Leveraged Trading: A professional approach to trading FX, stocks on margin, CFDs, spread bets and futures for all traders

by Robert Carver

  Unfortunately, it is very difficult to find a robot or EA whose track record can be trusted. The extraordinarily optimistic track records that can be found all over the internet are usually derived from back-testing and not real trading. Those back-tests are at best over-fitted, and many are completely fabricated. They have to be. Most system buyers will naively choose the system with the highest advertised return. You can’t beat the fakers if you’re honest, so to sell your system you have to heavily exaggerate.

  Copy trading is slightly better, in that the track records you see are usually from real life trading. However, all the copy trading sites I’ve seen use poor scoring methods. These encourage copy traders to take large amounts of risk to reach the top of the leader board. Also, they don’t properly account for different track record lengths. Copied traders may also set up multiple accounts, all trading differently. In the leader board you only see the one account that was successfu l by chance.

  Many providers of trading systems have dubious relationships with brokers. They get kickbacks from the broker every time you trade.

  The more you trade, and the higher your leverage, the more the trading system provider earns. This makes it even less likely that an expert advisor or robot system will be w orth buying.

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  ²79 Had I acted upon the information then it probably would not have been ‘insider trading’ – a criminal activity. Insider trading rules don’t normally apply to the government bond market.

  Naturally, I would have checked with a lawyer first.

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  ³70 Nobel laureates in the field of behavioural economics, the study of human failings in financial decision-making, so far include: Richard Thaler (2017), Robert Shiller (2013), and Daniel Kahneman (2002).

  ³¹ Technical note: This theory of changing risk aversion was developed by Daniel Kahneman and Amos Tversky, “Prospect Theory: An analysis of decision under risk” Econometrica 1979. Investors may also be suffering from other cognitive biases such as anchoring and framing.

  ³² Sometimes it can make sense to sell after good news. There is an old saying “Buy the rumour, sell the fact”. If you have bought in anticipation of good news, it is logical to sell once all the news is factored into the price. But it is hard to judge the point at which the price fully reflects the news, so most traders will sell too early, and would be better off waiting.

  ³³ Instead see my first book: Systematic Trading.

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  ³74 I discuss the mechanics of automated trading systems at length in multiple articles on my blog, at qoppac.blogspot.com 20

  ³75 This advice doesn’t just apply to amateur traders.

  Professional investors are also pretty lousy at deciding when they should sell. “While investors display clear skill in buying, their selling decisions underperform substantially – even relative to strategies involving no skill such as randomly selling existing positions.” From: Akepanidtaworn, K. et al,

  ‘Selling Fast and Buying Slow: Heuristics and Trading Performance of Institutional Investors’, https://ssrn.com/abstract=3301277

  (December 2018).

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  ³76 There have been several tests of momentum with large historical data sets. One study which goes back 200 years is by Christopher Geczy and Mikhail Samonov, ‘Two Centuries of Price-Return Momentum’, Financial Analysts Journal (2016).

  Part Two: Starting to Trade

  Chapter Four

  Concepts

  Trading has its own jargon.

  When I first started trading professionally, I was working on the exotic interest rate desk of Barclays investment bank. It was a few weeks before the conversations about yards, gamma, Bermudan swaptions, and bookies made any sense. I had the same problem

  when I moved into hedge funds. What was a high-water mark, and how did it relate to the draw-down? How much is ‘2 and 20’?

  Then I started trading my own money. I quickly found out that there was a whole new trading vernacular that I hadn’t yet come across; novel terms included candles, Bollinger bands, Ichimoku, 20

  and Fibbonaci. ³77

  In this chapter I explain some key ideas and terminology that you need to understand, before you begin trading with the Starter System, which I introduce in the n ext chapter.

