CFA Level II Exam · Analysis of Active Portfolio Management

Value Added by Active Management: Active Return Explained

Updated 7 October 2026 · Fact-checked

Active return is portfolio return minus benchmark return. It measures the value a manager adds, or loses, against the benchmark. You can also build it from active weights (portfolio weight minus benchmark weight) times each asset's return minus the benchmark return. Check the sign and the benchmark first.

Understand Value Added by Active Management

Every active manager is judged against a benchmark. The benchmark is the passive alternative: what you would have earned by simply holding the index. The manager's value added is the part of the return that the benchmark does not explain.

The measure is active return: portfolio return minus benchmark return. If the portfolio earns 9% and the benchmark earns 7%, the active return is +2%. If the portfolio earns 5% and the benchmark earns 7%, the active return is −2%. The manager destroyed value.

Active return comes from deviating from the benchmark. The deviation in each holding is the active weight: portfolio weight minus benchmark weight. A positive active weight is an overweight. A negative one is an underweight. Active weights across the whole portfolio sum to zero when both the portfolio and the benchmark are fully invested with no leverage or cash difference.

Active return can then be written as the sum of active weight times asset return across all holdings. Because active weights sum to zero, you can also subtract the benchmark return from each asset return. This shows the idea clearly: the manager adds value by overweighting assets that beat the benchmark and underweighting assets that lag it.

In an item set you will usually get a table of portfolio weights, benchmark weights and returns. Your job is to find the right columns, apply the formula, and read the sign correctly.

Key formulas to remember

Active return: RA = RP − RB; RP is portfolio return and RB is benchmark return for the same period. Positive means value added.
Active weight: Δwi = wP,i − wB,i; Portfolio weight minus benchmark weight for asset or sector i. Overweight is positive.
Active return from active weights: RA = Σ Δwi × Ri = Σ Δwi × (Ri − RB); The second form works because active weights sum to zero. Use it when the portfolio and benchmark are both fully invested.
Sum of active weights: Σ Δwi = 0; Holds when portfolio and benchmark weights each sum to 100%. A cash or leverage difference breaks this.

How to solve Value Added by Active Management questions

Use this method for any question on active return or active weights.

1Identify the portfolio and the benchmark. Note the period and whether returns are given as percentages.
2Write down the weights and returns in a small list, one line per asset or sector.
3Compute each active weight as portfolio weight minus benchmark weight. Check that they sum to zero.
4If total returns are given, compute RA = RP − RB directly.
5If only weights and asset returns are given, compute Σ Δwi × Ri for the active return, or use the second form with Ri − RB.
6Check the sign. A positive active weight in a sector that beat the benchmark adds value. An underweight in a lagging sector also adds value.
7State the answer in the units asked, such as percentage points or basis points, and match it to one option.

Quickest way: Active weight times return shortcut

When to use it: Use it when the vignette gives weights and sector returns and asks for the manager's total active return.

Subtract benchmark weights from portfolio weights for each sector.
Multiply each active weight by that sector's return.
Add the products. The total is the active return.
Sense-check: overweights in strong sectors should push the answer up.

Common mistakes in Value Added by Active Management

Subtracting in the wrong order, benchmark minus portfolio.
The word 'difference' hides the direction.
Fix: Always write portfolio minus benchmark. A manager who beats the benchmark has a positive active return.
Using portfolio weights instead of active weights when computing value added from allocation.
Students multiply familiar weights by returns and get the portfolio return.
Fix: Subtract benchmark weights first. Only then multiply by returns.
Forgetting that active weights sum to zero and not checking it.
Students skip the sanity check under time pressure.
Fix: Add the active weights. If the sum is not zero, you have an arithmetic slip or a cash position.
Mixing percentages and decimals or percentage points and basis points.
Options are often shown in different units.
Fix: Convert everything to decimals, compute, then convert back. 1 percentage point equals 100 basis points.
Comparing returns over different periods or against the wrong benchmark.
Vignettes may list several indexes and periods.
Fix: Match the benchmark named for the mandate and use returns for the same period as the portfolio.

Worked examples

Example 1

A fund returned 11.4% last year. Its benchmark returned 9.8%. (1) What is the active return? (2) If the fund had instead returned 8.5%, what would the active return be?

Show the solution

Active return = RP − RB.
(1) 11.4% − 9.8% = 1.6%.
(2) 8.5% − 9.8% = −1.3%.

Answer: (1) +1.6%, so the manager added value. (2) −1.3%, so the manager lost value against the benchmark.

Example 2

A portfolio and its benchmark hold three sectors. Portfolio weights: Technology 45%, Health Care 30%, Utilities 25%. Benchmark weights: Technology 35%, Health Care 30%, Utilities 35%. Sector returns: Technology 12%, Health Care 6%, Utilities 2%. (1) Find the active weights. (2) Find the active return from these weights. (3) Which decision added the most value?

Show the solution

(1) Technology: 45% − 35% = +10%. Health Care: 30% − 30% = 0%. Utilities: 25% − 35% = −10%. Sum is 0, as expected.
(2) Active return = Σ Δwi × Ri = 0.10 × 12% + 0 × 6% + (−0.10) × 2% = 1.2% − 0.2% = 1.0%.
Check with the second form. Benchmark return = 0.35 × 12% + 0.30 × 6% + 0.35 × 2% = 4.2% + 1.8% + 0.7% = 6.7%. Then 0.10 × (12 − 6.7) + 0 + (−0.10) × (2 − 6.7) = 0.53 + 0.47 = 1.0%.
(3) Technology contributed +1.2 percentage points. Utilities contributed −0.2 percentage points. Technology overweight added the most.

Answer: (1) +10%, 0%, −10%. (2) Active return of 1.0%. (3) The Technology overweight.

Exam tips

Read which benchmark the mandate uses before touching numbers. Vignettes often list more than one index.
Always compute active weights first. They also show you where the manager's bets are, which many questions ask about.
Check that active weights sum to zero. It catches errors fast and costs seconds.
Watch the units. Options may differ by 10 times or 100 times if you confuse percent and basis points.
No penalty for wrong answers, so answer every question even if you must estimate the sign and size.

Value Added by Active Management in other exams

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

Value Added by Active Management: frequently asked questions

What is the formula for active return in CFA Level II?

Active return equals portfolio return minus benchmark return. You can also compute it as the sum of active weights times asset returns. Both give the same result when portfolio and benchmark weights each sum to 100%.

What is an active weight?

It is the portfolio weight of an asset or sector minus its benchmark weight. A positive value is an overweight and a negative value is an underweight. The sum across all holdings is zero when both are fully invested.

Does a positive active return always mean skill?

No. A positive active return in one period can come from luck or from taking more risk. That is why the curriculum also looks at active risk and ratios such as the information ratio.

Can active return be negative?

Yes. If the portfolio earns less than the benchmark, active return is negative. It means the manager lost value relative to the passive alternative.