I recently listened to a podcast about one of the earliest human civilizations – the ancient Sumerians. Apparently, our system of minutes, hours, and days has been with us since the time of these ancient people, who developed it based on a simple base-12 counting system:

• There are three joints in each of the four fingers
• You can count twelve by tapping each joint in turn with the thumb of the same hand
• When you reach twelve, you hold up a thumb or finger on the opposite hand and start again
• When all five digits are outstretched, you’ve counted sixty – the number of seconds in a minute, and the number of minutes in an hour

The measurement of time is obviously a human construct. And our system for doing so is apparently based on human anatomy and then imperfectly aligned with our planet’s journey around its sun and rotation about its axis. Which all seems rather arbitrary.

This got me thinking.

Do arbitrary decisions about our frame of reference have implications for how we interpret the world?

That’s Interesting. But How Does it Relate to Trading?

Consider that a financial market consists of a series of events. For example, transactions where an asset changes hands (but also submitted and amended orders). These events are sequential in nature, that is, they happen one after another. But there are loads of them. An active market might have millions of transactions occur in a single day, and hundreds of millions in an entire year.

That poses a significant problem for an analyst. How can we possibly make sense of such an enormous amount of data in an efficient and meaningful way? Of course, it is possible to analyze a market on an event basis (that is, tick-by-tick, or order-by-order), but such analysis requires significant computing power and is largely impossible to inspect visually.

The familiar answer is that we typically group events into categories, summarize or report their most interesting characteristics, and then analyze these summaries rather than the events themselves.

Typically, we do this by grouping events by time, and then reporting some summary data that describes the group as a whole.

That, of course, is the familiar Open-High-Low-Close (OHLC) bar or candle that we see in the typical price chart.

We could also report the mean price of all the transactions if we wished, as well as any other statistical properties of interest.

Consequences of Summarizing

Consider what happens when we use summary data in our analysis. Let’s start with an OHLC bar from a daily chart. From potentially millions of events that occurred during the day, we derive four values: the price of the first and last transactions of the day, as well as the highest and lowest prices of the day. That’s useful, but it also results in an information loss.

For example, we might be able to infer possible evolutions of price during the day from the shape of the bar, but we can’t be sure exactly how events unfolded. OHLC bars also summarise the overnight session into two data points – the close of one bar and the open of the next. But again, we don’t get any detail.

One consequence of this is that simulations that rely on summary data have imperfect information. They may need to rely on assumptions.

For example, say we had a trade in the market, and both the stop loss and take profit levels of the trade were within the high-low range of a particular bar.

Which was hit first?

Thanks to the information loss associated with summarizing our data, we must make an assumption, which has a (potentially huge) impact on the simulation results and their accuracy.

Also, consider the open-close boundaries of our OHLC bar. In the 24-hour currency and cryptocurrency markets, when does a daily bar begin and end?

That decision directly impacts the OHLC data that we use in our analysis, and by extension, the results of that analysis.

This concept also extends to intra-day time periods.

For example, why do we typically summarize hourly data into hours that start and end neatly on the hour? Is there some principle related to the underlying market phenomena guiding this decision, or is it something that we have taken for granted without a lot of thought? What impact might this have – if any?

Shifting the frame of reference to our advantage

One consequence of the arbitrary nature of our frame of reference is that we can potentially pick a different arbitrary frame of reference to test various hypotheses or even to generate more data.

For example, say we use hourly price data in order to research a trading idea. We think we’ve found evidence of an edge. We can test the robustness of that edge by creating hourly bars that are offset by some number of minutes. If the edge is real, it should still show up on the offset data.

Conclusion

If there’s one thing I’ve learned about researching the financial markets, it’s that assumptions should always be tested.

Some assumptions are obvious – if I use closing prices in a backtest, then I’m assuming that I got filled at the closing price. If I use a fixed spread in calculating trading costs, then I’m assuming that it’s a reasonable estimate of the spread at the time I trade. Whether these assumptions actually matter is context-dependent.

Some assumptions are less obvious, but still very real. For example, if I use walk-forward optimisation, then I’m assuming that there’s some level of autocorrelation in the optimal parameter set.

There are other assumptions – such as our use of hours, minutes, and seconds to summarise price data – that are so fundamental to our view of the world that we don’t even realise we’re making them. Thinking about these assumptions can not only lead to deeper insights into the nature of the markets but also reveal creative research techniques.