting effect. This is the worst case for diversification: no combination of weights reduces risk below that weighted average. The option claiming maximized diversification benefit describes the opposite extreme, a correlation of -1, where risk can be reduced to zero at some weighting. The option claiming risk falls to zero confuses this case with perfect negative correlation. The option claiming identical expected returns is a non sequitur: correlation describes how two assets' returns move together, not whether their expected returns are equal, which is a separate and unrelated input.
Source: CFA Institute, Portfolio Risk and Return: Part I; Markowitz portfolio variance formula
An investment policy sets a long-term target of 60% equities and 40% bonds meant to stay in place for years, based on the investor's goals and risk tolerance. A portfolio manager also makes short-term adjustments around this target — for example, temporarily overweighting equities by 5% because they believe stocks are attractively priced this quarter. What are these two practices called, respectively?
ABoth practices are called strategic asset allocation; there is no separate term for short-term adjustments around a long-term target
BThe long-term target is called tactical asset allocation, and the short-term adjustment is called strategic asset allocation
CThe long-term target is called the efficient frontier, and the short-term adjustment is called the capital allocation line
DThe long-term target is called strategic asset allocation, and the short-term, opportunistic deviation from it is called tactical asset allocation
Correct answer: .
Strategic asset allocation is the long-term target mix set based on an investor's goals, time horizon, and risk tolerance, and it is meant to be revisited only infrequently as those underlying circumstances change. Tactical asset allocation refers to deliberate, typically short-term deviations from that target, taken in an attempt to exploit a manager's view that one asset class is temporarily mispriced or offers better near-term prospects. The option swapping the two definitions reverses which term applies to the long-term policy versus the short-term deviation. The option invoking the efficient frontier and capital allocation line misapplies terms that describe risk-return trade-offs among portfolios on a risk-return graph, not the strategic-versus-tactical allocation distinction. The option denying any separate term for short-term deviations ignores a standard and widely used distinction in portfolio management practice.
Source: CFA Institute, Portfolio Management: An Overview; CFA Institute, Basics of Portfolio Planning and Construction
A financial education course explains that portfolios commonly shift their target mix toward a higher proportion of bonds and cash and a lower proportion of equities as an investor's investment time horizon shortens. What is the primary risk-based rationale most commonly given for this pattern?
ABonds always produce higher total returns than equities over any time horizon, so shifting toward bonds improves expected returns regardless of the investor's time horizon
BA shorter time horizon leaves less time to recover from a market downturn before the funds are needed, so reducing exposure to equities' higher volatility lowers the risk of having to sell at a loss
CEquities become illegal to hold in tax-advantaged retirement accounts once an investor is within ten years of retirement, under securities regulations
DBond prices become less volatile than equity prices only after an investor turns 50, which is an age-based rule set by financial regulators
Correct answer: .
Equities historically carry higher short-term volatility than bonds, and a market downturn can take multiple years to recover from. An investor with a long time horizon can typically wait out such a downturn before needing to withdraw funds, but an investor approaching the point of needing the money has less time to recover and a higher chance of being forced to sell equities at a depressed price. Reducing equity exposure and increasing bonds and cash as the horizon shortens is a standard way to manage this shrinking recovery window, often implemented through a target-date fund's glide path. The option claiming bonds always outperform equities is false over most historical periods and horizons. The two remaining options invent fictitious legal restrictions and age-based regulatory rules that do not exist; no securities regulation prohibits holding equities in retirement accounts based on age, and bond volatility is a market phenomenon, not a rule tied to an investor's birthday.
Source: SEC, Investor.gov, 'Target-Date Funds'; CFA Institute, Basics of Portfolio Planning and Construction
An investor combines a single risky portfolio with a position in a risk-free asset (such as short-term government bills), varying the proportion invested in each. What does the resulting straight line of possible risk-return combinations represent?
AThe Capital Allocation Line (CAL): a straight line running from the risk-free rate through the chosen risky portfolio's risk-return point, showing all combinations available by mixing that portfolio with the risk-free asset
BThe efficient frontier, which by definition always includes the risk-free asset as one of its constituent holdings
CThe security market line, which plots expected return against a security's beta rather than against portfolio standard deviation
DA single fixed portfolio recommended for all investors regardless of their allocation between the risky and risk-free assets
Correct answer: .
The Capital Allocation Line plots every possible combination of expected return and standard deviation achievable by mixing one specific risky portfolio with the risk-free asset, forming a straight line from the risk-free rate (zero risk) through that portfolio's own risk-return point, and beyond it if borrowing at the risk-free rate to hold more than 100% in the risky portfolio is allowed. It is a single line tied to whichever risky portfolio was chosen, not the entire efficient frontier of risky-asset-only portfolios, which by construction excludes the risk-free asset entirely. The option describing the security market line confuses a different graph, one that relates expected return to a security's beta as part of the Capital Asset Pricing Model, not to combining a risky portfolio with a risk-free asset. The option describing a single universally recommended portfolio ignores that different investors choose different points along the same CAL based on their own risk tolerance.
