multiplier (IDM) is a relatively complex task, ¹70 74 so I’ve used my back-testing software to do it for you. Table 43 shows the multiplier you should use for different numbers of instruments.
The values in the first column assume that you’re adding
instruments to your portfolio from different asset classes to 20 20
provide the maximum diversification. ¹70 75 The second column shows the IDM to use if you are limited to a single asset class, for example, if you are a spot FX trader who can on ly trade FX.
Table 43: Instrument diversification multiplier (IDM) to use for a given number of instruments
Values calculated from back-tests using 37 futures instruments Higher values for IDM increase your leverage, so I have put a maximum ceiling on the IDM. It should never be larger than 2.5, regardless of how many instruments you ’re trading.
The diversification multiplier and risk targeting 20 20
Back in chapter five, ¹70 76 I calculated the optimal risk target of the Starter System and came up with a figure of 12%. This was determined by the performance of the system. The higher the expected Sharpe ratio (SR) of a trading strategy, the higher the 20 20
risk target can be. ¹70 77 The Starter System has a relatively modest 12% risk target because it has a relatively modest expected pre-cost SR of 0.24.
But with more instruments you can expect to get better performance. Earlier in this chapter, for the example of two instruments, the expected pre-cost return was increased from 4.88% to 5.74%. In general, the expected Sharpe ratio increases proportionally with the instrument diversification multiplier (IDM). I can prove this by taking formula 3 , for the pre-cost SR
of the Sta rter System:
SR old = (r – b) ÷ s old
Where r is the expected average return, b is the rate we can borrow at and s old is the original risk target. If we diversify our system and do not apply an IDM, then the standard deviation will reduce proportionally with the IDM, whilst the expected 20 20
returns remain unchanged: ¹70 78
SR new = (r – b) ÷ (s old ÷ IDM) = SR old × IDM
Applying leverage doesn’t affect the calculation of a Sharpe ratio. As the IDM is always greater than 1, applying the IDM will increase the Sharpe ratio, regardless of which risk target we de cide to use.
For example, the Starter System with a single instrument has r =
4.9%, with a standard deviation s old = 12%, and I assume a borrowing rate b = 2%.
SR old = (r – b) ÷ s old = (4.9% − 2%) ÷ 12% = 0.24
With two instruments from different asset classes, the IDM from tabl e 43 is 1.2:
SR new = 0.24 × 1.2 = 0.288
Table 44 shows how to use the IDM to calculate a new risk target if you are trading multiple as set classes.
Table 44: Instrument diversification multiplier (IDM), theoretical Sharpe ratio (SR), theoretical and recommended account level risk targets for multiple asset classes IDM values from table 43 (first column, multiple asset classes).
Recommended risk targets (D) are more conservative than the theoretical targets (C), as in back-tests the Sharpe ratio from higher diversification is lower th an expected.
The column A of table 44 is just a copy of the IDM values in the first column of table 43. Multiplying these IDM by the Sharpe ratio for the Starter System (0.24) gives a theoretical SR, which can be found in column B. From this, I can work out the theoretical risk target (column C), assuming I use the ‘half Kelly criterion rule’ that the risk target should be half the expected S harpe ratio.
In column D I’ve put the risk target that I’d actually recommend running your trading system at. These recommended risk targets don’t quite rise as fast as the theoretical values, because I find in my back-tests that actual improvements in performance tend to lag the increase that the IDM hopes y ou will get.
No matter how many instruments there are in your portfolio, you shouldn’t use a risk target of higher than 25%. This is the target I use myself – and I have nearly 40 instruments in my portfolio! I’ve also assumed here that the other determinants of risk target aren’t a constraint: broker leverage limits, prudent leverage limits, and your personal risk appetite. You should revisit the section starting on page 94 to check this f or yourself.
