Portfolio construction and analytics - Performance evaluatio...

Learning Outcomes

After reading this article, you will be able to measure a portfolio's absolute and relative performance against appropriate benchmarks, calculate risk-adjusted returns using ratios such as Sharpe and Jensen's alpha, and understand how performance attribution explains the sources of portfolio returns. These skills are essential for CFA Level 1 exam success and for practical investment analysis.

CFA Level 1 Syllabus

For CFA Level 1, 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. Focus your revision on:

• The calculation and interpretation of key risk-adjusted performance measures, including Sharpe ratio, Treynor ratio, and Jensen's alpha
• Distinction between absolute and relative portfolio performance
• The importance of benchmarks and their selection
• Principles of performance attribution—allocation, selection, and interaction effects
• Use of performance evaluation information in investment decision-making

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 risk-adjusted return ratio uses total portfolio risk, and when is it most appropriate to use?
2. Explain the main difference between performance measurement and performance attribution in portfolio analysis.
3. Which component of attribution analysis quantifies the portfolio manager’s value added from choosing stocks within a sector?
4. True or false? Jensen’s alpha uses systematic risk to evaluate performance and a positive alpha always means the portfolio outperformed its benchmark.

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 risks taken. This article covers the main performance measures and the steps of attribution analysis, providing the basis for sound investment appraisal.

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

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

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.

RISK-ADJUSTED PERFORMANCE MEASURES

Investment returns alone do not tell the full story. Risk-adjusted returns are critical for fair comparisons between strategies and for identifying genuine skill.

Sharpe Ratio and its Use

The Sharpe ratio expresses the excess return a portfolio generates for each unit of total risk taken.

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 Sharpe ratio is useful for comparing portfolios or managers when the investor’s total portfolio is not yet fully diversified, as it incorporates all risk.

Treynor Ratio and Jensen’s Alpha

Both Treynor ratio and Jensen’s alpha focus on systematic risk rather than total risk. They are most appropriate for evaluating the performance of well-diversified portfolios.

Key Term: Treynor ratio
The excess return earned per unit of portfolio beta (systematic risk).

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

Jensen’s alpha is interpreted as the absolute value an investor would be willing to pay a manager for their skill in generating returns above expectation, given risk.

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 = (14% - 3%)/15% = 0.73
(b) Treynor ratio = (14% - 3%)/1.2 = 9.17%
(c) Jensen’s alpha = 14% - [3% + 1.2 × (12% - 3%)] = 14% - 13.8% = 0.2%

Selecting the Appropriate Measure

Use the Sharpe ratio for portfolios where diversification may not be complete and total risk matters. Use the Treynor ratio or Jensen’s alpha for fully diversified portfolios and to assess manager skill versus systematic risk.

Exam Warning

Treynor ratio and Jensen’s alpha are only valid and comparable when portfolios are well diversified. Using them with concentrated portfolios can mislead risk evaluation.

ABSOLUTE AND RELATIVE PERFORMANCE ANALYSIS

Absolute performance refers to the portfolio’s return and risk over a defined period, regardless of a reference point. Relative performance compares returns to a benchmark to assess whether the manager “beat the market” or their designated standard.

Benchmark Selection

A benchmark should reflect the investor’s objectives and opportunity set. Common benchmark types include:

• Broad market indices (e.g., S&P 500)
• Strategy or style indices (e.g., value, growth, small cap)
• Custom blends or absolute return targets

Worked Example 1.2

A global equity manager with a US-dollar-based client uses the MSCI World Index as the benchmark. Over the past year, the portfolio returned 7% while the benchmark returned 5%. The portfolio's standard deviation was 12%.

Question: Did the manager outperform in absolute and relative terms? What other information is required for full evaluation?

Answer:
The manager outperformed the benchmark by 2 percentage points (relative performance). However, risk-adjusted measures (using the Sharpe or Treynor ratio) are needed to assess whether the outperformance was sufficient given the risk taken.

PERFORMANCE ATTRIBUTION

Performance attribution goes beyond measuring results to explain how active decisions led to outperformance or underperformance. It decomposes excess (active) return into allocation, selection, and interaction (sometimes called timing) components.

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

Attribution Effects

• Allocation effect: The value added from deviating from the benchmark’s sector or asset class allocations.
• Selection effect: The value added from choosing securities that outperformed the benchmark within a sector or segment.
• Interaction effect: The combined impact of both allocation and selection decisions.

Worked Example 1.3

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

Calculate the allocation and selection effects for Technology.

Answer:
Allocation effect (Tech) = (Portfolio weight - Bench weight) × Bench return = (60% - 50%) × 8% = 0.8% Selection effect (Tech) = Portfolio weight × (Portfolio return - Bench return) = 60% × (10% - 8%) = 1.2% The sum shows the value added from both overweighting Technology and outperforming in security selection.

Reporting and Interpretation

Attribution analysis helps investors and managers see where value was created or lost—whether from being overweight certain markets, sectors, or from stock-picking skill.

Revision Tip

For CFA exam questions, memorize the formulas for the allocation, selection, and interaction effects, and practice decomposing active return.

Summary

Performance evaluation is essential for determining whether an investment manager or strategy outperformed its benchmark, and for understanding whether the results were achieved by taking more risk or by skillful active management. Risk-adjusted return measures like the Sharpe ratio and Jensen’s alpha complement attribution analysis, which breaks down performance to identify sources of relative gain or loss. Always consider benchmark appropriateness and risk in your evaluation.

Key Point Checklist

This article has covered the following key knowledge points:

• Calculate and interpret Sharpe, Treynor, and Jensen’s alpha for portfolio performance
• Understand when to use absolute vs. relative performance measures
• Recognize the importance of benchmark selection and appropriateness
• Explain the components of performance attribution: allocation, selection, and interaction effects
• Distinguish between measurement and attribution analysis

Key Terms and Concepts

• performance measurement
• benchmark
• attribution analysis
• Sharpe ratio
• Treynor ratio
• Jensen’s alpha
• active return