Estimate the typical number of annual trades, and hence l ikely costs.
Check that it is profitable (or at least not significantly l oss making).
Decide on the weights to use when averaging it’s forecast with other tr ading rules.
Ideally you would perform steps 2, 3 and 4 by back-testing across a large number of instruments (including ones you may not yet be trading). Whilst it is possible to perform all of these steps in a spreadsheet, it’s much easier to use specialised software.
Unfortunately, this software makes it all too easy to commit the sins I highlighted in chapter three: taking excessive risks, trading too quickly, and assuming the past will repeat itself (
over-fitting ). Careful handling of the software is required to avoid making serio us mistakes.
There is much more I could say about the design and testing of trading rules. Naturally, I would recommend reading my first book, Systematic Trading , which covers all of these subjects in gre ater detail.
1. Semi-Automatic Trading
Perhaps you have concluded that systematic trading is not for you. It is way too boring mechanically following rules. You think you have some experience or insight into the market which cannot be implemented using a simple trading rule. You want to use your own subjective judgment to trade: discretion ary trading.
Way back in chapter three I wrote this:
“Trading systems ha ve two jobs:
Deciding when to open a new position, and whether to buy or sell.
Deciding the size of position you should have, and how long to hold it for.
I believe that everyone should use a system for the latter , and almost everyone should use a system for the former.”
Let me repeat that: even discretionary traders should use a system to decide on the size of their position and how long to hold it for. So, if you want to move away from pure systematic trading, I strongly recommend that you do th e following: Use your own judgment, analysis, subjective process, or examination of chicken entrails to decide whether to buy or sell a particular instrument. This step replaces the opening trading rule in the Sta rter System.
Size your positions according to the rules of the Sta rter System.
Use the stop loss from the Starter System to close you r positions.
In my first book Systematic Trading , I named this hybrid of person and machine, a semi-automatic trader . There is slightly more to Semi-Automatic Trading than blithely replacing your opening rule with a well-informed guess. Questions we need to addr ess include:
Performance monitoring
Initially semi-automatic traders should use the same stop loss fraction as in the Starter System, and a risk target no greater 20
than the 12% in the Star ter System. ¹74²
This might seem overcautious. These values are set using the performance expectations we had for the Starter System. But you are a brilliant human trader, much better than a dumb system!
Surely you will generate a much higher Sharpe ratio than the measly 0.24 expected for the Starter System, or the slightly higher performance you could expect to get from making the improvements in parts three and four o f this book?
If you are on course to make a seriously high Sharpe ratio then you can set a higher risk target. You could also trade faster, since the speed limit I set for costs is based on spending one-third of your expected returns. This would translate to a lower stop loss fraction, a shorter holding period, and more trad es per year.
Wait! Don’t get carried away. You don’t know how good you will be at discretionary trading until you’ve actually done it. It is better to start trading with the recommended values for risk target and stop loss, then monitor your live trading performance,
and if it is respectable enough you could consider changing your system parameters.
In this section I’ll explain how you can check to see if your trading is sufficiently profitable to justify an upwards revision of your performance expectations. In the next section I’ll discuss how you can use these expectations to adjust your risk target and stop l oss horizon.
You will not be recalibrating your system based on your average realised trading profits. Instead you will be using a conservative estimate of what your likely profitability will be.
If you perform significantly better than the Sharpe ratio expected for the Starter System, then your expected Sharpe ratio will be higher. But your expected future Sharpe ratio will always be set at a lower, more conservative, level than what you have actual ly achieved.
There are two ways to check performance; using daily returns, or the returns from each trade. Given you will be trading quite slowly it is more appropriate to use the returns from each trade.
Otherwise you can get several months of superficially attractive daily returns if you just happen to be the right way round on your first trade. Also, it is less work to use the returns from each trade, and if you are trading multiple instruments, you can gather evid ence faster.
