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Appendix B: Costs
Th is appendix:
explains in detail how to calculate costs, including calculations for the example instruments used in chapter six.
explores the relationship between costs and minimum trade size.
suggests some tactics you can use to reduce tr ading costs.
Spreadsheets that implement all the formulas in this appendix can be found on my website: systematicmoney.org/lever aged-trading Transaction costs
There are two typ es of costs:
Transaction costs, that we pay every ti me we trade.
Holding costs, which we pay for holding positions regardless of how oft en we trade.
First let’s calculate transaction costs. I will use the follow ing symbols:
S = spread in price units, e.g., if the trading spread is 100.01
to 100.02, then S=0.01
C = Commission to trade the instrument minimum size, in units of instrum ent currency
P = Current price o f instrument
TC ccy = Transaction cost per trade in instrum ent currency TC ratio = Transaction cost per trade, as a proportion of the exposure value of the minimu m size trade TC risk = Transaction cost per trade, r isk-adjusted Now we have the transaction cost as a percentage, we need to calculate the risk-adjusted cost (remember from chapter four that it makes sense to express costs in risk-adju sted terms).
Total risk-adjusted transaction cos t per trade: TC risk = TC ratio ÷ V
Where V = Instrument risk of instrument, measured as an annual standar d deviation.
For our example instruments:
Corn futures, V = 11.9%, TC risk = 0.0060% ÷ 11.9 % = 0.000504
AUDUSD FX, V = 6.84%, TC risk = 0.006% ÷ 6.84 % = 0.000690
Gold spread bet, V = 11.0%, TC risk = 0.023% ÷ 11. 0% = 0.00209
Euro Stoxx 50 CFD, V = 9.6%, TC risk = 0.0295% ÷ 9. 6% = 0.00307
S&P 500 SPY ETF margin trade, V = 16%, TC risk = 0.0383% ÷ 1 6% =
0.00239
Holding costs
Now we can calculate holding costs: the costs paid to own a position regardless of how often it is traded. These are expressed as an an nual figure.
Now we need to risk adjust the holding cost. Total risk-adjusted holding co st per year:
HC risk = HC ratio ÷ V
Where V = instrument risk, measured as an annual standar d deviation.
For t he examples:
Corn futures (dated), V = 11.9%, HC risk = 0.012% ÷ 11. 9% =
0.00101
AUDUSD spot FX (undated), V = 8.7%, HC risk = 0.3625% ÷ 6. 84% =
0.0417
Gold spread bet (dated), V = 11.0%, HC risk = 0.19% ÷ 11 .0% =
0.0173
Euro Stoxx 50 CFD (dated), V = 9.6%, HC risk = 0.236% ÷ 9 .6% =
0.0246
S&P 500 SPY ETF, margin trading (undated), V = 16%, HC risk =
0.125% ÷ 1 6% = 0.00781
These calculations ignore any account management fees or custody charges. They also assume that we always have a position on. For the Starter System, this will not be true (however, it is more likely to be true if you use a continuous trading system with no stop loss, as outlined in chapter nine). There will be times when the stop loss has been triggered, but the opening rule has not yet reversed its position. However, it is better to be conservative and assume that we always hold a position.
Total costs
The total expected annual cost for a trading system will be the transaction cost, multiplied by the expected number of trades, plus the annual h olding cost.
Total risk-adjusted cost, (i.e., in Sharpe r atio units): Ctotal = (TC risk × N) + HC risk
Where N = Expected number of trad es per year.
For the example instruments, using N = 5.4 for the Sta rter System:
Corn futures, C total = (0.000504 × 5.4)+ 0.001 01 = 0.00373
AUDUSD spot FX, C total = (0.000690 × 5.4) + 0.0 417 = 0.0454
Gold dated spread bet, C total = (0.00209 × 5.4) + 0.0 173 =
0.0286
Euro Stoxx CFD, C total = (0.00307 × 5.4) + 0.0 246 = 0.0412
S&P 500 margin trading, C total = (0.00239 × 5.4) + 0.00 781 =
0.0207
For the Starter System we require C total to be less than 0.08 to trade a given instrument and product.
