## **Learning Outcomes**

This article explains how risk budgeting and risk parity frameworks are applied to portfolio construction for the CFA Level 3 exam, focusing on how risk is intentionally allocated across assets and factors rather than simply by capital weights. It clarifies the objectives of risk budgeting, the meaning of risk contributions, and the mechanics of setting and implementing total and component risk budgets. The article examines how risk parity portfolios are constructed, including the use of leverage and adjustments to asset weights so that each asset or factor contributes equally to total portfolio risk. It analyzes factor risk, showing how exposures to systematic drivers such as equity, value, momentum, and credit can be decomposed, measured, and used to assess true diversification. The article distinguishes risk-based approaches from traditional mean-variance or capital-weighted allocations, highlighting strengths, limitations, and common exam traps. It also covers interpretation of optimization outputs, diagnosis of concentrated risk exposures, and formulation of portfolio adjustments that align realized risk contributions with stated risk budgets.

## **CFA Level 3 Syllabus**

For the CFA Level 3 exam, you are expected to understand how risk budgeting, factor risk, and risk parity contribute to robust portfolio construction, including the application and evaluation of risk budgeting in portfolio optimization, assessment of diversification by risk factor, and evaluation of portfolio exposures using risk parity frameworks. Revision in these areas supports effective preparation for relevant exam item sets, with a focus on the following syllabus points:

- Define and describe risk budgeting and its uses in portfolio management
- Explain risk parity and its application to portfolio construction
- Analyze factor risk and its effect on portfolio diversification
- Assess how to allocate portfolio risk across factors using risk budgeting and risk parity techniques
- Evaluate risk-based approaches versus traditional capital allocation
- Evaluate the effectiveness of diversification in risk-budgeted portfolios

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. How does a risk parity approach differ from a traditional capital-weighted portfolio allocation?
2. What is the primary objective of risk budgeting in factor-based portfolio construction?
3. Why is diversification by risk factor sometimes more robust than diversification by capital allocation alone?
4. Describe one potential shortcoming of a naïve equal risk budget approach.

## **Introduction**

Modern portfolio construction considers not just how much capital is allocated to each asset, but how risk is distributed among them. Risk budgeting and risk parity are frameworks designed to allocate risk efficiently, often with a focus on achieving better diversification through factors rather than just capital weights. By evaluating exposures to different risk sources, including systematic factors, these approaches create portfolios that are more resilient to concentrated losses and aligned with investor objectives and constraints.

> **Key Term: risk budgeting**
> A process that allocates risk across portfolio components, aiming to distribute risk efficiently among assets, factors, or strategies in accordance with an investor’s objectives and constraints.
>
> **Key Term: risk parity**
> A portfolio weighting method in which each selected asset or factor is designed to contribute equally to the portfolio’s overall risk, rather than allocating by capital or expected return.
>
> **Key Term: factor risk**
> The risk attributed to exposure to common economic or financial drivers (factors), such as value, size, momentum, or interest rates, which can affect multiple portfolio assets simultaneously.

## RISK BUDGETING CONCEPTS AND OBJECTIVES

Risk budgeting is central to modern portfolio optimization. Unlike traditional approaches, which focus on maximizing expected return for a given risk, risk budgeting emphasizes allocating risk (usually measured by volatility or VaR) intentionally across portfolio segments. The process starts by defining a total risk budget and then determines the optimal risk share for each asset, sub-portfolio, or risk factor to align with investor preferences and constraints. This framework can be used at various levels, from strategic asset allocation to implementation.

### How risk budgeting differs from traditional allocation

Traditional capital allocation portfolios may unintentionally concentrate risk in a few assets or factors—often equities—despite diversified capital weights. Risk budgeting highlights these imbalances and requires explicit risk distributions.

### Steps in risk budgeting

1. Set the total risk budget (e.g., target portfolio volatility).
2. Choose the dimension for risk allocation (by asset class, strategy, or factor).
3. Assign individual risk budgets to each component.
4. Optimize portfolio weights so that each component’s contribution matches its risk budget.
5. Monitor and rebalance as market conditions change.

> **Key Term: risk contribution**
> The proportion of total portfolio risk attributable to an individual asset, group, or factor, based on its correlation and volatility.

## RISK PARITY PRINCIPLES

Risk parity is a popular risk budgeting method that aims to allocate equal risk—instead of equal capital—to components of a portfolio. In a typical risk parity portfolio, each asset (or factor) is weighted such that its risk contribution (often measured as marginal contribution to volatility) is the same as every other selected component.

