If we have a short position, then everything is reversed. We close our positions if the price trades above the stop loss level. The high watermark will be the lowest daily price we’ve seen. We add the stop loss gap to the high watermark to get the stop loss level. If the closing price goes below the lowest daily price we have seen, then the stop loss will be moved down. The stop loss will always be higher than the current price (until it’s hit). If the price is falling, then the stop loss level will also be falling.
Formula 24: Stop loss level
Stop loss level (when long) = Highest price since trade opened –
s top loss gap
Stop loss level (when short) = Lowest price since trade opened +
s top loss gap
Let’s suppose we go long gold at $1,300 per ounce, with instrument risk of 11% a year. First, convert the instrument risk into price units ( formula 22):
Instrument risk in price units = 11% × $ 1,300 = $143
Next, we multiply this by the stop loss fraction (0.5), to get the stop loss gap in price units ( formula 23): Stop loss gap = $143 × 0.5 = $71.50
Finally, as we are long gold, we subtract the stop loss gap from the high watermark to get the stop loss level . As we have just opened the trade this will be the level that we purchased at, $1,300 ( formula 24):
Stop loss level = $1,300 – $71.50 = $1,228.50
Our stop loss level will be set at $1,228.50. If the daily closing price falls below this level, we will close the position.
But, if the daily closing price of gold goes higher than $1,300, then we increase our stop loss level appropriately. For example, if the price goes to $1,350 then we change our stop loss level to $1,350 – $71.50 = $1,278.50.
What proportion of my capital is at risk on each trade?
“Career day traders use a risk-management method called the 1
percent risk rule, or vary it slightly to fit their tradi ng methods.”
Some potentially dangerous advice from a trading blog Many traders recommend setting a fixed percentage of your capital that should be at risk on each trade. Values between 1% and 5%
are typical. However, in the Starter System we put on a position of a given size to target a certain level of risk, and then close it once a stop loss has been triggered. Why the difference?
Actually, the Starter System method is indeed equivalent to setting a percentage of capital at risk. Suppose we have a position in an instrument that had the same risk as the risk target for the Starter System: 12% a year. As instrument risk and target risk are equal, we would use a leverage factor of one, creating a notional exposure equal to our account value. The stop loss on this trade would be set at half the annual risk: 6%. So, 20 20
in theory, 6% of our capital is at risk on this trade. 76 79
We would get exactly the same result if the risk of the instrument was different. If the risk was doubled, we would deploy half our capital in the trade and the stop loss would be twice as large, which exactly offsets the change in position size. There would still be 6% of our capi tal at risk.
I can write this as a gene ral formula: Formula 25: Percentage of capital at risk on each trade Capital at risk per trade % = Risk target % × stop l oss fraction Capital at risk per trade % = 12 % × 0.5 = 6%
Although 6% might seem quite high, it is actually relatively small because the Starter System trades very slowly. Allegedly, more conservative figures of 1% or 2% for capital at risk are used by traders like the blogger above, who trade dozens or even hundreds of times a year. If I was trading that quickly with the Starter System I would have a lower stop loss fraction, and hence a much smaller proportion of capi tal at risk.
From table 12 earlier, if you were trading a hundred times a year then a stop loss fraction of 0.025 is appropriate. The capital at risk per trade would be 12% × 0.025 = 0.3%. Someone trading at least twice a day – 500 times per year – would risk even less.
Risking 1% on each trade as a day trader sounds conservative, but 1% is actually f ar too high.
In summary, it makes no sense to set an arbitrary constant percentage of capital at risk without considering your risk target, and how long you’re going to be holding positions for.
This is why I prefer to specify risk separately as (a) a risk target, and (b) a stop loss fraction. The former can be set according to the criteria I laid out earlier in the chapter, whilst the latter is determined by how quickly you can trade given the costs of your system.
How to implement stop losses
There are three principal methods for implementing stop loss rules:
When do we re-enter the trade after a stop has been triggered?
If we close a trade after a stop loss, when should we re-enter it?
There are two po ssibilities:
Why is day trading s o dangerous?
I’ve mentioned several times in this book that I’m not a fan of day trading – a type of trading where you have no active positions at the end of each day. This is a controversial and unpopular view. Closing out your positions before the end of each day sounds superficially appealing for seve ral reasons: You trade more often: more chances to make money.
If you are trading undated products like spot FX, you avoid paying fu nding costs.
It is safer, as you are not exposed to the market moving overnight. You cannot close positions in the middle o f the night.
You take less risk. Day traders frequently risk 1% or less on each trade compared to the 6% at risk in the Starter System (calculated o n page 113 ).
These arguments are all de eply flawed.
In theory, trading quickly is indeed more profitable. If you increase your frequency of trading by a factor of four, then this will double the maximum Sharpe ratio you can theoretical ly 20
achieve. 77³
However, this calculation ignores two key problems. Firstly, this is only a theoretical result. In reality, you are unlikely to see these sorts of improvements. Look again at figure 4 . Here the two fastest moving average crossover rules actually had worse performance than the slow er versions.