Minimum capital and costs
Why is there an inverse relationship between the minimum amount of capital required to trade an instrument and product, and how
costly they are to trade? Partly it’s because cheaper products like futures have larger minimum trade sizes, and because of minimum commissions, but it’s also related to inst rument risk.
To see why, consider the definition of minimum capital. Remember from chapter four that we try to achieve a risk target for our trading, and that for most instruments there is a minimum position size (FX lot, one CFD, futures contract, or bet per point).
Suppose an imaginary instrument has a notional exposure at its minimum position size of $1,000 and we’re trying to hit a risk target of 12% (annual standard deviation of returns).
If the returns of the instrument have a risk of 12%, then the risk of one minimum position unit is 12% × $1,000 = $120. We’d need at least $120 ÷ 12% = $1,000 of capital to trade this instrument. However, if the instrument has lower risk, say 6% per year, then we’d need just (6% × $1,000) ÷ 12% = $500 of capital instead. The converse is true: if the instrument risk was higher than 12% we’d need $2,000 in capital.
Now, how are costs and risk related? Let’s assume that it costs $20 in costs for the minimum trade of $1,000, or: 20 ÷ 1,000 =
2%. But we’re interested in risk-adjusted costs. So, with instrument risk of 12% the risk-adjusted costs work out at: 2% ÷
12% = 0.1667. However, with 6% risk the costs would be doubled: 2% ÷ 6%=0.3333. As table 75 shows, in this simple example there is a clear inverse relationship between minimum capital and risk-adjusted transa ction costs.
Table 75: Higher instrument risk means higher minimum capital, but lower costs
Minimum capital and costs for a hypothetical instrument at different levels of inst rument risk:
Of course, in real life it isn’t quite that simple, but broadly speaking this relationship holds within product categories and across instruments. The cheapest future I trade (Nasdaq equity index) is also one of the riskiest (risk around 19% per year), and the most expensive future (German 2-year bonds) is one of the safest (around 0.3 % per year).
Most instruments show a clear relationship: the lower the minimum capital required, the higher the costs you’ll need to pay.
Smarter execution to avoid the spread
Parts three and four of this book are all about improving the pre-cost expected returns of the Starter System. However, it’s also possible to increase your post-cost returns by reducing your costs. The traded spread that you pay when buying or selling is a significant part of the costs you have to pay when trading. The
good news is that most traders can avoid paying the spread at least some of the time, resulting in lower costs, and better returns. This section e xplains how.
How important is the spread cost?
On my screen right now, the price of corn is quoted at $374.30
per futures contract. But I can’t actually buy corn at that price, nor can I sell it. If I want to buy it will cost me $374.40, which is where the market is offering corn. Should I sell, I’d only receive $374.20, which is the market’s bid for corn. Essentially, $374.30 is the mid-market price , but I can’t actually trade at that level.
I define the spread cost as the difference between what I pay or receive, and the notional mid-market price. In both cases I’m paying a spread cost of $0.10 ($374.3 – $374.2, or $374.4 -
&nb
sp; $372.3). Alternatively, you can calculate this by taking the spread ($374.4 –$374.2 = $0.20) and halving it (half of $0.2 0 is $0.10).
Ten cents might not seem very much, but even with the limited amount of trading we do in the Starter System, it all adds up.
Have a look at table 76. The top row shows the risk-adjusted trading cost for some of the products I analysed in chapter six, when I introduced the Starter System. These costs assume that I have to pay the spread : buying at $374.40 and selling at $374.20
and paying $0.1 0 each time.
