Скачать книгу

2.1 illustrates a typical drawdown, the maximum drawdown, and the maximum drawdown duration of an equity curve. I will include a tutorial in Example 3.5 on how to compute these quantities from a table of daily profits and losses using either Excel, MATLAB, Python, or R. One thing to keep in mind: The maximum drawdown and the maximum drawdown duration do not typically overlap over the same period.

      Defined mathematically, drawdown seems abstract and remote. However, in real life there is nothing more gut-wrenching and emotionally disturbing to suffer than a drawdown if you're a trader. (This is as true for independent traders as for institutional ones. When an institutional trading group is suffering a drawdown, everybody seems to feel that life has lost meaning and spend their days dreading the eventual shutdown of the strategy or maybe even the group as a whole.) It is therefore something we would want to minimize. You have to ask yourself, realistically, how deep and how long a drawdown will you be able to tolerate and not liquidate your portfolio and shut down your strategy? Would it be 20 percent and three months, or 10 percent and one month? Comparing your tolerance with the numbers obtained from the backtest of a candidate strategy determines whether that strategy is for you.

      Even if the author of the strategy you read about did not publish the precise numbers for drawdowns, you should still be able to make an estimate from a graph of its equity curve. For example, in Figure 2.1, you can see that the longest drawdown goes from around February 2001 to around October 2002. So the maximum drawdown duration is about 20 months. Also, at the beginning of the maximum drawdown, the equity was about $2.3 × 104, and at the end, about $0.5 × 104. So the maximum drawdown is about $1.8 × 104.

      How Will Transaction Costs Affect the Strategy?

      Finally, there can be a delay between the time your program transmits an order to your brokerage and the time it is executed at the exchange, due to delays on the internet or various software-related issues. This delay can cause a slippage, the difference between the price that triggers the order and the execution price. Of course, this slippage can be of either sign, but on average it will be a cost rather than a gain to the trader. (If you find that it is a gain on average, you should change your program to deliberately delay the transmission of the order by a few seconds!)

      As an example of the impact of transaction costs on a strategy, consider this simple mean-reverting strategy on ES. It is based on Bollinger Bands: that is, every time the price exceeds plus or minus 2 moving standard deviations of its moving average, short or buy, respectively. Exit the position when the price reverts back to within 1 moving standard deviation of the moving average. If you allow yourself to enter and exit every five minutes, you will find that the Sharpe ratio is about 3 without transaction costs—very excellent indeed! Unfortunately, the Sharpe ratio is reduced to –3 if we subtract 1 basis point as transaction costs, making it a very unprofitable strategy.

      For another example of the impact of transaction costs, see Example 3.7.

      Does the Data Suffer from Survivorship Bias?

      A historical database of stock prices that does not include stocks that have disappeared due to bankruptcies, delistings, mergers, or acquisitions suffer from survivorship bias, because only “survivors” of those often unpleasant events remain in the database. (The same term can be applied to mutual fund or hedge fund databases that do not include funds that went out of business.) Backtesting a strategy using data with survivorship bias can be dangerous because it may inflate the historical performance of the strategy. This is especially true if the strategy has a “value” bent; that is, it tends to buy stocks that are cheap. Some stocks were cheap because the companies were going bankrupt shortly. So if your strategy includes only those cases when the stocks were very cheap but eventually survived (and maybe prospered) and neglects those cases where the stocks finally did get delisted, the backtest performance will, of course, be much better than what a trader would actually have suffered at that time.

      How Did the Performance of the Strategy Change over the Years?

      Most strategies performed much better 10 years ago than now, at least in a backtest. There weren't as many hedge funds running quantitative strategies then. Also, bid-ask spreads were much wider then: So if you assumed the transaction cost today was applicable throughout the backtest, the earlier period would have unrealistically high returns.

      Survivorship bias in the data might also contribute to the good performance in the early period. The reason that survivorship bias mainly inflates the performance of an earlier period is that the further back we go in our backtest, the more missing stocks we will have. Since some of those stocks are missing because they went out of business, a long-only strategy would have looked better in the early period of the backtest than what the actual profit and loss (P&L) would have been at that time. Therefore, when judging the suitability of a strategy, one must pay particular attention to its performance in the most recent few years, and not be fooled by the overall performance, which inevitably includes some rosy numbers back in the old days.

      Finally, regime shifts in the financial markets can mean that financial data from an earlier period simply cannot be fitted to the same model that is applicable today. Major regime shifts can occur because of changes in securities market regulation (such as decimalization of stock prices or the elimination of the short-sale rule, which I allude to in Chapter 5) or other macroeconomic events (such as the subprime mortgage meltdown).

      This point may be hard to swallow for many statistically minded readers. Many of them may think that the more data there is, the more statistically robust the backtest should be. This is true only when the financial time series

Скачать книгу