CFA Level II Exam · Using Multifactor Models

Factor Portfolios, Tracking Portfolios and Smart Beta Explained

Updated 7 October 2026 · Fact-checked

A factor portfolio has a sensitivity of 1 to one factor and 0 to all others. A tracking portfolio replicates a target's factor exposures using a set of assets. Smart beta tilts toward rewarded factors. You solve by matching betas, then reading active risk and active return from the exposure gaps.

Understand Applications: Factor Portfolios, Tracking and Smart Beta

A multifactor model says an asset's return is driven by a few common factors plus noise. Each asset has a sensitivity (beta) to each factor. A portfolio's sensitivity is the weighted average of its assets' sensitivities. This is what makes factor portfolios possible.

A factor portfolio is built to have a sensitivity of 1 to one chosen factor and 0 to every other factor. It isolates the return of that single factor. Investors use it to take a pure bet on one risk, or to hedge that risk out.

A tracking portfolio is built to match the factor sensitivities of a target, such as a benchmark. If every beta matches, the tracking portfolio behaves like the target in factor terms. The remaining difference is the target's specific risk, which the tracking portfolio does not copy. The tracking error is the standard deviation of the active return, which is portfolio return minus benchmark return.

In active management, a manager deliberately departs from benchmark factor exposures. This is a factor tilt: the portfolio has more or less of a factor than the benchmark. The active factor risk comes from these tilts. The active specific risk comes from security selection. In passive or rules-based approaches, smart beta uses fixed rules to tilt toward factors such as value, size, momentum, quality or low volatility. A multifactor smart beta product combines several tilts, which can diversify across factors.

You can also hedge a factor exposure. Add a position in a factor portfolio with the opposite sensitivity, so the net exposure to that factor is zero. Check the net beta, not just the sign of the position.

Key formulas to remember

Portfolio factor sensitivity: b_p,k = Σ w_i × b_i,k; Weighted average of asset sensitivities to factor k. Weights sum to 1 unless a cash or hedge position is stated.
Factor model return: R_i = a_i + b_i1 F1 + b_i2 F2 + … + b_ik Fk + ε_i; F are factor surprises or factor returns as defined in the vignette. ε is the specific return.
Pure factor portfolio: b_p,k = 1 for the chosen factor and b_p,j = 0 for every other factor j; Expected return is the risk-free rate plus that factor's risk premium in an APT-style setting.
Tracking portfolio condition: b_tracking,k = b_target,k for every factor k; Solve the weights from the matching equations plus weights summing to 1.
Active return: R_active = R_p − R_B; Portfolio return minus benchmark return.
Active factor tilt: Tilt_k = b_p,k − b_B,k; Positive means overweight to that factor relative to the benchmark.
Active return from factors: Σ (b_p,k − b_B,k) × F_k + active specific return; Splits active return into factor tilts and security selection.
Active risk (tracking error): Active risk = √(Active factor risk + Active specific risk); Variances add, not standard deviations. Active factor risk and active specific risk are variances.
Information ratio: IR = Active return ÷ Active risk; Active return per unit of tracking error.

How to solve Applications: Factor Portfolios, Tracking and Smart Beta questions

Use this order for any factor portfolio, tracking or smart beta item. Most marks come from reading the exposures correctly.

1Read the vignette and list the factors and their units (surprises, premiums or returns). Note whether the question uses the portfolio, the benchmark or both.
2Pull each asset's or portfolio's sensitivity to every factor from the exhibit. Write them in a small grid.
3Identify the task: build a factor portfolio, build a tracking portfolio, measure a tilt, hedge, or attribute return and risk.
4For building or hedging, write one equation per factor and one for weights summing to 1. Solve for the weights.
5For tilts, subtract benchmark betas from portfolio betas factor by factor. Keep the sign.
6For attribution, multiply each tilt by the factor return given. Add the specific return if the question asks for total active return.
7For risk, add variances, then take the square root only at the end. Compute the information ratio if asked.
8Check the answer against the story: an overweight to a factor that rose should add to return.

Quickest way: Beta-gap shortcut

When to use it: Use when the question asks for active return, tilt direction or hedge size and the exhibit gives betas for both portfolio and benchmark.

Compute the gap: portfolio beta minus benchmark beta for each factor.
Multiply each gap by the stated factor return and add them.
For a hedge, size the hedge position so its beta times its weight cancels the gap.
Eliminate options whose sign is wrong before doing any further arithmetic.

