Portfolio construction and analytics - Performance evaluatio...

Learning Outcomes

This article explains portfolio performance evaluation and attribution for CFA Level 1 candidates, including:

• measuring absolute portfolio performance using return and risk metrics over specified periods and interpreting results in an exam context
• comparing relative performance against appropriate benchmarks and recognizing the implications of consistent underperformance or outperformance
• calculating, interpreting, and contrasting key risk-adjusted measures, including Sharpe ratio, Treynor ratio, and Jensen’s alpha
• selecting the most suitable performance measure for diversified versus concentrated portfolios, based on the role of total and systematic risk
• describing the characteristics of effective benchmarks, including investability, transparency, and consistency with an investor’s objectives and constraints
• differentiating performance measurement from performance attribution and articulating why both approaches are needed in manager appraisal
• decomposing active return into allocation, selection, and interaction effects and explaining what each component reveals about manager skill
• using performance evaluation and attribution outputs to draw exam-style conclusions about risk, return, and the sources of value added
• recognizing practical issues in multi-period performance evaluation, including compounding and the choice of evaluation horizon

CFA Level 1 Syllabus

For the CFA Level 1 exam, you are required to understand the principles and techniques of portfolio performance measurement and to describe how risk, return, and attribution analyses inform the evaluation of investment managers and strategies, with a focus on the following syllabus points:

• calculation and interpretation of key risk-adjusted performance measures, including Sharpe ratio, Treynor ratio, Jensen’s alpha, and related concepts
• distinction between absolute and relative (benchmark-based) portfolio performance
• role and desirable characteristics of benchmarks in performance evaluation
• principles of multi-period performance evaluation and the need to adjust returns for risk
• basic concepts of performance attribution, including allocation, selection, and interaction effects
• use of performance evaluation and attribution information in investment decision-making and manager appraisal
• recognition of limitations and potential pitfalls in performance evaluation, including benchmark mis-specification and reliance on historical data

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which performance measure is most appropriate for ranking managers when investors hold fully diversified portfolios?
   1. Sharpe ratio
   2. Treynor ratio
   3. Standard deviation of returns
   4. Holding-period return
2. Which statement best describes the difference between performance measurement and performance attribution?
   1. Measurement adjusts returns for risk; attribution ignores risk
   2. Measurement focuses on historical returns and risk; attribution explains why performance differed from a benchmark
   3. Measurement compares performance to peers; attribution compares performance to cash
   4. Measurement uses gross returns; attribution uses net returns only
3. In sector-level attribution, which effect most directly captures stock-picking skill within a sector?
   1. Allocation effect
   2. Selection effect
   3. Interaction effect
   4. Currency effect
4. Jensen’s alpha is best described as:
   1. The excess return per unit of total risk
   2. The excess return per unit of beta risk
   3. The difference between the portfolio return and the CAPM-expected return based on beta
   4. The difference between the portfolio return and the risk-free rate
5. Which characteristic is least desirable in a benchmark used for performance evaluation?
   1. It is investable and transparent
   2. It is specified in advance
   3. It reflects the manager’s investment style and universe
   4. It is chosen after the evaluation period to best fit the manager’s results

Introduction

Portfolio performance evaluation is a core part of both the CFA curriculum and practice. Investors and analysts must assess whether a manager or strategy delivers superior results versus a benchmark, and whether those returns are commensurate with the risks taken. Performance evaluation is therefore not just about “how high” returns are, but whether the return–risk trade-off is attractive.

Over long periods, historical data show that higher-risk asset classes tend to earn higher average returns. For example, across many decades and countries, equities have shown higher standard deviations but also higher long-term average returns than government bonds or cash. Within equities, small-company stocks have tended to be more volatile but have earned higher long-run returns than large-company stocks. This positive relation between risk and return is often called the risk–return trade-off.

Because of this trade-off, very high returns are not automatically “good” if they were generated by taking very high risk. A portfolio that earned 15% when the equity market earned 20% is disappointing, even though 15% is a high absolute return. Similarly, a portfolio that earned 6% with very low volatility might be attractive relative to cash and bonds.

Performance evaluation is typically discussed within the broader portfolio management process:

• In the planning step, the investor’s objectives, constraints, and benchmark are set (for example, in an investment policy statement).
• In the execution step, the manager constructs and manages the portfolio.
• In the feedback step, performance is measured, attributed, and evaluated to see whether objectives have been met and whether changes are needed.

Key Term: performance measurement
The quantitative process of evaluating the historical return and risk of a portfolio or manager, sometimes relative to a benchmark or target.

Key Term: performance evaluation
The broader process of assessing whether historical performance was acceptable given the risk taken and the investment objectives, usually combining performance measurement, attribution, and qualitative judgment.

Key Term: benchmark
A relevant, predetermined standard used to compare and assess portfolio performance, such as a capital market index, style index, or custom strategy objective.

Key Term: risk-adjusted return
A measure of return that explicitly incorporates the amount of risk taken, allowing fair comparison across portfolios with different risk levels.

Key Term: attribution analysis
The process of explaining the sources of a portfolio’s active return relative to its benchmark, typically broken into allocation, selection, and interaction effects.

