Portfolio Management Pathway · Active Equity Investing: Portfolio Construction

Risk Budgeting and Constraints in Active Equity Portfolios

Updated 8 October 2026 · Fact-checked

Risk budgeting sets how much active risk, measured by ex-ante tracking risk, a portfolio may take and splits it across managers or bets. You compute tracking risk from active weights and covariances, allocate it where expected active return per unit of risk is highest, then check turnover, liquidity and position limits.

Understand Managing Risk Budgets and Portfolio Constraints

Active risk is the risk of deviating from the benchmark. You measure it as tracking risk (also called tracking error or active risk): the standard deviation of active returns, where active return = portfolio return − benchmark return. Ex-ante tracking risk is forward-looking and comes from a risk model. Ex-post tracking risk is backward-looking and comes from realized active returns.

A risk budget is the total amount of active risk the client or investment committee allows. It is set from the client's objectives and constraints: return target, risk tolerance, and how much underperformance the client can accept. You then allocate that budget. Across managers, you give more of it to those with higher expected active return per unit of active risk. Within a portfolio, you split it between sources such as stock selection, sector bets, and style factors.

The efficiency measure is the information ratio (IR) = expected active return ÷ tracking risk. The same IR logic gives a rule: with uncorrelated active returns, the allocation is efficient when each manager's marginal expected active return per unit of marginal active risk is equal. In practice, higher IR managers get larger budgets, subject to capacity and judgment.

Combining managers diversifies active risk. If active returns are uncorrelated, total tracking risk is the square root of the sum of squared weighted tracking risks. It is lower than the weighted average. If managers share the same bets, such as the same style tilt, correlation is positive and the benefit shrinks.

A risk budget is not used in a vacuum. Constraints limit how it is used. Common ones are maximum position size, sector or country deviation limits, minimum number of holdings, turnover limits, and liquidity limits, such as holding no more than a set share of a stock's average daily volume. Constraints reduce tracking risk and implementation cost, but they also reduce the ability to express views. A tight constraint set can leave part of the risk budget unused.

Key rules to remember

Active return: Active return = Rp − Rb; Rp is portfolio return and Rb is benchmark return.
Active weight: Active weight of asset i = wp,i − wb,i; Active weights sum to zero for a fully invested long-only portfolio.
Ex-post tracking risk: TR = standard deviation of (Rp,t − Rb,t); Uses realized history. Do not confuse it with ex-ante.
Ex-ante tracking risk (two-source, general): TR = √(σ1² + σ2² + 2 × ρ12 × σ1 × σ2); σ1 and σ2 are the active risk contributions of two sources, ρ12 is their correlation. For uncorrelated sources, drop the last term.
Ex-ante tracking risk (weights): TR = √(a′ Σ a); a is the vector of active weights and Σ is the covariance matrix of asset returns. Exam versions usually use two or three assets.
Information ratio: IR = E(active return) ÷ tracking risk; Higher IR means more active return per unit of risk and supports a larger budget.
Combined managers, uncorrelated active returns: TR = √(Σ wi² × TRi²); wi is the fraction of the portfolio given to manager i and TRi is that manager's tracking risk.
Risk contribution share: Share of variance of source i = (variance contribution of i) ÷ (total active variance); Budget by variance, not by standard deviation, because standard deviations do not add.

How to solve Managing Risk Budgets and Portfolio Constraints questions

Use this order for any risk budget or constraint question. Tie each choice back to the client's objectives and constraints.

1Read the command word and the client facts: return goal, maximum tracking risk, and any limits on turnover, liquidity, or position size.
2Identify what is given: active weights, covariances, manager tracking risks, IRs, or correlations.
3Work in variances. Square each tracking risk, apply weights, add the covariance terms, then take the square root only at the end.
4Compare managers or bets on IR. Direct more budget to the higher IR, and cap it where capacity or concentration is a concern.
5Check the result against the stated total tracking risk limit. Show the number, then say whether it is inside or outside the budget.
6Test the constraints: turnover, liquidity (days to trade at a set share of daily volume), and position limits. Say which are binding.
7State the recommendation in one or two sentences and link it to the client's objective or constraint.

Quickest way: Variance-first shortcut

When to use it: Use it for multiple-choice items asking for combined tracking risk or the budget split across managers.

Square every tracking risk to get variances.
If correlation is zero, multiply each by weight squared and add. If correlation is given, add 2 × ρ × product of the weighted risks.
Take the square root once at the end.
Sanity check: with zero correlation the answer must be below the weighted average of the tracking risks. With correlation of 1 it equals that average.
For liquidity, divide position size by (participation rate × average daily volume) to get days.

