Position holding time and volatility of returns

In this article we’re going to discuss the relationships between volatility of returns, average trade value, positions holding time and eventually to come to a conclusion about potential tradability of strategies depending on the aforesaid metrics. The research was made for cash fx markets, although it may be relevant to any other highly liquid market with large daily turnover.

Developing a robust trading strategy is typically a problem of finding a trade-off between a number of factors which may have a major impact onto the performance metrics. This trade-off is inevitable because each tradable opportunity in the market is not 100% the same as its predecessor, and therefore we cannot suggest a set of trading rules which would allow us to enter and exit a trade with 100% accuracy (read: buy at the very bottom, sell at the very top of a price movement). It is always possible that an eventually good trade starts with a drawdown, and it is also possible that a trade which starts with a nice run-up eventually is closed with a loss. Thus development of a trading strategy assumes that there is a certain compromise between winning and losing trades, between large and small drawdowns and run-ups.

Let’s consider an example. In Fig. 1 we can see an example of a trade which was initiated almost at the exact bottom, went into the positive zone almost immediately after the entry and was liquidated before any more or less noticeable drawdown might develop. However in hindsight it’s clear that this trade should have been held for a longer time, to gain much more substantial profit.

Fig. 1. Successful trade with a minimal position holding time. Price continues to go in the same direction.

On the other hand in Fig. 2 we can see that exiting a trade after only a brief period of time could be also quite beneficial, as in this case it prevents a far more considerable drawdown which  might have developed in case we held the position for a longer time.

Fig. 2. Unsuccessful trade with a minimal position holding time, price continues to go down.

And finally Fig. 3 presents a somewhat controversial picture where on the one hand exiting a position quickly indeed reduces the loss, but on the other hand staying in the same position for a longer time might have led us to at least a breakeven. By the way, this is the most typical situation of a “trader’s repentance”, when traders start to blame themselves for exiting a position prematurely, regret about missed potential profits and start to reopen positions which in turn often lead to another loss – but it’s another story which is beyond the scope of the present research.

Fig. 3. Unsuccessful trade with a minimal position holding time, price reverts to breakeven.

Thus we can see that using the same rule or set of rules for entering and exiting trades at first glance provides a somewhat controversial picture, and intuitively asks for a certain flexibility: say, in certain cases to indeed hold the position for a longer time, and in others to close it quickly to avoid unnecessary losses.

However such a problem can hardly be solved since price movements are non-stationary processes caused by a multitude of factors, most of which are unpredictable in the sense that one cannot successfully predict each price movement based only on past data. Therefore a robust trading strategy is always based on statistics: in simple terms, if we have more winners than losers and if the average winner is greater than the average loser then in the long run such a strategy will generate some profit. The question is only about the costs of generating this profit.

The structure of these costs consists of static costs, such as trading platform costs, spread and broker commissions, and dynamic costs, which can generally be attributed to systemic drawdowns. By systemic drawdowns we here assume those caused by trades closed in the negative zone, regardless of any commissions and/or any other static costs. In other words, we consider an idealistic picture where we were able to enter and exit at the very price we saw, and then subtract additional costs associated with the reality of the market.

Intuitively it’s clear that static costs are more or less constant (more or less – because spreads may vary), thus the volatility of returns will mostly be affected by the distribution of systemic drawdowns. Also it is intuitively clear that holding a position for a shorter time could reduce these drawdowns as in this case we close losing positions quickly, without allowing them to develop into even larger losses. Let’s see if this intuitive guess is correct and there is any relationship between the time in a position and the systemic drawdowns (volatility of returns).

First let’s consider a primitive strategy which opens a long position when price goes down and a short position when price goes up (a kind of a simplified mean-reversion strategy) and uses 1 minute resolution. In this case we seldom hold positions for more than 10 minutes, and we can expect the drawdowns to be rather small. Fig. 4 illustrates the theoretical performance of such a  strategy working in EURUSD between 2012 and today, and we can see that indeed the volatility of returns is indeed very low. If we consider numeric metrics, we have here an average positive monthly return of about 0.8% with an average monthly loss of 0.5%, and we can see no two months in the negative zone in a row – which means we can expect the following month to be always positive. An overall return of about 27,000 pips and more than 600 thousand trades, which might be considered as a sufficient statistical dataset to prove this as quite a stable and consistent growth rate.

