Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders
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With no leverage (leverage factor 1) our initial $1,000 earns 5%
in the first year, bringing us up to $1,000 × (1+0.05) = $1,050.
In year two, we lose 10% of $1,050 and are down to $1,050 × (1–
0.10) = $945. Things improve in year three, and we earn 20% on $945, giving us $945 × (1+0.20) = $1,134. Since $1.134 ÷ $1,000 =
13.4% we make a total of 13.4% over three years.
Leverage factor = 2
Applying a leverage factor of 2, we earn twice 5% in year one, less the interest we have to pay to borrow: (5% × 2) – 2% = 8%.
So, we end up with $1,080 at the end of the first year. The loss of 10% in year two really hurts, since with leverage it becomes (–10% × 2) – 2% = –22%. We actually have less cash at this point than we had without leverage ($842.40 rather than $945). For year three, our return of 20% becomes 38% with leverage and, in total, after three years we end up with a retu rn of 16.3%.
A little bit of leverage does indeed help. Doubling our leverage from 1 to 2 improves our returns a little, but does not double our profits.
Leverage factor = 3
For a leverage factor of 3, we have to borrow another $2,000 to have $3,000 to invest; we earn (5% × 3) – (2% × 2) = 11% in year one. After three years we end up with 14.3% more than we started with; less than the 16.3% we had with a leverage factor of 2.
Once leverage gets too high our total return sta rts to fall .
Leverage factor = 5
With a leverage factor of 5, our total returns have turned negative, as we cannot recover from the amplified effect of losing 10% i n year two.
Leverage factor = 8.5
With a leverage factor of 8.5, we end up completely broke. The modest loss in year two is magnified to the point where we lose everything. Even a profitable trading strategy can be wiped out if you use too mu ch leverage.
So too much leverage is bad, but insufficient leverage means you will be leaving some profit on the table. What is the right level of leverage?
Fortunately, there is a precise formula for determining how much you should bet given your expected profits which is known as the 20
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Kelly criterion. 74³ Under certain assumptions, 74 74 the Kelly criterion states that the optimal leverage f actor f* is: Formula 5: Optimal Kelly leverage factor Optimal leverage factor, f* = (r – b) ÷ s ²
Where r is the expected annual return, b is the interest rate that you can borrow at, and s is the expected standard deviation of returns of the instrument you are investing in. You can now calculate the correct risk target. This will be equal to the risk of the instrument s , multiplied by the optimal leverage f* : Formula 6: Optimal Kelly risk target
Optimal risk target = s × f* = s × (r – b) ÷ s ² = (r – b) ÷ s You may recognise this from earlier – it’s the Sharpe ratio from formula 3. The optimal Kelly risk target is equal to your expected S harpe ratio .
Minimum trades and minimum capital
Minimum and incremental trades
When calculating what position to take, you will usually get a number with some pesky decimal places attached; the system might say, “Please buy 42.3442 shares in Google”.
But you cannot buy less than one share of a company.
Theoretically the minimum trade size in a margin account is a single share, but minimum commission levels make this uneconomic.
For this reason, I recommend using a minimum of ten shares.
Similarly, you cannot usually buy less than 1,000 units of foreign currency when FX trading. The minimum stake when spread betting is typically $1 or £1 a point, and nobody will let you buy less than one futur es contract.
The minimum trade size is the smallest position you can possibly take in a given instrument and product. The incremental trade size is the smallest increase you can make to the minimum trade size.
In futures the minimum and incremental trade sizes are always the same: one futures contract. You have to buy a minimum of one contract, then if you want more exposure you buy another contract, and so on. In many cases FX, spread betting and CFD
trading brokers operate a similar system. You might have to buy a certain round number of lots of FX, £ or $ per point of spread bet, or contra cts of CFDs.
