## Market Risk Management in the Investments Fund Industry (Part 2)

Managing risk in alternative investment funds requires a combination of advanced techniques and a continuous effort to adapt to changing market conditions. Part 1 of this article explored approaches to evaluating and managing market risk. In Part 2, we will focus on the practical application of Value at Risk (VaR) and Expected Shortfall (ES) quantitative analysis techniques and delve deeper into the subject, providing examples and discussing new trends and approaches in the European Union (EU).

First, let’s look at the differences between VaR and ES techniques and how they can be practically applied in market risk management.

**Implementation of VaR and ES Statistics with Practical Examples**

Consider a hypothetical portfolio with a value of €10 million. With a one-day 95% confidence level, assuming a Z-Score of 1.645 (corresponding to a 5% tail risk), and a portfolio standard deviation of 2%, the VaR calculation would be: VaR = €10,000,000 × 1.645 × 0.02 = €329,000.

This implies a 5% probability that the portfolio will incur losses exceeding €329,000 in a single trading day under normal market conditions.

Expected Shortfall (ES), also known as Conditional Value at Risk (CVaR), builds upon VaR by quantifying the average loss in worst-case scenarios beyond the VaR threshold. ES provides additional insights into tail risk and helps prepare for extreme market events. The formula for ES is as follows: ES = (VaR / (1 - Confidence Level)) * Probability Density Function (PDF).

Continuing with the previous example, if the VaR is €329,000 with a 95% confidence level, and Probability Density Function (PDF) is a normal distribution with a mean of 0 and a standard deviation of 1, the ES calculation would be: ES = €329,000 × (1 / (1 - 0.95)) × PDF(z) = €6,580,000 × 0.1031* = €678,398.

Visualization of this calculation you can see at the graph below:

This means that in the worst 5% of cases, the average loss is expected to be €678,398. Applying VaR and ES in alternative investment funds involves certain unique challenges. These funds often hold illiquid assets for which historical price data may not be readily available, making it challenging to calculate VaR and ES. In such cases, managers may need to use other methods.

Effectively practical use of VaR and ES can divide into 5 main steps:

- Define the portfolio and identify risk factors. The risk factors impacting the portfolio are equity prices and interest rates.
- Collect historical data for non less than two years.
- Calculate portfolio returns using historical data.
- Calculate VaR and ES next, using a chosen methodology.
- Perform backtesting and validation. To ensure accuracy, the calculated VaR and ES measures must be backtested against actual losses. If the actual losses consistently exceed the calculated VaR, the models may need adjustments or recalibration.

Now that we have looked at the basic implementation of quantitative analysis techniques provided above let’s consider the latest market trends in the EU.

**5 New Trends and Approaches in 2023 in the EU Market**

In the EU market, risk management practices are continually evolving to adapt to changing regulations and market conditions. Here are some notable trends and approaches that will be crucial in 2023.

**Integration of Environmental, Social, and Governance (ESG) Factors**

With the growing emphasis on sustainable investing, risk management professionals are incorporating ESG factors into their VaR and ES models. This integration allows for a more comprehensive portfolio risk assessment, considering both financial and non-financial risks.

**2. Stress Testing and Scenario Analysis**

Stress testing and scenario analysis have gained prominence in addressing the limitations of VaR and ES. These approaches involve simulating extreme market conditions and evaluating the impact on portfolio performance. Risk managers can identify potential vulnerabilities and develop contingency plans by subjecting portfolios to severe scenarios.

**3. Machine Learning (ML) and Artificial Intelligence (AI)**

Advancements in ML and AI technologies have enabled risk managers to enhance their VaR and ES models. These technologies can analyse vast amounts of data, identify complex patterns, and improve risk estimation. Risk managers can obtain more accurate and dynamic risk measures by leveraging ML algorithms.

**4. Integration of Market and Credit Risk**

Risk management professionals are adopting a holistic approach by integrating these two risk dimensions in response to the interconnectedness of market and credit risk. This integration enables a more comprehensive understanding of portfolio risk and facilitates the identification of potential risk concentrations.

**5. Real-Time Risk Monitoring**

In an era of rapidly changing markets, real-time risk monitoring has become a vital component of risk management. Risk managers utilise advanced technological solutions to monitor portfolio risk in real-time, allowing for prompt decision-making and proactive risk mitigation.

**Conclusion**

The practical application of VaR and ES in managing portfolio market risk is a valuable toolset for risk management professionals. By implementing these measures, organisations can quantify and manage their exposure to potential losses. The EU market, in particular, has witnessed new trends and approaches that will play a crucial role in 2023. These are the integration of ESG factors, stress testing, machine learning, integration of market and credit risk, and real-time risk monitoring. These trends can enhance risk management practices and contribute to more robust and resilient AIF portfolios.

**Assuming we have access to a table of the standard normal distribution, we can find the value of the PDF(z) corresponding to the z-score of 1.645.*