Progressive Tradescapes (White Paper)
Sequential Time Tradescapes
There is an obvious extension to tradescapes. While we do not assume an entity's behavior is constant across time, it is a practical consideration to create an integrated historical picture and to view that as the expectation representative of that history.
In the signal processing world, a signal is considered stationary if its harmonic components remain of the same amplitude and frequency across time. That will not happen with real-world time series.
There will be periods in time where an entity's performance is dramatically better than a long term tradescape would indicate, and similarly there will be periods where it is far worse. In many instances, that is nothing more than a mirroring of what is happening in the overall markets. In other instances, it may be an entity-specific phenomenon.
Clearly the price of many entities are closely linked to the overall state of markets, national and global.
We look at reward to pain (or risk) ratios. There will be periods where the measure of reward will be diminished, where prices are generally contracting rather than expanding across most market entities. There will be periods where the measure of pain will be increased, where volatility is high and drawdowns are deep and prolonged. Not surprisingly, these tend to coincide. As a result reward to pain ratios will drop dramatically during the weaker periods and they can skyrocket during very strong periods.
While it can be instructive to see how well an entity has performed in different time periods, it is important to keep in mind that constancy is not likely to be seen in entities that tend to somewhat track the overall market.
Sequential time tradescapes, or progressive tradescapes, are individual tradescapes computed for different segments of time.
Once again we will use AAPL, Apple Computer, as an example. Here we see AAPL divided into four periods, each just under four years. The sequence includes the Internet bubble burst and the period where AAPL nearly folded, and the financial meltdown of 2008-2009. Clearly these four periods are sharply different. We scale the tradescapes to plot only those regions of the trading landscape where there is more reward than pain using the RRt metric.
The worst period is the 2001-2004 time. Prior and after were appreciably stronger. The most recent four years have been extremely strong with longer term trades.
If you look at the EM length 20 in all four plots, say at a lag fraction of 0.8, there is certainly a variation in reward-pain across time, but it is far smaller than one would see at different time horizons or lag fractions. A trading signaler operating in that range would have performed with something resembling constancy over these 15.5 years.
If you look at the EM length 60 in all four plots, say at a lag fraction of 0.9, there is a vast variation across time, from more pain than reward in the second time period to an exceedingly high reward-pain in the current time period. Financial times series are dynamic entities, ever shifting, and there will be periods where certain signalers will work poorly, and others where they can work remarkably well.
The Signaling Contribution
progressive tradescapes are particularly useful in testing for robustness in terms of the benefit derived from signaling on the order in the price movements of an entity. In the previous plot, we used a fixed scale for the RRt reward-to-pain performance metric. Only values where the reward exceeded the pain were plotted using the scaling option used. When searching for robustness across time, it can be more important to rescale the surfaces to have the threshold for plotting occur at the RRt for the underlying in each of the segments. While this does mean that each individual plot will not be directly comparable in terms of the gradient used for the contour or surface, this does make it possible to see where the signaling is generating a net positive benefit.
Ideally, we would like to see at least one time-horizon and lag region showing a strong benefit in each of the progressive tradescapes. We may not net more reward than pain, and we may not even net a profit, but we want the signaling to improve matters across all time segments. A tradescape finds the tradable order in a time series. For the purpose of robustness, we would like to see common zones where that order is effectively signaled. If we can find that, we know that trading a given time horizon, at a certain lag, and with an assumed accuracy, would have resulted in a system that consistently functioned well across time.
This is the progressive tradescape where the individual AAPL tradescapes are scaled so that a surface is only shown where the signaling improves upon the RRt of the underlying. The odd appearance of the fourth panel (the most recent four years) is due to the stratospheric growth AAPL has experienced in contrast to what is only modest pain by comparison. In our experience, it is an effort to design a signaling system where one realized three times the measure of reward relative to pain. In this time period, Apple Computer offered more than nine times reward to pain, and with no signaling required. It it is not surprising that no shorter term signaling can improve upon such. We thus look for consistency in the other three four-year time segments, and we can certainly find it. While there is no one single time horizon and lag that is optimal across all time periods, there is a very good reward-to-pain improvement common to all three periods.