Performance evaluation usually proceeds in three stages:

• Measurement stage: calculate portfolio and benchmark returns and risk over the evaluation period.
• Attribution stage: explain how much of the active (relative) return came from different types of active decisions (for example, sector weights versus stock selection).
• Appraisal stage: decide whether the manager added value, given the risk taken and the investment context, and whether any observed value added is likely to persist.

The rest of this article covers these steps, focusing on the risk-adjusted performance measures and attribution concepts that commonly appear in CFA Level 1 questions.

Risk-Adjusted Performance Measures

Investment returns alone do not tell the full story. A portfolio that returned 12% may be impressive if it was low risk, but not if it was extremely volatile and suffered large drawdowns along the way. Risk-adjusted return measures adjust for risk so that strategies with different risk levels can be compared on a more consistent basis.

In mean–variance analysis, risk is usually summarized by the variance or standard deviation of returns. For diversified portfolios in an equilibrium model such as the CAPM, only systematic (market-related) risk is rewarded.

Key Term: total risk
The overall variability of a portfolio’s returns, usually measured by the standard deviation of returns.

Key Term: systematic risk
The portion of total risk related to broad market movements that cannot be eliminated through diversification, commonly measured by beta.

Sharpe Ratio and its Use

The Sharpe ratio evaluates how much excess return a portfolio achieved per unit of total risk.

Key Term: Sharpe ratio
The excess return of a portfolio above the risk-free rate per unit of total portfolio risk, measured as standard deviation.

The formula is:

where:

• $R_p$ is the portfolio return over the period,
• $R_f$ is the risk-free rate over the same period, and
• $\sigma_p$ is the standard deviation (total risk) of portfolio returns.

Interpretation for exam purposes:

• A higher Sharpe ratio indicates more excess return per unit of total risk and is better.
• A Sharpe ratio of zero means the portfolio matched the risk-free rate.
• A negative Sharpe ratio means the portfolio underperformed the risk-free rate, which is undesirable.

The Sharpe ratio is most useful when comparing portfolios or managers when the investor’s total holdings may not be fully diversified – for example:

• evaluating a single balanced fund or multi-asset portfolio,
• comparing portfolios with very different asset mixes (equity-only, bond-only, and mixed funds),
• evaluating an investor who holds only one fund.

Because the Sharpe ratio uses total risk, it is especially relevant when:

• the portfolio is intended to be a complete portfolio, not just one component, or
• the investor is not yet well diversified and therefore cares about total volatility.

In practice, the Sharpe ratio is often computed using historical average returns and the historical standard deviation over a sample period (for example, monthly returns over five years). The choice of risk-free rate must match the return horizon (for example, a one-month Treasury bill rate when using monthly returns).

Treynor Ratio and Jensen’s Alpha

Both the Treynor ratio and Jensen’s alpha use systematic risk (beta) rather than total risk. They are most appropriate when the investor is well diversified, so that only market-related risk is relevant.

Key Term: Treynor ratio
The excess return earned per unit of portfolio beta, measuring reward for bearing systematic risk.

The Treynor ratio is:

where $\beta_p$ is the portfolio’s beta relative to the chosen market index.

Interpretation:

• A higher Treynor ratio indicates more excess return per unit of systematic risk.
• It implicitly assumes the portfolio is well diversified, so unsystematic risk is negligible.
• It is most meaningful when comparing portfolios that are all broadly diversified.

Key Term: Jensen’s alpha
The average return on a portfolio minus the return predicted by the Capital Asset Pricing Model (CAPM), measuring value added after adjusting for systematic risk.

Under the CAPM, the expected return on portfolio $p$ is:

where $E(R_m)$ is the expected market return.

Jensen’s alpha, often just called “alpha”, is:

where $R_p$ and $R_m$ are the realized portfolio and market returns over the period.

Interpretation:

• $\alpha_p > 0$: the portfolio outperformed what CAPM would predict for its beta; suggests value added beyond market exposure (though this may be due to skill or luck).
• $\alpha_p = 0$: performance was in line with market risk exposure.
• $\alpha_p < 0$: underperformance given the systematic risk taken.

In CAPM terms, alpha is the vertical distance between the portfolio’s point and the security market line (SML) in a beta–return diagram. A positive alpha means the portfolio lies above the SML.

Key Term: Jensen’s alpha
A measure of active performance: the difference between the actual portfolio return and the CAPM-expected return for that portfolio’s beta.

Note that alpha is an absolute measure in percentage terms (for example, “the portfolio added 1.2% per year on a risk-adjusted basis”), whereas the Treynor ratio is a relative measure per unit of beta.

Sharpe, Treynor, and Alpha in Combination

For exam questions, it is important to recognize:

• Sharpe ratio: uses total risk (standard deviation); suitable for non-diversified or standalone portfolios.
• Treynor ratio and Jensen’s alpha: use beta (systematic risk); suitable for portfolios that are parts of a larger, well-diversified whole.

When comparing several managers:

• If the investor holds only one of the funds (for example, choosing a single balanced mutual fund), focus on Sharpe ratios.
• If each fund would be one component of a diversified portfolio, comparison using Treynor ratios or alphas is more suitable, because investors can diversify away unsystematic risk themselves.