But suppose I could somehow avoid paying the spread. I could pay $374.30 for corn or receive the same if I sold. If I can trade at mid-market , I’d pay the costs shown in the second row of the table. There are no spread costs here, just commissions and holding costs. Better still, suppose I could capture the spread –
buying at the bid, and selling at the offer. If I can capture the spread I could buy corn cheaper than mid-market, at $374.20 (the market’s bid); and sell it higher, at $374.40 (the best offer in the market). Then I’d actually earn $0.10 every time I traded.
This would give me the risk-adjusted costs shown in the third row o f the table.
Table 76: Not paying the spread saves money Risk-adjusted trading costs with different execution assumptions
‘Pay the spread’ is the normal situation where we buy at the offer and sell at the bid. ‘Mid-market’ is where we can trade at the average of the bid and ask. ‘Capture the spread’ is where we buy at the bid and sell at the offer. In all cases commissions and holding costs are still paid.
Not paying the spread is worth doing in corn futures, where I can save almost half my costs if I can capture the spread. However, these are already very cheap to trade, so the benefits are
minimal. Similarly, in S&P 500 ETF trading, because we are trading ten shares at a time, the $1 minimum commission forms a large part of our costs and we still have to pay that even if we can avoid the spread. Avoiding the spread in spot FX markets is also of limited benefit. The holding costs, made up of the funding spread, make up the majority of total costs.
In CFDs and spread bets, the spread is far more important. Here there is no commission to pay and avoiding the spread by trading at mid-market will nearly halve the total costs. Earning the spread will reduce costs so that they are almost as low as in futu res markets.
Limit and market orders
How can you hope to trade at mid-market, or even better capture the spread? The solution is to use a limit order rather than the standard market order . Unfortunately, not all brokers offer limit orders. If yours does not, then get yourself a new broker or skip t his section.
A market order will be executed immediately at the best available price in the market at the time – the best bid if you’re selling, or the best offer if you’re buying. With market orders you always pay the spread.
In contrast, a limit order comes with a price tag attached and will only be executed if someone else in the market is willing to pay that price. Let us return to the example of corn futures, bid at $374.20 and offered at $374.40. To make the text readable I will now drop the $374 part of the price quote. Professional traders often do this when communicating with each other, and with their brokers. Using this method of quoting, a market buy order would cost 40, and I would get 20 if I was selling.
Suppose I want to buy. I could put in a buy limit order at the mid-market level of 30. Anyone putting in a market order to sell would trade with me, since my bid of 30 is higher than the current bid of 20. Similarly, if I was selling, I could enter a sell limit order at 30. The next buyer in the market would buy from me, since my offer is lower than the original offer of 40.
In both cases I would trade at the mid-market price of 30.
Better still, I could put my buy limit order in at 20. Markets work using a queuing system, so these orders would be behind 20 20
others at the same price which were submitted earlier. ¹75 70
However, once those orders were out of the way, the next market order to sell would be matched against my order. I’d capture the spread , by paying only 20 rather than the mid-market level of 30. The spread cost would actually be negative, as I earn $0.10
on each trade. This would also work if selling. I could put in a sell limit order at 40, and again end up earning $0.10 as a negative spread cost.
You might wonder why anyone would ever use a market order. Market orders have one huge advantage – they execute immediately. If you place a limit order there is a chance you will not trade at that level. For example, suppose you put in a buy limit order on corn at 20, hoping to capture the spread. Your order joins the queue of other orders at that price, but before it reaches the front of the queue some bullish news hits the market, and the price jumps to 60 bid and 80 offered.
Your order with a limit of 20 is now languishing behind all the better bids at 60, 50, 40 and 30. If you really need to trade then you have to cancel your bid and put in a new order. To reduce the risk of not trading this should be a market order . If you do it quickly enough, before the price rises further, you will end up paying the new offer price: 80. This is considerably higher than the original offer price of 40. You will pay $0.40
more than if you had submitted a market order in the first place.
In an effort to save money, you end up payi ng out more.
Who can execute smartly and how?
