## Introduction

Value of Risk (VaR) models are characterized by a series of shortcomings due to the many assumptions they make use of, including the confidence level, distribution, reference period, and holding period among others. In portfolio management, backtesting methods have become popular for checking the degree of accuracy of a VaR model. Therefore a systematic combination of at least two VaR models would facilitate substantial improvement in decision-making effectiveness, in providing support to the risk variable, and in setting the required market capital risk. This report explores the role of backtesting VaR models in portfolio management and the potential limitations of these models.

## The Role of Backtesting VaR Models in Portfolio Management

According to Lucas (2001), risk control in portfolio management will function optimally when the VaR is designed well with a limited occurrence of pre-existing real dangers. In such a situation, the degree of VaR accuracy becomes a vital aspect for measuring the level of risk in portfolio management in an organization, and thus the rationale for using different models of backtesting. However, despite the advancement of any backtesting model or system, the level of general accuracy is 75% and above. This means that it is next to impossible to generate a 100% accuracy level for VaR figures.

In the event of detecting potential flaws in a VaR model, applying a backtesting method might be a useful step in managing risks in a portfolio (Lucas 2001). Another role of VaR is quantifying the general portfolio risk as a determinant of the market risk capital requirement, which is equivalent to the set-aside size (Lucas 2001). This means that VaR modeling is an important tool for measuring the market risk as a component of quantifying the maximum possible loss that might occur over a fixed period of time at a given level of confidence.

Moreover, backtesting is a vital instrument in forecasting market risk management in a portfolio (Lucas 2001). In application, backtesting procedures are carried out through a comparative review of periodic profits and losses on a daily basis against estimated daily VaR, often by using a fixed annual time period.

Nevertheless, a systematic backtesting process can often be quite thorough in order to address the purpose of portfolio management and provide a complete view of the VaR software accuracy. As a result, it is possible to compute the required capital, which is associated with increasing the moral hazard to 75% (Lucas 2001). In order to avoid conflict of interest, portfolio management approaches should function within a universal or common standard, which also indicates the significance of backtesting. For instance, the risk-based required capital is positioned as the largest of either a portfolio management’s current assessment or 1% VaR.

In the banking industry, the 1% VaR for current assessment is set over a period of ten trading days against the previous sixty days, in addition to an amount reflecting the credit risk of a portfolio (Lucas 2001). This means that backtesting is instrumental in measuring the accuracy of calculations associated with value-at-risk in portfolio management. Ultimately, the value-at-risk calculated loss forecast is then compared with the real losses once the fixed time horizon lapses to determine the vicious cycle.

In application, backtesting simulates a strategy model using past data to determine its effectiveness and accuracy (Lucas 2001). The comparative review is significant for identifying the time horizon when the value-at-risk is undervalued or when the losses in the portfolio are larger than the projected value-at-risk. Based on the result, the value-at-risk may be recalculated in the event of inaccurate backtesting values, thus substantially lowering the risks associated with unexpected losses (Lucas 2001).

For example, when the value-at-risk for a period of one year of an investment portfolio is placed at $5 million at an estimated level of confidence of 95%, it suggests that the chance of experiencing losses exceeding $5 million is 5% over the fixed time horizon. Therefore, at a 95% confidence interval, the expected minimal loss over the period of trade cannot exceed $5 million. In the event that the past annual data of simulated value-at-risk and the definite losses in the portfolio are less than the expected risk losses, the computed value-at-risk is declared a suitable measure and vice versa (Lucas 2001).

## Associated Limitations of VaR Models

### Estimating the tail is difficult

The VaR is challenging to compute with large portfolios since a user has to estimate or measure the correlation, volatility, and return of individual assets. When the diversity and numbers of assets are growing, it is difficult to accurately compute VaR due to the exponential growth of the tasks to be accomplished (Lucas 2001). Since the VaR is not additive, estimating the tail is an uphill task, especially in the correlation of independent risk factors. For instance, the portfolio VaR consisting of assets K and L is not equal to the summation of VaR of asset L and VaR of asset K (Lucas 2001).

### Measuring risk is challenging

The VaR might give a ‘false sense of security’. Examining the risk exposure in the form of VaR may be misleading due to excessive focus on the losses, especially when the confidence interval is set at 99%. Even when a user comprehends the stated function of VaR, a high confidence level of 99% might give an artificial sense of security against risks (Lucas 2001). In reality, a 99% confidence interval is still far away from 100% and this assumption might lead to fatal results.

### VaR assumptions can be invalid

Different VaR models lead to dissimilar outcomes. The value of VaR varies depending on the method used. For instance, the Monte Carlo VaR, historical VaR, and variance-covariance parametric VaR methods give dissimilar values despite using the same portfolio. Consequently, the accuracy of each method may be questionable in terms of its representative value of VaR in estimating risks (Lucas 2001).

Moreover, the VaR does not quantify the worst-case loss. Although this loss might be greater than the VaR by a few percent, it should not be ignored since a loss of 1% is substantial and might result in the liquidation of a company. Therefore, it is impossible to compute the maximum possible loss simply by computing the VaR (Lucas 2001). This means that the VaR computation should be backed with other tools that consider the 1% worst-case scenario. On its own, the VaR is incomplete and might give invalid results.

### Insufficient data for computing VaR

The usefulness or result of VaR is dependent on the inputs used to generate the final values. In most cases, the assumption of a normal distribution of portfolios and return on assets with excess kurtosis or ‘abnormal skewness’ is unrealistic and might result in underestimation of the real risk (Lucas 2001).

## Conclusion

The value at risk (VaR) is an important statistical tool for risk management in a portfolio. The VaR quantifies and monitors the level of risk in any investment portfolio over a specified period of time. Specifically, the VaR measures the worst-case loss at a specified level of confidence in terms of its accuracy. However, this model is associated with limitations such as difficulty in estimating the tail, invalid assumptions, insufficient data, and challenges in measuring risk.

## Reference List

Lucas, A 2001, ‘Evaluating the Basle guidelines for backtesting banks’ internal risk management models’, *Journal of Money, Credit and Banking*, vol. 33, no. 3, p. 826-831.