It is common for rankings to differ:

• A portfolio with a very low total risk (perhaps because it holds a lot of cash) might have a high Sharpe ratio but a lower Treynor ratio if its beta is very small.
• Conversely, a portfolio with a high beta but relatively low volatility around the SML may have a strong Treynor ratio but a modest Sharpe ratio.

Worked Example 1.1

A portfolio has an annualized return of 14%, a risk-free rate of 3%, standard deviation of 15%, and beta of 1.2. The market return is 12%.

Calculate:
(a) the Sharpe ratio,
(b) the Treynor ratio, and
(c) Jensen’s alpha.

Answer:
(a) Sharpe ratio

$$\text{Sharpe} = \frac{14\% - 3\%}{15\%} = \frac{11\%}{15\%} \approx 0.73$$

This means the portfolio earned roughly 0.73 percentage points of excess return per 1 percentage point of total risk (standard deviation).

(b) Treynor ratio

$$\text{Treynor} = \frac{14\% - 3\%}{1.2} = \frac{11\%}{1.2} \approx 9.17\%$$

The portfolio earned about 9.17 percentage points of excess return per unit of beta risk.

(c) Jensen’s alpha
First compute the CAPM-expected return:

$$E(R_p) = 3\% + 1.2 \times (12\% - 3\%) = 3\% + 1.2 \times 9\% = 3\% + 10.8\% = 13.8\%$$

Then alpha:

$$\alpha_p = 14\% - 13.8\% = 0.2\%$$

The manager added a small positive alpha of 0.2 percentage points relative to what the CAPM predicts for this level of systematic risk.

The M-squared (M²) Measure

In the curriculum you may also encounter the M-squared measure, often written $M^2$. It is closely related to the Sharpe ratio.

Key Term: M-squared (M²) measure
A risk-adjusted performance measure that transforms a portfolio’s Sharpe ratio into a difference in return relative to the market portfolio, after adjusting the portfolio to have the same total risk as the market.

Conceptually, $M^2$:

• constructs a hypothetical portfolio that invests partly in the risky portfolio and partly in the risk-free asset so that the hypothetical portfolio’s standard deviation matches that of the market, and then
• compares the return on this risk-adjusted portfolio to the market’s return.

If $\sigma_p$ and $\sigma_m$ are the standard deviations of the portfolio and market, then the risk-adjusted portfolio return is:

and the $M^2$ measure is:

Interpretation:

• $M^2 > 0$: after scaling the portfolio’s risk to match the market’s risk, it earned a higher return than the market.
• $M^2 < 0$: the portfolio underperformed the market on a risk-adjusted basis.

Because $M^2$ is just a transformation of the Sharpe ratio, it ranks portfolios in the same order as the Sharpe ratio. Its advantage is that it is expressed in percentage return units (for example, “the portfolio outperformed the market by 1.5% per year on a risk-adjusted basis”), which is often easier to interpret than a ratio.

Worked Example 1.2

Suppose:

• Portfolio return $R_p = 11\%$,
• Portfolio standard deviation $\sigma_p = 8\%$,
• Market return $R_m = 9\%$,
• Market standard deviation $\sigma_m = 12\%$,
• Risk-free rate $R_f = 3\%$.

Compute the portfolio’s Sharpe ratio and $M^2$.

Answer:
Sharpe ratio:

$$\text{Sharpe} = \frac{11\% - 3\%}{8\%} = \frac{8\%}{8\%} = 1.00$$

Risk-adjusted portfolio return:

$$R_p^* = 3\% + \frac{12\%}{8\%}(11\% - 3\%) = 3\% + 1.5 \times 8\% = 3\% + 12\% = 15\%$$

$M^2$:

$$M^2 = R_p^* - R_m = 15\% - 9\% = 6\%$$

On a risk-adjusted basis (scaled to match the market’s volatility), the portfolio outperformed the market by 6 percentage points.

Selecting the Appropriate Measure

Use the different measures as follows:

• Sharpe ratio:

  • When evaluating a portfolio as a whole (for example, a single mutual fund that is the investor’s only holding).
  • When total volatility matters and the portfolio may not be fully diversified.
  • When comparing portfolios with different betas and different levels of total risk.

• Treynor ratio:

  • When comparing components of a well-diversified portfolio.
  • When the investor can diversify away unsystematic risk and cares mainly about market risk.
  • When portfolios are broadly diversified, so beta is an adequate summary of risk.

• Jensen’s alpha:

  • When focusing on the manager’s skill in generating returns beyond what is justified by beta.
  • When testing whether a portfolio lies above or below the CAPM security market line.
  • Often used to compare active managers within the same asset class or style.

• M² measure:

  • When you want a return-based comparison versus the market that directly incorporates total risk.
  • When communicating results to clients who may find “percentage outperformance” easier to understand than a Sharpe ratio.

Exam Tip:
If the question mentions that the investor holds a “well-diversified portfolio” and wants to compare funds as additions to that portfolio, think about Treynor ratio and Jensen’s alpha. If the investor is choosing one fund to hold as the entire portfolio, focus on Sharpe ratio (and $M^2$ if it appears).

Worked Example 1.3

An analyst is comparing three equity managers (A, B, and C). The market return is 8%, the risk-free rate is 2%.