The Quest for Robustness
If we do progressive tradescapes using shorter time periods, we would expect to see a much greater variability. We would expect to see one consist of much of the Internet bubble, another with much of the financial meltdown, and so on. The time period of each tradescape is now less than two years:
Here we plot only those zones where there is more reward than pain. This illustrates why trading system designers are constantly in dread of changing dynamics in overall markets, and in that of the entity being traded. Few systems are robust enough to win consistently across all conditions and states of the market.
What is immediately apparent is that five of these periods represent a very positive period for AAPL, and for the US markets in general. If one were to segment the market by sentiment, note that you can find common robust zones in the first, second, fifth, eighth, and ninth periods. Those same zones show little in the third, fourth, sixth, and seventh periods. The concept of partitioning time by sentiment prior to the primary signaling is addressed by sentimentscapes.
How Hard is It?
Let's look at SPY, the ETF that tracks the S&P 500 index. In the previous AAPL progressive tradescape, the lower Z in the gradient was 1, meaning that any reward to pain where there is more pain than reward shows as the gray background. Here we will change the lower Z in the gradient to 0, meaning that we will plot anything with a profit. The gray background corresponds to losses.
Bear in mind that the EM algorithm is designed to be as close to an ideal signaler as possible, and to respond as favorably as possible to order within the movements within the time series. Real-world signalers are, in general, not likely to do as well. Note also that these are long-only tradescapes. One has to mine an actual sustained growth in price in order to book a profit. In certain bleak market periods, that is next to impossible.
Indeed, the Internet bubble and financial meltdown periods are just that for SPY. No matter how well crafted any long-side signaler might be for that kind of market period, the net outcome is likely to be a loss over these periods.
If you look at the periods where there is a positive reward-pain, try to select a time horizon and a lag where there is a good reward-pain. It is hard even when only very positive periods are chosen. Clearly, this entity is a moving target. No matter how good one's signaling algorithm may be, if it is attempting to signal and book some portion of an upward price trend, it is going to be a nightmare.
Is Short-Side Trading any Easier?
Tradescapes measure the ability of an automated signaler to trade an orderly trend in a time series. Short-side trading is usually not suited to the trend trading paradigm since the panic aspect usually produces swift chaotic drops, and there are often sharp turns when the mood changes, as when the quarterly results suddenly reflect a favorable turnaround. It is not unusual on the short side to enter a position only after most of the drop has taken place, and to close a position after most of any given drop has vanished.
If we look at SPY with short-side progressive tradescapes, we do indeed see that we could have fared well during the bubble burst and especially during the financial crisis. In most periods, however, even with this very accurate signaling, the downside movements were too chaotic to signal for a profit across a number of the slightly less than two year periods.
On the short side, not only is it very difficult to select a robust time horizon, but in most periods nothing that one might do to trade order results in any profit at all.
This is also a good example of an overall market whose sentiment varies greatly from positive to negative across different time periods. A sentiment-augmented signaling system usually adds a very significant intelligence to the signaling, changing directions or taking one out of the market when the prevailing sentiment does not support the direction of a trade.
Progressive Tradescapes and the "Real" Pain of Trading System Design
With the ability to see what an ideal but lagged signaler can do, in approximating the best of what one might see in the real world, tradescapes illustrate quite well the real but hidden pain associated with trading systems. When will any given system cease to trade profitably? When that shift in dynamics takes place, how can one be certain a given system has outlived its useful life?
Here is a long-only 10-year tradescape for AMZN, the RRt lower gradient scale again set to 0 to show all trading where any profit at all is realized.
If you select a zone that you happen to like, say EM length=10 and lag fraction=0.8 and you design a signal that successfully realizes that, a progressive tradescape sequence will show you what that choice would have meant across time. Here are the long-only set of progressive tradescapes for AMZN, each just under two years time.
We thus conclude this discussion on a positive note. If we had been able to build a signaler with approximately the same 0.8 lag and full accuracy of the EM signal used in the tradescapes, at an effective time horizon of EM length 10, we would have seen a positive outcome across all nine of the periods. Some might have been weaker, some much stronger, but overall, such a choice would have have offered robustness across across time.
While it would certainly be welcome if the progressive tradescapes morphed smoothly from one time period to the next, clearly this AMZN example shows that to be unlikely. Sentiment doesn't smoothly change across wide time periods. It tends to change abruptly. That is why adjacent periods can look so very different in a progressive tradescape sequence.