Such insanely complicated rules are almost guaranteed to fail.
They are more likely to be over-fitted ; remember this means they are closely adapted to historical market movements, making them less robust if the future isn’t exactly like the past. They are very unlikely to meet the key characteristics I look for in a trading rule, which I outlined in chapter five: objective , simple , explicable , an d intuitive .
It is better to stick with simple intuitive rules, and to use several of these rules rather than a single, insanely complicated, rule. This chapter will explain how to use multiple trading rules to decide when to open positions, in addition to the single 16,64 moving average crossover rule used in the Sta rter System.
The case for diversification of trading rules Why are multiple rules better than one As with instrument choice there is no strong evidence that any particular trading rule is better than another. Figure 20
illustrates this. The six boxes on the left-hand side show the Sharpe ratio of the moving average cross over rule (MAC) introduced in chapter five for different crossover lengths, whilst the other seven boxes are for new rules which I will discuss later in this chapter. Remember the overlapping boxes and whiskers mean that we can’t be confident that one rule is significantly better t han another.
Figure 20: Comparison of Sharpe ratios for various trading rules If additional rules don’t provide higher returns, then why woul d we bother?
In fact, the logic for adding multiple trading rules is the same as for trading multiple instruments: they provide diversification
. The Starter System’s moving average crossover (MAC) 16,64 rule won’t always work. Sometimes markets will show clear trends lasting several weeks that the MAC 16,64 rule is looking for, but most of the time they won’t, and then other rules will com e into play.
What is the value of adding new trading rules?
In chapter seven I showed you could significantly improve the Starter System by taking one simple trading rule and applying it to many different instruments. This is a purely mechanistic task which doesn’t require much skill or intelligence. You would expect there to be much more value in the more creative and difficult task of finding new tr ading rules.
As figure 21 shows, there are indeed some benefits from adding trading rules. The first box on the left-hand side of this new figure 21 assumes we are trading the Starter System: a single
instrument, with one trading rule. This has a Sharpe ratio (SR) of 0.24. Now suppose we pick a randomly selected trading rule ¹¹¹
to add to the Starter System opening rule, and trade with both rules. Doing this improves our SR to 0.27. Adding a third rule improves it further, ¹¹² and so it continues. It’s clear that adding trading rules improves the expected performance of a tra ding system.
Figure 21: Sharpe ratio as trading rules are incrementally added But let us look more closely and contrast the improvements in figure 21 with those in figure 19 (from chapter seven, which showed the effect of adding more instruments). In table 47, I compare the increases in average Sharpe ratios for the two figures.
Table 47: Relative improvements in Sharpe ratios are higher when adding instruments than when adding trading rules Column A Sharpe ratios from figure 19, and column B fro m figure 21.
There is clearly more diversification from adding just a few instruments compared to the same number of rules. Going from one to two instruments improves the SR to 0.30, whilst moving from one to two trading rules results in a more modest rise in SR, to 0.27. The relative improvement from adding rules also tails off more quickly than the benefits from adding instruments. With 19
instruments we have a SR of 0.55, more than twice the performance of a single rule. But with 19 trading rules the Sharpe ratio i s just 0.36.
So, adding instruments is better than adding ope ning rules .
However, adding rules doesn’t require more money, whilst adding multiple instruments to the Starter System usually bumps up your minimum capital requirement. My advice is: first add as many instruments as you can afford to, given the capital you have available, and then consider adding tr ading rules.
My suite of trading rules
There are thousands of ideas for trading rules out there in books, and on the internet. But it’s difficult to sort the usable wheat from the vast quantity of chaff. To get you started I’ve included some more trading rules in this section. Like the moving average crossover, these are trading rules I use myself.
Although I won’t show you the data (to avoid making this book even longer), I’ve already checked that there is no evidence that any of these rules should be used on one instrument rather than on another. ¹¹³ At this stage I won’t be offering any advice as to which rules you should include in your system. That will come later in the chapter.
More moving average crossovers
In chapter five I introduced the general form of the moving average crossover rule, and then explained why I chose one specific variation for the Starter System: the 16-day moving average minus 64-day moving average. Depending on which instruments you are trading, some of the faster variations might be too expensive to trade (2 & 8 days, 4 & 16 days, 8 & 32 days).
I also said that the slower moving average pairs probably trade too infrequently (32 & 128 days, and 64 & 256 days).
However, it still makes a lot of sense to combine several moving average crossovers. By adding both faster and slower variations you can keep your expected number of annual trades – and also costs – at about the same level, whilst benefiting from the diversifying power of multiple rules. I’ll discuss how this is done later in the chapter.
Breakout
Consider the chart in figure 22, which shows crude oil from 2 010
to 2016.
Figure 22: Crude Oil (2010–2016)
Until late 2014 crude seemed to stay within a tight range , between $80 and $120. I started trading crude, amongst other instruments, with my own money in April 2014. Great timing because the price broke out of its range and then collapsed. My short position in crude was nicely profitable.