With market orders you have to pay higher costs, but with the certainty that they will execute quickly. That cost is pretty much fixed at half the size of the market spread. With limit orders you have the opportunity to pay lower or even negative costs, but with huge uncertainty about what those costs will be, and when your order will be filled. Neither order type is perfect. So, which should we use? It depends on what sort of trading yo u are doing.
Slow trend following (e.g., Starter System) The Starter System looks for trends that last for several weeks.
If you are holding a position for several weeks, it does not matter if it takes a few minutes or even hours to execute your trade. This style of trading is well suited to using limit orders. However, you need to have a plan B in case your initial limit order fails. Here is the tactical plan I use when submitting orders for my own tra ding system: I set an execution window during which I want my orders filled.
For my system this is an entire trading day.
At the start of the execution window I submit a limit order that would capture the sprea d if filled.
If the order fills, relax and open the metaphorical champagne: I have captured the spread.
If the order doesn’t fill, and there is an adverse price change so that I am no longer the best bid or offer (i.e., the market price has moved higher if I am buying, lower if selling): cancel the limit order and submit a market order. I will end up paying
significantly higher transaction costs, since the price has moved against me, and I’m also now paying the spread.
If the order hasn’t filled, and there is less than 10% of the execution window remaining (roughly 45 minutes if the window is a 20
whole trading day): ¹75¹ cancel the limit order and submit a m arket order.
I have built my own software that executes this plan. However, there is nothing to stop you using this method when trading manually. If you are not willing to spend all day monitoring your orders, then use a shorter execution window: an hour or even ten minutes is fine. Just be aware that with shorter windows you will end up with slightly higher costs. It is more likely you will end up with an unfilled order near the end of a shorter execution window and have to submit a market order. Impatience comes with a price tag.
How successful are the se tactics?
Table 77 shows the actual cost figures calculated from my own trading, since I started using this trading plan about four years ago. You can see that my actual costs were about halfway between what I would have paid if I had been paying the spread, and what I could have achieved if I was trading at the mid-
m arket price.
Table 77: My trading tactics mean I don’t always pay the spread Actual risk-adjusted trading costs from m y own system Cost includes holding and transaction costs, as a proportion of annual risk target, using data from actual trading between October 2014 and May 2019. A negative cost means I would have been pa id to trade.
Fast trend following
Suppose you are looking for trends that last a few hours, minutes or even seconds. You cannot spend an entire day patiently waiting for your orders to execute – you need to jump on the bandwagon now . In this situation, only market orders make sense. Traders looking for fast moving trends will always pay the execution spread. Combined with the high volume of trades this becomes a prohibitively expensive strategy, and hence not recommended.
Mean reversion trading
The opposite of trend following is mean reversion trading. Rather than expecting the market to move strongly in one direction or another, we hope that it will fluctuate around some equilibrium level. Mean reversion trading isn’t easy, since it’s hard to find assets that exhibit that kind of behavior. But the advantage they have is that they can use limit orders when opening new
positions, and they will always capture the spread when tradi ng normally .
Let’s look at an example. In early October 2018, the price of gold was stuck in a range between about $1,180 and $1,210 per ounce. To exploit this with a mean reversion strategy, I put in orders just inside that range: a buy limit order at $1,185, and a sell limit order at $1,205. As it happens, the price rallied and very early on 11 October, the market reached a level of $1,204.8
bid versus $1,205.0 offer (gold futures normally trade with a $0.20 spread). Before the price could move higher, someone had to buy from me at my offer level of $1,205. I went short at $1,205, and captured the spread.
When doing this kind of trading it’s vital to use stop losses, since the trading strategy doesn’t automatically cut positions 20
when the market moves against it. ¹75² I set a stop loss at $1,220. There were now two possible outcomes. Ideally, the price would begin to fall towards my bid of $1,185. I’d make a profit from this fall and, when the price reaches $1,185, I will capture the spread again when I clo se my trade.
Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders Page 24