Secondly, if you increase your frequency of trading, you will definitely pay higher costs. At a minimum, day trading involves doing two trades per day (an open, and a close). This will cost a fortune. For example, two trades a day in a gold spread bet works out at a risk-adjusted annual cost of 1.07, whilst for a Euro Stoxx 50 CFD it is 1.50. Whilst day traders can indeed avoid overnight funding costs on undated products, any saving is completely wiped out by the extra transa ction costs.
Futures are the cheapest product, but most of these are still too expensive for day trading. For example, day trading corn futures still costs a pricey 0.12 in risk-adjusted costs each year. There are a few instruments where day trading futures is feasible. Day trading the Nasdaq future would cost around 0.034 annually in risk-adjusted trading costs. But the minimum capital for Nasdaq futures is ov er $200,000!
Remember, I impose a speed limit on trading costs: you should never pay more than a third of your expected pre-cost Sharpe ratio out on costs. This works out at a speed limit of 0.08 in annual risk-adjusted costs for the Starter System. Hence, for day trading to make sense you nee d to either: Trade only very cheap futures like the Nasdaq. These require huge amounts of capital.
Increase the speed limit up to a higher proportion of your expected Sharpe ratio: perhaps a half, or even higher. This would make day trading feasible on most futures like corn, but this does not help traders who can’t afford the minimum trade sizes.
It is extremely risky given the uncertainty of expected Sharpe ratios. Do n’t do this .
Improve your pre-cost Sharpe ratio, so it is at least three times the cost of day trading.
Is it realistic to improve your pre-cost Sharpe ratio to the point when you could safely day trade? Consider AUDUSD spot FX, which is accessible to smaller traders and whose risk-adjusted cost when day trading is a relatively low 0.35 per year. To ensure you were under the speed limit – a maxim
um one-third of pre-cost returns paid out in costs – you need to be generating a pre-cost Sharpe ratio of 3 × 0.35 = 1.05. This is extremely optimistic. Only a few elite professional traders can confidently expect to make that kind of return when trading a single i 20 20
nstrument. 77 74
Now, let us consider the alleged lower risk of day trading.
Although you miss out on overnight moves as a day trader, you are still exposed to intra-day moves. Markets tend to move more during the day than overnight, as there is more news flow and trading activity during the day creates its own volatility. Also remember that the Starter System carefully calibrates position size, and thus risk, based on expected market volatility. Since instrument risk is estimated based on daily closing prices it will account for both intra-day and overnight marke t movements.
It is true that you cannot close positions overnight, but this should only be a concern for traders who are taking on far too much risk. Prices frequently gap up or down during the day. When gaps occur you would be unable to get out at your stop loss level, even though the mar ket is open.
A day trader will have a smaller amount of capital at risk on each trade, but as they trade more often this doesn’t necessarily make them any safer. Consider a trader trading the Starter System who does six trades in a particular year (remember the average is 5.4), each risking 6% of their capital (I calculated this figure back on page 113 ). We will compare them to a day trader risking
‘only’ 0.5% of their capital but opening and closing positions every day: roughly 250 t imes a year.
Let’s suppose both traders are unlucky and lose money consistently for two months straight – about one-sixth of a year.
The slower trader will expect to do a single trade and will lose 6% of their account. The day trader will lose on 250 ÷ 6 = 41.7
occasions. Losing 0.5% of your capital 41.7 times equates to a loss of around 0.5% × 41.7 = 21% . The smaller position size of the day trader is actually much riskier than the Sta rter System.
To have the equivalent amount of risk, the day trader will need to have an extremely small position size (around 0.14%), and hence a much lower risk target. With a lower risk target comes another problem – higher requirements for minimum capital. The day trader risking 0.14% of their capital will need more than forty times as much capital as is required in the Sta rter System.
Some day traders claim they can improve their returns by trading selectively. A day trader might only trade on 50 days of the year when they see the ‘best’ opportunities. This will reduce their costs somewhat; though they will still be many times higher than the costs of the Starter System. But it will also reduce their opportunities to make money relative to the Starter System, which is in the market the entire time. I am extremely sceptical that it’s possible to choose certain trades with a high enough success rate for selective trading to make sense.
If day trading is so difficult, why is it so heavily promoted by self-proclaimed internet trading experts? Well, most of these
‘experts’ are earning kickbacks from brokerage firms, and
brokerage firms love day traders as they generate much higher profits. Brokers also do their bit by creating nice mobile apps and websites that make day trading child’s play. Don’t be taken in by the hype – avoid day trading like the plague!
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74 78 Don’t worry if you don’t recognise all of the names or acronyms. They’re just labels for different instruments, and you don’t need to know which is which.
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74 79 Technical note: Specifically, if returns are independent and follow a Gaussian distribution, then the variance of the parameter estimate for Sharpe ratio is (1+0.5SR ² ) ÷ T, where T
is the number of observations.