20
First you need to calculate the performance ratio ¹74³ of y our trading:
Formula 33: Performance ratio
Performance r atio = r ÷ s
Where r is the average profit from each trade after all costs have been paid, and s is the standard deviation of your trade by 20 20
trade profits. ¹74 74 Once you have the performance ratio, plus the number of trades you have done so far, you can look them up in table 72. This will give you a conservative expected Sharpe ratio 20 20
after costs: ¹74 75 the Sharpe ratio (SR) you can be reasonably confident of achieving given what you’ve done so far.
Table 72: Conservative expected Sharpe ratio for a given performance ratio
We can be 75% confident that the Sharpe ratio is equal to or higher than the value shown, given the performance ratio. Where there are insufficient trades, I assume the expected Sharpe ra tio is 0.24.
Where the performance ratio is too low, or there is not enough history, then we are unable to say what the expected SR is with much confidence, and you should stick with the expected SR from the Starter System, 0.24. Notice also that I have capped the
expected Sharpe ratio at 1.0, even when theoretically it could be higher. This is to stop you using an excessively high- risk target.
Let’s take an example. Suppose you do 12 trades, and the average return on each trade after costs is 2% of your capital, with a standard deviation of 3.9% of your capital. The performance ra tio will be:
0.02 ÷ 0 .039 = 0.513
To be conservative we round this value down and look at the row in table 72 relating to a performance ratio of 0.5. We also round down 12 trades to ten. In the row for a ratio of 0.5, and the column for ten trades the conservative expected Sharpe ra tio is 0.39.
Using the original stop loss fraction and opening rule, it would take about two years to do 12 trades. A performance ratio of 0.513 is extremely good: it is more than four times better than 20 20
what I expect the Starter System to achieve. ¹74 76 So you can see that fairly strong evidence is needed to justify a higher expected Sharpe ratio, either in the form of a high performance ratio, or a very long track record of actual tradi ng, or both.
System calibration for semi-automatic traders From the last section you should have estimated your conservative expected Sharpe ratio after costs . Assuming this is higher than the 0.24 for the Starter System, you can now revisit chapter five ( page 94 ) to see if you can increase your risk target. Assuming that your own personal risk tolerance is high enough, and that you wouldn’t run into any problems with broker leverage limits, 20 20
¹74 77 this suggests you could increase your risk target to half the conservative expected S harpe ratio.
Formula 34: Risk target given conservative Sharpe ratio Risk target = Conserv ative SR ÷ 2
In the example above, given 12 trades with a performance ratio of 0.513, the conservative Sharpe ratio from table 72 was 0.39. The new risk target could be 0.39 ÷ 2 =
19.5% . This is an absolute maximum – you do not have to use that figure, but you must not 20 20
have a higher r isk target. ¹74 78
With a higher Sharpe ratio you can also afford to spend more on costs. Remember from chapter five that using my speed limit, the maximum risk-adjusted cost is equal to the pre-cost Sharpe ratio divided by 3. This is equivalent to setting your cost budget at 20 20
half your post-cost Sh arpe ratio. ¹74 79
Divide the expected conservative Sharpe ratio by 2. This gives you your risk-adjusted budget for total costs. Subtract holding
costs for the relevant instrument, which you have to pay no matter how often you trade, and you have your budget for transaction costs. Then divide what is left by the expected cost per trade for each instrument you are trading. This will give you the maximum number of trades you can afford to do per year, for a given instrument.
Formula 35: Maximum trades per year given a conservative estimate of Sharpe ratio
Maximum trades per year = [(Conservative SR ÷ 2) – holding costs]
÷ co st per trade
Now consult table 73 to see how you could change the volatility fraction and forecast horizon, for a given number of trad es per year.
Table 73: Stop loss fraction and forecast horizon to use for a given number of annual trades
Values calculated from back-testing different stop loss fractions over the instruments in my data set. Row in bold is Starter System. Figures are copied fr om table 12.
