Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders
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Instrument ri sk 3% a year
Price $119
Value of a point 0.01
Minimum and incremental trade size $1 per point Our notional exposure target, using formula 29, would s tart out at:
Notional exposure = [(forecast ÷ 10) × risk target % × capital] ÷
instr ument risk %
= [(10 ÷ 10) × 12% × $45,000] ÷ 3 % = $180,000
To work out the CFD bet per point we use the appropriate version of formula 20 introduced earlier in the book: CFD bet per point = (notional exposure × FX Rate × point s ize) ÷
price
= ($180,000 × 1 × 0.01) ÷ 119 = $15.13 per point = $15 per point (rounded)
Now, imagine that there was a market panic of a similar scale to 2008, where equities were brutally crushed and bonds rallied.
This would be great for our long bond position. But in those circumstances the risk of the US 10-year bond would also skyrocket. If the instrument risk rose to 9%, trading capital
rose to $50,000, and the forecast remained at 10, and we recalculate what our notional exposure targe t should be: Notional exposure = [(forecast ÷ 10) × risk target % × capital] ÷
instr ument risk %
= [(10 ÷ 10) × 12% × $50,000] ÷ 9% = $66,666.67
So, our current position (with a notional value of around $180,000) is nearly three times larger than it should be, and hence nearly three times riskier! This has been caused by the threefold increase in risk, slightly offset by the rise in capital. We need to reduce our position si gnificantly.
Adjusting position size without incurring heavy trading costs Your estimate of instrument risk and your trading rule forecast will change daily. Does this mean you should make small adjustment trades to our position every day? It’s a nice idea in theory, but every time you trade you lose money: the execution spread, and possibly commissions.
To avoid this, it’s necessary to avoid making frequent small adjustments, and only trade when your position is way off target.
To do this you need to compare your ideal notional exposure to the current exposure implied by your position. If these differ by more than 10% of the average exposure , then a trade is required.
Let’s look at the calculations in more detail.
First you need to calculate your ideal notional exposure using formula 29, on a daily basis:
Ideal notional exposure = [(forecast ÷ 10) × target risk % ×
capital] ÷ instr ument risk %
Next, work out the current exposure in home currency that is implied by the current position. If I rearrange the various versions of formula 20 I used to work out how much to bet, then I get these formulas for curre nt exposure: Formula 30: Calculating exposure, given current position Spot FX exposure = Value of FX position in h ome currency Spread bet exposure = (bet per point × price) ÷ (FX Rate × point size)
CFD (per contract) exposure = (CFD contracts × price × contract siz e) ÷ FX Rate
CFD (per point) exposure = (bet per point × price) ÷ (FX Rate ×
point size)
Futures exposure = (futures contracts × price × multiplie r) ÷ FX
Rate
Margin trade exposure = (number of shares × share pric e) ÷ FX
Rate
We will also need to work out the average exposure . This is the size of position for a for ecast of 10: Formula 31: Average exposure
Average exposure = [target risk % × capital] ÷ instr ument risk %
Now, if the current exposure deviates from your actual notional 20
exposure by 10% ¹³78 or more of the average exposure , then you 20
need an adjus ting trade: ¹³79
Formula 32: Deviation from ideal exposure Deviation % = (Ideal exposure – current exposure) ÷ average exposure
Let us return to the US 10-year bond ex ample above: US 10-year bond CFD on future, $ be t per point.
Capital $45,000. FX rate is 1.0.
Risk target 12%.
Forecast +10 (long).
Instrument ris k 3% a year.
Price $119.
Value of a point 0.01.
Notional exposure: $180,000 which works out to $15 per point (calculat ed earlier).
Suppose that the capital and forecast are unchanged, but the instrument risk now rises to 3.1% annually and the price has also changed, to $118. The ideal notional expo sure is now: Ideal notional exposure = [(forecast ÷ 10) × risk target % ×
capital] ÷ instr ument risk %
= [(10 ÷ 10) × 12% × $45,000] ÷ 3.1 % = $174,194
Now for our current exposure. We use the current price of $118, and a new exchange rate if that was relevant (it isn’t in this case). The point size is still 0.01, and the current position is $1 5 per point:
Current exposure, CFD (per point) = (bet per point × price) ÷ (FX
Rate × point size)
= ($15 × 118) ÷ (1 × 0.01 ) = $177,000
We also need the average exposure (which on this occasion is identical to the ideal exposure, since the fore cast is 10): Average exposure = [target risk % × capital] ÷ instr ument risk %
= 12% × $45,000 ÷ 3.1 % = $174,194
The ideal exposure is different from the current exposure by: Deviation % = (Ideal exposure – current exposure) ÷ aver age exposure
= (174,194 – 177,000) ÷ 17, 4194 = –1.6%
Since this is less than 10% we would not do any adjusting trade.
Now, imagine things get a little mo re exciting: Price rall ies to $120.
Capital rises to $48,000.
Forecast cha nges to +12.
Instrument risk goes up to 4.3%.
