Risk Budgeting
Risk budgeting is a strategic process in portfolio management where the total risk appetite of the portfolio is distributed among the various components of portfolio choice. This process is crucial in optimizing the portfolio’s exposures relative to the benchmark, ensuring efficient use of the active risk budget. The active risk budget is usually provided by the client.
Risk Management Process
The portfolio manager needs to perform the following tasks for an effective risk management process:
- Determine the type of risk measure: The type of risk measure is dependent on the manager’s strategy. For example, a manager of a hedge fund might prefer an absolute risk measure like total volatility of portfolio returns, while a manager of a mutual fund might prefer a relative risk measure such as active risk.
- Understand the strategy’s risk contribution: The total portfolio variance could be dominated by exposure to rewarded risk factors or by allocations to countries, sectors, or securities. If these exposures are dynamic, the timing of portfolio exposures also introduces risk. Therefore, understanding what drives a portfolio’s risk and ensuring the portfolio has the right kinds of specific risks is a crucial step in risk budgeting.
- Determine the appropriate risk budget level: The targeted levels of risk vary widely among managers and strategies. While there are general principles that limit the level of advisable risk in a specific strategy, it is also very much a policy issue.
- Properly allocate risk among individual positions/factors: Regardless of whether the risk measure is absolute or relative, managers must efficiently allocate their targeted risk budget.
Portfolio Management: Absolute vs Relative Risk Orientation
Portfolio management orientation, whether absolute or relative, heavily depends on the manager’s mandate and the investors’ objectives. If the goal is to outperform a benchmark like the S&P 500 over a specified period, the strategy focuses primarily on active risk management. In contrast, achieving a specific return, such as 10% annually, would shift the focus towards managing the volatility of portfolio returns.
Choosing Between Absolute and Relative Risk Measures
The selection between absolute and relative risk measures also reflects the personal beliefs of managers about their ability to add value. Managers like Warren Buffet, who believe that benchmark-relative constraints might restrict the potential of their investment strategies, tend to favor absolute risk measures, which allow more freedom, or relative measures with broader permissible deviations.
This freedom is evident in absolute risk measures where the risk threshold set must not be exceeded, giving managers like Ray Dalio the liberty to construct portfolios independently of any benchmark characteristics. Alternatively, a relative risk measure with extended boundaries allows substantial divergence from the benchmark while still anchoring the evaluation of risk and reward to it.
While some prominent institutional investors like BlackRock adopt strategies that disregard benchmarks entirely, focusing instead on absolute or total returns, or setting high active risk targets within a benchmark-relative framework, the majority of assets under management still operate under benchmark-relative mandates.
Irrespective of the risk orientation, the risks taken by a manager should reflect their perceived strengths. Extraneous risks should be diversified or minimized. For instance, market timers should focus on optimal timing of factor exposures, sector rotators on their sector exposures, and multi-factor managers on balancing their factor exposures. Understanding the basic drivers of absolute and relative portfolio risk is crucial in determining how to allocate risk effectively.
The Causes and Sources of Absolute Risk
The concept of absolute risk revolves around the potential for loss in a portfolio due to various factors. One of the key principles to grasp is that the total portfolio risk can increase if a manager adds a new asset to the portfolio that has a higher covariance with the portfolio than most current securities. For example, if a manager of a tech-focused portfolio adds a new tech stock that has a high correlation with the existing portfolio, the total risk will rise. This high covariance can be driven by a high variance or a higher correlation of the new security with the portfolio.
Factors Influencing Portfolio Risk
The portfolio variance is a function of the individual asset returns and the covariance of returns between assets. For instance, if a manager has a portfolio with 40% allocation to Apple Inc., and the covariance of Apple Inc. with the portfolio is high, it can account for a significant portion of the total portfolio variance.
The assets in a portfolio can be diverse, ranging from securities, sectors, countries, or pools of assets representing risk factors. If a manager specializes in sector rotation, replacing an allocation to one sector with an allocation to another sector having a higher covariance with the portfolio, total portfolio risk will increase.
A manager might also seek to understand how his portfolio variance can be attributed to factor exposures versus that which is unexplained by these factors. The risks a manager chooses to take should be related to his perceived skills. If the manager’s skills can be attributed to certain factors, then he would want to minimize the level of portfolio risk not explained by those factors.
Portfolio Variance and Factor Exposure
The segmentation of absolute portfolio variance into these two components—variance attributed to factor exposure and variance unexplained.
If the manager’s portfolio were the market portfolio, all the variance of the portfolio returns would be explained by a beta of 1 to the Market factor. Idiosyncratic risks would be fully diversified. However, as we move away from the market portfolio, total portfolio variance will be influenced by other factor exposures and other risks unexplained by factors.
The total portfolio variance \( V_p \) is expressed as:
\[ V_p = \sum_{i=1}^{n} \sum_{j=1}^{n} x_i x_j C_{ij} \]
Where \( x_i \) is the asset’s weight in the portfolio, and \( C_{ij} \) is the covariance of returns between asset i and asset j.
The contribution of each asset to portfolio variance \( CV_i \) is determined by :
\[ CV_i = \sum_{j=1}^{n} x_j x_i C_{ij} = x_i C_{ip} \]
where,
\( x_i \) is the asset’s weight in the portfolio,
\( C_{ij} \) is the covariance of returns between asset i and asset j,
\( C_{ip} \) is the covariance of returns between asset i and the portfolio.
