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Risk Assessment Made Easy with Historical Simulation Value-at-Risk

As discussed, the Value-at-Risk (VaR) measures the maximum potential loss that can occur on an investment under normal circumstances at a certain confidence level in a given time frame.

One of the most commonly used methodologies for VaR calculation is the Historical Simulation (HS) VaR method. As per the survey report - "Transition to the Internal Models Approach for Market Risk", the HS VaR is the most popular and highly used for VaR calculation in the industry followed by the Monte-Carlo Simulation (MCS) and Parametric-based (Variance-Covariance) VaR methodologies.

The HS VaR method leverages historical market data to assess the impact of market moves on a portfolio and eliminates the need for or application of complex statistical measures or distributional assumptions, instead, this model simply assumes that history will repeat itself, meaning that one of the past outcomes will repeat again in the future.

"one of the past outcomes" – to calculate the HS VaR, a hypothetical series of position returns or shock scenarios are created and ordered from worst return to best return (negative return to positive return), and sliced at a certain percentile given the desired confidence level.

Let's understand the HS VaR method with an illustration-

Past return outcomes of stock with $500m asset exposure are as follows-

-3.36%, -3.11%, -2.81%, -2.74%, -2.57%, -2.35%, -2.27%, -2.20%, -2.04%, -1.68%, -1.60%, -1.51%, -1.48%, -1.47%, -1.46%, . . . . . (252 observations) arranged from worst to best.

Calculate 1-Day 99% VaR assuming 252 trading days a year.

HS VaR = Nth observation sliced at the significance level


Significance Level = 1 - confidence level i.e., 1 - 99% = 1%

1-Day 99% Relative VaR = 1% of 252 i.e., 2.5th observation = -2.74% + [ ( -2.81% - -2.74% ) * 0.5 ] = -2.77%. Therefore, 1-Day 99% Absolute VaR is -$13.86m (-2.77% of $500m) is the maximum potential loss that can occur in a single day with a 1% probability of being exceeded (in the 1% of the abnormal circumstances, the losses can exceed $13.86m).

Drawbacks of the Historical Simulation Value-at-Risk Method

The HS VaR method, while widely used in the industry, is not without its limitations.

  • The HS VaR method assumes that history will repeat itself for which it relies solely on historical market data and does not account for expected changes that may impact the position(s) in the future.

  • Unlike the Parametric method, which incorporates the characteristics of all the available market data in the calculation of the key parameters such as mean and standard deviation, the HS VaR method is known for its inefficient utilization of such data as it only utilizes the bottom-line with equal weights given to each observation and the remaining data disregarded.

The HS VaR may not accurately capture the potential losses:

  • in extreme market conditions, as it relies on past data to estimate the risk, which may not account for rare but significant catastrophic events.

  • as it depends on the quality-quantity of the available historical market data. In cases where data is limited or unreliable, the results of the HS VaR method may not accurately reflect future market conditions.

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