Source: CFA Institute, Portfolio Risk and Return: Part II; Tobin, J. (1958), 'Liquidity Preference as Behavior Towards Risk'
An investor sets a target allocation of 60% stocks and 40% bonds for a $100,000 portfolio. After a strong year for stocks, the portfolio grows to $130,000, with stocks now worth $85,000 (about 65.4%) and bonds worth $45,000 (about 34.6%). To rebalance back to the 60/40 target, what should the investor do?
ASell all bonds and hold the entire $130,000 in stocks, since stocks have been outperforming and momentum suggests this trend will continue
BBuy more stocks and sell bonds, since the target percentages should be adjusted upward to match whichever asset class most recently outperformed
CSell approximately $7,000 of stocks and buy approximately $7,000 of bonds, bringing the portfolio to $78,000 in stocks (60%) and $52,000 in bonds (40%) of the $130,000 total
DDo nothing, because the current 65.4%/34.6% split is close enough to the 60/40 target that rebalancing would only incur unnecessary transaction costs
Correct answer: .
Rebalancing to a target allocation means restoring the original target percentages of the current total portfolio value, not the original dollar amounts. Sixty percent of the new $130,000 total is $78,000, and forty percent is $52,000. Since stocks are currently at $85,000, the investor sells $85,000 minus $78,000, or $7,000, of stocks, and uses the proceeds to buy $7,000 of bonds, raising bonds from $45,000 to $52,000. This mechanically forces selling some of what has recently risen in value and buying some of what has lagged, a built-in discipline rather than a market-timing judgment call. The option of moving entirely into stocks abandons the target allocation based on a momentum belief that isn't supported by the rebalancing rule itself. The option raising the target for the outperforming asset class defeats the purpose of having a fixed target in the first place. The option treating a 5.4 percentage point drift as negligible ignores that most rebalancing policies use materially tighter bands than that.
Source: CFA Institute, Portfolio Management: An Overview; SEC, Investor.gov, 'Rebalancing'
Research by Brinson, Hood, and Beebower (and later studies) analyzing the returns of diversified institutional portfolios found that most of the variation in returns between different portfolios over time was explained by which factor, rather than by security selection or market-timing decisions?
AThe specific individual stocks chosen within each asset class, since stock-picking skill is the dominant driver of portfolio return differences
BThe timing of purchases and sales within each asset class, since successfully buying low and selling high explains most of the variation between portfolios
CThe choice of brokerage firm and the fee structure negotiated with that firm, since costs are the single largest determinant of long-term portfolio variation
DThe portfolio's asset allocation — the broad mix between asset classes such as equities, bonds, and cash — since this policy-level decision explained the large majority of the variance in returns across the portfolios studied
Correct answer: .
The Brinson, Hood, and Beebower research, and subsequent studies replicating it, found that the broad policy decision of how much to hold in each major asset class explained the large majority of the variation in returns across the pension portfolios studied over time, far more than the specific securities chosen within each asset class or the timing of trades. This finding is often summarized as asset allocation being the dominant determinant of return variability among diversified institutional portfolios, which is why setting the strategic asset allocation is treated as the foundational step in portfolio construction. The option crediting individual stock selection overstates its relative contribution compared to the asset-allocation decision. The option crediting market-timing trading similarly overstates a factor the research found to be a much smaller contributor. The option crediting brokerage and fee choice is not what this body of research examined at all; it studied allocation, selection, and timing effects, not cost structures.
Source: Brinson, G., Hood, L., Beebower, G. (1986), 'Determinants of Portfolio Performance', Financial Analysts Journal; CFA Institute, Portfolio Management: An Overview
An investor holding a portfolio of only domestic stocks and bonds is considering adding an allocation to real estate investment trusts (REITs) and commodities, asset classes that have historically shown relatively low or inconsistent correlation with stocks and bonds. What is the main portfolio-construction rationale for adding them?
AREITs and commodities guarantee higher returns than stocks and bonds over any holding period, so adding them raises expected portfolio return with no added risk
BBecause their returns do not move in lockstep with stocks and bonds, adding a moderate allocation can reduce overall portfolio volatility for a given level of expected return, even though each asset class carries meaningful risk on its own
CCommodities and REITs are risk-free asset classes, so replacing bonds with them removes credit risk from the portfolio entirely
DAdding any additional asset class always improves a portfolio's Sharpe ratio, regardless of that asset class's correlation with existing holdings
Correct answer: .
The portfolio-theory rationale for adding asset classes with low or inconsistent correlation to existing holdings is that their price movements are not closely tied to the movements of stocks and bonds, so when one part of the portfolio falls, the added asset class is less likely to fall by the same amount at the same time. This can lower the overall portfolio's standard deviation for a given expected return, even though REITs and commodities are each individually risky and volatile on their own — the benefit comes from the combination, not from either asset class being safe in isolation. The option promising guaranteed higher returns with no added risk misstates diversification, which manages risk rather than eliminating it or guaranteeing outperformance. The option calling these asset classes risk-free is incorrect; both carry real price risk, including commodity price swings and REIT sensitivity to property values and interest rates. The option claiming any addition always improves the Sharpe ratio ignores that a highly correlated addition can leave risk-adjusted return unchanged or worse.