However, certain brokers are happy for you to make smaller incremental bets, over and above the minimum position. So, for example, my CFD broker has a minimum trade of ten contracts, each at £1 per point on the S&P 500. But they also allow one penny incremental increases to that trade size. My minimum trade size is £10 a point, but I can also place a trade for £10.01 or £10.0
2 per point.
The incremental trade size in a margin account is one share.
Buying 11 or 12 shares is as economically viable as buying the minimum t rade of ten.
Minimum required capital
An important implication of minimum position sizes is that there is a minimum amount of capital required to trade a given instrument using a specific product . We already saw this back in chapter two. To trade GBPUSD we used over £6,000 in capital for the futures trading example; the spread bet and the CFD for the same instrument came in at around £1,000 respectively, and we were able to trade spot FX with less than £100. Minimum capital requirements severely curtail the options that are open to traders who do not have six- or seven-figure accoun t balances.
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74 75
Costs
“ If you rationalise – hey, I am making profits, who cares if my trading costs are more than 40%. That would be like a pilot with 300 souls on board a flight across the Pacific ocean estimating their fuel based on a constant tailwind – when those headwinds show up, and they always do at some point – you crash.”
Excellent advice posted on elitetrader.com by ‘comagnum’
Costs are a key factor to consider when trading but are usually over-looked by novice traders. They prefer to think about which model of Ferrari they will buy with all the money they are bo und to make.
If you don’t know your costs, then you cannot make sensible decisions about how often you should trade. Should you trade quickly, incurring large costs, but possibly making more money.
Or trade more slowly to reduce your costs? Without estimating your likely costs, you cannot decide which instrument or product
you should trade, which trading rule you should use, or how quickly you should cut lo sing trades.
Risk-adjusted costs
I calculate all costs in risk-adjusted terms: as an annual proportion of target risk. That’s quite a mouthful! As an arbitrary example, if your target risk is 15% a year, and your annual costs are 1.5% of your capital, then your risk-adjusted costs will work out at 1.5% ÷ 15% = 0.10 = 10% of your target risk.
Why should you measure cost s that way?
Because this measure of costs is indifferent to leverage. If you double your leverage, then you also double your costs. Your positions are twice as big relative to your capital, and therefore will cost you twice as much. But doubling your leverage will also double your risk. In the arbitrary example, with costs doubled to 3% a year and risk of 30%, your risk-adjusted costs will be unchanged: 3% ÷ 30% = 0.10 = 10%.
Regardless of your leverage, your risk-adjusted costs will be identical. This also makes it easier to compare costs between different instruments that have different levels of risk. This measure of costs can also be thought of in terms of risk-adjusted 20 20
returns, as measured by the Sharpe ratio. 74 76 Dividing your costs by standard deviation will effectively tell you how much of your pre-cost Sharpe ratio will get eaten up by costs.
For example, suppose you are paying 2% costs with a risk target of 20%. Your risk-adjusted trading cost is 2% ÷ 20% = 0.10. You expect 0.10 units of your pre-cost Sharpe ratio to be paid out in costs. Let’s check this. If you can make 10% in annual pre-cost return, with a borrowing rate of 2% and target risk of 20% then your pre-cost Sharpe ratio will be ( from formula 3 ): Sharpe ratio = (
10% – 2%) ÷ 20% = 0.4
Now apply 2% costs. Your Sharpe ratio will be reduced to: Sharpe ratio = (10% – 2% - 2%) ÷ 20% = 0.3
As expected, this is a reduction of 0.10 Sharpe ratio units.
Cost calculations
There are two types of tr ading costs: Holding costs : costs we have to pay whilst holding a position.
These include the funding spread on any borrowing (for undated products: margin trading, spot FX, cash CFDs and daily funded spread bets), and the cost of rolling positions (for dated products: quarterly spread bets, futures, and instruments based o 20 20
n futures). 74 77
Transaction costs : cost of opening and closing our positions.
These comprise the trading spread, brokerage commissions, and any taxes we have to pay (like UK stamp duty on shares).
Let’s look at these co sts in turn.
