is higher than 1.898%. But the difference in interest rates here is tiny: 0.021%. A tiny change in the USD rate would cause the
rule to change its opinion about AUDUSD. This justifies a much smaller position in AUDUSD than the larger rate differential seen in GBPUSD. Similar arguments apply when trading carry in other leverag ed products.
Intuitively it seems to make sense to alter position size depending on how confident the opening rule is. But we are systematic traders, so let us check the evidence. Have a look at figure 32, which is an updated version of figure 24 from the previous chapter. In this figure I’ve shown the result of back-testing different variations of the Starter System; with and without binary trading and stop losses.
Figure 32: Removing the stop loss is good. Dropping binary trading is better. Effect of removing stop loss (NS), and also moving to non-binary trading (NS NB)
Figure 32 shows the average Sharpe ratio (SR) plus statistical uncertainty of three moving average rules, including the 16,64
pair used in the Starter System. The first box in each set of three shows the rule with a stop loss and binary trading, as used in the basic Starter System introduced in part two. The second box (suffix NS ) shows the effect of removing the stop loss. We have seen these statistics before, in figure 24 from chapter
nine. Finally, the third box in each triplet (suffix NS NB ) shows the effect of removing the stop loss and moving to non-bina 20
ry trading. ¹²77
You can see that moving to non-binary trading improves performance relative to the normal Starter System, and also compared to trading without a stop loss. Because the boxes and whiskers overlap the improvement isn’t statistically significant on any individual rule. But the consistent pattern means there is good evidence that non-binary trading will lead to higher risk-adjusted returns. We boost the expected SR by 13% when dropping the stop loss on the Starter System MAV 16,64 rule (SR goes from 0.24 to 0.27), and subsequently add another 26% by moving to non-binary trading (SR goes from 0. 27 to 0.34).
Because these results aren’t statistically significant you should not use these higher SR expectations to increase your risk target, as you would do if you were adding instruments or trading rules. It’s better to be conservative and limit yo ur leverage.
The forecast: A risk-adjusted prediction of the future How do we actually adjust positions depending on how confident our trad ing rule is?
Here is formula 14, which I introduced back in part two, for calculating required notional exposure for the Sta rter System: Notional exposure = (risk target × capital) ÷ instr ument risk %
The risk target will normally be 12%, but if using multiple instruments or trading rules then it should be adjusted using the calculations in chapters seven and eight. Now I am going to modify the formula as follows:
Formula 29: Notional exposure incorporating forecast strength Notional exposure = [(forecast ÷ 10) × risk target × capital] ÷
instr ument risk %
There is a new variable in the formula: the forecast . This is a prediction of what our risk-adjusted return is currently expected to be, compared to the long run average. The forecast is a scaled measure of how confident our trading rule c urrently is .
With a forecast of 10 the position will be the same as it is in 20
the original formula. Hence a forecast of 10 is average. ¹²78
Higher values for the forecast mean a larger position: a forecast of 20 is a position that’s double the average. A lower forecast equates to a smaller position: a forecast of 5 would give a position that is half the average.
Forecasts can be positive or negative; a positive forecast means we buy, and a negative implies we go short . In principal
forecasts could also be zero, which implies we do not know what the price w ill do next.
Importantly, I don’t use forecasts outside of the range –20 to
+20. If a forecast comes out larger than +20, I cap it at +20.
Strongly negative forecasts below –20 are flo ored at –20.
What’s wrong with larg e forecasts?
20
There are a couple of reasons ¹²79 why I don’t use forecasts that have absolute values larger than 20. Firstly, a larger forecast means you’re taking on more risk, and using more leverage. This will increase your potential loss if thin gs go wrong.
How bad can things get? Well, back in chapter six I showed you the likely losses from different risk targets. From table 10 the chance of a 25% monthly loss with the 12% risk target in the Starter System is tiny. However, suppose you had a rule that produced a forecast of 40? Then your current expected risk would be four times greater than the average of 12%, equivalent to a risk ta rget of 48%.
