FRM Exam Part II · VaR and Risk Budgeting in Investment Management

Risk Budgeting Framework and Asset Manager Risk

Updated 11 October 2026 · Fact-checked

Risk budgeting splits a total risk limit, usually measured by VaR or volatility, across asset classes and managers. Policy risk comes from the sponsor's strategic mix, benchmark risk from the chosen benchmarks, and active risk from deviations from benchmark. To solve questions, identify the layer, compute each risk, then combine them.

Understand Risk Budgeting Framework and Asset Manager Risk

Risk budgeting treats risk as a scarce resource. A plan sponsor, such as a pension fund, decides how much total risk it can bear. It then spends that risk where it expects the best reward. Asset allocation asks how much money goes to each asset. Risk budgeting asks how much risk goes to each asset or manager.

The budget works in layers. Policy risk is the risk of the sponsor's long-term strategic mix, the policy benchmark. It is usually the largest part of total risk. Benchmark risk (also called the manager benchmark or normal portfolio risk) is the risk of the benchmarks given to managers. The difference between the sum of manager benchmarks and the policy benchmark is a mismatch the sponsor should watch. Active risk is the risk of a portfolio's return relative to its benchmark. It is measured by tracking error (the standard deviation of active returns) or by relative VaR.

This decomposition lets you see where risk comes from. Total risk is the risk of the actual portfolio return. Active return equals actual return minus policy benchmark return. Active risk against policy includes both the benchmark mismatch and the managers' own active bets. Sponsors usually give each manager a tracking-error limit, and these limits are the manager-level risk budgets.

Because managers' active bets are often only partly correlated, total active risk is smaller than the simple sum of manager active risks. If active returns are uncorrelated, total active risk is the square root of the sum of squared weighted active risks. Diversifying across managers gives more total alpha per unit of risk. Sponsors then compare managers using the information ratio, which is active return divided by active risk, and move budget to those with the better ratio.

In VaR terms, the budget can be allocated by component VaR, which sums to total VaR and shows each asset's or manager's contribution. A decentralised structure sets limits for each manager and the sponsor monitors the overall total.

Key formulas to remember

Active return: Active return = Portfolio return − Benchmark return; Use the policy benchmark for sponsor-level questions and the manager benchmark for manager-level questions.
Tracking error (active risk): TE = standard deviation of (Rp − Rb); Also called active risk or relative risk. It is a standard deviation, not a VaR, unless you convert it.
Active risk from two components: σA² = σ1² + σ2² + 2ρσ1σ2; σ1 and σ2 are the active risks (or weighted active risks) of the two parts and ρ is their correlation. If ρ = 0, σA = √(σ1² + σ2²).
Relative VaR from tracking error: Relative VaR = z × TE × portfolio value; Assumes normal active returns with zero mean. z = 1.645 at 95% and 2.326 at 99% (one-tailed).
Information ratio: IR = Expected active return ÷ Tracking error; A higher IR means more active return per unit of active risk.
Component VaR: Component VaR(i) = wi × (marginal VaR of i); Σ component VaR = total VaR; Components add to total VaR, so they work as budget shares.

How to solve Risk Budgeting Framework and Asset Manager Risk questions

Use this order for most risk budgeting questions on the exam.

1Identify the level of the question: sponsor total risk, policy risk, benchmark mismatch, or manager active risk.
2Name the reference portfolio for that level. Active risk is always relative to a specific benchmark.
3Write down the inputs: weights, volatilities, correlations, tracking errors and portfolio value.
4Check units. Convert between annual and monthly, and between percent and currency, before computing.
5Combine risks correctly. Use the variance formula with correlation, not simple addition, unless correlation is stated as 1.
6Convert to VaR only if asked. Multiply by z and by portfolio value, and keep the horizon consistent.
7Interpret the result: compare it to the limit, state the share of the budget used, or rank managers by information ratio.
8Eliminate options that add risks arithmetically, mix up policy and active risk, or ignore diversification.

