Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders
Page 11
It is easier to consider the likely losses you could expect to see when running the Starter System at a given risk target.
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Tables 9 through 11 show my calculations 76¹ for the probabilities 20
76 ² of suffering losses of various severities over different tim e 20
horizons. 76³
Table 9: Chances of a given daily loss when running the Starter System
• Theoretically le ss than 0.01
Table 10: Chances of a given monthly loss when running the Starter System
• Theoretically les s than 0.01%
Table 11: Chances of a given annual loss when running the Starter System
• Theoretically les s than 0.01%
As an example of how to use these tables, suppose you are worried about a loss of 10% over a year. From table 11 (annual losses), the odds of losing 10% vary between 1.3% (with a risk target of 6%) and 39% (with a target of 192%). With a risk target of 24%
you expect to lose 10%, or more, about 26% of the time: one out of every four out of years. If you are uncomfortable with that, then you should choose a lower risk target.
My own personal tolerance for risk translates to a risk target of 24%, but you should make your own person al judgment.
Optimal risk level given system profitability How much risk should we take given our expected profitability? We need to use the Kelly Criterion formula from the previous chapter. There I showed you that under Kelly the optimal risk target is equal to your expected Sharpe ratio (SR) . For the Starter System the expected SR is 0.24 (from page 92 ), equating to a risk target of 24%. If you use a higher or lower risk 20 20
target, then you make less money in th e long run. 76 74
However, most professional traders are wary of using the optimum risk determined by the Kelly criterion. There are several reasons for their caution. Firstly, the Kelly criterion makes assumptions about the statistical distribution of returns which are rather unrealistic.
Secondly, there is a great deal of uncertainty about the real Sharpe ratio of any trading system. Look back at figure 4 , which 20 20
shows that there is a reasonable chance 76 75 the back-tested SR of the Starter System is actually less than 0.15, which would require a risk target below 15%. A risk target of 24% could be far too high. Also, back-tested returns cannot precisely forecast what we will earn in the future.
Finally, the SR of 0.24 is a pre-cost return. Using more expensive products to trade will bring the SR down substantially.
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76 76 With my speed limit we’re allowed to spend a third of our expected pre-cost SR on trading costs: up to 0.08. This would leave us with a SR o f just 0.16.
Most professional traders use a conservative version of the Kelly criterion known as half Kelly . Under half Kelly we use half the Sharpe ratio as our risk target:
Formula 18: Prudent ‘half Kelly’ risk target from Sharpe ratio Prudent risk target = Expected Shar pe ratio ÷ 2
For the Starter System, with a Sharpe ratio of 0.24, that implies a risk ta rget of 12% .
Determining the correct risk target
Let’s put together the various figures I’ve calculated for a hypothetical S&P 500 ETF margin trade to see what the correct risk target should be in t his example: Risk possible given maximum leverage allowed by brokers: 32% per year (calculated on page 94 ). This varies by instrument.
Risk possible given maximum prudent leverage: 21.3% per year (see page 95 ). This varies by instrument, and also depends on your appetite for losses.
Your own personal appetite for risk: I’ve used my own figure of 24% ( page 98 ). This is different for individ ual traders.
Optimal and prudent risk level given the expected profitability of your trading system: half the Sharpe ratio 12% ( page 98 ).
This depends on the trading system yo u are using.
The lowest and most conservative risk target from this list is the final figure based on expected profitability: 12%. Most of the time the expected Sharpe ratio will determine the leverage target you should use, unless you have a relatively conservative attitude to risk, or a broker who is unusually stingy with leve rage limits.
You should run the Starter System with an annual risk target of 12% . This might seem low, but risk targets for leading hedge funds typically range between 10% and 20%, and the profitability of these funds is expected to be much higher than that of the Sta rter System.
How much money could the Starter System make?
I can now work out the expected profitability of the Starter System. If we rearrange the Sharpe rati o formula 3 : SR = (r – b) ÷ s
We can use it to work out the expe cted return: Formula 19: Expected return from Sharpe ratio r = (SR × s) + b
Where SR is the Sharpe ratio, r is the average return, b is the rate we can borrow at and s is the standard deviation. The expected Sharpe ratio without costs SR = 0.24, the risk target I just calculated s = 12%, and b the rate we can borrow at is currently around 2.0%. So, our pre-cost expecte d return is: r = (0.24 × 0.12) + 0.02 = 4.9%
With a really cheap instrument we get an after-cost return which is pretty close to 4.9%. The most expensive instruments that I recommend trading would take away a third of our Sharpe ratio, leaving us with a post-cost expecte d return of: 21
r = (0.24 × [1 − 53] × 0.12) + 0.02 = 3.9%
An expected return between 3.9% and 4.9% may not seem very exciting. It is tempting to increase the risk target, apply more leverage and achieve a higher return. But this would be dangerous. You would need much higher performance expectations before it is safe to use a higher risk target.