From table 10 the chance of losing 25%, with an elevated risk target of 48%, is substantial: 3.6%. You could expect to lose a quarter of your capital every couple of years. Ouch. If, however, you capped your forecast at 20, equivalent to a risk target of 24%, then theoretically a loss of this magnitude will still be very unlikely (0.02% to be precise – once every 400 y ears or so).
Secondly, most trading rules don’t seem to work so well at extremes.
First, consider trend-following rules like the moving average crossover, and breakout rule. Very strong forecasts will appear when the market has been trending for some time. But after a prolonged bull market there is nobody left to buy, and a sell off becomes more likely. Sharp sell offs also produce strong negative forecasts for trend following rules, but markets tend to rally immediately after market crashes. (This is known as the ‘dead cat bounce’, since apparently dead cats bounce if you drop them off a building. I haven’t personally checked the veracity of this fact.) So, when trend forecasts are too strong, reversals become more likely, and the forecast for a continuing trend will oft en be wrong.
There are similar effects in carry trading. This is especially true in FX markets, where substantial differences in interest rates usually arise in emerging markets that are on the brink of a crisis.
For example, in Thailand interest rates reached around 11% in early 1997 versus 6% in the US. This produced a strong carry forecast, buying Thai baht and selling US dollars. For several years this had worked well as the Thai baht to US dollar FX rate was fixed, or in economist jargon it was ‘pegged’. Unfortunately, in July 1997 the Thai government was forced to drop the peg, and the Thai baht halved in value. There were catastrophic losses for ca rry traders.
Limiting your forecast to +20 or –20 reduces the harm you will do to your trading account when disas ter strikes.
Approximate position scaling for trading rules: eyeballing How do we go from charts, like figure 30 and figure 31, to a numeric forecast between –20 and +20? The simplest option is to eyeball the chart. At the end of figure 31 it looks like a really strong short forecast is required: perhaps –15 or –20. In contrast the forecast on our long position in figure 30 should be quite small; perhaps +5. Just make sure you have enough history on your charts to judge how strong a forecast is compared to historic al averages.
Precise position scaling for trading rules I don’t use the eyeballing method, since it is very subjective.
Instead I calculate the correct forecast systematically. The method for doing this will vary depending on the trading rule you are using, but there are usually four ste ps involved: Get the raw forecast from the t rading rule.
Divide the raw forecast by instrument risk to get a risk-adjusted forecast (we adjust forecasts for risk, because a forecast is a prediction of risk-adjust ed returns).
Rescale the risk-adjusted forecast so that the average value for a forecast is 10 (it is unlikely that the risk-adjusted forecast will have the right scaling, so a second adjustment is usua lly needed).
Cap any large forecasts at +20 or –20.
Moving average crossover
Let’s see how to work out the forecast for the Starter System rule, a moving average crossover (MAC). The calculation for a moving average pair of f (fas
t) and s (slow) days is formula 13: MAC f,s t = MA f t – MA s t
Moving averages are in the same units as prices, so MAC is in units of price difference. By coincidence in both figure 30 (Euro Stoxx) and figure 31 (corn) the difference between the two moving averages is 20 price units:
M AC corn = –20
MAC Euro Stoxx = +20
Now we need the instrument risk (step 2). To match the units of MAC this is measured in units of annual standard deviation of price returns . We derive this from the usual instrument risk, a standard deviation of returns in percentage terms, which I showed you how to estimate back in chapter six ( page 129 ). To convert this into price units we use formula 22 (which was originally introduced for stop loss calculations in ch apter five): Instrument risk in price units = Instrument risk as percentage volatility × c urrent price
The percentage standard deviation of returns for corn that I used in chapter six was 11.9% a year, and 9.6% for Euro Stoxx. The price of corn was 379, and 3,391 for Euro Stoxx; again from chapter six. So, the instrument risk in price units comes in at: Instrument risk in price units = 379 × 11.9% = 45 .10 for corn Instrument risk in price units = 3391 × 9.6% = 325.54 fo r Euro Stoxx
Now we need to divide the MAC value (–20 for corn and +20 for Euro Stoxx) by the inst rument risk.