Source: CFA Institute, Portfolio Risk and Return: Part I; SEC, Investor.gov, 'Diversification'
Building on the distinction between the efficient frontier and other portfolio-theory lines: when a risk-free asset is introduced and combined with the single risky portfolio that maximizes the reward-to-risk ratio (the tangency portfolio), the resulting line dominates every portfolio on the efficient frontier at every risk level except one point. What is this line called, and at which point does it touch the efficient frontier?
AThe security market line, which touches the efficient frontier at the portfolio with a beta of exactly 1.0
BThe Capital Allocation Line, which touches the efficient frontier at the lowest-risk portfolio on the frontier
CThe Capital Market Line, which touches the efficient frontier at exactly one point: the tangency (market) portfolio, the single risky portfolio combined with the risk-free asset that offers the best available reward-to-risk trade-off
DThe yield curve, which touches the efficient frontier only when short-term and long-term interest rates are equal
Correct answer: .
The Capital Market Line is the specific Capital Allocation Line drawn using the tangency portfolio — the one risky portfolio on the efficient frontier that produces the steepest possible line from the risk-free rate, meaning the best available reward per unit of risk. Because every other point on the efficient frontier produces a shallower line when combined with the risk-free asset, the Capital Market Line dominates the entire frontier at every risk level except where it touches the frontier at that single tangency portfolio, often called the market portfolio under further assumptions. The option describing the security market line confuses a different relationship, expected return plotted against beta for individual securities, which is a Capital Asset Pricing Model construct, not a line built by combining a risky portfolio with a risk-free asset. The option naming a generic Capital Allocation Line is imprecise, since any risky portfolio generates its own CAL, and only the one built from the tangency portfolio is the Capital Market Line. The option invoking the yield curve conflates an unrelated concept describing bond yields across maturities.
Source: CFA Institute, Portfolio Risk and Return: Part II; Sharpe, W. (1964), 'Capital Asset Prices'
According to the two-fund (mutual fund) separation theorem in portfolio theory, once a risk-free asset is available, every rational investor's optimal risky-asset holdings converge on the same single portfolio (the tangency portfolio), regardless of individual risk tolerance. Given this, what actually differs between a conservative investor and an aggressive investor under the theorem?
AOnly the proportion of total wealth each investor allocates between that single tangency portfolio and the risk-free asset — the conservative investor holds a larger share in the risk-free asset, while the aggressive investor holds a larger share in the tangency portfolio, or even borrows to hold more than 100% of it
BThe specific individual securities each investor selects within the risky portfolio, since risk tolerance determines which stocks and bonds are included
CNothing differs in practice; the theorem implies all investors should hold identical portfolios with no allocation differences whatsoever
DThe conservative investor holds a completely different risky portfolio with lower-beta stocks, while the aggressive investor holds a separate risky portfolio with higher-beta stocks
Correct answer: .
The two-fund separation theorem holds that the choice of the optimal risky portfolio (the tangency portfolio) can be made independently of an investor's risk preferences, since it is the single risky combination that offers the best reward-to-risk trade-off for every investor. Risk tolerance then only determines how an investor splits total wealth between that one risky portfolio and the risk-free asset: a conservative investor keeps a larger share in the risk-free asset and a smaller share in the tangency portfolio, while an aggressive investor holds a larger share of the tangency portfolio and may even borrow at the risk-free rate to hold more than 100% of it. The option claiming investors select different individual securities contradicts the theorem's core insight that everyone holds the same risky portfolio. The option claiming no differences exist at all ignores that the risk-free/risky split itself does differ and drives each investor's overall risk exposure. The option claiming each investor holds a separate risky portfolio built from different-beta stocks is exactly what the theorem says does not happen.
Source: CFA Institute, Portfolio Risk and Return: Part II; Tobin, J. (1958), 'Liquidity Preference as Behavior Towards Risk'
On the Markowitz minimum-variance frontier, one specific portfolio sits at the frontier's leftmost point: the single combination of the available risky assets that achieves the lowest possible standard deviation of any attainable portfolio, even though it is not necessarily the portfolio with the highest return for its risk level. This same portfolio also marks the starting point of the efficient frontier. What is this portfolio called?
AThe capital market portfolio
BThe minimum-variance portfolio
CThe tangency portfolio
DThe equally weighted (1/N) portfolio
Correct answer: .
The minimum-variance portfolio is the single combination of the available risky assets that achieves the lowest possible standard deviation of any portfolio on the minimum-variance frontier; it sits at the frontier's leftmost point and marks the start of the Markowitz efficient frontier, which runs upward and to the right from it toward higher risk and return. The option describing the capital market portfolio points to a different construct from capital market theory, the market-value-weighted portfolio of all risky assets, which need not have the lowest variance of any attainable combination. The option describing the tangency portfolio names the specific risky portfolio that maximizes the reward-to-risk ratio when paired with a risk-free asset; it sits further up the frontier, at a higher risk and return level than the minimum-variance point, and the two coincide only by coincidence, never by definition. The option describing an equally weighted (1/N) portfolio describes a naive rule that splits capital evenly across holdings; because it ignores each asset's volatility and correlation with the others, it produces the lowest-variance mix only by chance, not by construction.