  Some definitions

  An instrument is something you can trade, like the AUDUSD

  exchange rate or shares in Apple. A product is a specific way to trade a particular instrument, such as spread betting, CFD

  trading or futures. A dated product is an instance of an instrument expiring at a future date, such as June 2019 S&P 500

  futures. Dated products include futures, quarterly spread bets, and CFDs based on futures. Margin accounts, spot FX, daily funded spread bets and cash CFDs do not have an expiry; they are undat ed products .

  A trading rule is a systematic rule which determines how we trade. Initially, I will use one rule for deciding when to open positions, and a separate rule for closing them. A stop loss is a specific type of closing rule which, as the name suggests, is supposed to limit your losses. You would use a position sizing rule to calculate the size of your in itial trade.

  The total amount of cash you risk whilst trading is your capital

  . When you are trading you will be dealing with at least one type of currency. Your trading account will be denominated in your home currency : US dollars, British pounds, euros, or whatever.

  But you may be trading in products that have a different instrument currency , in which case you will use an FX rate to translate between currencies.

  Risk and return concepts

  Standard deviation

  The most important factor to consider when trading is risk . It is also the second and third most important. We don’t have much control over our profitability, but it is relatively easy to contr ol our risk.

  But what is risk? How do we define and measure it?

  There are many different ways to measure risk, but I use a specific method known as the standard deviation . I will also use the term volatility interchangeably with risk and standard deviation. The standard deviation is a measure of the extent to

  which actual returns deviate from the average return over a certain period. For example, suppose that an instrument has daily returns of +6%, –4%, +6%, –4%. The average return is +1%, and all the returns are 5% away from that average (+6% is 5% above the average of +1%, and –4% is 5% below it). In this simple case, the daily standard deviation would be exactly 5%.

  Notice that the standard deviation penalises unexpectedly good returns, as well as returns that are poorer than average. This might seem weird, since most people associate risk with the fear of losing money, not with unexpected gain. However, you should bear in mind that you cannot have upside risk without a high likelihood of downside risk. Even an exceptionally good trader 20

  can expect to lose money on around 46% of tr ading days. ³78

  Daily profits are relatively small relative to risk, even for exceptional traders. An exceptional trader with a standard deviation of 2% a day could expect to make an average daily profit of about 0.25%. On a typical good day, their profits will be one standard deviation higher than average: 2% + 0.25% = 2.25%

  . But on a typical bad day their profits will be one standard deviation lower than average: 2% – 0.25% = –1.75% . Even for this exceptional trader the downside and upside risk are almost identical. Hence, it makes sense to think about volatility in both directions.

  Another interpretation of the standard deviation is that it is the amount you could expect to lose on an average losing day (if we assume the average return is zero, which even for exceptional traders is a reasonable app roximation).

  In fact, we can be even more precise if we make another assumption. If we assume that returns follow a Gaussian normal distribution , then we can calculate exactly how frequently certain levels of returns are expected. A Gaussian normal distribution is sometimes called a Bell Curve, because it
is shaped like a bell with a fat middle (values near the average are common) and thin edges (extreme values are uncommon). Feel free to consult Wikipedia if you need more informat ion on this.

  If returns are Gaussian, then they will have the following properties (where m is the mean return, and s is the standard deviation):

  50% of the time above m , 50% of the time below m Around a third of the time (34.1%) they will be between m and m +

  s

  Around a third of the time (34.1%) they will be between m and m −

  s

  Around two-thirds of the time (68.2%) they will be between m − s and m + s

  2.2% of the time they will be higher than m + 2s 2.2% of the time they will be lower than m − 2s Around 95% of the time they will be between m − 2 s and m + 2s Finally, a health warning. Returns in financial markets are notoriously badly behaved and do not fit neat statistical models.

  In particular, really bad days in the market are far worse and more common than predicted by the Gaussian model. Be cautious about taking the values abov e as gospel.

  In this book I use annual standard deviations. A useful rule of thumb is that the annual standard deviation is about 16 times the 20

  daily standard deviation. ³79 The standard deviation of an equity index, like the S&P 500, is about 16% a year. Hence the daily standard deviation is 16% ÷ 16 = 1%. You can find methods for calculating standard deviations in chapter six, and appendix C.

