## **Learning Outcomes**

This article explains how passive and enhanced indexing strategies are designed, implemented, and evaluated within an exam context. It clarifies distinctions between price‑weighted, cap‑weighted, equal‑weighted, and factor‑based indices, and shows how construction and rebalancing rules drive portfolio holdings, turnover, and concentration risk. It analyses the mechanics of full replication, stratified sampling, and optimization as index‑tracking techniques, highlighting the cost, liquidity, and operational trade‑offs that influence method selection. It details how tracking error is defined, measured, and decomposed, and links key drivers—such as incomplete replication, cash drag, corporate actions, and transaction costs—to observed performance slippage versus the benchmark. It examines how enhanced indexing introduces small, systematic deviations from benchmark weights, including factor tilts and security‑level over‑ or underweights, with explicit tracking‑error limits. It also discusses when passive, sampled, or enhanced approaches are most appropriate given mandate risk budgets, implementation constraints, and market structure. Overall, the article equips CFA Level 3 candidates to interpret index‑tracking results, evaluate manager decisions, and articulate the strengths and limitations of alternative indexing approaches in portfolio‑management case scenarios.

## **CFA Level 3 Syllabus**

For the CFA Level 3 exam, you are expected to understand indexing as a portfolio management strategy, with a focus on the following syllabus points:

- Explain types of equity indices (e.g., price-weighted, capitalization-weighted, equal-weighted, factor-based) and their construction and rebalancing rules
- Distinguish between passive indexing and enhanced indexing in portfolio implementation
- Analyse causes of tracking error and assess tracking error mitigation methods
- Compare full replication to stratified sampling, optimization, and enhanced indexing approaches
- Explain how index selection and tracking methodology impact implementation effectiveness

## **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. Name three factors that may cause tracking error between a passive index portfolio and its benchmark.
2. Which method of index construction is most susceptible to excessive weight in a few dominant securities?
3. How can stratified sampling reduce tracking error compared to simple sampling?
4. In enhanced indexing, what is the main goal of small, systematic deviations from the benchmark weights?

## **Introduction**

Passive indexing is a central element of portfolio management, especially for investors seeking broad market exposure and low cost. Understanding how indices are constructed and managed, and how portfolios track an index, is critical for exam success. Enhanced indexing introduces modest, systematic deviations from the benchmark in search of incremental return, while still maintaining close adherence to the target index.

> **Key Term: Index construction**
> The process by which constituent securities are selected, weighted, and periodically rebalanced according to a defined set of rules.
>
> **Key Term: Tracking error**
> The standard deviation of the difference between the returns of a portfolio and its benchmark index over a specified period, reflecting deviations due to factors such as incomplete replication, cash flows, and trading costs.

## Index Construction: Core Methods

Indices can be constructed using several methodologies, each with particular features and consequences for replication strategy.

- **Price-weighted indices** assign weights based only on price per share (e.g., DJIA), giving undue emphasis to high-priced stocks regardless of overall company size.
- **Market capitalization-weighted indices** (e.g., S&P 500) use each company's proportion of total market value, making them more representative of aggregate wealth but susceptible to concentration in a few mega-caps.
- **Equal-weighted indices** weight all constituents the same, resulting in heavier exposure to small companies.
- **Factor-based and fundamental indices** select and weight securities using attributes like value or volatility, seeking alternative betas.

> **Key Term: Full replication**
> A passive investment technique where the portfolio owns every security in the index in exact benchmark weights, minimizing tracking error but potentially incurring high trading costs for large, broad indices.

## Approaches to Index Tracking

### Full Replication

Full replication means holding all index securities at the precise benchmark weights. This approach keeps tracking error very low, provided all trades are executed efficiently. However, for indices with hundreds or thousands of securities (like global all-cap benchmarks), full replication may be costly or impractical, due to illiquid or micro-cap constituents.

### Stratified Sampling and Optimization

Because full replication is not always feasible, managers may use:

- **Stratified sampling:** The index is divided into "cells" (by sector, size, style, etc.), and the portfolio seeks to match each cell’s aggregate characteristics using a subset of representative securities.
- **Optimization:** Quantitative models are used to select a subset and assign weights based on risk and return projections, subject to tracking error constraints and design limits on exposures.

