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The Super Guide to Risk Metrics: Why is the variance not enough?!
Risk measurement is an important concept in modern financial mathematics. Financial institutions such as banks and insurance companies often need to ensure that they have sufficient capital to cope with potential losses. This becomes even more important as market volatility increases. Traditionally, variance has been considered a method of measuring risk, but in recent years, as the market environment has changed, the understanding of risk measurement has also changed significantly.
Risk measurement should not only rely on the number of variance, but should be a more comprehensive assessment method.
The primary purpose of risk measurement is to determine the reserves that should be maintained on a set of assets (usually currency) so that the risks taken by the financial institution are acceptable to the regulator. Against the backdrop of market volatility and increasing risk management demands, people are beginning to re-examine the validity of variance as a risk measure.
The variance, or standard deviation, is often used as a traditional risk measure. However, its limitations gradually became apparent. The variance does not have the necessary transferability and is not monotonic, which means that relying solely on the variance in risk assessment may lead to wrong decisions.
Variation numbers do not adequately reflect extreme situations that are common in the market.
For example, for a random variable X, even if we increment it by a constant a, the variance is still Remain unchanged. This is enough to illustrate that when faced with the extreme volatility that can occur in a market, variance may not provide a meaningful risk assessment.
Compared with variance, current risk measurement methods such as "at-risk" and "excess risk" place more emphasis on market variability and uncertainty. These methods focus on the risks of extreme scenarios, such as using "expected shortfall" to measure the range of possible losses, providing a more comprehensive assessment tool.
Let's rethink how we can better measure risk.
In recent years, coherent risk measures and concave risk measures have been put into practice. These new methods emphasize certain mathematical properties, including transferability, monotonicity, and regularization, which can better describe risks in the market and thus improve the effectiveness and accuracy of capital management.
In this rapidly changing financial world, traditional approaches to risk measurement are increasingly seen as inadequate. However, how to create a comprehensive risk measurement framework remains an unresolved challenge. The market not only needs to measure past risk scenarios, but also urgently needs to predict possible risk scenarios in the future.
Future risk metrics should assess market conditions in a more holistic manner.
In practical applications, financial institutions have begun to adopt a new generation of risk measurement tools to cope with complex market conditions. For example, measures such as excess risk and expected shortfall not only help analyze general risk but also provide sensitive assessments of market sell-offs and liquidity risks.
The actual needs of the market and financial supervision under the new situation call for us to conduct comprehensive reflection and improvement on the risk assessment standards. Obviously, relying solely on variance to guide capital retention strategies is no longer comprehensive and effective enough.
Therefore, when we re-examine the topic of risk measurement, it is worth thinking about what direction risk measurement should develop in the future to adapt to the ever-changing market environment and regulatory requirements?