  Calculating the risk of a position

  What sort of financial danger are we exposed to if we buy an S&P

  500 futures contract, or go long a CFD, or place a spread bet at

  £1 a point? There is a simple formula to wo rk this out: Formula 1: Annual risk of a position

  Annual risk = Notional exposure home currency × annual standard deviati on % returns

  I mentioned above that the standard deviation of the S&P 500

  index was about 16% a year. With a notional exposure of $10,000

  to the S&P 500, the annual risk is 16% × $10,000 = $1,600. Often to find out your risk you first have to convert the notional exposure into home currency. For example, if we were British, then we convert $10,000 into GBP. At a rate of 1.33 that works out to £7,519. Then we calculate the annual risk: 16% × £7,5 19 =

  £1,203.

  That is all very interesting, but how do we calculate our notiona 20 20

  l exposure? 74 70

  Formula 2: Notional exposure formulas

  Risk-adjusted returns

  Suppose you know two traders, Bill and Carol. Bill makes an average of 10% a year, whereas Carol makes just 8% a year. Who is the more succes sful trader?

  The answer might seem obvious: surely, it’s Bill?

  Examining the track record of Bill and Carol more closely, you realise that Bill has a much riskier strategy. Some years he makes over 50%, whilst in others he incurs large losses. The

  standard deviation of Bill’s returns comes out around 20% a year; whilst Carols more pedestrian trading produces a standard deviation of just 10% a year.

  Given the choice I would invest in Caro l, not Bill.

  Why?

  Well, suppose I had $1,000 to invest. If I put money into Bill’s strategy, I earn 10% a year on average ($100), with a standard deviation of 20% ($200). But if I borrow another $1,000, I could invest a total of $2,000 in Carol’s strategy. I would receive double her normal return of 8%, less the cost of borrowing the extra money. If I can borrow at 2% a year then I earn: (8% × $2,000) – (2% × $1,000) = $ 140 per year As a proportion of my original $1,000, I will receive 14%

  annually. The annual standard deviation of my returns is 10% × $2

  ,000 = $200.

  Using the same capital of $1,000, Carol’s trading strategy now has the same standard deviation as Bill’s ($200), but with a higher return ($140 rather than $100). After adjusting the strategies so they have the same risk, Carol is more profitable.

  To properly compare trading strategies, we need to calculate a return that is adjusted for risk. A measure that does this is the S harpe ratio .

  Formula 3: Sharpe ratio (SR)

  SR = (r – b) ÷ s

  Where r is the expected annual return of our trading strategy (without leverage), b is the annual interest rate we can borrow 20

  at 74² and s is the standard deviation of the trading strategy, before any leverage is applied.

  So, Bill’s Shar pe ratio is:

  SR B = (10% – 2%) ÷ 20% = 0.4

  This is lower than Carol’s, which c omes out at: SR C = (8% – 2%) ÷ 10% = 0.6

  Carol gets more return for the risk she takes, and hence has a higher Sh arpe ratio.

  The advantage of using the Sharpe ratio to compare strategies is that it isn’t affected by leverage. For example, let us calculate the Sharpe ratio of Carol’s strategy with a leveraged investment of $2,000 (a leverage factor of 2). I will earn 14% on my original investment, so r = 14%. The borrowing rate, b = 2%.

  Finally, if I apply a leverage factor of 2 it will double the standard deviation of Carol’s strategy, s = 20%. Now I can recalculate the S harpe ratio:

  SR C = (14% – 2%) ÷ 20% = 0.6

  This is the same as before. Let’s unpick this calculation in more detail:

  With leverage factor L , we will earn L × r in returns, where r are the returns of the unlever ed strategy.

  But we also have to pay to borrow, at a rate of b . With leverage factor L we will borrow L −1 (remember that a leverage factor of 1 corresponds to no borrowing at all). So, we have to pay (L − 1)

  × b in borr owing costs.