Holding costs
We can work out the risk-adjusted holding cost of an instrument
, by dividing holding costs with the instrument risk, measured in annual standard devi ation terms.
Formula 7: Risk-adjusted holding costs Risk-adjusted holding cost = Annual holding cost ÷ ins trument risk
As an example, it costs around 0.033% a year to hold the US 2-year bond future, which has risk of around 0.54% a year. In risk-adjusted terms the hold ing cost is:
Risk-adjusted holding cost = 0.033% ÷ 0 .54% = 0.061
How is this cost affected by leverage?
Let’s find out. If your target risk was 20% a year, then using formula 4 you need to apply a leverage factor of 20% ÷ 0.54% =
37.04. At a leverage factor of 37.04 it would cost you 37.04 ×
0.033% = 1.22% of your capital every year to hold a position in the US 2-year bond future:
Risk-adjusted holding cost = 1.22% ÷ 20% = 0.061
Holding cost as a proportion of risk is unchanged after applying all th at leverage.
Transaction costs
Transaction costs should also be calculated as a proport ion of risk.
Formula 8: Risk-adjusted transaction costs Risk-adjusted cost per transaction = Cost per transaction ÷
natural ins trument risk
Again, let’s look at an example. Suppose it will cost you 0.1% of your capital to trade your typical position in US 2-year bonds, with a target risk of 20% per year. Then the cost for each transaction, as a proportion of your ri sk, will be: Risk-adjusted cost per transaction = 0.1% ÷ 20% = 0.005
To work out the annual cost we need an additional piece of information, which is the expected number of trades that will be execute d each year.
Formula 9: Risk-adjusted annual transaction costs Risk-adjusted annual transaction costs = Risk-adjusted cost per transaction × # of tra des per year
For example, if you do five trades per year, at a risk-adjusted cost of 0.005 per transaction then i t will cost: Risk-adjusted annual transaction cost = 0.005 × 5 = 0.025
Total annual trading costs are just the sum of transaction and ho lding costs:
Formula 10: Total risk-adjusted costs
Total risk-adjusted cost = Risk-adjusted transaction cost + Risk-adjusted holding cost
For the simple example our total costs each year would be 0.061
in holding costs, plus 0.025 in transaction costs, for a total annual risk-adjusted cost of 0.061 + 0.025 = 0.086.
Alternatively, you can think of this as giving up 0.086 of your Sharpe ratio in transaction costs every year. If your Sharpe ratio before costs was 0.4, then after costs it would be 0.4 – 0.
086 = 0.314.
Appendix B explains in more detail how to calc ulate costs.
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³77 A yard is traders slang for a billion. Gamma is a kind of risk that options traders are exposed to. Bermudan swaptions are a particular type of product that we traded. Bookies – a shortened version of bookmakers – was a derogatory term for a broker. You hit a high watermark when your fund’s price hits a new peak. The draw down is the cumulative loss since you last reached a high watermark. ‘2 and 20’ is a common fee structure in the hedge fund industry: a management fee of 2% which is paid regardless, plus 20% of any profits that you’ve made. A candle is a method for displaying a range of price movements on a chart. Bollinger bands are used to find the range of price changes, whilst Ichimoku and Fibbonaci are both psuedo scientific techniques for calculating key price levels (I don’t use or recommend any of these methods).
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³78 Technical note: All calculations for the exceptional trader assume an annual Sharpe ratio of 2, daily standard deviation of 2%, and returns drawn from a Gaussian normal distribution.
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³79 Technical note: This is because standard deviation scales with the square root of time (if we make certain simplifying assumptions), and there are roughly 256 trading days in a year.
The square root of 256 is 16.
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74 70 Technical note: Should we care about currency risk when speculating in an instrument that isn’t denominated in our home currency? For example, if you buy US stocks as a GBP investor you are exposed to both US stock prices and also to the GBPUSD rate (if GBP appreciates, you will lose money). My own research indicates that currency risk forms only a small part of the overall risk of most investments. For traders using derivatives this is less important than for other traders, as they are only exposed to currency risk on their margin, not the entire position.