The total variance of the portfolio (\( V_p \)) can be decomposed into two components—variance attributed to factor exposure and variance unexplained and is given by :
\[ V_p = \text{Var} \left( \sum_{i=1}^{K} (\beta_{ip} \times F_i) \right) + \text{Var} (\varepsilon_p) \]
Where,
\( \beta_{ip} \) represents the sensitivity of the asset i returns with respect to the market factor \( F_i \),
\( F_i \) is the return of factor i, and
\( \varepsilon_p \) is the idiosyncratic risk of the portfolio.
Causes and Sources of Relative/Active Risk
Relative risk is measured using the variance of the portfolio’s active return, also known as Active Variance (AV). The AV is calculated using the formula:
$$AV_p = \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i – b_i) (x_j – b_j) RC_{ij}$$
Where:
\( x_i \) = the asset’s weight in the portfolio
\( b_i \) = the benchmark weight in asset i
\( RC_{ij} \) = the covariance of relative returns between asset i and asset j
Each asset’s contribution to the portfolio active variance (CAV) is calculated as:
$$CAV_i = (x_i – b_i) RC_{ip}$$
Where,
\( RC_{ip} \) = the covariance of relative returns between asset i and the portfolio.
It’s important to note that an asset’s risk level doesn’t necessarily affect the active risk. For example, a low-risk asset could increase active risk if it has a low correlation with the equity benchmark. Conversely, a high-risk asset might reduce active risk if it has a high covariance with the benchmark. The key factor is the asset’s relative (active) volatility compared to the benchmark.
Practice Questions
Question 1: A portfolio manager is working on a long/short equity strategy and is benchmarked against a cash plus target. As part of the risk management process, the manager needs to determine the type of risk measure to use. Which risk measure would the manager most likely prefer to use?
- Active risk
- Total volatility of portfolio returns
- Capitalization-weighted index
Answer: Choice B is correct.
In this scenario, the portfolio manager would most likely prefer to use the total volatility of portfolio returns as a risk measure. This is because the manager is working on a long/short equity strategy and is benchmarked against a cash plus target. In a long/short equity strategy, the manager takes long positions in stocks that are expected to increase in value and short positions in stocks that are expected to decrease in value. The total volatility of portfolio returns is a measure of the overall risk of the portfolio, taking into account both the long and short positions. It provides a comprehensive view of the risk associated with the portfolio and is particularly relevant for a long/short strategy, where the risk can come from both the long and short positions. The total volatility of portfolio returns is a key input in the risk management process and can help the manager to make informed decisions about the portfolio’s risk profile.
Choice A is incorrect. Active risk, also known as tracking error, is a measure of the risk of a portfolio relative to a benchmark. In this case, the benchmark is a cash plus target, which is not a typical benchmark for a long/short equity strategy. Therefore, active risk would not be the most appropriate risk measure in this scenario.
Choice C is incorrect. A capitalization-weighted index is a type of stock market index in which each component of the index is weighted according to its market capitalization. It is not a risk measure and therefore would not be appropriate for the manager to use in this scenario.
Question 2: A portfolio manager is working on a long-only equity strategy and is benchmarked against a capitalization-weighted index. The manager is in the process of understanding the strategy’s risk contribution. Which of the following factors could potentially dominate the total portfolio variance?
- Exposure to rewarded risk factors
- Allocations to countries, sectors, or securities
- Both A and B
Answer: Choice C is correct.
Both exposure to rewarded risk factors and allocations to countries, sectors, or securities could potentially dominate the total portfolio variance. In a long-only equity strategy benchmarked against a capitalization-weighted index, both these factors play a significant role in determining the portfolio’s risk contribution. Rewarded risk factors refer to those factors that are expected to generate a positive return over time. These could include factors such as value, size, momentum, and quality. The portfolio’s exposure to these factors can significantly influence its risk and return characteristics. Similarly, the portfolio’s allocations to different countries, sectors, or securities can also have a substantial impact on its risk profile. For instance, a portfolio heavily concentrated in a particular sector or country could be subject to higher risk if that sector or country experiences a downturn. Therefore, both these factors could potentially dominate the total portfolio variance, making Choice C the correct answer.
Choice A is incorrect. While exposure to rewarded risk factors can influence the total portfolio variance, it is not the only factor that could potentially dominate it. As explained above, allocations to different countries, sectors, or securities can also have a significant impact on the portfolio’s risk profile.
Choice B is incorrect. Similarly, while allocations to different countries, sectors, or securities can influence the total portfolio variance, they are not the only factors that could potentially dominate it. The portfolio’s exposure to rewarded risk factors can also significantly influence its risk and return characteristics.
Glossary
- Active Risk: The risk (standard deviation) of the difference between the portfolio return and the benchmark return.
- Total Volatility: The standard deviation of the portfolio returns.
- Absolute risk measure: A risk threshold that the portfolio risk must not exceed.
- Relative risk measure: A risk measure with wide bands around a central target, implying a benchmark-relative approach.
- Covariance: A measure of how much two random variables vary together.
- Variance: A statistical measurement of the spread between numbers in a data set.
- Idiosyncratic risk: Risk that is specific to a particular asset and can be reduced through diversification.
- Factor exposure: The sensitivity of a security’s returns to a particular factor.
Portfolio Management Pathway Volume 1: Learning Module 3: Active Equity Investing: Portfolio Construction;
LOS 3(e): Discuss the application of risk budgeting concepts in portfolio construction