CAs at Risk

Accountancy SA,  Sep 2003  by Tosen, Graeme

Tags: Computer Associates International Inc.

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There are several truths about the training of CAs. One is that most newly qualified CAs will be well trained and conversed in the subjects of hedging, hedge effectiveness and risk disclosures, but would know little about the actual economic risk measures and risk management implementation. Another is that most employers would not understand why this is so - "you are a CA, aren't you?"

The fact is that you can only manage to include that much into one professional designation, except if we had an extra three years to do some high-level mathematical and statistical courses as an add-on to accounting, tax, audit, business management, cost management, financial management, investment concepts; the list goes on and on and on.

Given the number of CAs that hold senior management positions at a rather early stage in their lives and the increasingly complex financial environment, shouldn't we at least attempt to know the basics? Added to this, these concepts are central to the Basel accord and Basel II. So if you are one of those people that still think that a dynamic hedging strategy has to do with advanced gardening techniques and that VAR is the way English speaking people pronounce the Afrikaans equivalent of "where," then this series of articles are just for you.

The series is aimed at introducing the regular accountant to risk tools, hedging techniques, a bit of stats and a lot of acronyms. Just enough to keep you awake in the next board meeting.

This first introductory article will focus on the concept of Value at Risk (VAR). Later in the series, we will look at duration and convexity, the "greeks" and other option related risk measures and concepts, a number of economic hedging strategies, risk analysis techniques and briefly look at credit, liquidity and operational risk measurement.

INTRODUCTION TO VALUE AT RISK (VAR) I The most important risk development in recent years has most probably been the increased use of VAR. There are several ways to skin the VAR cat, each having its own advantages and disadvantages. By definition, VAR is the amount of loss relative to a mean return. From this definition, it should be clear that for a calculation of VAR you would need to define a mean return (this is often done by way of a probability distribution of possible returns) and some measurement of the dispersion from the mean (or volatility). The standard deviation of such a distribution is commonly used as the dispersion measurement.

A normal distribution is a specific type of probability distribution, which, because of its special characteristics, is most suited to value at risk calculations. The handy factor about a normal distribution is the dispersion rule. In a normal distribution, for a one-tailed test (VAR only measures the downside from the mean), approximately 90% of possible values fall within 1.28 standard deviations from the mean, 95% fall within 1.65 standard deviations, 97.5% within 1.96 standard deviations and 99% of all values within 2.33 standard deviations.

Using the standard normal distribution, VAR can be calculated as a multiple of standard deviations below the mean. For example, suppose you have a mean return of R3 million and a standard deviation of R7 million. At a 95% confidence interval (i.e. 1.65 standard deviations), you can calculate your value at risk as being R 8.55 million [R3 mil - (1.65 x R7 mil)]. What we are saying is that for a given time period, there is a 95% change that the loss for that period will not exceed R8.55 million, or conversely; for 5% of the time, the loss will be at least R8.55 million. The larger your chosen confidence interval, the larger the possible loss, but the smaller the probability of that loss occurring.

The use of market volatility in the calculation of VAR leads to a greater VAR number in more volatile markets over a given time period. This characteristic is very helpful in the explanation of the risk that is taken over a specific period, as it should be clear that markets that change rapidly can lead to sudden drops or increases in value of, for example, long equity future positions where the firm has a fixed future delivery date. Because of large short-term movements, you run the risk of having to take a loss on the position due to a sudden price change just before delivery. Your risk of loss is thus higher because of higher volatility, which is measured by standard deviation, an important input of the VAR model.

IMPORTANT FACTORS WHEN DISCUSSING VAR I

* From the example above, it is clear that VAR gives an indication of the probability of a loss, but not of the magnitude of that loss. So, although your risk professionals can inform you that you can loose at least R8.55 million 5% of the time, you do not have an indication of how much that loss will actually be. Sensitivity testing and back testing of models become vitally important.

* Secondly, VAR is calculated for a given time horizon. If the returns you used above were daily returns, the probability of a loss is a daily one. You could, in our example, expect to lose at least R8.55 million for 5% of the days in a year (13 days if we assume 250 working days a year). It is possible to change the time period you look at by using statistical techniques. Not that this is of vital importance, but to change a daily VAR figure to a ten-day VAR figure, you multiply the daily VAR by the square root of ten.