This idea of a breakout from a range is a classic trading strategy. There are numerous ways to define a range, and to determine when a price has broken out of a range. I use the following definition, where P t is the pric e at time t : Formula 28: Breakout calculations
Rolling maximum over last N days, R MAX N = Max(P t , P t−1 , P
t- 2 , … P t−N+1 )
Rolling minimum over last N days R MIN N = Min(P t , P t−1 , P t−
2 , … P t−N+1 )
Rolling average over last N days R AVG N = (R MAX N + R MIN N ) ÷
2
Scaled price in range = (P t – R AVG N ) ÷ (R MA X N – R MIN N ) The scaled price will vary between +0.5 (if the current price is at the top of its range) and –0.5 (if the price is at the bottom
of the range). Because I like to catch breakouts early, I will open trades if the scaled price is greater than zero (i.e., the price is greater than the average, which would be a long), or lower than zero (the price is lower than average : a short).
This makes the rule work a little differently from breakout trading strategies you might have seen elsewhere. In particular there is nothing special about the price reaching the edge of its previous range. Arguably ‘breakout’ is the wrong name for this rule, but I couldn’t think of a better one.
The breakout rule has a single parameter, N . If N is small then we look at the price range just for the last few days. We will identify lots of breakouts, but the large number of resulting trades could be expensive. Conversely if N is large the rule will look further back into the history of the price, and there will be fewer trades. We’ll have fewer opportunities, but it will be cheap er to trade.
Figure 23: Crude oil with rolling minimum, maximum and average values
I’ve added the rolling minimum, maximum and average values to the price of crude oil in figure 23, using N =320 (since the N in my trading software is measured in b
usiness days, this is about 15
20
months). ¹¹74 The wiggly line is the original price, and the two ranges are in grey; halfway between them is the average. Remember the rule will go short if the price is below the average line and go long when it is abo ve the line.
The price is mostly near the bottom of the range from mid-2014 to the end of the year: a clear signal to go short. Here is my calculation for the breakout signal on 13 August 2014: Rolling maximum R MAX 320 = 107.78
Rolling minimum R M IN 320 = 98.76
Rolling average R AVG 320 = (R MAX 320 + R MIN 320 ) ÷ 2 =
(107.78 – 98.76) ÷ 2 = 103.3
Scaled price in range = (P t – R AVG N ) ÷ (R M AX N – R MIN N )
= (100.3 – 103.3) ÷ (107.78 – 98.76) = –0.33 [Sho rt Position]
As we saw in chapter five, when considering the choice of moving average lengths, selecting the right N involves considering both expected pre-cost returns, and costs. Figure 20 at the start of this chapter showed there is no evidence that any single value of N is significantly better than another on a pre-cost basis. That leaves us with just costs to consider. Table 48 has all the relev ant numbers.
Table 48a: Indicative trading costs for different length breakouts, in risk-adjusted units
• An instrument / rule combination is too expensive to trade: the cost is higher than the speed limit of one-third of pre-cost Sharpe ratio shown in the se cond column.
Total cost is H + (TC×T) where T is the number of trades per year (first column), TC transaction cost per trade, and H annual holding cost. All costs are calculated in appendix B.
Table 48b: Indicative trading costs for different length breakouts, in risk-adjusted units
• An instrument / rule combination is too expensive to trade: the cost is higher than the speed limit of one-third of pre-cost Sharpe ratio shown in the se cond column.
Total cost is H + (TC×T) where T is the number of trades per year (first column), TC transaction cost per trade, and H annual holding cost. All costs are calculated in appendix B.
I’ll explain exactly which value(s) of N you should use later in the chapter. Spreadsheets which help you to implement this, and all the rules in this book, are available from the book’s website: systematicmoney.org/levera ged-trading .
Carry
The moving average crossover and breakout rules work best when prices trend strongly in one direction or another. Carry is a trading rule which makes a profit when nothing happens. Carry is defined as the return that you expect if asset prices remain stable . We have already learned about carry in chapter one. You may want to re-read that section before continuing.
For physical products like margin trades and spot FX the carry is equal to any interest or dividends we receive, less financing and borrowing costs. For derivatives like futures, CFDs and spread bets, the carry is received through the price of the derivative changing even when the spot price re mains fixed.
For the carry rule we define the carry return as the expected annualised percentage return on a long position if the underlying price remains unchanged . The underlying price is the actual price for physical products, and for derivatives the price of the product they are based on. If we expect a positive carry return then we would go long (to capture the positive carry). If the carry return is negative then we would go short (which should be profitable if carry is negative for a lon g position).
The exact calculation of carry is different depending on which leveraged product you a re trading.
Equities bought with margin
The trading rule expects the carry return to be identical in magnitude for both long and short positions. This is fine for derivatives, but for physical products it will not be the case because of the financing spread we learned about in chapter one.
To get around this we calculate carry for physical products by taking an average of (i) the carry for long positions, and (ii) the carry for short positions with a minus sign. Hence, the carry calculation excludes the funding spread, as this is already accounted for in our holding cost c alculations.