Risk-adjusted MAC forecast = MAC ÷ instrument risk in price units That gives us risk-adjusted f orecasts of: Risk-adjusted MAC forecast = –20 ÷ 45.10= –0. 443 for corn Risk-adjusted MAC forecast = +20 ÷ 325.54 = +0.061 fo r Euro Stoxx
As the charts suggest, once we have accounted for volatility the forecast for corn is much stronger than that of Euro Stoxx .
Next, we need to rescale the forecast (step 3). Scaling factors for the MAV pair used in the Starter System, plus several others, 20
¹³70 are shown in table 65. Sometimes the magnitude of the scaled forecast will come out at more than 20; if this happens you should limit it to +20 (for a long) or –20 (for a shor t) (step 4).
Rescaled forecast if long = Min(+20, Risk-adjusted forecast × sca ling factor)
Rescaled forecast if short = Max(–20, Risk-adjusted forecast ×
sca ling factor)
Table 65: Scaling factors for different MAV pairs Scaling factors calculated by averaging across back-tests of 37
instruments.
Let’s return to the two instruments I’ve been using as an example. For the 16,64 moving average crossover used in the Starter System, the scaling factor is 57.12. We multiply the risk-adjusted forecasts by this number, and apply a limit –20 or
+20:
Rescaled forecast = Max(–20, –0.443 × 57.12) = Max(–20, –25.3) =
–20 for corn
Rescaled forecast = Min(+20, +0.061 × 57.12) = Min(+20, +3.5) =
+3.5 fo r Euro Stoxx
As expected, the forecast for corn, which we’d cap at –20, is much stronger than the forecast for Euro Stoxx a t just +3.5.
Breakout
Here is a reminder of the final step in the calculation of the breakout rule I introduced in chapter eight, formula 28: Scaled price in range = (P t – R AVG N ) ÷ (R M AX N – R MIN N ) This 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). This calculation is already risk-adjusted, ¹³¹ so all we need to do is multiply the scaled price by a scaling factor. ¹³²
These can be found in table 66. Notice that these are quite different from those in table 65. This is quite normal, different rules can legitimately have completely different scaling factors.
Remember to cap any forecasts lower than –20 or high er than +20.
Table 66: Scaling factors for different breakout look backs Scaling factors calculated by averaging across back-tests of 37
instruments.
As an example, here’s the raw and scaled forecast calculation using N=320 for crude oil, with the values I used as an example in chapter eight, and with the appropriate scaling factor of 33.5
(final row o f table 66):
Scaled price in range = (P t – R AVG N ) ÷ (R MA X N – R MIN N )
= (100.3 – 103.3) ÷ (107.78 – 98 .76) = –0.33
Scaled forecast = Max(–20, risk-adjusted forecast × scal ing factor)
= Max(–20, –0.33 × 3 3.5) = –11.1
We’d be short crude oil in this situation, with a forecast a little stronger than the av erage of 10.
Carry
Back in chapter eight I defined the carry rule as the expected annual percentage return . This means that volatility scaling is simple; we just need to divide by the instrument risk , which I explained how to estimate back in chapter six. We also need the scaling factor. After back-testing I would recommend using a scaling factor of 3 0 for carry.
Table 67: Example of carry forecast calculation as of June 2018
Expected percentage return (A) calculated in chapter seven, page 201 onwards. Instrument risk (B) from table 16. Scaling factor (D) calculated using a back-test averaging across 37 instruments.
Table 67 shows how I’d calculate current values of the carry forecast for the example instruments in chapter six, using the expected annual percentage carry returns I worked out in chapter eight, and annual standard deviation figures from chapter six.
Notice the capped forecasts in the final column. It’s possible for scaled carry forecasts to come out with an absolute value greater than 20, so you should cap forecasts as I’ve done he re for gold.