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75 70 Using 68% and 95% confidence intervals might seem completely arbitrary, but these are the standard values used in statistics for these kinds of plots. They relate to the proportions of the most widely used statistical distribution, the ‘Gaussian Normal’, which we met in chapter four. The two intervals encompass the regions that are one standard deviation (68% confidence) and two standard deviations (95% confidence) around the central estimate.
You might ask why there is no 100% confidence interval. In fact, we can never be 100% sure what the Sharpe ratio really is no matter how long the back-test is.
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75 ¹ The explanation for this is too large to fit into this footnote. If you are interested it is in appendix B, on page 300
.
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75 ² If trading is your primary source of income and you make consistent returns then you may be liable to pay UK income tax on trading profits, and it’s possible this could also apply to spread betting winnings. I should also point out that legislation is subject to change and interpretation, and I’m not a lawyer or an accountant.
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75 ³ I am not making these up: all are charting patterns used by traders.
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75 74 This last pattern is a fake. It was made up by banking analyst Suvi Platerink to mock traders who use such techniques.
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75 75 Technical note: My favourite explanation of momentum returns comes from behavioural finance, specifically prospect theory.
This explains why traders become more risk averse and wish to sell once the price has gone up. Conversely when the price has fallen, they become risk loving and are reluctant to sell. This leads to recent risers being undervalued, and recent fallers being overvalued.
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75 76 Several historical tests of momentum have been done, one which goes back 200 years, is by Christopher Geczy and Mikhail
Samonov, ‘Two Centuries of Price-Return Momentum’, Financial Analysts Journal , (2016).
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75 77 You will notice that I fixed the ratio of the fast and slow moving averages at exactly 4 (so for example f =2 and s =8 which gives a ratio of 8 ÷ 2 = 4). This is to reduce the number of possibilities I had to consider. Any ratio between around 2 and 6
works equally well. You will also notice that the fast moving average length goes up in multiples of 2: f =2,4,8,16 and so on.
Crossovers which use the missing intermediate values for the fast moving average (f=3,5,6,7,9...) end up being extremely similar to the crossovers I’ve shown here.
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75 78 I’ll explain why I chose these particular products in the next chapter.
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75 79 It is not compulsory to add profits to your capital. For example, I regularly withdraw any profits that I make from my trading account and invest them elsewhere. This means I do not benefit from the compounding of returns in my account but it is safer.
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76 70 Another formula that will directly give you the required leverage factor (remember this is equal to notional exposure ÷
capital) is: Leverage factor = Target risk % ÷ instrument risk %.
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76 ¹ Health warning: Do not take these figures at face value. They make some assumptions about how likely different market returns are. Larger daily and monthly trading losses are more common in reality than the tables suggest. For example, the current instrument risk of the S&P 500 equity index is around 16% a year; according to the assumptions used to build these tables the chances of a 7% daily drop are extremely small; so small that such a drop should only happen once every 3.4bn years. But there have been six such falls in the last 40 years; four in 2008
alone!
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76 ² Technical note: The values in these tables have been calculated assuming that returns are drawn from a Gaussian normal distribution with a Sharpe ratio of 0.24 (the expected pre-cost return of the Starter System).
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76 ³ You may be wondering why all the risk targets shown are multiples or fractions of 12%. 12% is the risk target I recommend using in the Starter System, for reasons I explain on page 99 .
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> 76 74 In fact, if you use a risk target that’s more than double your expected Sharpe ratio you’ll end up expecting to lose money, no matter how good your opening rule is.
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76 75 From figure 4 there is a 95% chance that the SR is between 0.15 and 0.34; hence there is a 5% chance the SR is outside of this range, implying a 2.5% chance the SR is below 0.15. All this
assumes that a trading system continues to work as well in the future as it did in the past.
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76 76 Strictly speaking, we should use a risk target based on the expected after costs Sharpe ratio, which would be different for each product. However, this would make the book much more complicated, and using half Kelly is sufficiently conservative assuming you stick to the speed limit for trading costs.
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76 77 As you’ll see later in the book diversifying your trading across multiple instruments can easily improve your expected Sharpe ratio (SR) by a factor of 2.5. A fund making a SR of 2.4
on an individual instrument would have an overall SR across all of their instruments of 2.4 × 2.5 = 6. This is very high. Some professional traders will occasionally make this level of return for short periods, but very few have consistently made that kind of Sharpe ratio. The elite firms which manage to do this employ extremely sophisticated technology which is not accessible to amateur traders.
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76 78 Technical note: To separate the effect of the opening rule, I used a random opening rule which entered long trades with 50%
probability with an equal chance for short trades. I then measured the trading frequency across 37 different futures contracts and took a weighted average.
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76 79 Actually, it’s unlikely we’d close our position exactly at the stop loss level so it’s probably a bit more than 6%. But this is also true if you set your position size as an explicit fraction of your capital.
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77 70 This means you’ll keep a position open if a price briefly hits a stop during the day and then bounces back before the close.
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 12