Introduction

In the realm of risk assessment and Value at Risk (VaR) calculation, the delta-normal method stands as a widely used approach, particularly for linear derivatives. However, as with any methodology, the delta-normal method is not without its limitations. Understanding these limitations is crucial for practitioners to make informed decisions and consider alternative techniques where appropriate.

The delta-normal method simplifies VaR computation by assuming a normal distribution of portfolio returns and using the delta of the underlying assets to estimate the change in portfolio value. This simplicity allows for quick calculations, especially in liquid markets. Nevertheless, it’s important to acknowledge the inherent shortcomings of this method.

Limitations of Delta-Normal Method

1) Non-Normality of Returns: The central assumption of the delta-normal method is that portfolio returns follow a normal distribution. However, financial market returns often exhibit fat tails and skewness, deviating from a true normal distribution. In such cases, relying solely on the delta-normal approach can lead to inaccurate VaR estimates.

2) Extreme Market Conditions: During extreme market conditions, such as market crashes or sudden volatility spikes, the assumptions of normality can break down. The delta-normal method may not adequately capture the tail risk associated with such events, leading to underestimated VaR estimates.

3) Non-Linear Instruments: While the delta-normal method is suitable for linear derivatives, it becomes less accurate for non-linear instruments like options and other derivatives. These instruments exhibit non-linear relationships between underlying assets and option values, making the delta approximation less reliable.

Example: Consider an options portfolio that includes out-of-the-money put options. The delta-normal method might not capture the convexity of option payoffs accurately, leading to underestimation of potential losses during extreme market moves. Similarly, during a financial crisis, the delta-normal method may not adequately account for the increased volatility and correlations among assets.

Mitigating Strategies

To address the limitations of the delta-normal method, practitioners often resort to more advanced techniques like historical simulation or Monte Carlo simulation. These methods account for non-normality, extreme events, and non-linear instruments, providing more accurate and robust VaR estimates.