Have some patience! The Starter System is designed to help you learn the principles of good trading. Improvements that I will introduce in parts three and four will substantially improve these expec ted returns.
Beware of systems with extremely high advertised returns, these can only be achieved by taking far too much risk, or by creating track records that are over-fitted or entirely fabricated.
From notional exposure to position size Once you have determined the risk target, and calculated your required notional exposure using formula 14 , you need to work out the size of your trade. This depends on the type of product: Formula 20: Position sizes from notional exposure Minimum required capital
We can now calculate the minimum capital , a concept I introduced in chapter four. This figure is necessary to decide which instrument and product we can trade. First, I use the position sizing formula ( formula 14):
Notional exposure = (target risk % × capital) ÷ instr ument risk
%
Substituting in the minimum notional exposure and minimum capital, and then rearranging:
Formula 21: Minimum capital
Minimum capital = (Minimum exposure × instrument risk %) ÷ t arget risk %
Where the minimum notional exposure is the exposure of the minimum trade , calculated using the formulas for notional exposure starting on page 59 .
Minimum capital and the siren call of leverage Minimum capital is an annoying concept, since it often prevents traders from trading the products they want, or even trading at all. Looking at formula 21 there are three ways that minimum capital levels can be reduced:
Finding an instrument with a lower minim um exposure.
Finding an instrument with lower inst rument risk.
Increasing the target risk.
Options 1 and 2 are fine, in theory. In reality, as I have already discussed, you will probably end up paying higher costs for instruments that have higher mini mum capital.
Option 3 is the dangerous one. It is particularly dangerous because a trader using the Starter System will usually be using much less leverage than the brokers permitted maximum. I suggest using a leverage factor of 1.25 to trade Euro Stoxx 50 CFDs, but my broker has a maximum of 20 (for retail customers: professionals can use even more). I could use a target risk that is ten times higher (120%), and still end up with a leverage factor
that is well below the maximum (12.5, much less than 20).
Even better, I would only need one-tenth of the minimum capital
: just $645.
But remember once more the formulas used to determine the appropriate target risk:
Risk possible given maximum leverage allowed by brokers: sure, no p roblem here.
Risk possible given maximum prudent leverage: with leverage of 12.5 a 4% move would wipe out half your capital. Moves that size are not uncommon in the equ ity markets.
Your own personal appetite for risk: Look again at tables 9 to 11
and decide whether you are comfortable with a 120% risk target. I wouldn’t be.
Optimal and prudent risk level given the expected profitability of your trading system: half the Sharpe ratio. You would need a Sharpe ratio of 2.4 to justify a risk target of 120%. This is
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much better than almost any other trader on the planet 76 77 can expect to achieve when trading a single instrument!
Please do not be lured down this path by the brokers. Stick to the risk target I recommend and keep your le verage down.
Here are some examples showing how minimum capital is calculated, using the target risk of 12% for the Starter System, and my current estimates of inst rument risk: Position sizing and minimum capital requirements Remember from earlier in the chapter that we use the current value of our account for calculating trade sizes. This can lead to problems for smaller traders who start with only just eno ugh capital.
Suppose you started trading US Eurodollar futures with $12,000.
According to my calculations these currently require a minimum capital of $11,000. You start with $1,000 more than you need.
Sadly, in this particular example things don’t go well. After a few losing trades you’re down to $10,900. This is insufficient to meet the minimum capital requirement.
You have three options to deal with this problem. Firstly, you can ignore it and carry on trading . This means that you will have too much risk relative to your current capital. If you make further trading losses your account will be emptied: quickly. Do n’t do this .
Secondly, you can add money to your account to replenish your losses and get you back to $11,000. I really don’t recommend this
. Topping up your account when you lose money is like repeatedly pushing coins into a slot machine. It probably won ’t end well.
The third option is to increase your starting capital . Then you can lose some money but still continue trading. For example, if you initially had $22,000 in your account then you could continue to trade Eurodollar futures until you had lost half your money. I recommend starting with twice the minimum capital for your preferred instrument – more if possible.
A fourth option is to switch to trading a different instrument with lower capital requirements, once you’re below the minimum level for the instrument you initially selected. That might make sense if the alternative instrument is still cheap enou gh to trade.
When should positions be closed?
Too many traders fall in love with a position and then refuse to close it. If you never close positions then you are investing, not trading. There is nothing wrong with investing – I do it myself – but this is a book about trading. Other traders will close their trades prematurely, before any potential profits have been realised. Deciding when to close your positions should not be down to personal whims and fancies. It should be subject to the same level of discipline as deciding when to ope n positions.
What type of closing rule?
There are a number of different methods that traders typically use for closin g positions:
How do we determine the right stop loss level?
Do you prefer your stops tight or loose? A tight stop loss implies the price barely has to budge from its recent high (or low if you’re short) before the trade gets closed. Tight stops keep losses small, but you will be prematurely stopped out of many trades that could have been profitable. With a loose stop you will see larger losses before the rule closes each trade, but by sticking with the position and not getting shaken out by small price fluctuations there might be a better chance of m aking money.
