Risk Targets

Understanding risk targets and their implications is crucial in portfolio management. Different mandates have varying risk targets, and establishing the appropriate level of risk is a subjective exercise. This document delves into the different risk targets for various mandates, the process of establishing an appropriate level of risk, the importance of clear communication of risk orientation, and practical risk limits.

Risk Targets for Different Mandates

Various mandates have different risk targets. For example:

• A market-neutral hedge fund like Bridgewater Associates may target an absolute risk of 10%.
• A long-only equity manager like Warren Buffet might aim for an active risk of less than 2%, making them a closet indexer.
• A long-only manager like Peter Lynch could target an active risk of 6%–10%, making them benchmark agnostic.
• A benchmark-agnostic equity manager like Seth Klarman might aim for an absolute risk equal to 85% of the index risk.

Establishing Appropriate Level of Risk

Establishing the appropriate level of absolute or relative risk is a subjective exercise. It is highly sensitive to managers’ investment style and their conviction in their ability to add value using the various levers at their disposal. For instance, a value investor like Benjamin Graham may have a different risk appetite compared to a growth investor like Philip Fisher.

Communication of Risk Orientation

Managers must clearly communicate to investors their overall risk orientation. For instance, a manager following a high-risk, high-return strategy should make this clear to potential investors.

Practical Risk Limits

There are practical risk limits that provide insights into risk management. These include:

• Portfolios may face implementation constraints that degrade the information ratio if active risk increases beyond a specific level.
• Portfolios with high absolute risk targets face limited diversification opportunities, which may lead to a decrease in the Sharpe ratio.
• There is a level of leverage beyond which volatility reduces expected compounded returns.

Implementation Constraints in Portfolio Management

Managers strive to efficiently utilize their active risk, regardless of its targeted level. This efficiency is gauged by the information ratio, a measure that compares active return to active risk. For instance, two managers could have the same information ratio but varying levels of active risk.

Suppose an investor is comfortable with a higher level of active risk. In that case, a manager might escalate his active risk to align with another manager’s active risk level. This can be accomplished by scaling up the active weights, thereby increasing the manager’s excess returns while preserving the same information ratio.

Constraints in Scaling Active Risk

• Short positions may not be increased if the investment policy prohibits them.
• Overweights may not be increased if the policy disallows leverage.
• Leveraging positions with poor liquidity may be unwise and could also impact trading costs.
• If the policy limits maximum position sizes, a manager may be unable to proportionately scale his active risk.

Limited Diversification Opportunities in High Absolute Risk Targets

In the field of investment management, a manager with a high absolute risk target may encounter limited diversification opportunities. Despite possessing a higher risk tolerance, the manager’s objective is to utilize risk efficiently. However, it’s crucial to understand that a twofold increase in absolute risk doesn’t necessarily yield a twofold return. This principle is effectively illustrated by the Markowitz efficient investment frontier.

The Markowitz efficient investment frontier demonstrates a concave relationship between return and risk. As risk escalates, expected returns also rise, albeit at a diminishing rate. This underscores the diminishing returns of assuming additional risk.

Moreover, portfolios with elevated risk/return targets eventually exhaust high-return investment opportunities, leading to a decrease in efficient diversification. This inability to diversify efficiently can result in a lower Sharpe ratio, a measure of risk-adjusted return. A diminished Sharpe ratio signifies that the portfolio isn’t generating adequate returns for the level of risk assumed.

Leverage and its Implications for Risk

According to Sharpe’s theory, there exists a linear relationship between absolute risk and return in a one-period setting, provided there is a risk-free rate at which investors can borrow or lend. This suggests that managers can proportionately scale expected returns and absolute risk up or down, thereby maintaining a constant, optimal Sharpe ratio.

A manager can utilize leverage to extend the implementation limits of a strategy. However, excessive leverage can lead to a reduction of expected compounded return in a multi-period setting. This constraint is also implicit in the full fundamental law of active management, which expresses the main sources of active returns.

Transfer Coefficient and Active Risk

The transfer coefficient is a measure of a manager’s ability to translate portfolio insights into investment decisions without constraint. If a manager is limited in his ability to implement his strategy, the transfer coefficient will decline. If he attempts to maintain the same level of active risk, his information ratio will also decline. In this case, there is an optimal/maximum level of active risk.

Expected Compounded/Geometric Return

The expected compounded/geometric return of an asset \(R_g\) is approximately related to its expected arithmetic/periodic return \(R_a\) and its expected volatility \(\sigma\) as per the formula:

$$R_g = R_a – \frac{\sigma^2}{2}$$

For instance, consider an asset with a 20% standard deviation and a 10% expected arithmetic return. The expected compounded return for this asset is 8%. If we leverage the asset by a factor of 2, the expected compounded return increases to 12%. However, if we leverage the asset by a factor of 3, there is no additional improvement in return.

Impact of Leverage Cost

When the cost of funding leverage is incorporated, the active return is reduced while the volatility remains proportional to the amount of leverage. The Sharpe ratio will decline even faster. For example, a portfolio with a leverage of 3× would have the same expected return as an unlevered portfolio if the cost of funding leverage were 2%.