Don’t forget, changing the risk target for your entire trading account will also affect the risk target you have for each instrument. You should multiply the account level risk target by the IDM to get the instrument level risk target. The recommended values for instrument level risk targets are shown in column E of table 43.
For the two instruments I’ve used as examples in this chapter, which are from different asset classes, the IDM from table 43
will be 1.2 (a little more conservative than the value we worked out earlier), and the recommended account level risk target from table 44 is 13%. That means the instrument level risk target will be 1.2 × 13% = 15.6%.
Table 45 calculates the recommended account level, and instrument level, risk target when your instruments come from a single asset
class. There is less diversification, so the IDM and expected Sharpe ratio s are lower.
Table 45: Instrument diversification multiplier (IDM), theoretical Sharpe ratio (SR), theoretical and recommended account level risk targets for a single asset class IDM values from table 43 (second column, single asset class).
Recommended risk targets (D) are more conservative than the theoretical targets (C), as in back-tests the Sharpe ratio from higher diversification is lower th an expected.
The diversification multiplier and minimum capital requirements To recap: if you have a diversified set of instruments then you will: (a) be running at a higher overall risk target for your account due to improved performance expectations, and (b) applying a diversification multiplier to the risk targets on each individual instrument. Together these imply that the risk targets on each instrument will be higher than the 12% we used in the Starter System. One useful side effect of this is to reduce the minimum capital required to trade each instrument: the higher your risk target, the lower the capital that is required.
To calculate minimum capital we use formula 21 : Minimum capital = (Minimum exposure × instrument risk %) ÷ t arget risk %
To adjust minimum capital for a different risk target we multiply by the ratio of the original and the new instrument level risk target:
Formula 27: Adjust minimum capital for different risk target New minimum capital = Minimum capital × (original target risk ÷
new ta rget risk %)
For the two instruments I’ve used as an example in this chapter (Euro Stoxx and US 10-year bonds, both traded via CFDs), the correct risk target for each instrument is 15.6% (from table 44, as they are in different asset classes). The minimum account sizes are $6,500 (Euro Stoxx) and $6,000 (10-year bonds). To adjust for higher risk targets, I multiply the minima by the ratio of the original and new risk target. For Euro Stoxx: New minimum capital = 6,500 × (12% ÷ 15. 6%) = $5,000
For US 10 -year bonds:
New minimum capital = 6,000 × (12% ÷ 15. 6%) = $4,165
Remember, if you start with multiple instruments, you don’t need to apply the rule of using twice the minimum capital. To start trading these two markets you need just $5,000 + $4,165 = $9,165.
This is less than the $13,000 required to trade Euro Stoxx in the 20 20
Starter System for a single instrument! ¹70 79
Trading the Starter System adapted for multiple instruments Before you start trading
There is a bit more work to do before you begin trading with multiple instruments.
Running the system
Here are the changes required to the Starter System’s trade plan for multiple instruments:
Once you’ve done the initial setup, then running the Starter System for multiple instruments is just like running many individual systems, each with its own capital allocation and its own instrument level risk target (which is equal to the account level
risk multiplied by the IDM).
Monitor minimum account size: removing and adding instruments Trading with multiple instruments does involve one additional task: making sure that you can still meet the minimum instrument capital requirements for your current account size. If you cannot, then you need to remove instruments, starting with the last instrument you added in the setup stage, then the penultimate instrument you added, and so on (remember: ‘last in, first out’).
If you subsequently make your money back, then you can start adding back the instruments you’ve removed, starting with the most recently removed (‘last out, first back in’). If you’re lucky and get a rise in your account value above what you began with, then you can add additional instruments into your trading account, using the same logic that you used in the system d esign phase.
Let’s look at an example. Suppose you are trading Euro Stoxx and decide to add US 10-year bonds as your second instrument. You begin with $12,000 in capital. A couple of pages ago I calculated that the minimum capital required to trade these two instruments was $9,165 ($5,000 + $4,165). If you start with $12,000 you could split that 50/50 and put $6,000 in each instrument.
