The military doesn’t acquire a new transport plane without considering its purpose—do they need a heavy-lift aircraft to fly into established airports, or do they require a lighter plane to deliver small payloads to unfinished drop zones? A value-at-risk measure, like a transport plane, is a tool. Before we implement one, we need to know its purpose. This might be:
- Regulatory reporting and regulatory capital adequacy requirements under the Basel Accords: The prescribed value-at-risk metric is 10-day 99%value-at-risk. Due to the practical challenges of modeling intra-horizon events, this is calculated as one-day 99%value-at-risk and then scaled by the square root of ten—essentially assuming a static portfolio for ten days and independent daily P&L’s.
- Internal reporting, economic capital adequacy requirements andvalue-at-risk limits within financial institutions and other trading organizations: These are different applications, but a single value-at-risk measure is often implemented to support two or all three of them. Various quantile-of-loss value-at-risk metrics are used.
- Corporate disclosures: Item 305 of the SEC’s Regulation S-K requires that large corporations disclose certain qualitative and quantitative information on market risks arising from interest rates, foreign exchange, commodities, and other sources. Quantitative information can be presented as tabular data on individual positions, a sensitivity analysis, or quantile-of-lossvalue-at-risk.
- Quantitative asset-allocation or portfolio optimization models: These generally incorporate a value-at-risk measure, although it may not be called that. Harry Markowitz’s pioneering work in the 1950’s employed linear value-at-risk measures with either a one-year variance of return or one-year standard deviation of return value-at-risk metric. Today, these techniques are sometimes called risk budgeting.
- Optimizing tracking error of investment portfolios against a benchmark: A standard deviation of return value-at-risk metric might be used. The value-at-risk measure is applied, not to the portfolio, but to the portfolio combined with a short position in the benchmark. Tracking error is optimized by adjusting the portfolio’s composition, balancingvalue-at-risk against the portfolio manager’s desire to make active bets.
- Hedge optimization: Situations arise where some liquid instrument is used to hedge some less liquid position. If the correlation between the two is imperfect, some market risk will remain. The question arises as to how many units of the hedging instrument will provide the optimal hedge. This can be answered by applying a value-at-risk measure to the total position (original position plus the hedge) and adjusting the hedge to determine the number of units of the hedging instrument that minimizes thevalue-at-risk. One-day standard deviation of P&L is a typical value-at-risk metric for this purpose, but a quantile of loss might also be used.
Needless to say, different applications may call for very differentvalue-at-risk systems. On one extreme are financial institutions that can spend tens of millions of dollars on avalue-at-risk implementation for risk monitoring,value-at-risk limits and/or capital calculations. Much of the expense can be for interfacing with other systems, security, redundancy and coding a model library that can handle all the instruments the institution trades. Coding the actual analytics for calculatingvalue-at-risk can be a more modest task.
At the other extreme are simple spreadsheet value-at-risk measures. One of these might be used each week by a commodities wholesaler to track market risk, or once each reporting period by a corporation to satisfy its disclosure requirements. Spreadsheet value-at-risk measures tend to be linear value-at-risk measures, but add-on software may facilitate Monte Carlo or other analytics. Inputs tend to be manual. Security is minimal—perhaps “locking” the spreadsheet to prevent a user from inadvertently deleting or changing a formula.
This chapter describes how to implement avalue-at-risk system, focusing primarily on larger implementations that support financial risk management or regulatory reporting requirements for banks. We present the perspective of a financial risk manager who might be involved in the process.