Source: CFA Institute, Portfolio Risk and Return: Part II (minimum-variance and efficient frontiers); Markowitz, H. (1952), 'Portfolio Selection,' Journal of Finance
Under the Capital Asset Pricing Model (CAPM), two investors hold portfolios with identical systematic risk (the same beta). One investor's portfolio is a handful of stocks concentrated in a single industry, carrying substantial unsystematic risk on top of that beta; the other investor's portfolio is broadly diversified, carrying almost no unsystematic risk. Does CAPM predict that the market compensates the concentrated investor with a higher expected return than the diversified investor, since the concentrated investor is bearing more total risk?
AYes, because CAPM prices total risk, measured by standard deviation, not just the systematic portion
BYes, but only for small-capitalization stocks, which earn an extra premium specifically to compensate holders for their higher unsystematic risk
CNo, but only because exchange rules cap the return any single concentrated position may legally earn
DNo, because unsystematic risk can be eliminated at no cost simply by holding a diversified portfolio, so the market does not pay a premium for a risk an investor could have avoided
Correct answer: .
CAPM predicts expected return as a function of systematic risk (beta) alone; both investors have the same beta, so CAPM predicts the same expected return for both, regardless of how much unsystematic risk the concentrated investor is additionally carrying. The reasoning is that unsystematic risk can be diversified away at essentially no cost by holding more securities, so a rational market has no reason to pay a premium for a risk an investor could simply have avoided by diversifying; a return earned from a concentrated bet reflects stock-picking luck or skill, not a structural risk premium. The option claiming CAPM prices total risk measured by standard deviation describes a different framework, not CAPM, which explicitly prices only the covariance-with-the-market (beta) component. The option invoking a small-capitalization premium confuses a separate, empirically observed market anomaly debated in asset-pricing research with CAPM's basic assumptions, which make no such carve-out. The option invoking exchange rules on concentrated positions describes a regulatory constraint that doesn't exist in this form and has nothing to do with CAPM's actual economic reasoning.
Source: CFA Institute, Portfolio Risk and Return: Part II (the CAPM); Sharpe, W. (1964), 'Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,' Journal of Finance
A portfolio manager maintains a target asset allocation and must decide WHEN to rebalance back to target, as distinct from how much to trade once a rebalance is triggered. Under one approach, a trade is triggered only when an asset class's actual weight drifts beyond a predefined band around its target (for example, more than 5 percentage points away), regardless of how much time has passed since the last rebalance. What is this approach called, and how does it typically compare with simply rebalancing on a fixed calendar schedule (e.g., once a year) regardless of how far the portfolio has drifted?
AThreshold (tolerance-band) rebalancing; compared with a fixed calendar schedule, it generally keeps allocations closer to target with fewer, better-timed trades, since it reacts to actual drift rather than the passage of time
BThreshold rebalancing; compared with a fixed calendar schedule, it typically drifts further from target, since it triggers a trade only a small number of times per decade on average
CCalendar rebalancing; in practice it produces results identical to a tolerance-band approach, since normal market volatility guarantees a band breach within any given year regardless of the band's width
DStrategic asset allocation; unlike a tolerance-band approach, it periodically replaces the portfolio's target weights themselves rather than trading the existing portfolio back toward an already-set target
Correct answer: .
This approach is threshold, or tolerance-band, rebalancing: trades are triggered only when an asset class's actual weight drifts beyond a predefined band around its target, independent of how much calendar time has elapsed. Compared with calendar rebalancing, which trades on a fixed date regardless of how far, or how little, the portfolio has actually drifted, threshold rebalancing reacts directly to the thing that matters, drift away from target, so it tends to keep the portfolio closer to its intended risk profile while often triggering fewer unnecessary trades during calm markets. The option claiming threshold rebalancing drifts further from target inverts this relationship. The option claiming the two approaches produce identical results ignores that a band's width is a deliberate design choice, and a calm period can easily pass an entire year without breaching even a fairly narrow band. The option describing strategic asset allocation names a different concept entirely, the process of setting the long-term target weights themselves, not a rule for when to trade an existing portfolio back toward an already-established target.
Source: CFA Institute, Overview of Asset Allocation (rebalancing policy); Vanguard Research, 'The Rebalancing Edge: Optimizing Target-Date Fund Rebalancing through Threshold-Based Strategies'
An investor builds a portfolio with two distinct pieces: roughly 70% in a widely diversified, low-cost index fund held long-term as a stable foundation, and the remaining 30% split across a handful of actively managed or thematic positions the investor adjusts more frequently to pursue specific opportunities or views. What is this portfolio construction approach called?
ADollar-cost averaging
BThe barbell strategy
CTactical asset allocation
DCore-satellite investing
Correct answer: .
This structure is core-satellite investing: a large 'core' of broadly diversified, low-cost holdings (commonly 60-80% of the portfolio) provides a stable foundation tracking overall market performance, while a smaller 'satellite' sleeve of more actively managed or thematic positions is adjusted more frequently to pursue specific opportunities. Dollar-cost averaging describes a timing rule for how new contributions are invested over time, equal amounts at regular intervals, not how the resulting portfolio is structured into tiers, so it doesn't describe this two-part split. The barbell strategy combines two extremes with little in the middle, most commonly very short-duration and very long-duration bonds, which is a different structural idea from a large passive core paired with a smaller active satellite. Tactical asset allocation describes temporary, short-term tilts away from a portfolio's existing long-term target weights to exploit a near-term view, not a standing two-tier division between a stable core and an actively managed satellite sleeve.