(a) Compute the Sharpe ratio for each manager.
(b) Compute the Treynor ratio for each manager.
(c) If an investor will choose one manager as a complete portfolio, which seems most attractive?
(d) If the investor will hire two of the managers as part of an already well-diversified portfolio, which two are most attractive on a beta-adjusted basis?

Answer:
Excess returns (over risk-free):

• A: $10\% - 2\% = 8\%$
• B: $9\% - 2\% = 7\%$
• C: $11\% - 2\% = 9\%$

(a) Sharpe ratios:

$$S_A = \frac{8\%}{18\%} \approx 0.44,\quad S_B = \frac{7\%}{10\%} = 0.70,\quad S_C = \frac{9\%}{22\%} \approx 0.41$$

On a total-risk basis, Manager B ranks highest.

(b) Treynor ratios:

$$T_A = \frac{8\%}{1.2} \approx 6.67\%,\quad T_B = \frac{7\%}{0.7} = 10.0\%,\quad T_C = \frac{9\%}{0.9} = 10.0\%$$

Managers B and C have the same Treynor ratio and both exceed A.

(c) For an investor choosing a single manager as the whole portfolio, total risk matters. Manager B has the highest Sharpe ratio and the lowest volatility, so B is most attractive.

(d) For an investor adding managers to an already well-diversified portfolio, systematic risk is more relevant. Managers B and C have higher Treynor ratios than A, so B and C are most attractive on a beta-adjusted basis.

Limitations and Practical Issues

When interpreting these measures in exam scenarios, keep in mind:

• They depend on the chosen benchmark (market index) and risk-free rate:
  • Using an inappropriate market index to estimate beta will distort the Treynor ratio and alpha.
  • Using a risk-free rate that does not match the evaluation horizon can bias Sharpe ratios.
• They are often based on historical data, which may not repeat in the future.
  • A high historical Sharpe ratio does not guarantee future outperformance.
  • Short sample periods lead to more estimation error.
• Rankings may differ across measures:
  • A portfolio could have a high Sharpe ratio but a lower Treynor ratio if its total risk and beta differ markedly from peers.
• They assume return distributions are reasonably stable and approximately normal:
  • For assets with highly skewed or fat-tailed returns (some alternative investments, option strategies), standard deviation may understate risk.
• They assume linear relationships between portfolios and the market:
  • Strategies with significant options exposure may have non-linear payoffs, making beta and alpha harder to interpret.

Exam Warning:
Treynor ratio and Jensen’s alpha are only meaningful when portfolios are well diversified, so that beta is an adequate measure of risk. Using them with highly concentrated portfolios can mislead risk evaluation.

In addition, comparisons of Sharpe, Treynor, or $M^2$ should be made over the same time horizon and using consistent definitions of return and risk (for example, all annualized, all using the same risk-free rate, and all gross or all net of fees).

Multi-Period Performance and Compounding

Performance evaluation usually covers multiple periods (for example, three, five, or ten years). Two important concepts are:

• Holding-period return (HPR): the total return over a single period, including price change and income.
• Average returns: summary measures of performance over many periods.

Two common averages:

• Arithmetic mean return: the simple average of periodic returns; useful for expected one-period returns.
• Geometric mean return: the compound average rate at which an initial investment would have grown to its ending value; appropriate for describing multi-period investor experience.

If returns in periods 1 to $n$ are $R_1, R_2, \dots, R_n$:

• Arithmetic mean: $$\bar{R}_{\text{arith}} = \frac{1}{n}\sum_{t=1}^n R_t$$
• Geometric mean: $$\bar{R}_{\text{geom}} = \left[\prod_{t=1}^n (1 + R_t)\right]^{1/n} - 1$$

Because of volatility, the geometric mean is always less than or equal to the arithmetic mean (equal only when all period returns are identical). For long-term performance evaluation, the geometric mean is generally more appropriate.

Worked Example 1.4

A portfolio has the following annual returns over three years: +10%, −5%, and +15%. Compute:

(a) The arithmetic mean return.
(b) The geometric mean return.

Answer:
(a) Arithmetic mean:

$$\bar{R}_{\text{arith}} = \frac{10\% + (-5\%) + 15\%}{3} = \frac{20\%}{3} \approx 6.67\%$$

(b) Geometric mean: First compute the cumulative value of 1 invested:

$$(1.10) \times (0.95) \times (1.15) = 1.20175$$

Then:

$$\bar{R}_{\text{geom}} = 1.20175^{1/3} - 1 \approx 1.0632 - 1 = 6.32\%$$

The geometric average (6.32%) is slightly lower than the arithmetic average (6.67%) because volatility reduces the compound growth rate.

In multi-period performance evaluation, risk-adjusted measures such as the Sharpe ratio are often computed using arithmetic mean returns and standard deviations of periodic returns, while the geometric mean is quoted to summarize the investor’s long-term realized growth rate.

Absolute and Relative Performance Analysis

Performance can be viewed in absolute terms (standalone) or relative to a benchmark.

Key Term: absolute return
The portfolio’s return over a specified period, without reference to any benchmark or target.

Key Term: relative return
The difference between the portfolio’s return and the return on a chosen benchmark over the same period.