Example: S&P 500 SPY ETF, bought with margin We would go long S&P 500 because the carry return is (jus t) positive.
Equities: undated contracts for difference (CFDs) or spread bets Spot FX
Here is an example, for AUDUSD. With a long position in AUDUSD we make money if the USD depreciates and AUD gets stronger.
Therefore, we are effectively borrowing in USD, to dep osit in AUD.
This is negative, so we’d have a short positio n in AUDUSD .
Derivatives: Futures, and CFD or spread bet based on futures To calculate the carry for derivatives we compare the price of the derivative with the price of something else that we expect the derivative price to converge on. There are three different methods, depending on what other prices ar e available.
Method one: Relative to nearer contract price To calculate the carry for a future, or another derivative product based on a future, we compare the price of the contract we are trading with a near er contract: Sharper eyed readers may realise that we know whether to go long or short by step three of these calculations (spot level minus spread bet level). Nevertheless, it’s important to know how to work out the expected annualised return, since we’ll need to use that in part four o f this book.
Example: Corn future
Negative carry return, so we go short corn .
To calculate carry using method one we need to ensure that we aren’t holding the nearest contract, since this method only works if there is a nearer contract relative to the contract we are trading. This is why back in chapter six I rolled corn from December 2018 to December 2019, in late September before the September 2018 contr act expired.
Method two: Relative to spot price
If you can only trade the nearest contract you obviously can’t use method one. If a spot price is available for your instrument, then you can compare the dated price to the spot price.
Example: Dated gold spread bet based on future Carry return is negative so we’d go short gold.
Method three: Relative to spot price
Sometimes no spot price is available. In that case you can use the following method, which assumes you can get the same amount of carry on the first two availabl e contracts: 20
Example: Euro Stoxx 50 based on future ¹¹75
We are trading the nearest Euro Stoxx (September 2018). The next contract was De cember 2018.
We’d go long Euro Stoxx when using the carry rule.
Trading costs
The trading costs of the carry rule are similar to those of the 16,64 moving average crossover used in the Starter System. As table 49 shows, that means we can trade it with all the instruments I used in chapter six.
Table 49: Estimated risk-adjusted trading costs for carry strategy
Values shown in body of table are total cost calculated as H +
(TC × T) where T is the number of trades per year (first column), TC is the transaction cost per trade and H is the annual holding costs; all costs are risk-adjusted. T has been estimated as an average over back-tests for all the instruments in my own data set. Costs calculated using the formulas in appendix B.
How do we use multiple trading rules?
There can only be one opening rule...
How can we use multiple opening rules in the Starter System? For example, suppose that we are trading gold using three rules: the moving average 16,64 rule from the Starter System, the carry rule I introduced in this chapter, plus one of the new bre akout rules.
If all three rules think we should go long, then it’s a slam dunk: we should buy the market. But what if two rules think we should go short, and the other rule wants to go long? With more rules the number of permutations gets increasingly mi nd boggling.
There are a few possible solutions here, but only one which I recommend:
I discuss how we calculate weights for trading rules later in the chapter.
Improvement in Sh
arpe ratio
Back in chapter four I explained that the more optimistic your expectation of Sharpe ratio, the higher your account level risk target could be. In chapter seven I used this result to increase the risk target on trading systems which had more than one instrument. Similarly, adding more trading rules also improves our expected Sharpe ratio. With more trading rules we can use a higher risk target.
Table 50 shows the recommended account level risk target as more trading rules are added to the Starter System. As I did for instruments, I started with the improvement in Sharpe ratio as trading rules are added, from figure 21. Then I halved the Sharpe ratio to get a theoretical risk target. Finally, I came up with some recommended risk targets, which are a little more conservative than the theoret ical values.
Table 50: Account level risk target when trading rules are added to the Simple System
Expected Sharpe ratios (A) from figure 21. Theoretical risk target (B) is half expected Sharpe ratio. Recommended risk target is a conservative target derived from the theore tical value.
What if you are fortunate enough to have both multiple instruments and multiple rules in your trading system? You need to multiply the proportionate increase in Sharpe ratio for instruments (from table 44 or 45 in chapter seven) by the relevant ratio for trading rules (above in table 50). I’d also recommend that you never use an account level risk target higher than 30%, to avoid your leverage getti ng too high.
So, for example, suppose you are trading three instruments which are drawn from multiple asset classes, using five different trading rules. From table 44, which is relevant for multiple asset classes, the recommended account level risk target (column D) for three instruments is 14%. This is a proportionate increase on the Starter System of 14% ÷ 1 2% = 1.1667.
From table 50 the recommended account level risk target for five trading rules is 15%. Proportionally the increase is 15% ÷ 12% =
1.25. If I multiply the two proportionate increases together, I get 1.1667 × 1.25 = 1.458. To find the recommended risk target I multiply this by the Starter System target: 1.458 × 12% = 17.5%, or 18% rounded.
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 18