Non-binary trading with multiple trading rules With multiple rules you should use the same weighting scheme I suggested in chapter eight. However instead of weighting values of +10 and –10 you should weight the forecasts from each rule.
¹³³ There is also no need to round the value of the weight ed forecast.
For example, suppose your weights are 40% for the moving average 16,64 rule, 10% for a breakout rule, and 50% for the carry rule.
If their respective forecasts are +6, –12, and +10; then the weighted aver age will be:
[0.4 × (+6)] + [0.1 × (-12)] + [0.5 × ( +10)] = +6.2
In this simple example we’d use a forecast of +6.2 to calculate our position using formula 29.
Do we need more capital for non-binary trading?
Non-binary trading makes a lot of sense, but it also has a big disadvantage: it requires more capital – at leas t in theory.
Imagine that you are trading the Euro Stoxx, which is the instrument I recommended in chapter six for CFD traders. This 20
requires a minimum of $6,500 to trade a single contract, ¹³74 and
ideally twice that: $13,000. With $13,000 you can trade the binary Starter System using two CFD contracts, and should you lose some money you would revert to trading a sing le contract.
Now suppose you decide to change the size of your position according to forecast strength, again with initial capital of $13,000 for an average position of two contracts. On average (forecast of +10 or –10) the trading rule will tell you to buy, or sell, two contracts. With a weak forecast (+5 or –5) you would trade one contract, and if the forecast is exceptionally strong (+20 or –20) you would hold four contracts. So f ar, so good.
Your problems begin if you lose some money and end up with less than $13,000. Now, instead of an average of two contracts, you can only hold one. With a very strong forecast you’d buy or sell twice the average: two contracts. But if your forecast is weaker than average you can’t buy or sell half a contract, so you would end up with no position at all. This somewhat reduces the benefit of non-bin ary trading.
One solution is to begin with even more capital: four times the absolute minimum. So, for Euro Stoxx CFD trading, you would have 4 × $6,500 = $26,000. This means you could take an average position of four contracts; owning up to eight contracts if the forecast was strong, and less than four for weaker forecasts. If you lost half your money, you would be down to an average of two contracts, but you could still reduce your position to a single contract if the foreca
st was weak.
But I do not advise this. Instead, if you have extra capital you’re almost certainly better off using it to diversify your 20
trading strategy across multiple i nstruments. ¹³75
20
Let me explain. From chapter seven, ¹³76 going from one to two instruments improves the expected Sharpe ratio (SR) of the Starter System from 0.24 to 0.30, an increase of 0.06 SR units.
From earlier in this chapter, the benefit of non-binary trading, assuming you’ve already dropped the stop loss, is the same: 0.06
SR units. This looks like a dead heat, but although similar in magnitude, the improvement from adding extra instruments has greater statistical significance than the benefits of non-bin ary trading.
Additionally, you would still keep some of the benefit of non-binary trading, even if you end up trading with reduced capital.
20
¹³77 Only traders who have lost money, and who subsequently have weak forecasts, are affected. We expect smaller profits when forecasts are weak, so we are not giving up much return. In my own back-testing, I have found that the average degradation in performance from having insufficient capital with non-binary trading was minuscule: less than 0.02 SR units. The gains from diversifying across two instruments (0.06 SR units) exceed the small cost of occasionally not being able to hold a position.
In summary, you should not use extra capital to ensure you can continue non-binary trading when losses occur; instead use it to add more instruments to your system. You can ignore the theoretical requirement for higher minimum account size when conducting non-bin ary trading.
Adjusting position size for risk
If our forecast changes, then our position should also be adjusted. However, there is another important factor that affects position sizing: the current risk of an instrument .
When instrument risk changes you should, in theory, change the size of your position. To understand why, consider the follow ing example:
US 10-year bond CFD on future, $ b et per point Capital $45,000. FX rate is 1.0.
Ris k target 12%
Forecas t +10 (long)
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 21