Absolute Performance

Absolute performance focuses on:

• the actual return achieved (for example, 7% annual return), and
• the risk characteristics (for example, standard deviation, beta, drawdowns) over the evaluation period.

Absolute performance analysis answers questions such as:

• Did the portfolio meet the investor’s required return (for example, 6% per year to meet long-term goals)?
• Was the volatility acceptable given the investor’s risk tolerance?
• Were there large drawdowns that might have caused liquidity or behavioral issues?

Absolute performance is particularly important for investors with explicit targets, such as:

• an endowment that must earn at least inflation plus a spending rate,
• a pension fund that must meet actuarial return assumptions,
• an individual with a required rate of return stated in the investment policy statement (IPS).

However, absolute performance does not tell you whether the manager did better or worse than a passive alternative facing similar market conditions.

Relative Performance and Active Return

Relative performance uses a benchmark to provide context.

Key Term: active return
The difference between portfolio return and benchmark return, representing relative outperformance or underperformance.

Formally:

where $R_b$ is the benchmark return.

Interpretation:

• Positive active return: portfolio beat the benchmark (outperformance).
• Negative active return: portfolio lagged the benchmark (underperformance).
• Zero active return: portfolio matched the benchmark (ignoring fees and costs).

Relative performance is essential for assessing whether a manager is adding value beyond simply tracking the market.

A manager might deliver a positive absolute return but still underperform the benchmark if the benchmark was even stronger. For example:

• Portfolio return: +7%
• Benchmark return: +10%

The active return is −3%. This would typically be viewed as disappointing performance for an active manager, even though the absolute return is positive.

Similarly, during a market downturn:

• Portfolio return: −5%
• Benchmark return: −12%

The active return is +7%. This indicates strong relative performance (the manager lost less than the market), which may be regarded as successful defensive management.

Benchmark Selection

A benchmark should reflect the investor’s objectives and opportunity set. A poorly chosen benchmark can make a weak manager look good or a strong manager look bad.

Common benchmark types include:

• Broad market indices:
  • For example, a global equity index for a global equity mandate, or a domestic bond index for an investment-grade bond mandate.
• Style or strategy indices:
  • For example, value, growth, small-cap, or sector indices, used when managers specialize in particular styles.
• Custom blends of indices:
  • For multi-asset portfolios, a weighted mix of equity, bond, and other indices reflecting strategic asset allocation.
• Absolute return targets (cash-plus benchmarks):
  • For example, “3-month T-bill rate + 3%”. Common for absolute-return or hedge fund strategies.
• Peer group benchmarks (less ideal):
  • Comparing a fund to the median or average performance of similar funds. This is less precise and can be subject to survivorship bias.

Effective benchmarks typically have the following characteristics:

• Specified in advance: Defined before the evaluation period begins, not chosen afterwards to flatter results.
• Relevant and appropriate: Reflects the manager’s investment universe and style. A US small-cap manager should not be evaluated against a global large-cap index.
• Measurable and transparent: Returns are readily and objectively calculated and widely published.
• Unambiguous: Constituents and weights are clearly known (for example, list of stocks and their index weights).
• Investable: It is feasible to replicate or approximate the benchmark in practice, at least in principle.
• Consistent with objectives and constraints: Aligns with the client’s risk profile, time horizon, and constraints set in the investment policy statement.

An inappropriate benchmark can lead to incorrect conclusions. For example:

• Evaluating a real estate fund against the S&P 500 equity index is misleading because real estate has different risk and return characteristics.
• Evaluating a low-volatility equity strategy against a high-beta growth index may make the strategy look weak in strong bull markets, even if it meets its risk-focused objective.

Worked Example 1.5

A global equity manager with a US-dollar-based client uses the MSCI World Index (developed markets) as the benchmark. Over the past year:

• Portfolio return: 7%
• Benchmark (MSCI World) return: 5%
• Portfolio standard deviation: 12%

(a) Did the manager outperform in absolute and relative terms?
(b) What other information is required for a full evaluation?
(c) Suppose you later discover that the manager invests only in emerging market equities. What does this imply about the benchmark choice?

Answer:
(a) Absolute performance: The portfolio delivered a 7% return. You would compare this to the client’s required return (for example, a 6% target). If the required return was 6%, the portfolio met the absolute objective.

Relative performance: The manager outperformed the benchmark by 2 percentage points (7% − 5% = 2%). This is positive active return.

(b) Further evaluation should consider:

• Risk-adjusted measures such as the Sharpe ratio to assess whether the 2% outperformance was achieved efficiently, given the 12% volatility.
• The manager’s beta relative to the MSCI World index to determine Jensen’s alpha.
• Whether the return and risk figures are net or gross of fees, as clients experience net returns.
• The evaluation period length; a single year may be too short to judge skill.

(c) If the manager invests only in emerging market equities, MSCI World (developed markets only) is not an appropriate benchmark. Emerging markets have different risk and return characteristics. A more appropriate benchmark would be an emerging markets index, or a combination of developed and emerging market indices matching the mandate. The apparent outperformance versus MSCI World may reflect different asset class exposure rather than skill.