Common mistakes in Managing Risk Budgets and Portfolio Constraints

Adding tracking risks directly instead of variances.
Weighted averages feel natural, and standard deviations look like they add.
Fix: Square first, combine with weights and correlation, and take the square root last. Only perfectly correlated risks add directly.
Forgetting to weight a manager's tracking risk by its share of the portfolio.
The manager's tracking risk is quoted against its own mandate, so it is easy to overlook that it applies only to its allocation.
Fix: Multiply each manager's tracking risk by its portfolio weight before squaring.
Confusing ex-ante and ex-post tracking risk.
Both are called tracking error.
Fix: Ex-ante comes from a model and current holdings and looks forward. Ex-post comes from realized return differences and looks back.
Allocating the risk budget on expected active return alone.
High return is attractive, but it may come with high risk.
Fix: Rank on information ratio, then check capacity, correlation to other managers, and the client's total limit.
Treating constraints as free.
Constraints look like pure protection.
Fix: State the trade-off. Tight position, turnover, or liquidity limits lower tracking risk and costs but can leave the risk budget unused and weaken the ability to act on views.
Ignoring liquidity when sizing a position in a small-cap or large portfolio.
Students focus on the risk number and skip the days-to-trade check.
Fix: Compute position size ÷ (participation rate × average daily volume) and compare with the allowed trading horizon.

Worked examples

Example 1

A client allocates 60% of a portfolio to Manager A (tracking risk 4%) and 40% to Manager B (tracking risk 5%). Their active returns are uncorrelated. Calculate the combined ex-ante tracking risk.

Show the solution

Weighted risk of A = 0.60 × 4% = 2.4%. Variance = 5.76.
Weighted risk of B = 0.40 × 5% = 2.0%. Variance = 4.00.
Because correlation is zero, add the variances: 5.76 + 4.00 = 9.76.
Take the square root: √9.76 = 3.124%.
Check: the weighted average is 2.4 + 2.0 = 4.4%, and 3.12% is lower, as expected.

Answer: Combined ex-ante tracking risk ≈ 3.12%.

Example 2

Using the same managers, the client has a total tracking risk limit of 3.0%. Manager A has expected active return 1.6% and Manager B 1.5%. The correlation of their active returns is 0.30. Calculate the new combined tracking risk and state whether it is within the limit. Then state which manager has the higher information ratio.

Show the solution

Weighted variances: A = 5.76, B = 4.00 (as before).
Covariance term = 2 × 0.30 × 2.4 × 2.0 = 2.88.
Total variance = 5.76 + 4.00 + 2.88 = 12.64.
Tracking risk = √12.64 = 3.555%.
3.56% is above the 3.0% limit, so the limit is breached.
IR of A = 1.6 ÷ 4 = 0.40. IR of B = 1.5 ÷ 5 = 0.30.

Answer: Combined tracking risk ≈ 3.56%, which exceeds the 3.0% limit. Manager A has the higher IR (0.40 vs 0.30), so any cut in total risk should come from B's allocation first, because A delivers more active return per unit of risk.

Exam tips

Show the squared terms and the correlation term on paper. A correct final number earns full credit, but visible steps help if you slip.
When the question asks you to recommend, name the client constraint (risk limit, liquidity, or horizon) and tie your answer to it in one sentence.
Read whether tracking risk is for the whole portfolio or for one manager's mandate, and weight it accordingly.
If a constraint is named, say what it does to tracking risk and to implementation cost. Examiners look for the trade-off.
Give only the number of responses requested, in the order asked.

Managing Risk Budgets and Portfolio Constraints: frequently asked questions

How do you calculate ex-ante tracking risk?

Take the active weights and the covariance matrix of asset returns, and compute the square root of a′Σa. With two risk sources, use √(σ1² + σ2² + 2ρσ1σ2). It is forward-looking, based on current holdings.

What is the difference between ex-ante and ex-post tracking risk?

Ex-ante is estimated from current positions and a risk model. Ex-post is the standard deviation of actual past active returns. Ex-ante guides the budget, and ex-post checks whether the manager stayed within it.

How is active risk allocated across managers?

Compare information ratios and correlations. Managers with higher expected active return per unit of risk get more of the budget, subject to capacity and the total tracking risk limit. Low correlation between managers makes combined risk smaller.

Why do turnover and liquidity constraints matter in active equity?

Turnover drives trading costs, which erode active return. Liquidity limits determine how fast a position can be built or exited without moving the price. Both restrict how much of the risk budget can be used in practice.