The ideal notional exposure has fallen further to: Ideal notional exposure = [(forecast ÷ 10) × risk target % ×
capital] ÷ instr ument risk %
= [(12 ÷ 10) × 12% × $48,000] ÷ 4.3 % = $160,744
The current exposure is at $15 p er point is: Current exposure = (bet per point × price) ÷ (FX Rate × point size)
= ($15 × 120) ÷ (1 × 0.01 ) = $180,000
Average expo sure is now:
Average exposure = [target risk % × capital] ÷ instr ument risk %
= (12% × $48,000) ÷ 4.3 % = $133,953
The deviation from the ideal exposure is: Deviation % = (Ideal exposure – current exposure) ÷ average exposure
= (160,744 – 180,000) ÷ 133, 953 = – 14.4%
This is larger than 10%, so at this point we do a trade necessary to reduce our exposure. The bet per point required by the ideal exposure of $160,744 is:
$ bet per point = (Ideal exposure home currency × FX Rate × point s ize) ÷ price
= ($160,744 × 1 × 0.01) ÷ 120 = $13.4 = $13 rounded As we are long $15 per point, we need to close $2 per point of our position. Any adjusting trades also have to be larger than any minimum specified by the broker for the product and instrument you’re using. If your account value is modest it’s quite likely that many of your adjusting trades won’t meet the minimum trade size. You will have to keep your position at th e same size.
These calculations have been pretty gruesome but remember in practice that you would be using a spreadsheet to au tomate them.
Practical non-binary trading
Updated trade plan
Here are the required updates to our trade plan for non-bin ary trading:
Example of position management
Let’s see how the initial trades from chapter six would have been different if I take forecast values i nto account.
Step one
Work out the required notional exposure ( formula 29): Notional exposure = [(forecast ÷ 10) × target risk × capital] ÷
instr ument risk %
Table 68: Notional exposure for initial trades in June 2018, including forecasts
Instrument risk (A) from table 16. Capital (B) from chapter six, page 121 . Forecasts (C) calculated using MAC 16, 64 trading rule and formulas on page 246 onwards. Notional exposure (D) calculated with 12% target risk using formula 29.
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Table 68 shows the notional exposure calculations for the initial example trades, using the appropri ate capital.
Step two
Calculate how large the position should be in the appropriate units for each product (formula 20). All the values are from chapter six and are correct as of 18 June 2018. Instrument
parameters are from table 14, prices from table 15, and the FX
rates are the same I used to calculate the original notional exposures in chapter six, on page 135 .
Example of position management
You should check daily that the exposure implied by your open positions hasn’t deviated too much from the ideal exposure. The ideal exposure is calculated using the latest forecast, current instrument risk, and the level of capital in your broker age account.
Let’s see how this could be done with the example trades from chapter six, and the prices and risk that were prevailing in the market on 4 July 2018, a few weeks after the original trades were put on.
The first step is to work out my ideal notional exposure , as shown in table 69. I have also calculated the average exposure, as that will be nee ded shortly.
Table 69: Ideal notional and average exposure on 4 July 2018
Instrument risk (A) estimated on 4 July 2018. Capital (B) includes profits or losses made since initial trade. Forecasts (C) calculated using MAC 16, 64 trading rule and formulas on page 246 onwards. Notional exposure calculated with 12% target risk using formula 29. Average exposure calculated using formula 31.
Step two is to work out my current exposure using the various 20 20
flavours of formula 30. I’m using up-to-date prices ¹74 70 from 4
July 2018 and, when required, updated FX rates from t he same day.
Notice that the current exposure is long for Euro Stoxx, but the ideal exposure is short: the sign of the forecast has changed since the original trade was put on.
Step three is to check the deviation ( formula 32): Deviation % = (Ideal exposure – current exposure) ÷ aver age exposure
If this deviates from my actual notional exposure by 10% of the average exposure , then I need to make an adjusting trade. Table 70 checks this for ea ch position.
Table 70: Comparing ideal and current exposure on 4 July 2018
Ideal exposure (A) and average exposure (C) from table 69.
Current exposure (B) as calculated above. Deviation (D) calculated using formula 32.
Apart from the gold spread bet I will need adjusting trades all of my positions. Finally, I recalculate what my positions would
be with the ideal exposure (using the various versions of formula 20, with prices and FX rates for 4 July 2018), and check to see if the resulting trade i s feasible:
Table 71: Summary of adjusting trades required Table 71 summarises the adjusting trades. In practice, some of these trades would have happened earlier, had I checked them every day rather than waiting a few weeks. However, this book would have been even longer and extremely dull had it included several months of daily exposure c alculations!
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¹²74 Footnote for poker experts: I realise this is a gross oversimplification that ignores the big and small blinds, and the possibility of bluffing.
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¹²75 If we were using non–binary trading, and also retaining a stop loss, then we’d size our original position according to forecast strength, but then keep it constant. Except for our first trade, we’d likely have a very weak signal, since we open a new position when the trading rule has only just changed sign.
We’d then keep this very small position until a stop loss was hit. That makes no sense.