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74 ¹ So-called because there is a larger S&P 500 contract which is worth five times as much. But nobody trades that as virtually all the activity in this instrument has moved to the E-mini future.
As I was completing this book in early 2019, a new S&P 500 micro future was launched which is worth one-tenth the value of an Emini. The new future is still very illiquid, and at present is much more expensive to trade than the E-mini.
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74 ² You might see this called the risk-free rate elsewhere.
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74 ³ John Kelly, ‘A new interpretation of information rate’, Bell System Technical Journal , (1956).
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74 74 Technical note: Returns need to be serially independent and drawn from a Gaussian normal distribution. Negative skew or high kurtosis will reduce the optimal leverage. Whilst these assumptions are not realistic for most trading strategies, in most they do not usually affect the level of optimal leverage to any significant degree. For FX carry, a strategy I will introduce in part three, which has modest negative skew, the optimal leverage is reduced by around 5%.
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74 75 I discuss exactly how to calculate the minimum capital required for a particular trading strategy in chapter five.
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74 76 From formula 3 the Sharpe ratio is equal to your expected return, minus the interest rate you can borrow at; all divided by the standard deviation of your returns.
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74 77 Importantly the cost of carry is not equal to the holding cost (and if carry was positive, we would not automatically have negative holding costs). If holding costs were zero, we would earn carry that was equal in magnitude on long and short positions. The effect of holding costs is to reduce positive carry and increase negative carry. For example, if I can earn 5%
from a deposit in one currency, and borrow at 1% in another currency, then my theoretical positive carry would be 4%, or –4%
if I reversed the trade. But if my broker applies a financing spread of 0.5% then I will earn 4.5% on deposits, and borrow at 1.5%. My positive carry has been reduced to 3%, 1% lower than before, hence my holding costs are 1%. Similarly, the negative carry would be the difference between borrowing at 5.5% and
depositing at 0.5%, or –5%; again, the holding costs have increased the negative carry by 1%.
Chapter Five
Introducing the Starter System
I dabbled in shares during the tech bubble that ended in 2000, but my first encounter with serious trading was working for an
investment bank as an options tra der in 2002.
When I joined I had no idea h ow to trade.
I had spent several months on the bank’s graduate training scheme, but this involved taking classes that were mostly completely irrelevant to life on the trading floor. The received wisdom was that trading was best learned by osmosis; sitting junior traders next to experienced veterans, in the hope they would eventually learn something useful. Until then, they could handle the senior traders’ co ffee orders.
I quickly learned the technical aspects of the job, such as how to work out a price for the products we were trading, and that my boss’s preferred drink was a skinny latte with a double shot. But nobody taught me how trading decisions were made. I could not answer simple questions like: should I buy or sell? How big should my positions be? When should I clos e my trades?
At least initially, I could have really done with some kind of system. Something like: “If you see this pattern then buy. This one means sell. Here is the calculation you need to work out your positions. Finally, if this happens, then close your trade.”
Then, when I had gained in confidence, I could have started to make my own decisions; gradually tweak the system, keeping the most important parts, and over-riding it where appropriate. Of course, to do that I would need to know which parts of the system were sacrosanct, and which could be saf ely ignored.
I am going to give you the help I never had: in this chapter, I’m going to introduce the Starter System. It is a complete system which tells you when to trade, how large your trades should be, and when you should close your trades. As you read through the rest of the book you will learn how and when to change it, and which parts are too importan t to change.
An overview of the system
The Starter System is a trading system which is as simple as possible and is designed to be suitable for beginner traders with minimal capital. Here are the main elements that it contains: In this chapter I introduce each part of the system and explain how I designed it. The next chapter will show you how to actually
implement and trade the system. Then, in the rest of the book, I explain how to adapt and improve the Sta rter System.
Which instrument and product to trade?