Absolute vs Relative Risk

Just as returns can be analyzed in absolute and relative terms, so can risk:

• Absolute risk: measured by the volatility (standard deviation) of portfolio returns.
• Relative risk: the variability of active returns (portfolio minus benchmark).

At Level 1, the focus is mainly on absolute risk (standard deviation) and beta. The concept that the standard deviation of active returns measures how tightly a manager tracks the benchmark is useful to understand, even if the term “tracking error” is not emphasized.

A manager who seeks to closely track the benchmark will have:

• small active returns (close to zero),
• therefore low relative risk (returns tightly clustered around the benchmark).

A highly active manager will typically have:

• large deviations from benchmark weights,
• larger active returns, both positive and negative,
• therefore higher relative risk.

Understanding this helps in interpreting attribution results and risk-adjusted performance.

Performance Measurement vs Attribution

Before covering attribution in detail, it is important to distinguish it from simple performance measurement.

• Performance measurement answers: “What were the returns and risk?”

  • Example: The portfolio returned 8% with a 10% standard deviation, while the benchmark returned 6%.
  • It includes calculating returns (point-to-point or average) and risk statistics (standard deviation, beta).

• Performance attribution answers: “Why did performance differ from the benchmark?”

  • Example: Outperformance came mainly from overweighting technology and successful stock selection in healthcare.
  • It decomposes active return into components linked to the manager’s decisions.

Both approaches are needed in manager appraisal:

• Measurement tells you how much value (or loss) occurred.
• Attribution tells you where it came from (asset allocation, sector bets, stock selection, currency positions, and so on).

A manager might slightly lag the benchmark overall but show strong stock selection that was offset by poor sector allocation. This detail is only visible through attribution.

Performance evaluation in practice combines:

• Quantitative analysis: returns, risk, risk-adjusted metrics, attribution effects.
• Qualitative assessment: team stability, investment process, style consistency, and whether observed performance seems repeatable.

Performance Attribution

Performance attribution goes beyond measuring results to explain how active decisions led to outperformance or underperformance. It decomposes active return into a set of effects associated with different types of decisions.

At CFA Level 1, the focus is on Brinson-style attribution for equity and multi-asset portfolios at a simple, conceptual level.

Attribution Effects

At a high level, three effects are commonly discussed:

Key Term: allocation effect
The portion of active return attributable to the manager choosing different asset class or sector weights from the benchmark.

Key Term: selection effect
The portion of active return attributable to the manager choosing securities that perform differently from the benchmark securities within the same sector or asset class.

Key Term: interaction effect
The portion of active return that arises from the combined impact of having both different weights and different security performance within sectors.

In a simple sector-level equity attribution:

• Allocation effect:
  Did overweighting or underweighting certain sectors (such as technology or healthcare) help or hurt relative performance, assuming benchmark-like returns within each sector?

• Selection effect:
  Within each sector, did the chosen securities outperform or underperform the sector’s benchmark, given the sector weight used?

• Interaction effect:
  Captures the cross-effect of simultaneously having different weights and different returns in a sector. In practice it is often smaller than the first two effects but can be positive or negative.

There are several formal attribution models in practice, each with slightly different formulas. At CFA Level 1, the emphasis is primarily on the economic interpretation of these effects and simple calculations following given formulas.

Simple Sector-Level Attribution Formulas

One common, simplified set of formulas (used in exam questions) for sector $i$ is:

• Allocation effect (sector $i$):

  $$\text{Allocation}_i = (w_{p,i} - w_{b,i}) \times R_{b,i}$$

• Selection effect (sector $i$):

  $$\text{Selection}_i = w_{p,i} \times (R_{p,i} - R_{b,i})$$

• Interaction effect (sector $i$):

  $$\text{Interaction}_i = (w_{p,i} - w_{b,i}) \times (R_{p,i} - R_{b,i})$$

where:

• $w_{p,i}$, $w_{b,i}$ are portfolio and benchmark weights in sector $i$,
• $R_{p,i}$, $R_{b,i}$ are portfolio and benchmark returns in sector $i$.

The total sector contribution to active return is the sum:

Summing over all sectors:

subject to rounding.

Worked Example 1.6

A portfolio and its benchmark are composed of two sectors: Technology and Healthcare. The information is:

• Technology:

  • Portfolio weight: 60%
  • Portfolio return: 10%
  • Benchmark weight: 50%
  • Benchmark return: 8%

• Healthcare:

  • Portfolio weight: 40%
  • Portfolio return: 6%
  • Benchmark weight: 50%
  • Benchmark return: 5%

Calculate the allocation and selection effects for Technology using the simple formulas below.

• Allocation effect (Technology):

  $$(\text{Portfolio weight} - \text{Benchmark weight}) \times \text{Benchmark sector return}$$

• Selection effect (Technology):

  $$\text{Portfolio weight} \times (\text{Portfolio sector return} - \text{Benchmark sector return})$$

Answer:
Allocation effect (Technology):

$$(60\% - 50\%) \times 8\% = 10\% \times 8\% = 0.8\%$$

Overweighting Technology by 10 percentage points increased the portfolio’s return by 0.8 percentage points relative to the benchmark.

Selection effect (Technology):

$$60\% \times (10\% - 8\%) = 60\% \times 2\% = 1.2\%$$

The manager’s Technology stock picks outperformed the Technology sector benchmark by 2%, and with a 60% sector weight this added 1.2 percentage points to active return.

