Introduction
Where in the past VaR was primarily used by big banks, we see a lot more companies in food and agri use VaR in their suite of risk management tools. Although VaR is very good to have as a risk management tool it is equally important to understand the limitations of using Value at Risk.
In this article, after a short introduction on the definition and past usage, we will focus on the advantages and limitations of using VaR. We will conclude by outlining the best practice to use Value at Risk for risk management purposes.
Definition of VaR
VaR is defined as follows: For a given portfolio, time horizon t, and probability p, the p-t-VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is p. As an example, set the VaR horizon at 5 days and the probability p at 95%. When the calculated VaR is 1mm, this means that there is a 5% chance that the cumulative loss for the next 5 days is larger than 1mm when the position is being kept unchanged.
Short History of Value at Risk
Although early forms of Value at Risk have been in use since the beginning of the 20th century we did not see VaR as a distinct concept until the late 80s. One of the main drivers behind the development of Value at Risk as a risk measurement tool was J.P. Morgan. Their methodology published in 1994 puts more emphasis on recent data than data in the past and is still one of the most used methods to calculate VaR.
In the commodity trading world interest in VaR picked up much later. One of the more notable events sparking interest in VaR was in October 2006 when hedge funds entered the futures markets for commodities and volatility spiked tremendously. Interest and use further increased after the financial crises of 2008.
Advantages
There are many advantages to using VaR as a risk management tool. The most important one is that VaR provides a quantification of the risk for the entire portfolio in just one number. This enables management to quickly see what the status of the company is at any point in time.
VaR also provides a way to see how well diversified the portfolio is by looking at the diversification benefit of a group of portfolios. By this we mean, how much the VaR goes down when a set of portfolios is taken together. The VaR for the group of portfolios will always be less or equal to the sum of the individual VaR numbers. The amount by which the VaR goes down we call the diversification benefit.
Other types of analysis are also possible with VaR. We can for instance calculate an optimal hedge ratio between two products by minimising VaR for the 2 products combined in one portfolio. Say we want to hedge a long wheat position with CBOT Wheat futures. We could hedge on a 1 to 1 basis by taking as many tons short CBOT Wheat as there are tons long of physical wheat. However, this might not be the optimal hedge as the correlation between the two is not 1 and the volatilities will not be equal meaning that the prices don’t move in the same way. The ratio between the two which minimizes VaR will be the optimal hedge ratio.
VaR can also assist in setting of position limits as it functions as a link between budgets and positions needed to accomplish that budget. This works as follows. We start with the risk appetite of the company. Usually this is a percentage of the equity. This number should be equal to the maximum amount the company is willing to lose within a certain horizon with a certain statistical confidence. Most used will be a 10-day 99% number. Depending on the reporting needs, this number can be scaled to the desired time frame and probability. This will be the company VaR limit. The VaR now needs to be distributed over several product lines. This can be done by running a number of scenarios to determine what the diversification benefit between the product lines will be. This will result in VaR limits per product line. From a VaR per product line we can get to volumetric limits by running scenarios on VaR calculations per product line.
Limitations
While there are many advantages to using VaR as a risk management tool, it is important to also realize there are limitations to VaR. By no means is it a measure on which can be trusted blindly.
VaR gives a loss amount with a percentage chance and a time horizon. This also means that with a chance of 1-p the loss will be larger than the VaR. However, how much larger is unknown and this can be substantially larger as we have seen in the past, for instance with the financial crisis of 2008. Losses at that moment were much larger than the estimated VaR numbers at that time. This brings us directly to the second limitation. VaR can only be based on historical data. Usually this is no more than 1 year of data. When a macroeconomic event happens which puts markets in a different regime, this cannot be predicted by a VaR engine as this has not happened in the past.
Data availability can be another limitation. The estimation of VaR is only as good as the underlying data on which it is calculated. Especially for products which are traded in less liquid markets the availability of price data can be limited. This can be solved by using proxy price series for these products, but the question remains whether this is a good fit or not.
Best practice for use of VaR
We have now seen the advantages but also the limitations of VaR but how should VaR be best utilized?
First, we want to go a bit deeper in to the VaR Horizon and probability. These need to be set before any VaR can be calculated. The horizon will depend mostly on the availability of prices. When prices are available on a daily basis, a daily VaR is possible. When prices are only available weekly, a weekly VaR would make more sense. For the percentage it is more up to the risk manager to determine what is appropriate. A percentage of 99% will be broken less but the numbers reported will be significantly higher. Especially when introducing VaR it can sometimes be easier to report lower numbers as higher numbers can be more off-putting.
The best use of VaR comes when the user knows the limitations. VaR works very well within a set of risk management tools. It is a great addition to the more conventional position limit structure. A high VaR when way below the position limit indicates for instance that the position limits must be reviewed and vice versa, a low VaR with positions at the position limit indicate that the position limits could be extended.
In combination with scenario stress testing VaR works very well to give a straightforward picture of the current situation. VaR serves as a tool to measure the “normal” situation where the stress test can function for the extreme case scenario.
Concluding we can state that as long as the limitations of VaR are taken into consideration and VaR is used within a suite of risk measures it is an excellent risk management tool.