Source: CFA Institute, Overview of Asset Allocation; Investopedia, 'Core-Satellite Investing'
A portfolio strategy allocates capital across stocks, bonds, and commodities so that each asset class contributes an equal share of the portfolio's total volatility, rather than allocating an equal dollar amount or an equal percentage of capital to each. Because bonds are typically far less volatile than stocks, this approach ends up putting a much larger dollar amount into bonds than a simple equal split would, often applying leverage to the lower-volatility sleeve so its expected-return contribution becomes comparable to the rest of the portfolio. What is this strategy called?
AEqual-weighted (1/N) allocation
BRisk parity
CThe 60/40 portfolio
DStrategic asset allocation
Correct answer: .
This is risk parity: instead of allocating an equal dollar amount or an equal percentage of capital to each asset class, it sizes each position so every asset class contributes an equal share of the portfolio's total volatility. Because bonds are typically far less volatile than stocks, achieving equal risk contribution requires allocating a much larger dollar amount to bonds than a simple equal-split approach would, and often applying leverage to the lower-volatility sleeve so its expected-return contribution becomes comparable to the rest of the portfolio. Equal-weighted (1/N) allocation does the opposite: it equalizes dollar amounts, not risk contributions, which in a stock-bond mix leaves equities dominating the portfolio's actual volatility despite being a minority of invested capital. A 60/40 portfolio is a specific, fixed equity-bond split chosen for its return profile, not a rule for equalizing each asset class's risk contribution; in fact, the concentration of risk in the equity sleeve of a typical 60/40 mix is exactly the imbalance risk parity is designed to correct. Strategic asset allocation describes the general practice of setting a stable, long-term target mix based on an investor's goals and risk tolerance; it doesn't specify any particular rule, such as equalizing risk contributions, for how that mix should be derived.
Source: Qian, E. (2005), 'Risk Parity Portfolios: Efficient Portfolios through True Diversification,' PanAgora Asset Management; Bridgewater Associates, 'Risk Parity Is About Balance'
An investor holds a portfolio of 5 randomly selected stocks across different industries and is deciding whether to add more holdings to reduce risk further. Based on research on the relationship between portfolio size and risk reduction, what should the investor expect as more randomly selected stocks are added, say up to 20-30 holdings and then well beyond that?
AUnsystematic (company-specific) risk falls quickly at first, but most of the achievable reduction occurs within roughly the first 20 to 30 holdings; adding far more holdings beyond that yields only marginal further reduction, since market-wide systematic risk remains no matter how many stocks are added
BUnsystematic risk keeps falling at a constant rate per additional stock no matter how many are already held, so a 100-stock portfolio diversifies company-specific risk twice as effectively as a 50-stock portfolio
CAdding more stocks eventually eliminates both unsystematic and systematic risk entirely once the portfolio holds enough names, since diversification removes all forms of risk given a large enough number of holdings
DAdding more stocks increases risk rather than reducing it, because each additional holding introduces its own company-specific risk on top of the risk already present in the portfolio
Correct answer: .
Classic research on portfolio size, beginning with Evans and Archer's 1968 study and echoed in later work commonly citing roughly 20 to 30 holdings as capturing most of the benefit, finds that company-specific risk falls sharply as the first several holdings are added, but the marginal reduction shrinks quickly, so that beyond roughly 20 to 30 well-diversified holdings, further additions remove only a small sliver of remaining unsystematic risk. The option describing a constant per-stock reduction rate is wrong because the relationship is curved, not linear: the risk reduction from the next holding gets smaller as the portfolio grows, not constant. The option claiming systematic risk eventually disappears entirely is wrong because market-wide risk, by definition, affects nearly every security simultaneously and cannot be diversified away by holding more names, however many there are. The option claiming more holdings increase overall risk is wrong because, while each stock does carry its own idiosyncratic risk, those risks are not perfectly correlated with each other, so combining them still reduces the portfolio's overall unsystematic risk rather than adding to it.
Source: Evans, J.L. & Archer, S.H. (1968), 'Diversification and the Reduction of Dispersion', Journal of Finance
An individual investor splits a lump sum equally across 10 different stocks (10% each), rather than using a mean-variance optimization model that would compute 'optimal' weights from each stock's estimated expected return, variance, and covariance with the others. Academic research comparing this simple equal-weighting approach (often called the '1/N rule') against optimized mean-variance portfolios, tested on actual future returns, has found which of the following?
AThe 1/N rule always underperforms mean-variance optimization out of sample, because equal weighting ignores all information about each stock's expected return and risk
BMean-variance optimization always outperforms the 1/N rule out of sample, confirming that using more statistical information about expected returns and covariances produces better real-world portfolios
CThe 1/N rule has performed comparably to, or better than, many mean-variance-optimized strategies out of sample in several studies, largely because estimation error in the inputs (expected returns and covariances) often outweighs the theoretical benefit of optimizing with them
DMean-variance optimization and the 1/N rule produce mathematically identical portfolio weights whenever more than ten assets are included, so the comparison is moot for larger portfolios
Correct answer: .
