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VaR: Demystified - Views on News from Equitymaster
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  • Aug 7, 2001

    VaR: Demystified

    In what some would consider a significant decision to modernize stock markets, the SEBI announced, on May 31, 2001, that starting from July 2, 2001 the margin requirements for scrips in the compulsory rolling settlement mode would be determined based on a scientific model, i.e. the Value- at-Risk (VaR) model.

    The regulation, stated broadly, prescribes a scrip-wise 99% VaR to be computed as equal to 3.5 times the daily volatility of each scrip, with the latter being computed using the same exponentially weighted moving average method that is currently used for index futures. The daily scrip - wise margins are computed as a multiple (at least 1.5 times) of the daily VaR. The exchanges are expected to calculate and display the scrip-wise margins on a daily basis. Margins for each trading member is arrived at by summing up scrip-wise margins based on scrip-wise VaRs multiplied by their positions in each stock, and this margin would be applicable for transactions to be carried out in the next day.

    The new margining system would remove the limitation of an across-the-board margin wherein volatile stocks are inadequately covered and less volatile stocks are handicapped by more than required margin, by linking the margins explicitly to measures of risk / volatility of stock prices. Naturally, the effectiveness of the risk based margining system would critically depend upon the accuracy with which the proposed VaR model characterizes the risk of a portfolio. In this article I discuss the properties and limitations of the VaR model in the context of setting margins. VaR defines the maximum loss a portfolio can suffer within a time horizon (say a day) at a pre- specified probability level. For example, if a 99% VaR is specified as Rs 10, it should be interpreted as in 99 out of 100 days the loss the portfolio can suffer will never exceed Rs 10. Note that this is not the same thing as saying VaR is the maximum possible loss when the markets turn unfavorable. The maximum potential loss a portfolio can suffer when things turn unfavorable is the entire value of the portfolio itself.

    To put it in simple terms, a 99% VaR will indicate the maximum loss that a portfolio can suffer in 99 percent of times. Conversely, it is the minimum loss that a portfolio can suffer in 1 percent worst cases. Therefore, VaR can be interpreted as the best of the worst scenarios or the worst of the best scenarios.

    A related point is that two portfolios, with different catastrophic risk profiles (stream of large losses), can have the same VaR. For example, out of 500 past returns the worst 5 losses on portfolio A may be 15, 14, 13, 12 and 10, while for portfolio B they may be 25, 15, 15, 13, 10. The 99 percent VaR number for both would be, assuming the same volatility, Rs 10, although the portfolio B is far more riskier than portfolio A. The point to be noted here is that VaR does not measure the intensity of potential losses (say the average worst losses) that can occur when markets turn unfavorable. This in turn would imply that setting margins equal to the daily VaR cannot fully cover for the average worst losses that various trading positions can incur.

    In the context of bank capital regulation, Basle committee suggests holding a scalar multiple times the VaR to cover for such losses. One could attribute the SEBI guideline that specifies a scalar multiple factor of at least 1.5 on a daily VaR to arrive at safe margins to this factor. Whether this factor is sufficient to cover the observed losses (simulated on historical returns) is an empirical issue, and the SEBI circular is silent on the rationale behind these multiplying factors. The exchanges must, therefore, undertake such exercises before implementing the new guidelines in order to make sure that they would not be holding excessively large or small levels of margins that could adversely affect the market activity.

    Another aspect of the proposed regulation is that the daily VaR be computed scrip-wise and multiplied with each trader™s position in each stock to arrive at margins to be applicable for a trader™s transaction the next day. An obvious limitation of this regulation is that it treats the risk of a portfolio as equal to the sum of risks of each scrip in the portfolio, thereby ignoring the fact a portfolio is a diverse set of correlated positions. The risk of well- diversified portfolios is expected to be less than that of the sum of the risks of individual parts, and margins based on the latter will be too high for this portfolio, possibly adversely affecting the market activity. A related technical point, not often recognized, is that VaR of a portfolio could be greater or less than the sum of VaRs of individual securities in the portfolio depending upon the composition of portfolio. In particular, for portfolios consisting of options this property of lack of sub-additivity becomes important. This would mean that by setting margins based on scrip-wise VaRs, the exchanges can not be sure that they are being conservative all the time and hence safe. For the margins to be determined in a scientific manner, as is being claimed, the SEBI must encourage the exchanges to develop models to compute the VaR of a portfolio as a whole and not by parts.

    Finally, VaR is obviously related to the volatility (variance) of the underlying stock price, but it is not a measure of volatility. Under some assumptions about how stock returns are statistically distributed (the so-called normal distribution), one can compute 99% VaR as 2.33 times the stock volatility. The SEBI guidelines require daily VaR to be computed as 3.5 times the daily volatility may be factoring in, in a crude way, for the possibility that stock returns are not normally distributed. Whether this factor is sufficient or not to account for the extreme, but rare, losses is again an empirical matter that needs to be established in the Indian context. Further, one can not be sure that the VaR model, based on historical return data, would remain stable and applicable during the ‚crisis™ periods for which it is designed in the first place as stock prices may behave very differently during the crisis periods than otherwise. The regulator and exchanges will have to use some other auxiliary measures to deal with such situations.

    * This article titled Value-at-Risk and Margin Requirements - Opportunities and Pitfalls has been written by Gangadhar Darbha for NSE News. The article was carried in the June 2001 edition of NSE News.



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