The Gateway to Algorithmic and Automated Trading

Alphability

Published in Automated Trader Magazine Issue 06 July 2007

This issue of Automated Trader marks the launch of a new set of tradability statistics called Alphability. Andy Webb outlines some examples of their construction and their application as tools to expedite the development of automated and algorithmic trading models.


Alphability statistics are intended to provide an indication of the relative ease of capturing alpha from specific markets and time frames using generic categories of trading model. The two categories presented here are trend and reversal strategies. (Metrics and a database of matching engine rules for scalping and other 'order book' type strategies will be added later.)

In addition to the metrics published in these pages, more comprehensive Alphability statistics, including a larger range of time frames and volatility weighted scores, will shortly be available at www.automatedtrader.net. Automated Trader subscribers will also be able to download historical datasets from there.

Why?

The main motivation for introducing Alphability is the growing need among market practitioners to develop more models and to develop them faster. The objective is that Alphability metrics should assist by guiding practitioners towards the optimum marriage of market/time frame characteristics and model type.

Readers of Automated Trader have been increasingly telling us that the expanding availability and sophistication of financial modelling tools and financial data appear to have reduced the life expectancy of trading models. Easier is perhaps not the mot juste, but advances in modelling and testing tools have certainly streamlined the development process. Combining

this with the huge increase in the popularity of automated and algorithmic trading has inevitably driven greater interest in and adoption of such tools. However, this has in turn lead to greater competition for the same trading opportunities, which appears to be resulting in a compression in the timeline for capturing market inefficiencies.

In the past, a trader or quant might spend months building and testing a trading model, but at least had the reasonable expectation that (if robust) it would continue to capture alpha for a reasonable period of time. But in many cases that expectation is now looking far less reasonable. It is by no means unheard of for high frequency stat-arb programmes to have to recalibrate their automated trading models several times a day. But now it seems to be a case of more rapid wholesale deterioration that cannot be fixed by tweaking a few parameters. An intraday model that might have been good for two years' live performance five years ago might now be pushed to survive for six months. We appear to be entering an era of 'disposable models'.


Figure 1 - Daily HiLo Alphability DAX Sep 07

Another factor in the need for faster and more prolific model development has been the growing interest in using weak form alpha models for algorithmic trading. Here, the objective is not so much the outright capture of alpha, but the reduction of transaction costs. If a model can finesse the placement of a trade being entered on the basis of another decision mechanism (such as a fund manager's fundamental analysis) then every basis point saved feeds straight through to the trade's bottom line. For example, a weak form reversal model that only captures one or two basis points may be inadequate as an alpha model, but will add value as part of an algorithmic model by predicting shortterm peaks and troughs to optimise the timing of order slices.

What?

It should be stressed that Alphability metrics are just environmental statistics and not a set of trading models. Nor are they any sort of judgement as to whether a particularly market is 'good' or 'bad'. Instead, they provide historic measures intended to assist those building trading models/systems in determining which markets and timeframes are most favourably responsive to which generic types of model. Obviously, as the Alphability data are historic and market characteristics are not usually static, there is no guarantee that a market that responds well to, for example, a trend-following model today will do so tomorrow. Nevertheless, it is possible to infer general indications of the trading characteristics of markets and time frames and their interrelationships from the Alphability statistics and this will hopefully assist models builders in creating the appropriate types of model for the market or time frame concerned.

Trend Alphability

The Alphability stats for defining the 'trend friendliness' of markets are largely based upon determining the amount of noise around a hypothetical trend. For example, one of the simplest Trend Alphability metrics is the R2 (coefficient of determination) of a linear regression line plotted through the data points between the bars on which the low and high of a trading session were made (or the reverse if the high was made first). The calculation is based on the mid point of price bars in a variety of time frames.


Figure 2 - Daily HiLo Alphability FTSE Sep 07

Figure 1 shows the values for this metric for the DAX index future from late March to early July (spliced continuation contract rolled from June on June 15th). The high/low regression was plotted across five-minute price bars. Buying the low and selling the high (or vice versa) is obviously an idealised scenario but Trend Alphability gives an indication of the amount of noise around this largest possible movement of the trading session. Trend Alphability values also vary considerably among similar types of instrument; Figure 2 shows the same component for another stock index future - the FTSE - for the same period as the DAX in Figure 1. At 0.59 the average R2 for the period is appreciably lower than the DAX's 0.70. As is probably apparent from the chart, the variance of the daily Alphability metric is also considerably higher in the case of the FTSE at 0.078 versus 0.048 for the DAX.