Quickest way: Square-root-of-sum-of-squares shortcut

When to use it: Use it when the question gives several manager tracking errors and says their active returns are uncorrelated.

Multiply each manager's tracking error by its weight in the total fund.
Square each result and add them.
Take the square root to get fund-level active risk.
Compare with the simple sum to confirm the answer is smaller, as a sanity check.
If asked for VaR, multiply by z and the fund value.

Common mistakes in Risk Budgeting Framework and Asset Manager Risk

Adding tracking errors of managers directly.
Students treat risk like money, which adds.
Fix: Combine variances with correlation. Only a correlation of 1 makes risks add.
Confusing policy risk with active risk.
Both are called risk, and both appear in the same budget.
Fix: Policy risk is the risk of the strategic benchmark mix. Active risk is the deviation from a benchmark.
Treating risk budgeting as the same as asset allocation.
Both decide how to divide a portfolio.
Fix: Asset allocation divides capital. Risk budgeting divides risk, such as VaR or tracking error, which can differ greatly from capital shares.
Ignoring the mismatch between manager benchmarks and the policy benchmark.
Students assume manager benchmarks always sum to the policy benchmark.
Fix: Check it. A gap is a source of active risk for the sponsor even if every manager sits exactly on its benchmark.
Applying z to tracking error without adjusting for horizon or confidence.
Tracking error is quoted annually and VaR questions use a shorter horizon.
Fix: Scale by √(time) first, then multiply by z. Use 1.645 for 95% and 2.326 for 99%.

Worked examples

Example 1

A fund has two managers, each with 50% of assets. Manager A has tracking error 4% and Manager B has 3%. Their active returns are uncorrelated. What is the fund's active risk?

Show the solution

Weighted active risk of A = 0.5 × 4% = 2%.
Weighted active risk of B = 0.5 × 3% = 1.5%.
Variance = 2² + 1.5² = 4 + 2.25 = 6.25.
Active risk = √6.25 = 2.5%.

Answer: 2.5%, which is less than the simple weighted sum of 3.5%.

Example 2

A ₹2,000 crore plan has fund-level tracking error of 2.5% a year against its policy benchmark. Assuming normal, zero-mean active returns, what is the one-year 95% relative VaR?

Show the solution

Relative VaR = z × TE × value.
z at 95% one-tailed = 1.645.
TE × value = 0.025 × ₹2,000 crore = ₹50 crore.
Relative VaR = 1.645 × ₹50 crore = ₹82.25 crore.

Answer: About ₹82.25 crore. With 95% confidence, the plan should not underperform its policy benchmark by more than this over one year.

Exam tips

Always read which benchmark the question uses. Policy and manager benchmarks give different active risks.
Expect questions that ask you to pick the right interpretation, such as why total active risk is below the sum of manager limits.
Memorise z values of 1.645 and 2.326 and check whether the question uses one-tailed values.
When a question asks how to reallocate budget, think information ratio and component VaR, not just total return.
Watch for wording that separates risk budgeting from asset allocation: risk budgeting allocates risk, not capital.

Practice questions from VaR and Risk Budgeting in Investment Management

Risk Budgeting Framework and Asset Manager Risk: frequently asked questions

What is risk budgeting in portfolio management?

It is the process of setting a total risk limit and dividing it across asset classes, strategies or managers. The risk is measured by volatility, VaR or tracking error. The aim is to spend risk where the expected reward is highest.

What is the difference between policy, benchmark and active risk?

Policy risk comes from the sponsor's long-term strategic mix. Benchmark risk comes from the benchmarks given to managers. Active risk is the risk of deviating from a benchmark, usually measured as tracking error.

How is risk budgeting different from asset allocation?

Asset allocation sets the share of capital in each asset. Risk budgeting sets the share of risk. A small capital share in a volatile asset can use a large share of the risk budget.

How do sponsors use tracking error limits?

Each manager gets a tracking error limit that works as a manager-level risk budget. The sponsor monitors the combined active risk, which is lower than the sum of limits when manager bets are not perfectly correlated.