Unfortunately, you now start to lose money. Initially you should reduce your capital equally in each instrument, until there is $5,000 in each. After further losses, since you have to leave the absolute minimum $5,000 in Euro Stoxx, you start reducing your allocation to US 10-year bonds, which have a lower minimum capital ($4,165). Then, once your total capital is under $9,165, you will have to drop US 10-year bonds entirely, since they were the last instrument you added (‘last in first out’) and their
capital allocation would otherwise be under the minimum leve l of $4,165.
With a single instrument (Euro Stoxx), your account level and instrument level risk target will be back to the 12% used in the Starter System. The minimum capital required for Euro Stoxx is now the original $6,500 from chapter five. You do not apply the rule of requiring double the minimum capital, since that only applies when you start trading with a single instrument.
If your losses reach the point where you have less than $6,500, you will have to stop trading entirely or find a new instrument with an even lower minimum capital requirement. Naturally, once 20
you get more than $9,165 in capital, ¹¹70 you can start trading US
10-year bonds again, assuming that the opening rule confirms you s hould do so.
This process is summarised in table 46.
Table 46: Example of a trading plan to add or remove instruments as profits or losses are made
Plan assumes we are trading two CFDs. First CFD chosen: Euro Stoxx, with minimum capital of $5,000 when trading two instruments, or $6,500 when trading one instrument. Second CFD
chosen: US 10-year bonds, with minimum capital of $4,165 when trading two instruments.
When removing instruments, do not close existing trades . Wait until a position has been closed naturally by hitting a stop loss before taking it out of your portfolio. Otherwise, if your account balance moves around near the $9,165 threshold, you will end up incurring additional trading costs from constantly closing and reope ning trades.
Until you close your position, you will be temporarily taking on too much risk. To alleviate this, you should avoid opening new positions in other instruments if that means you are trading more markets than you’d idea lly want to.
For example, suppose we were trading Euro Stoxx and US 10-year bond CFDs and our capital has just dropped below $9,165. We want to stop trading US 10-year bonds. What happens next depends on our current positioning:
No position in anything : Don’t open a new position in US 10-year bonds. When the opening rule dictates it, open a new position in Euro Stoxx.
Position in Euro Stoxx, not in US 10-year bonds : Don’t open a new position in US 10-year bonds: from now on only trade Euro Stoxx.
Position in US 10-year bonds, nothing in Euro Stoxx : Wait until you have closed your US 10-year bond trade – do not open up a position in Euro Stoxx. When your US 10-year position is closed, stop trading US 10-year bonds and open up a new Euro Stoxx position when your opening rule dictates it.
Position in both US 10-year bonds and Euro Stoxx : Wait until one of the positions is closed by a stop loss, then see the relevant procedure for a single position in one instrument.
Eventually you will only be trading Euro Stoxx.
20
79 ³ Although, to be fair, this quote was aimed at stock investors rather than traders.
20 20
79 74 See page 92 .
20 20
79 75 Because a diversified system has a higher expected return for the same level of risk, it will also have a higher expected Sharpe ratio. As we saw in part two ( page 98 ) a higher Sharpe ratio means that it is safe to set a higher risk target for the account as a whole. I will discuss how we can quantify this effect later in the chapter.
20 20
79 76 Sometimes the average performance goes down slightly when an instrument is added. The average returns depend on exactly which instruments are drawn randomly, and sometimes we are unlucky and happen to get a set of instruments whose returns is slightly worse. But this slight degradation in performance isn’t significant or meaningful.
20 20
79 77 Table 5 .
20 20
79 78 Page 78 .
20 20
79 79 If you are familiar with correlations, you may be surprised to see how low these values are. However, they are the correlations of trading systems for particular instruments, not the correlations of returns in the actual instruments . The correlation of trading systems for a given pair of instruments is nearly always much lower than the correlation of the underlying returns.
