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Market Risk Measurement Methodologies: Value-at-Risk |
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| Value-at-Risk |
| Most fund managers usually ask about how much our portfolio had gained today, which is a backward looking question. In the opposite, modern risk managers would like to know how much we could loose tomorrow, which a forward-looking and risk-defensive question. Imaging a risk manager of a company trying to explain how much the level of risk is he can just tell you something like: not very much, sort of risky or very risky. However, if you still want to know how much exactly our portfolio would be the lost, “value-at-risk” (VaR) is the standardized answer which is risk comparable. |
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| The basic concepts in measuring risk, we have first to find a portfolio’s profit and loss function then mapping the equation into the identified risk factors and finally find the distribution of profit and loss directly or indirectly from the distribution of the risk factors. Here are some of the examples of mapping of risk factors |
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| A foreign-currency portfolio’s profit and loss ( D V t) is weighted sum of return on each foreign currency. |
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| A stock portfolio’s profit and loss ( D V Dt ) can use the CAPM’s beta to approximate the portfolio’s return that can help to reduce number of risk factors to a mangeable size. |
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| A bond portfolio’s profit and loss ( D V t) is able to mapping into spot yield change ( D y i) in different maturity. |
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There are number of approximation methods of portfolio valuation or profit and loss and assumption on distribution such as “delta-normal” method, “delta-gamma-normal” method and Cornish-Fisher approximation, etc.
The followings are three major types of techniques that widely used to calculate VaR. |
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1. Historical Simulation Method |
This is a straight forward non-parametric method which requires no assumption on distribution. We simply observe the profit and loss behavior of our current position of portfolio by observing from the historical change in risk factors that determine the value of portfolio. |
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| 2. Analytical Method |
This is a parametric method, based on the assumption that the returns are normally distributed. Historical data is to estimate the means, standard deviations and correlations as the key parameters for calculation formula. |
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This method is very popular and easy to use so it can be called as variance-covariance method. |
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3. Monte Carlo Simulation Method |
It constructs simulated value of risk factors from a given distribution and dependence structure. We then have the distribution of the profits and losses over the large number of simulation runs. This is a very flexible and powerful method that analyst can measure risk on complicated derivative products and perform variety of stress testing based on his creative imagination.
The measurement of future risk is very challenging job and we would like to know what would happen beyond VaR. The following methods are very useful and necessary as complements to the VaR. |
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| Back Testing |
It is a procedure, which is required by regulator, in which one can check how often the actual losses have exceeded the risk level predicted by VaR. This prevents banks from setting the VaR too low that is too risky to the available capital. It also prevents banks from loosing business if the VaR is too high. |
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| Stress Testing |
It is very useful to artificially generate extreme scenarios of the main factors driving the portfolio returns by exposing it to data different from the data used when specifying and estimating the profits and losses. |
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| Advancement in VaR |
Other than the above 5 basic procedures, VaR has been widely fine tuned with a lot of research in order to make it as a good predictors of future risk. Those who interest in advancement in VaR may have to study further in the following topics: expected shortfalls, extreme value of loss, time-varying volatility (GARCH), quasi Monte Carlo simulation, Copula simulation, etc. |
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