Volatility, Leverage and Compounded Return

If the realized volatility is significantly greater than expected, such as in crisis time, the combined impact of volatility and leverage on compounded return could be dramatic. The information ratio and the Sharpe ratio will not always be degraded by a reasonable rise in active or absolute risk, and a reasonable level of leverage can increase expected compounded return. The appropriate tactics must be evaluated by the manager in the context of his investment approach and investors’ expectations.

Practice Questions

Question 1: A portfolio manager is considering different risk targets for various mandates. He is considering a market-neutral hedge fund, a long-only equity manager, and a benchmark-agnostic equity manager. He is also aware of the implications of his risk orientation and the practical risk limits. Based on these considerations, which of the following statements is most likely to be true?

1. The market-neutral hedge fund is likely to target an absolute risk of less than 10%.
2. The long-only equity manager might aim for an active risk of 6%–10%, making them a closet indexer.
3. The benchmark-agnostic equity manager might aim for an absolute risk equal to 85% of the index risk.

Answer: Choice A is correct.

A market-neutral hedge fund is likely to target an absolute risk of less than 10%. Market-neutral hedge funds aim to eliminate market risk by taking long and short positions in different securities with the goal of achieving a zero beta, i.e., no correlation with the market. This strategy is designed to produce returns that are independent of the overall market direction. Therefore, the absolute risk, which is the total risk of the portfolio, is likely to be less than 10%. This is because the hedge fund’s strategy is designed to neutralize the impact of market movements, thereby reducing the overall risk of the portfolio. The absolute risk is a measure of the total risk of a portfolio, including both systematic and unsystematic risk. In a market-neutral strategy, the aim is to minimize systematic risk, which is the risk associated with market movements, thereby reducing the absolute risk.

Choice B is incorrect. A long-only equity manager might aim for an active risk of 6%–10%, but this would not make them a closet indexer. A closet indexer is a fund manager who claims to actively manage a fund while actually mirroring a benchmark index. An active risk of 6%–10% indicates a significant deviation from the benchmark, suggesting active management rather than closet indexing.

Choice C is incorrect. A benchmark-agnostic equity manager might aim for an absolute risk, but it is unlikely to be equal to 85% of the index risk. Benchmark-agnostic managers do not use a benchmark to guide their investment decisions or risk levels. Instead, they focus on absolute returns and may take on higher or lower risk levels depending on their investment strategy and market conditions. Therefore, their absolute risk is not likely to be closely tied to the risk of a benchmark index.

Question 2: A portfolio manager is communicating his risk orientation to his investors. He understands that he must clearly communicate his overall risk orientation, and that his investors must understand the implications of this risk orientation. Which of the following is most likely to be a correct statement about this communication?

1. Managers should communicate that a strategy can be executed at any level of risk.
2. Managers should not communicate their risk orientation to investors.
3. Managers should clearly communicate their risk orientation, but this does not mean that a strategy can or should be executed at any level of risk.

Answer: Choice C is correct.

Managers should clearly communicate their risk orientation, but this does not mean that a strategy can or should be executed at any level of risk. It is crucial for portfolio managers to communicate their risk orientation to their investors. This is because the risk orientation of a portfolio manager can significantly impact the performance of the investments. However, this does not imply that a strategy can or should be executed at any level of risk. The level of risk that a portfolio manager is willing to take should be in line with the risk tolerance of the investors. If the risk orientation of the portfolio manager is not in line with the risk tolerance of the investors, it could lead to significant losses for the investors. Therefore, while it is important for portfolio managers to communicate their risk orientation, they should also ensure that their strategies are executed at a level of risk that is acceptable to their investors.

Choice A is incorrect. While it is true that managers should communicate their risk orientation, it is not accurate to say that a strategy can be executed at any level of risk. The level of risk that a strategy can be executed at depends on a variety of factors, including the risk tolerance of the investors, the market conditions, and the specific characteristics of the investments.

Choice B is incorrect. It is not correct to say that managers should not communicate their risk orientation to investors. On the contrary, it is crucial for managers to communicate their risk orientation to investors, as this can significantly impact the performance of the investments. Investors need to understand the risk orientation of their portfolio manager in order to make informed decisions about their investments.

Glossary

• Active Risk: The risk (or standard deviation) of the difference between the portfolio return and the benchmark return.
• Information Ratio: A measure of portfolio returns above the returns of a benchmark, usually an index, compared to the volatility of those returns.
• Sharpe Ratio: A measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations.
• Information Ratio: A measure that compares active return to active risk.
• Active Return: The difference between the portfolio’s return and the benchmark’s return.
• Sharpe Ratio: A measure of risk-adjusted performance.
• Transfer Coefficient: A measure of a manager’s ability to translate portfolio insights into investment decisions without constraint.
• Expected Compounded/Geometric Return \((R_g)\): The return of an investment over a specified period, calculated in a way that assumes that profits are reinvested.
• Expected Arithmetic/Periodic Return \((R_a)\): The simple average of a series of periodic returns.
• Expected Volatility \((\sigma)\): The standard deviation of the return on an investment.

Portfolio Management Pathway Volume 1: Learning Module 3: Active Equity Investing: Portfolio Construction;

LOS 3(f): Discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction;