This book hopes to pave the way for a new approach in measuring risks, one that is unrestrained by ingrained notions of being independent and identically distributed (i.i.d.), stationarity, and normality of financial variables. Without such assumptions, mathematical risk models will lose a degree of tractability but will gain a practical ability to handle the risk of fat tails and procyclicality. Essentially, we have lost precision but have gained accuracy, and hence become less “wrong” in our assessment of risks.
The removal of these strict mathematical conditions leads to an open arena for further development of the basic bubble value at risk (buVaR) framework beyond what is described in this book. Some potential directions for further research include:
1. Calibration: Determining a more elegant theoretical upper limit for buVaR calibration. In this book, we used an average of the largest daily changes encountered in all history capped by a possible circuit-breaker (cap on day loss) imposed by the exchange. The weakness is that some markets do not have circuit-breakers (such as commodities and FX markets) and nascent markets will not have enough history of downturns for proper calibration. Ideally, the upper limit should be based on some natural limit imposed by the financial system environment. Such a limit should be intuitively justified and should not come from mathematical abstractions.
2. Benchmarking: The computation of the bubble measure is highly dependent on the availability of continuous data. For some emerging markets, illiquid prices make the measure inaccurate. In such cases, using benchmarks may be a better alternative, for example, using an equity index as a benchmark to derive the bubble measure for an illiquid stock. A potentially better idea is to use a group of suitable benchmarks to derive the bubble measures for all assets in the financial markets. Using benchmarks can be appropriate because we are actually interested in the cycle of the general market. And benchmarking will certainly lead to more stable results.
3. Performance testing: Because buVaR is “non-i.i.d.,” back tests and most statistical tests will not be meaningful, which leaves us to rely on performance testing not unlike that done for trading systems. In such tests, the practitioner is more concerned with accuracy (shown up as positive performance) than with statistical precision. Hence, one area of research is in designing a better gauge of “goodness” or effectiveness for the buVaR model. A well-defined test metric will be useful for the purpose of optimizing the parameters in buVaR.
4. Systemic risk: One advantage of buVaR is that it outputs profit and loss (PL) vectors, which makes it compatible for use with other new risk tools such as CoVaR and network models. These new models attempt to measure the spillover and transmission of systemic risks (see Chapter 12). Given that buVaR itself preempts many major sell-offs in history, it will be interesting to explore its effectiveness when used in combination with network models and Contagion VaR (CoVaR). Will it provide an early warning of systemic events?
5. Risk indicators: It is worth exploring whether risk indicators can be used to create an alternative
bubble measure for application in buVaR. A risk indicator is a proprietary indicator, which banks use to gauge market sentiment; hence, it is usually very cyclical.
1 Applying rank filter (see Section 13.3) to it may produce the necessary counter-cyclical quality.
6. Ultralow volatility problem: We observed in the tests in Chapter 15 that on a few occasions (see
Figure 15.26) the buVaR peaked and then
fell back just before the crash, even though the
bubble measure correctly timed the crash. This was due to the extremely low volatility that preceded the crash—the ETL (and VaR) was so low and depressed that, despite the multiplier effect, the buVaR declined. This is not ideal. Future research may attempt to correct for this “calm before the storm” effect. Under such a rare circumstance, the buVaR will dip from its peak before the crash, but VaR in comparison will always be too late—it will register a big reading when the crash occurs.
7. By looking at the result charts in Chapter 15, it is apparent buVaR inherited the plateau effect problem (see Section 2.7) from using the equally weighted historical simulation approach. It is proper to use decaying weights so that data rolling off the observation window will have a smaller impact. We abstain from including a decay factor in Chapter 13 because we wish to simplify the illustration of the buVaR idea and because the author does not have a strong view on the choice of decay schemes. We leave this to future research.