CFA Level II · CFA Level II Exam

Analysis of Active Portfolio Management for CFA Level II

Analysis of active portfolio management measures whether a manager adds value beyond a benchmark. You compute active return, active risk, the information ratio and the Sharpe ratio, then use the fundamental law, IR ≈ TC × IC × √BR, to link skill, breadth and constraints to expected performance.

What this chapter covers

This chapter asks one question: is an active manager worth paying for? It starts with value added, which is the portfolio return minus the benchmark return. It then builds the tools to judge that value per unit of risk: the Sharpe ratio for total risk and the information ratio for active risk.

Next comes the fundamental law of active management. It says the information ratio depends on skill and on how many independent bets you make. The basic form is IR = IC × √BR. The expanded form adds the transfer coefficient: IR ≈ TC × IC × √BR. You then split active risk into the part from factor tilts and the part from security selection, and you solve for the level of active risk that maximises the expected utility of the portfolio.

This chapter links to Portfolio Construction, Equities and Fixed Income. It also uses ideas from Quantitative Methods, such as standard deviation and regression. Level II questions come in item sets, so you will usually get a short vignette with a table of weights, returns, or ratios. You then pick the right formula and apply it.

Portfolio Construction carries a 10-15% topic weight, and this chapter is one of the most calculation-friendly parts of it. The formulas are short, the inputs are given in the vignette, and the same few relationships appear again and again. If you know which ratio to use and how active risk is built, you can pick up reliable points with little reading time. It also helps with judgement questions in other topics, such as whether a manager's reported results show real skill or just more risk.

Analysis of Active Portfolio Management: topics in the order to study them

1Value Added by Active ManagementStart here because everything else measures this: active return is portfolio return minus benchmark return, and you need that definition first.
2Sharpe Ratio and Information RatioThese two ratios turn value added into return per unit of risk, and you need them before the fundamental law makes sense.
3Fundamental Law of Active ManagementIt explains what drives the information ratio, so you study it once you know what the information ratio is.
4Active Risk and Active Return DecompositionThis splits active risk and return into factor and security selection parts, which builds on the active return and risk ideas already covered.
5Optimal Active Risk and Portfolio ConstructionStudy it last because it combines the information ratio, active risk and the benchmark into one decision on how much active risk to take.

How to prepare Analysis of Active Portfolio Management

Treat this chapter as a small set of linked formulas. Aim to know what each input means, not just the arithmetic.

Write down the definitions first: active return, active weight, active risk (tracking error) and the information ratio. Say each out loud in one sentence.
Learn the Sharpe ratio and information ratio side by side. Note which one uses total risk and which uses active risk, and what benchmark or risk-free rate each one subtracts.
Practise the fundamental law in both forms. Do questions where you solve for IR, then questions where you solve for IC, breadth or the transfer coefficient.
Work through active risk decomposition with a vignette: split active risk into factor and security selection parts and check that the parts add up in the way the curriculum shows.
Solve for optimal active risk, noting how it rises with the information ratio and falls with risk aversion. Practise reading which inputs the vignette actually gives you.
Finish with full item sets under time. For each one, mark the data you used and the formula you chose, then review any wrong answers by cause: wrong formula, wrong input or arithmetic.
Make a one-page sheet of formulas and conditions, and review it a few times in the last week.

Common mistakes in Analysis of Active Portfolio Management

Using the Sharpe ratio when the question asks about skill versus a benchmark.
Fix: Look at the denominator the question implies. If it is about active return against a benchmark, use the information ratio with active risk.
Dividing by portfolio standard deviation instead of tracking error in the information ratio.
Fix: Find the figure described as active risk, tracking error, or standard deviation of active returns, and underline it in the vignette.
Treating breadth as the number of stocks in the portfolio.
Fix: Count independent investment decisions made over the period. Ask whether the bets are truly independent before counting them.
Ignoring the transfer coefficient and applying only IC × √BR.
Fix: If the vignette mentions constraints, such as no short selling or position limits, check for a transfer coefficient and use the expanded form.
Mixing time periods, such as monthly active return with annual active risk.
Fix: Convert everything to the same period before computing any ratio, and state the period next to each number as you work.
Memorising formulas without understanding what moves each one.
Fix: For each formula, ask what happens to the answer if one input rises. Practise this on item sets so conceptual questions become easy.

Last-day revision: Analysis of Active Portfolio Management

Active return = portfolio return − benchmark return.
Active weight = portfolio weight − benchmark weight.
Sharpe ratio = (Rp − Rf) ÷ σp, which uses total risk.
Information ratio = active return ÷ active risk, where active risk is the standard deviation of active returns (tracking error).
Basic fundamental law: expected IR ≈ IC × √BR, where IC is the information coefficient and BR is breadth.
Expanded form: expected IR ≈ TC × IC × √BR, where TC is the transfer coefficient.
A transfer coefficient below 1 means constraints stop the portfolio from using all of the manager's insights.
Breadth means the number of independent decisions per year, not just the number of securities held.
Active risk squared = factor risk squared + security selection risk squared, under the curriculum's decomposition.
Optimal active risk rises with a higher information ratio and falls with greater risk aversion.
Use the Sharpe ratio to compare total-risk performance and the information ratio to judge active skill against a benchmark.
Check the units: use consistent periods (annual or monthly) for returns and risk before dividing.

Analysis of Active Portfolio Management in other exams

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

Analysis of Active Portfolio Management: frequently asked questions

What is the difference between the Sharpe ratio and the information ratio?

The Sharpe ratio divides excess return over the risk-free rate by the standard deviation of the portfolio. The information ratio divides active return over the benchmark by active risk. Use the Sharpe ratio for total risk and the information ratio for skill relative to a benchmark.

What does the fundamental law of active management tell you?

It says the expected information ratio rises with skill (the information coefficient) and with the square root of breadth. The expanded form multiplies by the transfer coefficient, which shows how well the portfolio puts those insights into practice given constraints.

How do I solve fundamental law questions in an item set?

Pick out the given inputs from the vignette and decide which form of the law applies. Rearrange the formula if you need to solve for IC, breadth or TC. Check whether the vignette mentions constraints, which signals that the transfer coefficient matters.

Is this chapter mostly calculations or concepts?

Both appear. Expect some short calculations with ratios and the fundamental law, and some questions asking how a change in one input affects the result. Study the formulas and also practise explaining what moves each one.