Improving on Var the Maths of Delvar

A nalytic variance-covariance value-at-risk is an established technique for measuring exposure to market-based financial risk (Smithson, 1996i and 1996ii). Given a description of the market characteristics and the user’s portfolio, the objective of VAR is to determine how much value might be lost over a given time, with a given level of probability, in a given currency. For example, JP Morgan’s RiskMetrics provides a comprehensive analytical methodology for assessing VAR. This form of VAR begins by replacing a portfolio, or the trades within it, with a set of cashflows reflecting those trades’ current values and their risk attributes. (This process is sometimes separately referred to as “shredding” the trades.) The resulting cashflows (which can be in any currency, commodity or other price risk source) are then aligned upon certain “vertices” representing standardised maturities and credit levels for the markets in which the cashflows are traded, again preserving their value and risk characteristics. (For example, six-month Libor Deutschmark and two-year dollar swap market flows might each represent a vertex.) The complete process of translating a trade into vertex cashflows is called “mapping”. Having thus arrived at the “cashflow map” (ie, the net result of mapping a portfolio of trades), one next combines this map with a covariance matrix whose index set is the set of vertices, which yields the desired result, the VAR number. Yet after VAR is assessed, there remains an important question: “What can one do to reduce VAR?” In this article, we introduce an approximation mechanism for improving VAR, referred to here as DelVaR. To present the issues in more concrete terms, consider what feedback the VAR calculation should provide to the trading activity of an institution. Which new trades will improve VAR and which will degrade it? And precisely how will we implement trading limits based upon VAR, when such limits evidently depend not only upon the proposed trades themselves but also on the way in which these trades interact with the existing portfolio of the institution? Unfortunately, the nonlinear nature of VAR requires us to create a new portfolio incorporating the proposed trades, and then reassess the VAR of this augmented portfolio. Among other things, this means that the VAR limits imposed upon any proposed new trade necessitate the re-evaluation of all trades (perhaps tens of thousands of these) in the institution’s revised portfolio, which can be a demanding process. The DelVaR approach offers a more economical means for evaluating any new proposed trade in terms of its effect on institutional VAR, without the extensive recalculation of total VAR. This permits the realisation of rapid evaluation of candidate trades, so that real-time VAR trading limits become practical. Also, by adding one additional feature to the DelVaR mechanism, called “trade normalisation”, it becomes possible to determine not just whether certain trades will increase or decrease VAR but, indeed, what relative ranking those trades should enjoy for VAR reduction purposes.