20 20
¹70 70 Incidentally, don’t feel you have to trade every asset class, even if you have the capital to do so. Never add an instrument which is too expensive to trade (risk-adjusted costs greater than one-third of the expected Sharpe ratio: 0.08 for the opening rule specified in the Starter System). You may have good reasons for avoiding other asset classes entirely, for example, I don’t trade cryptocurrencies.
20
¹70¹ Okay in theory you could add the MXPUSD CFD, but the minimum capital requirement is so large that, if you could afford it, you would be better off trading futures.
20
¹70² Total capital 6,500 + 6,000 = $12,500. Share of Euro Stoxx 6,500 ÷ 12,500 = 52%, share of US 10-year bonds 6,000 ÷ 12,500 =
48%.
20
¹70³ There is more detail in my first book, Systematic Trading .
(If your account value is large enough to be in this position you can probably afford to buy another trading book.) 20 20
¹70 74 Technical note: Given N trading subsystems with a correlation matrix of returns H and instrument weights W summing to one, the diversification multiplier will be 1 ÷ [ ( W x H x W
20
20
T ) 70.75 ].
20 20
¹70 75 The IDM for two instruments with multiple asset classes (1.2), is a little lower than the value I calculated for the earlier example of Euro Stoxx equity and US 10-year bonds (1.3).
My recommended IDM is based on taking an average across many instruments. It is better to use this, rather than a value calculated for just one specific pair of products.
20 20
¹70 76 Page 99 .
20 20
¹70 77 As long as it is no higher than the risk target implied by broker leverage limits, prudent leverage limits, or your own personal tolerance for risk.
20 20
¹70 78 This calculation also assumes that all instruments have the same costs. As you will see I am quite conservative with my Sharpe ratio expectations, partly to account for any higher costs when additional instruments are added.
20 20
¹70 79 Of course, ideally you should put $5,000 in each so they’ve got the same capital allocation.
; 20
¹¹70 These figures all assume that the minimum capital required will remain the same, but in practice this needs recalculating as instrument risk changes.
Chapter Eight
Adding New Trading Rules
When asked to describe my last proper job working for a large systematic hedge fund, I’d usually waffle, saying something like,
“Looking for patterns in data to predict the movements in financial markets.” (That was before the 2008 financial crisis.
After the crisis had struck, once hedge fund managers and bankers had become public enemies number one and two, I used to mumble that I did, “Something with computers”, and then hurry away before I was unmasked as a capitali st scumbag.)
“Looking for patterns in data...” suggests that I spent my office hours carefully searching for one, amazing, new trading rule.
Surely this is the path to riches, requiring great expertise and skill? Isn’t this what every trader should be doing – combing
through charts, trying to find the undiscovered opening rule which will earn mass ive profits?
Such a rule would no doubt have to very complicated, such as this horrendous example which was ‘generously’ shared by the author in an online tr ading forum:
“S&P Overnight – If Top 3 30-Minute Candles the Same Colour Trades Inverse 3rd Tallest Volume Candle Colour – If Flat Subsequent (S&P & Nasdaq Rotate Between Excluding Open & Close & Including Open & Close Including 16:00 Candle) Overnight Sunday Trades 3rd Highest 30-Minute Candle Volume Including Opening & Close Including 16:00 Candle from 18:00–00:30 & 00:30–9:30 Trades 3rd Highest Volume Excluding Opening & Close but Including 16:00
Candle (Overnight Thanksgiving from Trades 3rd Highest Open Excluding Opening & Close from 16:00–3:00 am & Trades 3rd Highest Volume Including Opening & Close but Including 16:00 Candle from 3:00–9:30)” …and so it continues for another 620 words.
Trading rule posted on elitetrader.com Traders love such complexity as it validates the time and effort they spend searching for patterns and increases the chance that they have found something unique. They think it gives them an edge. I t does not.
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 17