Fig. 4. Theoretical returns of a strategy with very short position holding time.

Does it look like we have found the ultimate winning strategy and don’t have to continue the research? We shouldn’t forget that besides dynamic costs which are very efficiently reduced in this strategy there are still static costs. Since static costs are something we can’t really reduce, at least substantially, it is important that the average trade generated by the strategy exceeded them, and the more it exceeds these costs, the better. 

The average trade value generated by this strategy is the very bottle-neck here. On average such a strategy yields only 0.05 of a pip – and the broker commission in the best case could be as low as 0.1 pip. So, even disregarding the spread which also adds to the costs, this strategy is unable to even cover broker commissions – and thus in real world such a strategy is not tradable.

Let’s consider another example, a strategy which holds positions for quite a considerable time, sometimes for a number of days. The performance chart shown in Fig. 5 shows that the volatility of returns generated by this strategy is much greater than that of the previous one.

Fig. 5. Theoretical returns of a strategy with long position holding time.

Speaking numbers, we have an average positive monthly return of about 0.47% and an average monthly loss of 0.46% – so, this strategy may generate consistent profits only because of the greater number of winning trades/months than losing ones. However the total net return generated within the same period of time (2012-2018) is very similar to the first strategy, and given an average trade of over 33 pips it’s clear that this strategy is quite tradable in real life even if broker’s commissions are 1 pip, and the spread exceeds a typical value of 1-2 pips. The disadvantage here is in the distribution of returns over time – for this strategy it is quite normal to generate negative returns for 2 and even 3 months in a row. Therefore investing with such a strategy would require quite some patience to allow it to recover from drawdowns.

Looking at these two examples we may come to an empirical conclusion that the larger the holding time of a position, the greater the volatility of returns – but at the same time the greater the average trade. To prove or disprove this hypotheses let’s consider the third strategy which holds positions for several hours – something in between minutes in the first example and days in the second one.

From a chart shown in Fig. 6 it is clear that the volatility of returns here is more significant than in the first example where positions are held for some minutes, but lower than that of the second strategy, where positions are held for days.

Fig. 6. Theoretical returns of a strategy with medium position holding time.

To get to numbers, we have here an average monthly return of about 0.24% and an average monthly loss of 0.11%. In absolute values these numbers are smaller than the respective metrics of the first, 1-minute strategy, but the ratio between them is quite similar, and it exceeds the corresponding ratio of the second (day) strategy almost 2 times. At the same time the average trade value of this strategy is above 7 pips, which definitely makes it tradable with most STP or ECN brokers. Besides that, quite similar to the first strategy in our overview this one also very seldom generates negative returns for more than 1 month in a row, which makes it really attractive for most investors. Of course there is no free lunch here as well – the absolute return falls to slightly above 7000 pips versus 23000 pips generated by the previous strategy which holds positions for longer time (days).

Now we can briefly summarize the results. The table below features key metrics of the three strategies considered above with their theoretical performance generated between 2012 and today.


Let’s make some conclusions.

First, we can clearly see that if we reduce the holding time below a certain threshold we cannot generate positive returns because the average trade value falls below the absolute minimum of trading costs. Perhaps we could speculate about reducing these very costs, but for the majority of buy-side traders it doesn’t seem to be possible.

Second, increasing the holding time we increase the average trade value and the overall net return, but sacrifice the recovery rate (the time required to recover from a drawdown). Therefore there is no universal advice as to which kind of strategy to employ: those running for greater absolute returns may want to follow a strategy which holds positions for days, and be prepared to have sufficient patience to allow it to recover from drawdowns. Those who prefer more consistent returns may want to use strategies with shorter holding time, which reduces the time in a drawdown, but be ready to miss some potential profits if we talk about absolute numbers.

Lastly we need to note that all the aforesaid is relevant to trading without reinvestment. This means that in all theoretical examples shown above we assumed that we traded the same position size all the way from beginning till end. In reality of course we may take advantage of reinvestment, and it may substantially change the picture in favor of shorter-term strategies. We will consider it in one of the future articles.

— Alex Krishtop

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