  Hence, our net leveraged return after borrowing cos ts will be: (L × r ) – ( L – 1 ) × b = ( L × r ) – ( L × b ) + b The numerator (top part) of the Sharpe ratio equation is the net leveraged return minus the borrowing rate, i.e.,

  [( L × r ) – ( L × b ) + b ] – b = ( L × r ) – ( L × b ) = L × (

  r – b )

  This is identical to the leverage factor L multiplied by the numerator for the unleveraged Sharpe ra tio ( r − b ).

  So, the numerator of the Sharpe ratio will double if leverage doubles , and so on.

  The denominator (bottom part) of the Sharpe ratio equation is the standard deviation. This will also double if leverage doubles, and so on. Mathematically the denominator wi ll be L × s .

  Since both the numerator and denominator of the Sharpe ratio scale exactly with leverage, it is unaffected by the amount of leverage used. Or to put it mathematically, the L is ca ncelled out.

  No matter what leverage I use, the Sharpe ratio will be the same

  . Hence, for traders who can use leverage, the Sharpe ratio is the most appropriate measure of risk-adjus ted returns.

  Knowing your expected risk-adjusted return is very important. As you will learn later in the book, traders with higher Sharpe ratios can safely use more leverage, and they can afford to pay h igher costs.

  Risk targeting

  “Hi guys and gals, i [ sic ] have a daily target of $1,000 per day, what is yours and [ why ] you have that target”

  Posted on forexfactory.com Inexperienced traders focus on profits . They want to make a certain amount of money on every trade, or set a target for each day, week, mo nth or year.

  Experienced traders target risk . They understand that returns are pretty random, particularly at shorter time intervals. But risk – the volatility of returns – is relatively predictable. If you know your expected risk, you have a good idea of how much you could reasonably expect to make or lose over a given ti me interval.

  In this book, I specify target risk as an annualised standar d deviation .

  Instrument risk and leverage factor

  What if you have a trading risk target of 25% a year, but are trading an instrument like German 2-year government bonds, whose risk, measured by the annual standard deviation of returns, is currently just 0.3%? You will need some leverage, b ut how much?

  Formula 4: Required leverage facto
r

  Required leverage factor = Target risk ÷ ins trument risk To go from an instrument risk of 0.3% to get to a target of 25% a year you’ll need a leverag e factor of: Required leverage factor = 25% ÷ 0.3% = 83.3

  If you had $1,000 in capital, then your required exposure would be $83,300 in German 2 -year bonds.

  We won’t always need to use leverage. A leverage factor of less than 1 would be required where the instrument risk is greater than your target. For example, suppose that you are trading a risky cryptocurrency with an instrument risk of 100% a year, and your own risk target is just 20%. The required leverage factor is 20% ÷ 100% = 0.2. With $1,000 in capital, your position would b e just $200.

  Getting the right level of risk

  Most traders assume that you should always take more risk if you can. If you expect to earn 10% a year trading with no leverage (a leverage factor of 1), then surely it makes sense to use the maximum amount of leverage your broker will allow you: 30, 50 or even 200 times. But beware, even profitable traders can be wiped out if they use excessi ve leverage.

  Consider this simple example: we have a trading strategy that earns 5% in year one, loses 10% in year two, and makes 20% in year three. What would have happened if we ran it at different

  degrees of leverage, assuming we can borrow money at 2% a year?

  Table 2 has the answer.

  Table 2a: Some leverage is good. Too much is bad Effect of increasing leverage factor on a hypothetic al strategy.

  Table 2b: Some leverage is good. Too much is bad Effect of increasing leverage factor on a hypothetic al strategy.

  In the table, columns show the growth of $1,000 at the end of each year given the relevant leverage factor, where leverage = 1

  is no leverage; assuming a borrowing fee of 2% a year. The final row shows the total percentage growth in your account from the start of year one to the end of year three.

  Leverage factor = 1