Together, these effects show that the manager added value both by overweighting a strong-performing sector and by picking superior stocks within that sector.

In a full attribution, you would repeat these calculations for Healthcare and, if needed, calculate an interaction effect. Summing the sector-level effects would approximate the total active return.

Full Two-Sector Attribution

Continuing with the previous example, let us complete the attribution.

Worked Example 1.7

Using the same data as in Worked Example 1.6, compute:

(a) The portfolio and benchmark total returns.
(b) The total active return.
(c) Allocation, selection, and interaction effects for Healthcare.
(d) Verify that the sum of effects approximates the active return.

Answer:
(a) Portfolio and benchmark total returns:
Portfolio:

$$R_p = 0.60 \times 10\% + 0.40 \times 6\% = 6\% + 2.4\% = 8.4\%$$

Benchmark:

$$R_b = 0.50 \times 8\% + 0.50 \times 5\% = 4\% + 2.5\% = 6.5\%$$

(b) Active return:

$$R_p - R_b = 8.4\% - 6.5\% = 1.9\%$$

(c) Healthcare effects:
Allocation (Healthcare):

$$(40\% - 50\%) \times 5\% = (-10\%) \times 5\% = -0.5\%$$

Underweighting a sector with a positive return slightly hurt performance.

Selection (Healthcare):

$$40\% \times (6\% - 5\%) = 40\% \times 1\% = 0.4\%$$

Stock selection in Healthcare added 0.4%.

Interaction (Healthcare):

$$(40\% - 50\%) \times (6\% - 5\%) = (-10\%) \times 1\% = -0.1\%$$

For Technology, using the earlier data:
Interaction (Technology):

$$(60\% - 50\%) \times (10\% - 8\%) = 10\% \times 2\% = 0.2\%$$

(d) Sum of effects:
Allocation total:

$$0.8\% + (-0.5\%) = 0.3\%$$

Selection total:

$$1.2\% + 0.4\% = 1.6\%$$

Interaction total:

$$0.2\% + (-0.1\%) = 0.1\%$$

Sum of all effects:

$$0.3\% + 1.6\% + 0.1\% = 2.0\%$$

The total of 2.0% is very close to the actual active return of 1.9%; the small difference is due to rounding.

Interpretation: Most of the value added came from selection (1.6%), with smaller contributions from allocation (0.3%) and interaction (0.1%).

Interpretation of Attribution Results

Attribution analysis helps investors and managers see where value was created or lost:

• Positive allocation effect, negative selection effect:

  • The manager was good at choosing which sectors or asset classes to overweight or underweight, but did not pick stocks well within sectors.

• Negative allocation effect, positive selection effect:

  • The manager picked stocks well but hurt performance through poor sector or asset class allocation.

• Consistent positive selection effect across multiple periods:

  • Suggests persistent stock-picking skill in the manager’s chosen universe.

• Consistent positive allocation effect with neutral selection:

  • Suggests skill in top-down asset allocation (for example, deciding when to overweight equities versus bonds or specific sectors).

At CFA Level 1, you may be asked:

• to compute simple allocation or selection contributions for a sector,
• to identify which effect (allocation, selection, interaction) a described decision relates to, or
• to interpret whether a manager’s skill lies more in top-down allocation or bottom-up selection.

Worked Example 1.8

Suppose a portfolio and its benchmark each have two sectors, A and B.

• Sector A:

  • Portfolio weight: 30%
  • Portfolio return: 15%
  • Benchmark weight: 20%
  • Benchmark return: 10%

• Sector B:

  • Portfolio weight: 70%
  • Portfolio return: 8%
  • Benchmark weight: 80%
  • Benchmark return: 7%

Using the simple formulas for allocation and selection effects, identify whether the manager’s value added came more from allocation or selection.

Answer:
Sector A allocation effect:

$$(30\% - 20\%) \times 10\% = 10\% \times 10\% = 1.0\%$$

Sector A selection effect:

$$30\% \times (15\% - 10\%) = 30\% \times 5\% = 1.5\%$$

Both overweighting Sector A and superior stock selection within A added value. The selection contribution (1.5%) is larger than the allocation contribution (1.0%).

Sector B allocation effect:

$$(70\% - 80\%) \times 7\% = (-10\%) \times 7\% = -0.7\%$$

Underweighting B hurt performance slightly because Sector B’s benchmark return was positive.

Sector B selection effect:

$$70\% \times (8\% - 7\%) = 70\% \times 1\% = 0.7\%$$

Stock selection in Sector B added value.

Overall, the manager’s value added came more from selection (1.5% + 0.7% = 2.2%) than from allocation (1.0% − 0.7% = 0.3%). This suggests stronger stock-picking skill than sector allocation skill.

Attribution in Multi-Asset and Global Portfolios (Conceptual)

Attribution is not limited to equity sectors. In multi-asset portfolios, typical attribution levels include:

• Asset allocation:
  How much of active return came from overweighting or underweighting major asset classes (equities, bonds, cash, real estate) relative to the policy benchmark?

• Within-asset-class selection:
  Within equities, did choosing particular regions, styles, or stocks add value? Within fixed income, did security selection (duration, credit quality, sector) add value?