Common mistakes in Applications: Factor Portfolios, Tracking and Smart Beta

Treating a factor portfolio as having zero betas everywhere.
Students confuse pure factor exposure with a market-neutral position.
Fix: A factor portfolio has beta 1 on the target factor and 0 on all others. Check both conditions.
Adding standard deviations to get active risk.
It feels natural to add the factor and specific risk figures.
Fix: Add variances: active factor risk plus active specific risk, then take the square root.
Using the portfolio's absolute beta instead of the beta gap versus the benchmark.
The exhibit lists portfolio betas first and students stop there.
Fix: Active exposure is portfolio beta minus benchmark beta. Only the gap drives active return.
Believing a tracking portfolio removes all differences from the target.
Matching factor betas sounds like full replication.
Fix: It matches factor exposure only. Specific risk of the target is not copied, so some tracking error remains.
Forgetting the weights-sum-to-1 equation when solving for a tracking portfolio.
Students solve only the factor equations.
Fix: Always write the budget equation, or include cash or the risk-free asset if the vignette allows it.
Calling smart beta active stock picking.
Both depart from market-cap weights.
Fix: Smart beta is rules-based and transparent. It targets factor exposure, not manager judgement on individual securities.

Worked examples

Example 1

A benchmark has factor sensitivities of 1.00 to Market and 0.20 to Value. A portfolio has 1.10 to Market and 0.50 to Value. In the period, the Market factor return was 4.0% and the Value factor return was 2.0%. The portfolio's active specific return was 0.3%. (1) What is the active exposure to each factor? (2) What is the active return from factor tilts? (3) What is the total active return?

Show the solution

Market gap: 1.10 − 1.00 = 0.10. Value gap: 0.50 − 0.20 = 0.30.
Market contribution: 0.10 × 4.0% = 0.40%.
Value contribution: 0.30 × 2.0% = 0.60%.
Factor tilt return: 0.40% + 0.60% = 1.00%.
Total active return: 1.00% + 0.3% = 1.30%.

Answer: (1) +0.10 to Market and +0.30 to Value. (2) 1.00%. (3) 1.30%.

Example 2

A manager's active factor risk is 4.00 (variance, in %²) and active specific risk is 5.00 (variance, in %²). Active return is 2.4%. (1) What is the tracking error? (2) What is the information ratio? (3) The manager reduces active specific variance to 0 and keeps all else equal. What is the new tracking error?

Show the solution

Total active variance: 4.00 + 5.00 = 9.00.
Tracking error: √9.00 = 3.0%.
Information ratio: 2.4% ÷ 3.0% = 0.80.
New active variance: 4.00 + 0 = 4.00.
New tracking error: √4.00 = 2.0%.

Answer: (1) 3.0%. (2) 0.80. (3) 2.0%.

Exam tips

Read the exhibit for the benchmark row before the portfolio row. The question usually needs the difference.
Check whether the vignette gives risk as variance or standard deviation before adding anything.
For smart beta questions, link the tilt to the factor named in the vignette and judge the claim against rules-based, transparent construction.
When asked to hedge, confirm the net beta is zero after the hedge. Do not stop at choosing the opposite sign.
With no penalty for wrong answers, never leave an item blank. Eliminate wrong signs and guess from what remains.

Applications: Factor Portfolios, Tracking and Smart Beta in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

FRM Part IIFactor Portfolio Construction and Smart Beta

Applications: Factor Portfolios, Tracking and Smart Beta: frequently asked questions

What is the difference between a factor portfolio and a tracking portfolio?

A factor portfolio has a sensitivity of 1 to one factor and 0 to the others. A tracking portfolio copies the factor sensitivities of a chosen target. The first isolates a factor. The second replicates a benchmark's factor profile.

How do you build a tracking portfolio from a factor model?

Write one equation for each factor, setting the weighted average beta equal to the target's beta. Add an equation that weights sum to 1. Solve the system for the weights.

What is smart beta in a multifactor context?

Smart beta uses fixed rules to tilt a portfolio toward factors such as value, momentum, quality or low volatility instead of market-cap weights. A multifactor version combines several tilts to spread factor risk. It is usually positioned between passive and active management.

How does a multifactor model separate active risk?

Active risk splits into active factor risk from tilts versus the benchmark and active specific risk from security selection. Their variances add. The square root of the sum is the tracking error.