Introduction to Value-at-Risk (VaR)
Value-at-Risk (VaR) is a statistical measure that quantifies the potential loss in the value of a portfolio over a specified time horizon, given a certain confidence level. It answers the question:
What is the worst expected loss that won’t be exceeded with a given probability over a specific period?
If a portfolio has a one-day 95% VaR of $1 million, it means that there is a 95% probability that the portfolio will not lose more than $1 million in a single day. However, in 5% of cases, the loss could exceed this amount.
VaR can be computed using three primary approaches: (1). Historical Simulation Method, (2). Parametric Method (also known as Analytical Method), and (3). Monte-Carlo Simulation Method.
Interpretation: A risk manager using 95% VaR expects losses to exceed this threshold 5% of the time. A 99% VaR threshold is extreme, meaning losses exceeding this level happen only 1% of the time. Beyond the VaR threshold, extreme losses are possible but are not captured by VaR—this is why Expected Shortfall (ES) is often used.
Limitations of Value-at-Risk (VaR)
It though has some valid reasons for its popularity, especially within investment banks and other big financial institutions, but it comes with a few limitations. Understanding these limitations is crucial for effective risk management, especially in periods of market stress.
Dependence on Historical Data: VaR calculations rely heavily on historical data to predict future risks. If the historical data does not include extreme market conditions, the VaR estimates may be too optimistic.
Lookback Periods: The lookback period, or the timeframe of historical data used, can significantly impact VaR calculations. If the lookback period is too short or does not capture periods of market stress, the VaR will not accurately reflect potential extreme losses.
Market Stress: VaR does not account for potential losses during periods of extreme market stress not captured in the lookback period. This limitation became evident during the 2008 financial crisis when many portfolios experienced losses far exceeding their normal VaR estimates. for example: during the 2008 financial crisis, market conditions were much more volatile and severe than in previous years. Many financial institutions relied on VaR models that did not account for such extreme scenarios, leading to underestimation of risk and significant financial losses.
Correlation: When it comes to determining the risk of a portfolio, a risk measure is expected to incorporate the correlation between each pair of assets. However, with the increased number of assets and diversity of positions in the portfolio, it becomes very difficult to calculate and incorporate the correlations precisely for risk reduction.
Non-Additive Measure: Speaking about the first limitation, this risk measure becomes non-additive. "the value-at-risk of asset A plus the value-at-risk of asset B is not equal to the value-at-risk of a portfolio containing asset A and B due to the correlation that exists between them."
VaR Method Selection: As mentioned earlier, one has to choose between the methods that can be used to calculate the value-at-risk number. However, different methods eventually lead to different results. It becomes difficult to make the right choice between these methods: The Historical Simulation Method, Parametric Method, and Monte-Carlo Simulation Method.
Beyond VaR: Value-at-Risk does not measure the worst-case loss i.e. unexpected loss beyond the confidence level. 99% 1-Day VaR means that in the remaining 1% of the cases, the losses are expected to be greater than that 99% 1-Day VaR number. This measure does not say anything about the severity of the losses within that 1% case.
Interview Answer
VaR is a statistical measure that quantifies the worst expected loss at a given confidence level over a specific time horizon. It is widely used in market risk management to estimate potential losses under normal market conditions.
There are three main approaches to calculating VaR: parametric (variance-covariance), historical simulation, and Monte Carlo simulation.
While VaR is useful for setting risk limits and regulatory capital requirements (such as under Basel III and FRTB), it has limitations—particularly its inability to capture extreme losses beyond the threshold, which is why Expected Shortfall is often preferred to capture extreme losses.
In practice, traders and risk managers use VaR alongside other risk measures to monitor portfolio exposure and ensure compliance with risk limits.
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