Figure 3 - R2 to Return Ratio DAX Sep 07

Multiplying this daily Alphability metric by the high/low range for the day (expressed as a percentage change) gives a ratio of 'trendiness' to the maximum available reward. See Figure 3 for an example of this. The overall score is therefore obviously affected by both the size of the potential trend (the move from high to low) and the R2 of the linear regression. Therefore the overall score can be reduced if a major trend is offset by a high degree of noise, while a high R2 will be offset by a small daily range. For this particular variant of Trend Alphability, any score over 2 for more volatile instruments such as stock index futures typically indicates exceptionally benign conditions for a low frequency intraday trend following model. Any score between 1 and 2 still represents a reasonable environment. Below 1 (and especially below 0.5) intraday conditions would probably be best characterised as 'choppy'. Commensurate values for less volatile instruments such as bond futures are typically a third of those for stock index futures.

Reversal Alphability


Figure 4a - Trough Reversal (long entry)

Reversal Alphability follows similar general principles to Trend Alphability in that it provides a metric for the ease or difficulty of capturing a hypothetically optimal alpha. As the name implies, the differences lie in the generic types of model used.


Figure 4b - Peak Reversal (short entry)

One example of these hypothetical models uses a pair of very simple reversal patterns, illustrated in Figures 4a and 4b. The trigger value is the mid point of each bar, so for a long position the entry logic is a bar (Bar 3) with a mid valueless than the preceding and succeeding bars. In both cases the preceding and succeeding bars are descending/ascending, so in the case of Figure 4a the mid point of Bar 2 must be less than that of Bar 1, while the mid point of Bar 5 must be greater than that of Bar 4.


Figure 5

The metric is calculated by assuming that the model reverses to and fro between these signals and is always in the market intraday, but does not hold positions overnight. If a trough reversal is followed by more than one successive peak reversal, the first peak reversal is taken (and vice versa). The number of reversals in a day are calculated and divided into the sum of the percentage change of the moves from each reversal to the next. (From the low of each trough reversal to the high of each peak reversal for long positions, and vice versa for shorts.)

Figure 5 illustrates the reversal model on an intraday basis applied to five-minute price bars for just short entries on the DAX future (highlighted in red as in Figure 4b). The histogram shows the accumulated 'profit' and the overlaid red plus signs indicate the accumulated short trade count for the day. As can be seen, the market was essentially range trading on this day so the hypothetical performance was predictably good. This particular variant of Reverse Alphability operates on a narrower value scale than its Trend Alphability counterpart outlined above. A score of more than 0.4 (for stock index futures) indicates a very positive environment for

reversal models, 0.3-0.4 is still benign while scores below 0.3 (and especially 0.2) would be regarded as adverse conditions. As with Trend Alphability scores, the values for instruments such as bond futures are typically a third the size. (Online versions of Alphability will include volatility weighting to normalise these values.)

Again, it should be emphasised that (as with the daily high/low used in Trend Alphability) this example of Reversal Alphability is in no way intended as a functional trading model. It acts only as a mechanism for capturing the hypothetical maximum return for just one example of a reversal technique. Its limitations as a live trading model should be apparent; for example, the rules display a major 'peek ahead' in that for both long and short trades the return is calculated from the high/low of the third bar in the patterns when the actual formation of the patterns would not of course be confirmed until the fifth bar.

Alphability: Stock Index and Bond Futures Metrics Sep 07 Expiry


Figure 6 - Daily Trend Alphability : Stock Index Futures

Figure 7 - Daily Trend Alphability : Bond Futures

Figure 8 - Reversal Alphability : Stock Index Futures

Figure 9 - Reversal Alphability : Bond Futures

Future Expansion


The initial Alphability stats have been created in response to reader requests and discussions. For reasons of space, the data presented here are a relatively restricted subset of that which will be available online. The intention is very much that the future evolution of Alphability be driven by the readership of Automated Trader. Therefore, if you have any specific suggestions regarding instrument coverage, time frames or other enhancements, please contact the Editorial Director, Andy Webb