A widely cited study by DeMiguel, Garlappi, and Uppal (2009) compared the simple equal-weighted 1/N portfolio against 14 different mean-variance-optimization-based strategies across several real-world datasets and found that none of the optimized strategies consistently beat the 1/N rule on risk-adjusted return, certainty-equivalent return, or turnover out of sample. The reason is that mean-variance optimization requires estimating expected returns and the covariance matrix from historical data, and those estimates carry substantial error; feeding noisy estimates into an optimizer can amplify that noise into extreme, poorly performing weights, a problem sometimes called the 'error-maximizing' property of optimization. The option claiming the 1/N rule always underperforms gets the empirical finding backwards. The option claiming optimization always wins makes the same mistake in the opposite direction and ignores the well-documented estimation-error problem. The option claiming the two approaches produce identical weights above ten assets is simply false: equal weighting assigns the same weight to every asset regardless of its data, while mean-variance optimization's weights depend entirely on the estimated inputs and will generally differ sharply from equal weights.
Source: DeMiguel, V., Garlappi, L. & Uppal, R. (2009), 'Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?', Review of Financial Studies
A financial advisor prepares a formal written document for a new client before building any portfolio. This document states the client's return objectives and risk tolerance, the client's time horizon, and constraints such as liquidity needs, tax situation, and legal or regulatory restrictions, but does not yet specify which individual stocks or bonds to buy. What is this foundational document called, and what role does it play in the portfolio management process?
AA prospectus, which is the document a mutual fund issues to all prospective investors describing the fund's investment objective, fees, and historical performance
BAn Investment Policy Statement (IPS), which documents the client's objectives and constraints and, combined with capital market expectations, forms the basis for setting the strategic asset allocation that follows
CA trade confirmation, which is the receipt generated after each individual buy or sell order is executed in the client's account, confirming price and quantity
DA proxy statement, which is the disclosure document a public company sends to its shareholders ahead of a shareholder vote, describing the matters to be voted on
Correct answer: .
An Investment Policy Statement (IPS), as described in CFA Institute's portfolio management curriculum, is a written document prepared early in the portfolio management process that sets out a client's return objectives and risk tolerance over the relevant time horizon, along with constraints such as liquidity needs, tax considerations, regulatory requirements, and any unique circumstances. Rather than specifying individual security selections, the IPS is combined with capital market expectations to form the basis for the client's strategic asset allocation, the broad mix of asset classes the portfolio will target before any individual securities are chosen. The option describing a prospectus is incorrect because a prospectus is a disclosure document a fund issues about itself to the investing public, not a document capturing an individual client's own objectives and constraints. The option describing a trade confirmation is incorrect because that is a transaction-level receipt generated after a trade executes, unrelated to upfront planning. The option describing a proxy statement is incorrect because that document concerns a public company's own shareholder vote, not an investment advisor's planning process with a client.
Source: CFA Institute, 'The Portfolio Management Process and the Investment Policy Statement', Level I curriculum refresher reading
A portfolio is made up of two assets: 70% invested in Stock A, which has an expected return of 12%, and 30% invested in Bond B, which has an expected return of 4%. Ignoring any correlation between the two assets, which affects portfolio risk rather than expected return, what is the portfolio's expected return?
A4.0%, the expected return of the lower-weighted asset alone, since diversification pulls the combined return toward the safer asset
B8.0%, the simple (unweighted) average of the two assets' expected returns, treating each asset as if it made up half the portfolio
C12.0%, the expected return of the higher-weighted asset alone, since it makes up the majority of the portfolio
D9.6%, the weighted average of the two expected returns using each asset's actual portfolio weight: (0.70 x 12%) + (0.30 x 4%)
Correct answer: .
A portfolio's expected return is always the weighted average of its individual holdings' expected returns, using each asset's actual weight in the portfolio, not an equal or simple average. Here that calculation is (0.70 x 12%) + (0.30 x 4%) = 8.4% + 1.2% = 9.6%. This weighted-average relationship holds regardless of how the two assets are correlated with each other; correlation affects the portfolio's risk (standard deviation), not its expected return, which is a simple linear combination of the components' expected returns. The option giving the lower asset's return alone incorrectly assumes diversification pulls the combined return toward the safer asset, which is not how expected return combines; only risk, not return, benefits from a diversification effect. The option using a plain 50/50 average ignores the actual 70/30 weighting entirely, implicitly treating the two assets as equally sized. The option giving the higher asset's return alone ignores the 30% allocation to the lower-returning asset altogether, as if it contributed nothing to the blended figure.
Source: Bodie, Z., Kane, A. & Marcus, A., Investments, chapter on Portfolio Theory and Diversification
The Capital Asset Pricing Model (CAPM) explains an asset's expected return using a single factor: its beta (sensitivity to the overall market). The Fama-French three-factor model, developed by Eugene Fama and Kenneth French, extends CAPM by adding two further factors that help explain differences in stock returns not captured by market beta alone. What are these two additional factors?
