Question

Describe some advantages and disadvantages of Value at Risk (VaR) as a risk measure relative to other risk measures

Answer 1

Value At Risk is a widely used risk management tool, popular especially with banks and big financial institutions. There are valid reasons for its popularity . But for using Value At Risk for effective risk management without unwillingly encouraging a future financial disaster, it is crucial to know the limitations of Value At Risk.

VAR does not measure worst case loss

99% percent VAR really means that in 1% of cases (that would be 2-3 trading days in a year with daily VAR) the loss is expected to be greater than the VAR amount. Value At Risk does not say anything about the size of losses within this 1% of trading days and by no means does it say anything about the maximum possible loss.

The worst case loss might be only a few percent higher than the VAR, but it could also be high enough to liquidate your company. Some of those “2-3 trading days per year” could be those with terrorist attacks, Kerviel detection, Lehman Brothers bankruptcy, and similar extraordinary high impact events.

You simply don’t know your maximum possible loss by looking only at VAR. It is the single most important and most frequently ignored limitation of Value At Risk.

Besides this false sense of security problem, there are other (perhaps less frequently discussed but still valid) limitations of Value At Risk.

Value At Risk gets difficult to calculate with large portfolios

When you’re calculating Value At Risk of a portfolio, you need to measure or estimate not only the return and volatility of individual assets, but also the correlations between them. With growing number and diversity of positions in the portfolio, the difficulty (and cost) of this task grows exponentially.

Value at Risk is not additive

The fact that correlations between individual risk factors enter the VAR calculation is also the reason why Value At Risk is not simply additive. The VAR of a portfolio containing assets A and B does not equal the sum of VAR of asset A and VAR of asset B.

The resulting VAR is only as good as the inputs and assumptions

As with other quantitative tools in finance, the result and the usefulness of VAR is only as good as your inputs. A common mistake with using the classical variance-covariance Value At Risk method is assuming normal distribution of returns for assets and portfolios with non-normal skewness or excess kurtosis. Using unrealistic return distributions as inputs can lead to underestimating the real risk with VAR.

Different Value At Risk methods lead to different results

There are several alternative and very different approaches which all eventually lead to a number called Value At Risk: there is the classical variance-covariance parametric VAR, but also the Historical VAR method, or the Monte Carlo VAR approach (the latter two are more flexible with return distributions, but they have other limitations). Having a wide range of choices is useful, as different approaches are suitable for different types of situations. However, different approaches can also lead to very different results with the same portfolio, so the representativeness of VAR can be questioned.