These methods are easier and less costly to implement, but typically create higher tracking error than full replication, especially if market conditions change rapidly or if optimization models are misspecified.

> **Key Term: Enhanced indexing**
> A passive-plus strategy that introduces small, systematic deviations from index weights in an attempt to add modest alpha while limiting active risk and maintaining benchmark-like behavior.

## Tracking Error: Definition and Drivers

Tracking error quantifies how closely the portfolio return matches the benchmark over time. Understanding its sources enables better management and expectation-setting.

**Major sources of tracking error:**

- Incomplete or approximate replication (sampling error)
- Index reconstitution lags (delayed trades after index changes)
- Corporate actions and events not mirrored instantaneously
- Cash drag (uninvested cash levels due to client flows or dividends)
- Trading costs and liquidity shortfalls, especially for thinly traded securities
- Tax or dividend treatment differences
- Currency management errors (for multinational indices)

### **Worked Example 1.1**

A mutual fund seeks to track the FTSE All-World Index, which has 3,700 stocks. The portfolio manager uses stratified sampling to select 500 securities that replicate the sector, size, and regional weights of the index. Over the next year, several countries add new companies to the index, and two sectors experience sudden volatility. The portfolio’s return lags the index by 0.20%. What likely contributed to this tracking error?

> **Answer:** Key causes likely include imperfect sector and country representation—sampling fewer securities means some country and sector characteristics were missed. Also, trading lags during constituent changes and high implementation costs for frontier market additions may have added to tracking error.

### **Worked Example 1.2**

Suppose an ETF tracks an equal-weighted index of 300 stocks, rebalancing quarterly. Over the past year, large-cap stocks outperformed small-caps. Explain how index construction and rebalancing contributed to tracking error.

> **Answer:** An equal-weighted index will systematically overweight smaller companies, which likely underperformed in this scenario. Frequent rebalancing forced the ETF to sell large-cap winners and buy small-cap laggards, further hurting tracking. The ETF’s costs from high turnover also raised tracking error versus a cap-weighted alternative.

## Enhanced Indexing Strategies

Enhanced indexing, or passive-plus, uses quantitative or rules-based techniques to make minor, systematic deviations from the index in order to add modest returns (expected "alpha") while maintaining tight control of tracking error.

- Examples: tilting toward value, momentum, or quality characteristics using multifactor screens; exploiting tax management opportunities; or systematically excluding higher-cost, illiquid names.
- Advantages: Slightly higher expected return than pure passive with similar risk profile.
- Limitations: Still prone to underperformance if factor tilts lag, if models are faulty, or if costs exceed added value.

### **Worked Example 1.3**

A manager runs an enhanced index fund designed to track a cap-weighted index with a permitted tracking error of 1%. Each quarter, the manager overweights stocks with above-average dividend yield and underweights those with the lowest yield, making sure to keep all sector- and size-based exposures within 0.5% of benchmark. In a year when dividend yield underperforms, what is the expected outcome for the fund’s excess return and tracking error?

> **Answer:** The fund would likely see modest negative excess return versus the benchmark, as the yield tilt detracted. Tracking error would remain within the intended 1% range, as the exposure limits force close adherence to index-like risk characteristics.

### **Revision Tip**

> Focus your CFA exam revision on how tracking error, portfolio construction, and rebalancing interact. Know examples of when enhanced indexing may outperform or underperform pure passive funds.

## **Summary**

Accurate index construction and replication methods are central for passive and enhanced indexing strategies. Tracking error arises from sampling, reconstitution delays, trading costs, market frictions, and index methodology effects. Enhanced indexing allows for modest, systematic alpha-seeking with limited active risk. Understanding these interactions helps CFA candidates evaluate the strengths and weaknesses of different passive tracking approaches in real-world portfolios.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Distinguish between price-weighted, cap-weighted, equal-weighted, and factor-based index construction methods
- Explain full replication, stratified sampling, and optimization approaches to index tracking
- Identify the main sources of tracking error in passive index strategies
- Describe how enhanced indexing strategies aim to deliver modest alpha within tracking error limits
- Compare the tradeoffs between implementation cost, tracking error, and expected return for different indexing approaches

## **Key Terms and Concepts**

- Index construction
- Tracking error
- Full replication
- Enhanced indexing

Passive and enhanced indexing - Index construction and tracking error