AA size factor (the historical return spread between small-capitalization and large-capitalization stocks) and a value factor (the historical return spread between stocks with high and low book-to-market ratios)
BA momentum factor (the historical return spread between recent winning and losing stocks) and a quality factor (the historical return spread between highly profitable and weakly profitable companies)
CAn inflation factor (the sensitivity of returns to unexpected changes in inflation) and an interest-rate factor (the sensitivity of returns to changes in the risk-free rate)
DA liquidity factor (the historical return spread between highly liquid and illiquid stocks) and a currency factor (the historical return spread attributable to exchange-rate movements)
Correct answer: .
Fama and French found that, alongside market beta, two additional factors helped explain the cross-section of average stock returns: a size factor, commonly labeled SMB ('small minus big'), capturing the historical tendency of small-capitalization stocks to earn different average returns than large-capitalization stocks, and a value factor, commonly labeled HML ('high minus low'), capturing the historical tendency of stocks with high book-to-market ratios (value stocks) to earn different average returns than stocks with low book-to-market ratios (growth stocks). A stock or portfolio's returns are regressed on all three factors (market, SMB, and HML) to estimate its sensitivity, or loading, to each one. The option describing momentum and quality factors is incorrect because those are well-known factors from later research, momentum from Carhart's four-factor extension and quality/profitability from the later Fama-French five-factor model, not part of the original three-factor model. The option describing inflation and interest-rate factors is incorrect because those belong to macroeconomic multi-factor asset pricing models, not the Fama-French model, which is built from stock-characteristic-based factors. The option describing liquidity and currency factors is incorrect for the same reason, since those are separate factors studied elsewhere in asset pricing research, not the two factors Fama and French added to CAPM.
Source: Fama, E.F. & French, K.R. (1993), 'Common Risk Factors in the Returns on Stocks and Bonds', Journal of Financial Economics; also covered in CFA Institute's factor-based strategies curriculum
A defined-benefit pension fund has a stream of future benefit payments it must make to retirees over the coming decades. To protect the plan's funded status from interest rate changes, the fund's manager builds a bond portfolio whose interest-rate sensitivity is matched to the pension's future obligations, rather than simply maximizing the bond portfolio's yield. What is this asset-liability matching approach called, and what specific bond-portfolio characteristic is matched to the liabilities?
ATactical asset allocation, where the manager shifts the bond-to-equity mix within the pension portfolio based on short-term views about which asset class looks more attractively priced
BSecurities lending, where the manager lends out a portion of the pension's bond holdings to other market participants in exchange for a fee, generating extra income for the plan
CLiability-driven investing (LDI), using duration matching, where the bond portfolio's duration is set equal to the duration of the pension's future liabilities so that a given change in interest rates affects the value of the assets and the liabilities by a similar amount, helping stabilize the plan's funded status
DDollar-cost averaging, where the manager invests a fixed amount into the bond portfolio at regular intervals over time, regardless of current bond prices or interest rate levels
Correct answer: .
Liability-driven investing (LDI) is a pension or insurance portfolio management approach that starts from the institution's future liabilities, the benefit payments it must make, rather than only from a return target, and constructs the asset portfolio to track those liabilities' behavior under changing market conditions. The classical technique for managing interest rate risk this way is duration matching, also called immunization: because duration measures a bond portfolio's approximate percentage price sensitivity to a given change in interest rates, setting the asset portfolio's duration equal to the liabilities' duration means a parallel shift in rates moves the present value of the assets and the liabilities by a similar amount, which helps keep the plan's funded status, assets minus liabilities, more stable than if the bond portfolio were managed purely to maximize yield without regard to the liability stream. The option describing tactical asset allocation addresses a different decision, the equity-bond mix based on short-term views, not matching the liabilities' interest rate sensitivity. The option describing securities lending is an unrelated income-generating practice that does nothing to manage interest rate risk against liabilities. The option describing dollar-cost averaging is an unrelated purchase-timing discipline, not an asset-liability risk management technique.
Source: CFA Institute, Fixed-Income Portfolio Management curriculum on liability-driven strategies; Redington, F.M. (1952), classical immunization theory
Two lines from modern portfolio theory and the Capital Asset Pricing Model are often confused with each other: the Capital Market Line (CML) and the Security Market Line (SML). Which statement correctly distinguishes what each line plots on its horizontal axis and which assets can lie on it?
AThe CML plots expected return against beta and includes only efficient portfolios combining the risk-free asset with the tangency portfolio, while the SML plots expected return against standard deviation and includes every individual security or portfolio, efficient or not
BThe CML and SML are two names for the same line; the choice of name depends only on whether the investor is analyzing individual stocks or entire portfolios
CThe CML plots expected return against total risk (standard deviation) and includes every individual security or portfolio, efficient or not, while the SML plots expected return against systematic risk (beta) and includes only efficient portfolios combining the risk-free asset with the tangency portfolio
DThe CML plots expected return against total risk (standard deviation) and includes only efficient portfolios combining the risk-free asset with the tangency portfolio, while the SML plots expected return against systematic risk (beta) and includes every individual security or portfolio, efficient or not
Correct answer: .