For example, if equities in a 60/40 equities/bonds portfolio are much riskier than bonds, they will dominate total risk, and diversification is poor. In risk parity, borrowing may be used on low-risk assets (e.g., bonds) and capital is reduced for higher-risk assets (e.g., equities) so that each contributes equal risk. This can increase diversification and may improve portfolio robustness across different market environments.

### Why risk parity

- Avoids concentration of risk in dominant assets (e.g., equities)
- Creates portfolios with more balanced exposures to economic scenarios
- Reflects investors’ risk tolerances better than naïve capital weighting

## FACTOR RISK AND DIVERSIFICATION

Modern risk budgeting and risk parity are often applied within a factor model context, especially for multi-asset or equity portfolios. Here, the portfolio is decomposed into exposures to systematic factors like value, momentum, credit spreads, or inflation. Each factor’s contribution to total portfolio risk can be estimated using a variance-covariance framework or factor model.

Risk budgeting frameworks allocate risk to factors, not just asset classes, potentially increasing true diversification. This helps avoid overexposure to a few risk sources and achieves more stable portfolio performance.

### **Worked Example 1.1**

A global portfolio consists of US equities, global bonds, and commodities. The total portfolio volatility target is set to 10%. The current estimated risk contributions are 80% equities, 15% bonds, and 5% commodities. The investment committee wishes to construct a risk parity portfolio. What changes are needed?

> **Answer:**
> To achieve risk parity, reduce exposure to equities (the dominant risk contributor), increase exposure to bonds and commodities, and (if needed) use borrowed funds to raise the risk contributions from bonds and commodities so that all three approach 33% of risk each. The resulting portfolio may use less equity capital and more bond and commodity capital, and possibly even employ borrowed funds.

## RISK BUDGETING IN PORTFOLIO OPTIMIZATION

Risk budgeting can be embedded into portfolio optimization procedures (such as mean-variance or risk-based optimization). The optimization seeks to allocate weights so that each asset or factor’s risk contribution is consistent with its budget. The process may use equality constraints (as in risk parity) or unequal allocations for custom preferences.

Optimization is often performed using iterative algorithms since an asset’s contribution depends on its volatility, correlation, and portfolio weight. Risk budgeting is particularly valuable in multi-factor settings. Diversification is measured not by the number of positions but by effective risk contributions.

### **Worked Example 1.2**

An investor wants to allocate among four factors: equity, value, momentum, and credit. The total volatility target is 12%. The investor sets a risk budget of 6% volatility for equity and distributes the rest equally among the other factors. How should capital weights be set?

> **Answer:**
> The optimal solution is found by allocating portfolio weights so that each factor’s risk contribution matches its assigned percentage of total volatility. Because each factor's volatility and correlation differ, capital allocations will not be equal—in fact, historically riskier or more correlated factors will receive smaller weights. The optimization aims for equity contributing 6% to portfolio volatility, with value, momentum, and credit each contributing 2%.

## RISK BUDGETING PRACTICALITIES AND LIMITATIONS

While risk budgeting and risk parity portfolios can provide greater diversification, some limitations and considerations are essential for candidates:

- Risk parity may overweight low-volatility assets and underweight assets with fat-tail risk or deep drawdowns.
- The true number of independent risk factors may be lower than the total number of positions.
- Highly correlated assets/factors may have overlapping risk exposures, reducing diversification benefit.
- Model sensitivity and estimation error can distort risk allocations.
- Practical implementation may require periodic rebalancing as asset risk and correlation change.

### **Exam Warning**

> The CFA exam commonly tests understanding of the difference between capital allocation and risk contribution. Remember: equal capital does not mean equal risk, and a "diversified" portfolio may still be risk-concentrated in one asset or factor.

### **Revision Tip**

> When assigned a risk budgeting question, always check for dominant risk contributors—especially equities—and consider how optimizing risk contributions (not just weights) would address this.

## **Summary**

Risk budgeting and risk parity provide frameworks to distribute risk more efficiently across assets or factors. By focusing on risk contributions rather than capital weights, portfolios can achieve better diversification and stability in changing markets. Factor risk budgeting further increases true diversification by spreading exposures across multiple economic drivers. Candidates must be able to distinguish key differences between traditional, capital-focused and risk-based portfolio construction.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define risk budgeting, risk parity, and factor risk, and explain their differences from traditional capital allocation.
- Describe and justify portfolio optimization approaches based on risk allocation.
- Demonstrate how risk budgeting can improve factor diversification in a portfolio.
- Recognize potential shortcomings and practical challenges with risk-budgeted and risk parity portfolios.
- Identify CFA exam questions where evaluating risk contributions (rather than only weights) is essential.

## **Key Terms and Concepts**

- risk budgeting
- risk parity
- factor risk
- risk contribution

Risk budgeting and portfolio optimization - Risk parity factor risk and diversification