For example, suppose you’re trading the Euro Stoxx CFD. This has risk-adjusted holding costs of 0.0246 per year, and transaction costs per trade of 0.00307 (figures calculated in appendix B).
Suppose you estimate your conservative SR at 0.39: Maximum trades per year = [(Conservative SR ÷ 2) – holding costs]
÷ cos t per trade
= [(0.39 ÷ 2) – 0.0246] ÷ 0. 00307 = 55.5
You can afford to trade no more than 55 times a year. Looking at table 73 you could get away with using a stop loss fraction of 0.1 , which is expected to trade 46.9 times per year. You don’t have to lower the fraction that much, but you must not use an even low er fraction.
If you do change your stop loss fraction then you must also change your forecast horizon, which for a fraction of 0.1 will be eight days. You will be now be making predictions at a shorter time scale, with a horizon of around a week. Are you confident that your subjective method for picking trades will work with a one-week horizon? If you aren’t comfortable predicting market movements with a shorter horizon then use a larger stop lo ss fraction.
Incidentally, it isn’t compulsory to adjust your risk target or stop loss – it’s completely okay to ignore these recommendations and stick with the levels used in the Starter System, or to make a partial adjustment towards the new levels. It’s also fine to
adjust the risk target, and leave the stop loss fraction alone, or vice versa.
What if your performance gets better or worse?
You should monitor your performance ratio regularly. If it improves then you can raise your conservative expectation of Sharpe ratio; and also consider making upward adjustments to the risk target and stop lo ss fraction.
If you hit a losing streak, and your performance ratio begins to degrade, then you must recalibrate your trading system to reflect a lower expectation for Sharpe ratio. If you find that your volatility target and stop loss fraction are too high, then they must be reduced.
Let us return to the example of a Euro Stoxx CFD trader who had a run of good performance. They had an expected Sharpe ratio of 0.39, after costs. Based on that the trader decided to change their stop loss fraction to 0.1, and their risk targ et to 19.5%.
Now suppose they hit a rocky patch, and after a total of 20
trades their performance ratio has fallen to 0.38. Rounding down to a ratio of 0.35 we can see that the expected Sharpe ratio in table 74 has fallen to 0.26 . That equates to a maximum account level risk target of 0.26 ÷ 2 = 13% . Their current risk target of 19.5% is too high, and they nee d to cut it.
What about the volatility fraction? Euro Stoxx CFD has risk-adjusted holding costs of 0.0246 per year and transaction costs per trade of 0.00307 (figures calculated in appendix B). Using formula 35:
Maximum trades per year = [(Conservative SR ÷ 2) – Holding costs]
÷ cost per trade = [(0.26 ÷ 2) – 0.0246 ] ÷ 0. 00307 = 34.3
From table 73 the maximum volatility fraction they could use is 0.20. Their current fraction of 0.1 is too high, and this parameter also needs to be changed.
20
¹74¹ If you want to know where these figures come from: Starter System ( page 92 ), instruments ( page 170 ), trading rules (
page 195 ), stop loss ( page 227 ), and non-binary trading (
page 243 ).
20
¹74² If they are trading one instrument. For multiple instruments, it is okay to use a higher account level risk target to reflect the diversification in their portfolio, and to apply an instrument diversification multiplier to instrument level risk targets. See chapter seven.
20
¹74³ This is a bit like a Sharpe ratio (an average return over a standard deviation), except there is no borrowing rate and it is calculated per trade, rather than per year.
20 20
¹74 74 I explain how to calculate these figures in appendix C, page 315 .
20 20
¹74 75 Very technical note: We can be 75% confident that the Sharpe ratio is equal to or higher than the values shown in the table, given the performance ratio. Assuming 5.4 trades per year as in the Starter System and a borrowing rate of 2% I can imply the annualised Sharpe ratio from the performance ratio. This in turn gives the mean estimate for the Sharpe ratio distribution. For Gaussian returns the variance of the sampling estimate for a Sharpe ratio is given by (1+0.5SR ² )/N, where N is the number of periods. I then take the 25% percentile point from the resulting implied distribution of the Sharpe ratio estimate.