The Capital Market Line (CML) is the specific Capital Allocation Line formed by combining the risk-free asset with the tangency portfolio, the single risky portfolio offering the best available reward-to-risk trade-off. Its horizontal axis measures total risk via standard deviation, and only portfolios that are efficient combinations of the risk-free asset and the tangency portfolio actually lie on it; an individual stock, or an inefficiently diversified portfolio, does not sit on the CML. The Security Market Line (SML) comes directly from the Capital Asset Pricing Model and measures systematic risk via beta on its horizontal axis; because CAPM holds that only systematic risk is priced, every security and every portfolio, efficient or not, is predicted to sit on the SML according to its own beta. The option assigning beta to the CML and standard deviation to the SML has the two lines' risk measures reversed, while keeping the efficient-portfolios-only restriction on the wrong line. The option claiming the two lines are simply the same line under different names ignores that they use different risk measures and apply to different sets of assets entirely. The option assigning standard deviation to the CML and beta to the SML correctly but then restricting the CML to every asset and the SML to only efficient portfolios has the scope exactly backwards: it is the CML, not the SML, that is limited to efficient combinations of the risk-free asset and tangency portfolio, while the SML applies to any security or portfolio regardless of efficiency.
Source: Bodie, Z., Kane, A. & Marcus, A., Investments, Chapter 9 (Capital Asset Pricing Model); Sharpe, W. (1964), 'Capital Asset Prices', Journal of Finance
A portfolio manager is dissatisfied with naive mean-variance optimization because small changes in the historical expected-return estimates she feeds into the optimizer produce wildly different, often extreme and concentrated portfolio weights. The Black-Litterman model addresses this problem by blending a particular starting point for expected returns with the manager's own specific views. What does the Black-Litterman model use as that starting point, and how does it combine it with the manager's views?
AIt starts from each asset's own long-run historical average return taken in isolation, then simply overrides the historical figure with the manager's view for any asset where the manager holds a strong opinion
BIt starts from the expected returns implied by reverse-solving the market's current capitalization-weighted portfolio through the standard mean-variance equations, the 'equilibrium' returns, then statistically blends those equilibrium returns with the manager's own views, weighted by how confident the manager is in each view
CIt starts from zero expected return for every asset, treating all securities as equally attractive by default, and then sets each asset's final expected return equal entirely to the manager's own view, with no blending at all
DIt starts from the risk-free rate as the expected return for every asset, then adds a single, identical risk premium to every asset regardless of the manager's views, ignoring any asset-specific opinions altogether
Correct answer: .
The Black-Litterman model, developed by Fischer Black and Robert Litterman, begins with the 'equilibrium' expected returns that can be reverse-engineered from the market's actual current capitalization weights: given the covariance matrix of asset returns and a risk-aversion coefficient, one can solve the standard mean-variance equations backwards to find the set of expected returns that would make today's market-cap-weighted portfolio the mean-variance-optimal choice. These equilibrium returns serve as a stable, market-based starting point, a statistical prior, rather than noisy historical averages. The manager's own views, each stated with an associated confidence level, are then combined with this equilibrium prior using a Bayesian-style weighting, producing a posterior set of expected returns that shifts away from equilibrium only for the specific assets the manager holds a view on, and shifts further the more confident that view is. If the manager holds no views at all, the model's output simply reproduces the market-cap weights. The option describing isolated historical averages overridden by opinion ignores the model's actual reverse-optimization starting point and its statistical blending step entirely. The option starting from zero expected return for every asset describes neither the equilibrium prior nor any step in the actual model. The option starting from the risk-free rate plus one identical risk premium for every asset ignores both the equilibrium step, which differentiates expected returns across assets based on their actual market weights and covariances, and the incorporation of the manager's own views.
Source: Black, F. & Litterman, R. (1992), 'Global Portfolio Optimization', Financial Analysts Journal
About Portfolio Theory & Asset Allocation
Before 1952, investors mostly judged one security at a time. Harry Markowitz's paper that year, published in the Journal of Finance (later work for which he shared the 1990 Nobel Prize in Economics), reframed the question around the whole portfolio: because different assets rarely move in perfect lockstep, combining them can lower a portfolio's overall volatility below the average of its individual holdings' volatility, without necessarily lowering expected return. Plotting every combination of risk and expected return produces the efficient frontier — the set of portfolios that deliver the highest expected return for a given level of risk, or the lowest risk for a given expected return; a rational, risk-averse investor should hold a portfolio somewhere on that frontier, not below it.
This is also where the common risk/return vocabulary comes from: unsystematic (idiosyncratic) risk — the risk specific to one company or sector — can be reduced by diversifying across enough imperfectly-correlated holdings, while systematic (market) risk affects nearly everything at once and cannot be diversified away. The two-asset portfolio variance guide works the underlying covariance math for the simplest possible case: two assets.
In practice, most investors implement these ideas through asset allocation — choosing a broad split across stocks, bonds, and cash that matches their risk tolerance and time horizon — and periodic rebalancing, selling down whichever asset class has grown to exceed its target weight and adding to whichever has fallen below it, which forces a disciplined sell-high, buy-low habit rather than reacting to recent performance.