Whic h is better?
Some traders use fixed sto p loss gaps:
“I always close my position when the price has retraced by $1”
Paraphrased from an anonymous trading blog But more sensible people understand that setting stop losses is a little more complicate d than that.
There are a number of factors that traders usually consider when setting their stop losses. Typically, th ese include: The size of their account (smaller accounts need tighter stops, because small movements in price have a large effect on a sma ll account).
The size of their position (larger positions need tighter stops, because smaller movements in price quickly get magnified into la rge losses).
In fact, these are both completely irrelevant.
If you use account size when setting stop losses, then smaller traders end up with tighter stops than the larger traders. As a result, smaller traders will trade more frequently than those
with more capital, regardless of whether that makes sense or not for a given instrument. This is nonsensical: the market doesn’t know or care how big your account is, or how large your po sitions are.
But surely it is dangerous to ignore the size of your account and position size when setting s top losses?
In fact, if you have used a position sizing rule, then the risk of your trade will already have been calculated taking account size into account. It is then unnecessary to consider account size or position size when setting you r stop loss.
These are the three factors that actually matter when determining stop losses:
The current risk of the instrument.
Interaction with the o pening rule.
Tr ading costs.
It is fairly obvious why instrument risk is important when setting stop losses. It would make no sense to use the same stop loss on both US 2-year and 10-year bonds. US 2-year bonds have about one-quarter the volatility of 10-year bonds. A stop that is correct for 2-year bonds will be far too tight fo r ten years.
A stop loss gap that is fine for quiet and peaceful periods will be far too tight when things get crazy. By regularly re-estimating instrument risk we can ensure the stop loss is appropriate for the market environment. If you use the current level of instrument risk to calculate your stop, then you will have wider stop losses when markets are jumpier. The position sizing rule will automatically calculate smaller positions when risk is higher, so you do not need to worry about the risk of losing more money if you widen your stops when instrument r isk goes up.
So, you should set your stop loss gap as a fraction of the relevant instrument’s current volatility , i.e., as a fraction of instrument risk , measured as an annual standard deviation of returns .
But what fraction should you use? A small fraction such as 0.1
will give a very tight stop, whilst a large fraction like 1.0
translates to a relatively wide stop. For example, consider the S&P 500 with instrument risk of 16% a year. A fraction of 0.1
translates to a stop loss gap of 0.1 × 16% = 1.6%. A move of that size can easily happen over a few hours. Conversely a fraction of 1.0 produces a stop loss gap of 1.0 × 16% =16%. Normally it takes several months for the price to mov e that much.
To make this decision we need to consider the remaining factors from the list above: the interaction of the stop loss with our opening trading rule , and tr ading costs .
It would be nuts to use a wide stop loss with a relatively fast pair of moving average crossovers, like MAC 2,8. We would end up opening a position based on a trend that was just a few days old, and then stay in the trade for months. Equally, it makes no sense to use a tight stop loss with a slow pair of crossovers. Imagine
– you wait patiently for weeks, until the market shows a clear trend, before placing your trade. Then just a few hours la
ter you are stopped out when the price moves slightly against you.
Trading costs are also important when setting the stop loss volatility fraction. With tighter stop losses we trade more frequently, which will result in costs that are too high for most instruments and products. However, I calibrated the opening rule with costs in mind. So, we don’t need to explicitly consider costs again, as long as the closing stop loss rule is properly aligned with the o pening rule.
To calibrate the stop loss fraction, I did some back-testing. I estimated the average length of time that different levels of 20 20
stop loss fraction 76 78 held a position. I then matched these fractions to the moving average crossover (MAC) rule with the most similar trading frequency. The results are in table 12. For the Starter System, which uses the MAC 16,64 crossover pair, the table implies we should use a stop loss frac tion of 0.5 .
Table 12: Faster trading rules need tighter stop losses Trades per year for different stop loss fractions, matched to opening trade rule with different cross over speeds.
• None of the crossover pairs I use have the same trading frequency as the stop loss fraction shown in this row.
All values calculated from back-testing different MAV opening rules and stop loss fractions over the instruments in my data set. Row in bold is Sta rter System.
Stop loss calculations
Instrument risk is usually measured as an annualised standard deviation of percentage returns. When calculating your stop loss gap it’s better to measure the instrument risk in price units rather than percentage units . This is because we need to set our stop level, and thus our stop loss gap, in price units.
Formula 22: Price unit volatility
Instrument risk in price units = Instrument risk as percentage volatility × c urrent price
Formula 23: Stop loss gap
Stop loss gap = Instrument risk in price units × stop l oss fraction
If we are long , to calculate the stop loss level we subtract the stop loss gap from the high watermark . This is the highest daily closing price since the trade was opened. If at any point the daily closing price falls below the stop loss level, we close the position. The stop loss will always be lower than the current price (until it is hit). If the price is going up, then the stop loss level will be going up.