20 20
¹74 76 The expected performance ratio of the Starter System is about 0.18. In reality we have to pay costs that would reduce that.
20 20
¹74 77 See page 94 .
20 20
¹74 78 For traders with multiple instruments: This calculation is the same, even if you started with a higher account level risk target to reflect the diversification in your account. You will need better performance history to justify raising your expected Sharpe ratio even further, compared to a trader with only one instrument. Also, this is the account level risk target . If you are using multiple instruments you should still use an instrument diversification multiplier (IDM) to work out your instrument level risk target. The value of the IDM will remain unchanged, regardless of any increase you make to your account level risk target.
20 20
¹74 79 Let SR pre be the pre-cost Sharpe ratio (SR), SR post be the after cost SR, and c the risk adjusted cost. SR post = SR pre –
c. Then if c = SR pre ÷ 3 −› c = SR post +c −› 2c = SR post −› c
= SR post ÷ 2.
Epilogue
“A little learning is a dangerous thing”
Alexander Pope, ‘ Essay on Criticism ’ 1709
“The tyro knows nothing, and everybody, including himself, knows it. But the next, or second grade thinks he knows a great deal …
It is this semi-sucker rather than the 100% article who is the real all-year-round support of the commission houses.”
Edwin Lefevre, ‘ Reminiscences of a Stock Operator ’ 1923
Newcomers to trading don’t (usually) do anything too crazy. They are naturally sceptical of the whole business; and their instinct tells them to behave cautiously and keep their bets small. Many new traders speak of feeling frozen, like rabbits in the
headlights of a car, when they try and make their first trade.
Trading too often is unlikely to be a problem for novices.
The danger comes when you acquir
e a little learning and some experience. You graduate from being a ‘tyro’ (a beginner) and achieve the grade of ‘semi-sucker’. You have some good luck –
several trades in a row without any losses. You begin to think that nothing can possibly go wrong. You start to think you’re a trading genius. You get greedy. You ignore your trading plan. You start to take unnecessary risks, use too much leverage, and increase the frequency of y our trading.
Do not get carried away. A few good trades do not mean you’ve found the holy grail. Be careful – things can still go b adly wrong.
Remember:
Stick to your system
Don’t use excessive leverage – keep your risk ta rgets modest Don’t trade too often – keep your tradi ng costs low St ay sceptical
Glossary
Words in bold refer to other entries in t he glossary.
Appendices
Appendix A: Useful Information
Further reading
Systematic Trading , Robert Carver, 2015, Ha rriman House My first book. Essential reading for traders who wish to develop their own trading systems (but then you would expect me t o say that).
Following the Trend , Andreas F. Clenow, 2012, Wiley Great resource for developing a futures trading strategy if you have the capital to diversify across many different instruments.
The Complete Turtle Trader , Michael W. Covel, 2009, Har per Business
True life story of a set of novice traders who learned to trade sys tematically.
Building Winning Algorithmic Trading Systems , Kevin J. Davey, 2014, Wiley
Kevin is a ‘celebrity trader’, but unlike most he actually knows what he is doing.
Trading Systems and Methods, 5th Edition , Perry J. Kaufman, 2013, Wiley
The bible of trading strategies. Great resource for trading rule ideas.
Fortunes Formula , William Poundstone, 2005, Hill & Wang Excellent and very readable book about the Kell y Criterion.
Technical Analysis , Jack Schwager, 1995, Wiley This is just one of many excellent books that Jack has written.
Fooled by Randomness , Nassim Taleb, 2 007, Penguin Taleb has written a series of books on the nature of risk, especially in trading. This book, his first, is the best.
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 23
