Quality Money Management : Process Engineering and Best Practices for Systematic Trading and Investment

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where   1 is the speed of mean reversion toward the long-run value u , and the

variance is proportional to the level of the interest rate, r.

● Generate a path for each stochastic variable.

● Value the portfolio given the random variables as inputs, that is, mark-to-market.

● Repeat the generation of random paths and portfolio valuation, say 10,000 times.

● Compile a distribution of portfolio values, from which a 2 standard deviation VaR

(95% confidence bands) can be measured.

As we discussed in K | V 4.1, portfolios generally contain more than one source of finan-

cial risk. The Monte Carlo methodology can be easily extended to a general multivariate

case, to account for any number of risk sources. Some random variables may be corre-

lated, others uncorrelated. In the case of correlation, a correlation coefficient must be

added. This is often done using Cholesky factorization.

Monte Carlo simulation is by far the most powerful method to calculate Value at Risk.

First and foremost, it can consider any number of financial risks: nonlinear price risk,

volatility risk, model risk, credit risk, time varying volatility, nonnormal distributions and

fat tails, implied parameters, and extreme or user-defined scenarios. The only drawback

is the computation cost. Monte Carlo is expensive in terms of time and money. When

portfolios contain complex derivative instruments, full portfolio valuation can take a long

time and a lot of technological and intellectual horsepower to calculate. We recommend

that these calculations be done using standard, internal, existing systems or third-party

stand-alone systems COTS. The reason for this recommendation is twofold:

1. The calculations in these systems should be industry standard, not proprietary.


2. The time to build these complex systems can be measured in years. To get a trading
   system up and running quickly, a firm should not spend six months to a year to get
   an attribution system and/or VaR system built. (As with all vendor components, the
   organization must confirm COTS package ’ s ability to satisfy the intended applica-
   tion when used in the monitoring and measuring processes. This confirmation must
   be accomplished prior to initial use and reconfirmed as necessary.)

We do recommend that you program a custom database that stores all the inputs and

outputs of these systems, so that all the output data can be graphed and monitored using

SPC, and data mined during the kaizen process. The proper storage of these results and

analysis should allow a system to beat any competition that does not store and statisti-

cally analyze the performance output data for continuous improvement.

We recommend that you adopt a VaR framework, not only to view risk, but also to

have a tool that accurately measures “ what-if ” scenarios. This what-if analysis becomes

a key tool of the kaizen process. The kaizen team can make changes to the portfolio con-

struction and run the Value at Risk. The results will either confirm or disprove the root

cause of the system and allow a kaizen team to move forward with scenario analysis.

27.4. Summary

While many, mostly small, trading groups ignore risk metrics or perform the minimum

calculations, we recommend all firms embrace real-time performance and risk metrics.

Firms should view risk and performance as a continuum from single point estimates to

beating a benchmark to what-if scenarios.

27.4. SUMMARY