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¹²76 You will sometimes hear traders talk about pyramiding or, as one online pundit describes it, “adding to winning positions with new trades, when prices reach key technical levels”. These levels, like the entry into the initial trade, are often determined subjectively. If the trading rule you are using is a trend following rule, like in the Starter System, then your non-binary trading will look a lot like pyramiding. But non-binary trading using trading rules is superior to pyramiding – it doesn’t use subjective judgement and is simpler (as you don’t need a separate stop loss rule for each new trade you put on).
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¹²77 I haven’t shown results for systems that have non-binary trading combined with a stop loss as this doesn’t make any sense.
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¹²78 The choice of scaling factor is arbitrary, I prefer to use 10
but other values are equally valid.
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¹²79 Other more technical reasons are elucidated in Systematic Trading , page 113 (print edition).
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¹³70 All the scaling factors in this chapter have been calculated using a back-test over my own set of 37 instruments, and verified using an even wider set of artificial data. However, they are valid regardless of what you are trading, as my estimates are very similar across different markets.
¹³¹ We don’t use instrument risk explicitly in the breakout calculation. However, we do divide by the price range, and instruments with larger price ranges also have greater
volatility, so it has roughly the same effect as dividing by instrument risk.
¹³² Technical note: You might expect that the scaling factor would be around 40, since an average value for breakout rules is probably about 0.25 (in the middle of the range from 0 to 0.5), and we require a scaled forecast of around 10: 10 ÷ 0.25 = 40. In fact, as table 66 shows, (a) the correct scaling factors are all under 40, and (b) come in slightly differently depending on the value of N. This is because (a) the raw breakout signal is not uniformly distributed, and (b) square root time scaling effects.
¹³³ Technical note: In theory we should compensate for the diversification benefit across forecasts by applying a second diversification multiplier; in Systematic Trading this factor is the ‘forecast diversification multiplier’ (FDM). Without the FDM
the mean absolute value of our combined forecasts will not be equal to the desired value of 10, but will be slightly lower.
Omitting the FDM makes the system simpler and safer, and hence I have not included it in this book.
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¹³74 From table 5 .
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¹³75 In fact the capital required with multiple instruments may be even lower than for a single instrument, because (i) we drop the requirement for double the absolute minimum capital, (ii) the effect of the instrument diversification multiplier, and (iii) higher account level risk targets, due to the expected benefits of diversifying.
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¹³76 Page 183 .
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¹³77 I discuss this in a blog post: qoppac.blogspot.com/2016/03/
diversification-and-small-account-size.html 20
¹³78 Technical note: The optimal size of the non trade region depends on the trading costs, and a few other factors. 10% is a sufficiently conservative value given the costs paid by smaller traders using the leveraged products in this book.
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¹³79 We use the average exposure as the denominator in this formula, not the current exposure. Otherwise when current exposure is low this percentage will be meaninglessly large.
20 20
¹74 70 Of course, 4 July is a US holiday, so there was no price for corn futures or the S&P 500 that day. I’ve used the price from the previous day.
Chapter Eleven
What Next?
The Starter System is designed to help you learn how to trade safely. However, it’s unlikely that anyone will want to use it for the rest of their trading career. I’m sure you will want to
use your new found knowledge of the markets to develop your trading and increase your expected pr ofitability.
What comes next for someone who is confidently trading the Star ter System?
There are three possible routes y ou can take: Improve upon the Starter System, using the ideas in part three and part four o f this book.
Learn how to design and back-test your own systematic tr ading rules.
Move into Semi-Automatic Trading where you use your own experience and judgment to decide when to open positions, but use the system for risk control and position management.
Let’s look at each of th ese in turn.
1. Improvements to the Starter System
The basic Starter System, introduced in chapters five and six, delivers a back-tested Sharpe ratio (SR) before costs of around 20
0.24, equating to pre-cost returns of around 4.9 % per year. ¹74¹
The improvements you can make will depend on your available capital, time, and expertise. Here is a recap of the upgrades you could make to the Starter System, listed in order of potential improvement, with the best first:
Adding multiple instruments , as in chapter seven, will improve your SR by a factor of around 1.25x (for two instruments) and 2.3x (for 20 or more). So, with two instruments your expected SR
would rise to 0.24 × 1.25 = 0.30. This option is only available if you have sufficient capital to share between multiple instruments.
Introducing new trading rules , like those in chapter eight, will increase your back-tested SR by a factor of between 1.13x (for two trading rules) and 1.48x (for 20 or more). However, using multiple trading rules can be tim e consuming.
Dropping the stop loss , as in chapter nine, improves the expected SR by a factor of around 1.13x. This can also result in more work, since trading rule forecasts need to be moni tored daily.
If you have already dropped the stop loss then moving to non-binary continuous trading , which I discussed in chapter ten, increases the SR by a factor of about 1.25x.
1. Back-testing and designing your own system
If you are hooked on systematic trading you might want to continue developing the Starter System, beyond what is covered in this book. I recommend that you continue using the Starter System, and then add your own novel opening rules (if you aren’t using a stop loss then these rules would also be used for closing positions). I strongly advise keeping all the other parts of the Starter Sy stem intact.
Here are the steps I take when I’m implementing a new t rading rule:
Design the t rading rule.
If you’re using continuous trading, modify the rule so it’s risk-adjusted, and estimate the required scaling factor (see c hapter ten).