The Idea of VaR

Finance is essentially about the valuation of uncertain cashflows in the future. Dealing with this uncertainty, and the relationship between risk and return, is the basic challenge faced by everyone in finance, whether in banking or fund management or securities.

Traders and firms need to be extremely careful when dealing with risk. Some amount of risk is inescapable, for otherwise the average returns would be extremely low. Some kinds of risk do not yield higher returns, and are just not worth bearing. Risk and return have to be thought out at the portfolio level, whereas many people are instinctively used to looking at individual securities. The risk of the overall portfolio has to be calibrated to suit the risk tolerance of the principals, and maximise the average returns that can be attained by these levels of risk.

This is not a simple challenge. Traditionally, coping with risk has been done by pure intuition. This is becoming increasingly hard given the complexity of the modern financial system, and the competitive pressures generated by `quantitative' firms. There is a considerable body of pre-scientific "folk medicine" which is widely used in finance. This has generated many disasters, some of which have made front page news.

One of the most difficult facets of risk in the financial sector is the relationship between shareholders and managers. The owners of a finance company need to define a "risk policy" which the managers that they hire should obey. If risk and return lie at the heart of finance, then shareholders need to locate the firm on the risk--return tradeoff, and ensure that managers cater to the choices of the shareholders. The definition of risk policies in this context requires an explicit specification of risk. This gives an impetus for a more explicit treatment of risk using modern financial economics.

In recent years, the notion of "Value at Risk" (VaR) has come into prominence as a tool towards the risk measurement. In order to measure the risk of a portfolio in terms of its VaR, we need to specify two things: (a) a horizon and (b) a probability level. Hence there is no such thing as a single VaR, instead there is a different VaR for different time horizons and for different probability levels. The VaR at a 99% level on a one--day horizon is the one--day loss that will only be exceeded on 1% of the days. Similarly, the VaR at a 95% level on a one--week horizon is the one--week loss that will only be exceeded on 5% of the weeks.

If we assume there are 250 trading days a year, a 1% VaR on a one--day horizon is the loss that will be exceeded for two to three days a year. If Nick Leeson's supervisors had known the one--day VaR of his positions, they would have never allowed these positions.

Thus the notion of a VaR reduces the total risk of an entire portfolio -- and not an instrument -- into a numerical measure of the losses that will be experienced on bad days on the portfolio. VaR has one great advantage: managers can understand and comprehend it. The chairman of a company can discuss the drafting of a risk policy in terms of VaR, even if he is not familiar with advanced financial economics.

To be sure, the implementation of systems to measure VaR require advanced financial economics. But the beauty of VaR is that the output that comes out of a VaR implementation is comprehensible. When we deal with complex combinations of spot equity, index futures, index options, forward positions on the currency market, etc., the creation of a VaR system is technically demanding. Yet, any manager would know that something is amiss when the 95% VaR on a one--day horizon of a position exceeds the net worth of the company.

VaR is measured at a portfolio level. VaR is not about any one instrument, it is about the total risk of a portfolio. It is not particularly meaningful to ask: "what is the VaR of the September Nifty futures". The idea of VaR correctly focusses upon the bottom line: the risk of the portfolio as a whole.

VaR is closely connected with initial margin requirements of clearing corporations. The initial margin is supposed to be large enough to cope with one--day losses on most days. At the Chicago Mercantile Exchange, initial margin is normally set at a 95% VaR on a one--day horizon.

Once again, portfolio analysis is important: it is not possible to assign an initial margin to each futures contract and obtain the total risk of the portfolio by summing up. A portfolio "buy August futures and buy September futures" is very different from a portfolio "buy August futures and sell September futures". The first position is speculating on both prices rising. The second position is hedged, it has no price exposure, and has a much lower VaR.

Regulators have long been interested in risk measurement with the objective of limiting the leveraged positions that are adopted. The leverage of banks is limited by the Basle norms. These norms are naive in that they do not use portfolio analysis. VaR ideas would yield better prudential regulation for banks.

In the securities industry, VaR is starting to be adopted by many regulators. In India, the L. C. Gupta Committee on exchange--traded derivatives has refrained from micro--managing markets as far as specifying margins are concerned; instead the Committee recommends that SEBI should ensure that the collateral pledged with the clearing corporation always exceeds the 99% VaR on a one--day horizon (this is more stringent than requirements in the US, which typically target the 95% VaR on a one--day horizon). The Committee additionally recommends that this condition should even apply intra--day, in real--time. When SEBI employs such ideas, it would be making a historic shift away from the crude specification of initial margin as percent of gross exposure, which is currently used on the spot market.

This use of VaR is a milestone in the regulation of financial markets in India, and is progressive even by international standards. The safety obtained using the 99% VaR requirement for futures trading exceeds the safety of the equity cash market on all exchanges in the country other than NSE.

As we go into an increasingly complex financial sector, explicit risk measurement is essential. There are innate conflicts of interest between the risk appetite of traders, the risk appetite of managers, and the risk appetite of the board. The use of VaR would help enable appropriate control structures which guide activities towards the objectives of shareholders. In addition, the use of VaR at the clearing corporation in the context of derivatives trading would ensure that certain minimum collateral (and hence net worth) always exists, thus putting a floor upon the fragility of a firm.

(For further details on what VaR is and how it can be used, see Value at Risk: A Conceptual Examination by Ajay Shah, Chapter 23 in Derivatives Markets in India Tata McGraw Hill, April 1998).

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