For global portfolios, there can also be:

• Currency effect:
  The impact of active currency positioning relative to the benchmark. A manager might hold securities in a given country but hedge or not hedge currency exposure, affecting returns when exchange rates move.

Though detailed multi-level attribution (for example, within fixed income) is beyond Level 1, you should be comfortable with these basic ideas and able to interpret descriptive statements about them.

Reporting and Use in Manager Appraisal

In practice and in exam-style questions, attribution results are used to:

• understand a manager’s style and strengths (for example, allocation-focused versus selection-focused),
• assess whether outperformance is likely to be repeatable (for example, consistent selection skill is more convincing than a single strong year),
• detect style drift (deviations from the stated style, such as a value manager drifting into growth stocks),
• support decisions to retain, increase, or reduce allocations to managers.

Attribution does not guarantee that skill will persist, but:

• A pattern of stable positive selection effects over time is stronger evidence of skill than sporadic, volatile results.
• A manager who relies heavily on big allocation bets may have more volatile relative performance and may be harder for clients to stick with.

Performance Evaluation for Alternative Investments (Conceptual Extension)

Alternative investments (private equity, real estate, hedge funds, infrastructure, and so on) present additional challenges for performance evaluation:

• Illiquidity and infrequent pricing:

  • Many alternative assets are not traded daily. Appraisal-based valuations can smooth returns, understating volatility and overstating Sharpe ratios.

• Complex fee structures:

  • Performance fees (carried interest, incentive fees) and high management fees reduce net returns. Gross performance may look strong, but investors experience net performance.

• Long and uneven cash flow patterns:

  • Private equity and some real estate funds have long life cycles with phases of capital commitment, deployment, and distribution. Standard time-series measures must be interpreted carefully.

• Use of leverage:

  • Hedge funds and private equity often use borrowed funds to increase returns. Higher volatility increases the importance of risk-adjusted measures.

At Level 1, you are not expected to compute specialized alternative investment performance measures, but you should understand that risk-adjusted evaluation is even more important when returns are non-normal and cash flows are irregular.

Key Term: investment life cycle (alternative investments)
The sequence of phases—capital commitment, capital deployment, and capital distribution—through which many alternative investment funds pass, affecting the timing and pattern of returns.

Summary

Performance evaluation is essential for determining whether an investment manager or strategy has added value and whether the results were achieved by taking more risk or through skillful active management.

Key ideas include:

• Absolute performance analysis looks at return and risk on a standalone basis relative to investor objectives.
• Relative performance analysis introduces a benchmark and focuses on active (excess) return.

Risk-adjusted measures such as the Sharpe ratio, Treynor ratio, Jensen’s alpha, and M-squared allow returns to be compared fairly across portfolios with different risk levels:

• Sharpe ratio uses total risk and is appropriate for standalone or not fully diversified portfolios.
• Treynor ratio and Jensen’s alpha use systematic risk (beta) and are appropriate for well-diversified portfolios where unsystematic risk is negligible.
• M-squared translates the Sharpe ratio into an easily interpreted percentage outperformance relative to the market at the same risk level.

Appropriate benchmark selection is critical. Benchmarks should be:

• specified in advance,
• relevant to the manager’s style and universe,
• transparent, measurable, and investable,
• consistent with the investor’s objectives and constraints.

Performance measurement tells you what happened in terms of risk and return, while performance attribution explains why performance differed from the benchmark:

• Attribution decomposes active return into allocation, selection, and interaction effects.
• The pattern and sign of these effects highlight where the manager added or destroyed value.
• Over multiple periods, consistent positive selection or allocation effects may suggest skill.

Combining risk-adjusted performance measures with attribution results enables more informed judgments about manager skill, style consistency, and suitability for an investor’s objectives and risk tolerance—exactly the kind of reasoning you are expected to demonstrate in CFA Level 1 exam questions.

Key Point Checklist

This article has covered the following key knowledge points:

• Distinguish between absolute and relative portfolio performance and calculate active return.
• Calculate and interpret Sharpe ratio, Treynor ratio, Jensen’s alpha, and understand the M-squared measure.
• Decide when to use total-risk measures (Sharpe, M²) versus beta-based measures (Treynor, alpha).
• Recognize the characteristics of an effective benchmark and why benchmark choice matters.
• Understand multi-period performance concepts, including arithmetic and geometric mean returns.
• Differentiate performance measurement from performance attribution and understand their distinct but related roles.
• Explain and interpret the allocation, selection, and interaction effects in attribution analysis.
• Use attribution outputs to infer whether a manager’s strengths lie in top-down allocation or bottom-up selection.
• Appreciate practical limitations of performance measures, including reliance on historical data and benchmark specification.
• Recognize additional challenges in evaluating performance for alternative investments.

Key Terms and Concepts

• performance measurement
• performance evaluation
• benchmark
• risk-adjusted return
• attribution analysis
• total risk
• systematic risk
• Sharpe ratio
• Treynor ratio
• Jensen’s alpha
• M-squared (M²) measure
• absolute return
• relative return
• active return
• allocation effect
• selection effect
• interaction effect
• investment life cycle (alternative investments)