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Mechanical trading systems - Weissman R.L.

Weissman R.L. Mechanical trading systems - Wiley publishing , 2005 . - 240 p.
ISBN 0-471-65435-3
Download (direct link): mechanicaltradingsystems2005.pdf
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Price Risk Management
down. In contrast to doubling the volumetric risk after each loss, those employing averaging down strategies double their existing volumetric exposure on losing positions whenever the position held loses half of its value. A common stock shifting from growth to bankruptcy reveals the inherent flaw in utilization of such a strategy.
Because Martingale and Martingale look-alikes, such as averaging down, are disastrous as volumetric risk management methodologies, strategies that increase volumetric exposure during and/or after increases in equity under management should provide us with an attractive alternative. Such strategies are collectively known as anti-Martingale methods. The most simplistic anti-Martingale technique would entail doubling our position size after each gain and returning to our original volumetric exposure after a loss. Although such a position sizing technique might be robust enough to be effective in price risk arenas in which per-position profits and losses were identical, the technique is generally considered a suboptimal answer to the issue of volumetric price risk management in the financial markets because of the nature of trading strategies employed (e.g., trend-following—inequality of profits and losses) as well as the heteroskedastic-ity of the assets traded.
A more robust anti-Martingale methodology is known as fixed fractional money management. The basic premise behind fixed fractional money management is that volumetric exposure increases or decreases as equity under management fluctuates. For example, if we were trading a system that experienced a worst peak-to-valley drawdown in equity of $10,000 on a $100,000 portfolio during the backtested period and we intended to trade this system with $1,000,000 under management, we could trade 10 contracts for each signal generated while still retaining the expectation of a worst peak-to-valley drawdown in equity of 10 percent. Once our account equity increased to $1,100,000 we could increase our position size to 11 contracts while retaining the same 10 percent worst peak-to-valley expectation. On the other hand, a decrease in equity to $900,000 would force a reduction of our position size to 9 contracts to retain this same 10 percent worst peak-to-valley drawdown expectation.
One of the major benefits in utilizing the fixed fractional money management methodology is that it forces both a slowing of the rate of equity deterioration during drawdowns and simultaneously accelerates market exposure during periods of increases in account equity.4

Although an in-depth discussion of the various methods of calculating VaR is beyond the scope of this book, I will provide a general overview of the
topic and why it is an important complement to traditional methods of price risk management (e.g., stop-loss and volumetric price risk management).5
Value-at-risk methodologies attempt to quantify the standard deviation (or historical volatility) of a trading asset or portfolio of assets and the historical correlations between these assets in order to answer the question: What is the likelihood of our losing X dollars or more over a specified time horizon under normal market conditions?” For example, a particular hedge fund might have a daily VaR of $30 million at the 95 percent confidence level. This would translate into there being a 95 percent probability of the portfolio not experiencing a loss in excess of $30 million over the next 24 hours.

Although VaR provides traders and risk managers with a multitude of benefits, its most touted benefit—the introduction of probability of loss for a given portfolio over a specified future time horizon—is applicable to all market participants. The key feature here is VaR’s incorporation of historical volatility and correlations for a specific portfolio to forecast future price risk with some notion of likelihood over a given holding period.
Risk managers and system developers utilizing traditional measures such as stop-loss and volumetric price risk analysis can tell us many essential aspects of portfolio risk, such as the likelihood of an account trading specific assets with a particular methodology experiencing a 20 percent peak-to-valley drawdown over the course of the past 10 years. Moreover, they can determine how many times such an account would have endured daily losses in excess of a particular monetary threshold (e.g., $10 million). In fact, this ability to determine the number of times that a portfolio experienced a daily loss in excess of $10 million is a nonstatistically based VaR methodology known as historical VaR.
Historical VaR allows us to establish some notion of probability in regard to losses over a given historical time horizon (such as one year) simply by counting off the worst occurrences of the trading account until we have identified the desired percentage of largest losing trading days. For example, if last year contained 255 trading days and we were interested in determining the historical VaR for a trading account with a 95 percent probability or confidence level over a 24-hour holding period, we could simply count off the 13 days in which that account experienced its largest daily losses. This is because 5 percent times 255 trading days gives us roughly 13 trading days for the calendar year in question. As a result, if last year’s thirteenth least severe daily loss was $5 million and last year’s average daily trading result was a profit of $2.5 million, then the historical VaR for last year would be $7.5 million.
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