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Harm Elderman
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I am currently working in the financial industry in Europe, London. I am a former quant. Quote: "It is well enough that people of the nation do not understand our banking and monetary system, for if they did, I believe there would be a revolution before tomorrow morning." Disclaimer:... More
  • Trading With Leverage, What Everyone Should Realize! The Mathematics Of Growth! 1 comment
    Jun 22, 2014 5:32 AM

    This article will discuss the advantages of using statistics in your day to day use of wandering around in the world of financial markets.

    During my period of being a student at university (bless those days), I was studying for an economics and econometrics BSc & MSc degree. The majority of my friends were all investing their student money in CFDs and other derivative products alike. Some of them were using substantial amounts, far exceeding 10k per portfolio. That is quite daunting for someone who just reached the age of 20 years old, but hey, you are young, you can take the risk right?

    I was at the time a frequent user of many online day trading communities. During those university years I saw so many traders come and go. Many of them blew up their portfolios with a lot of precision. I couldn't have done it better myself if I wanted to. Back in the day most of them were all asking, how many % was I making? I said I was already happy with 1% a week. Most couldn't believe what I said. They rather saw their portfolio double in a week. What they failed to understand is that 1% a week is still a solid 67% (1.0152) return a year. Everyone knows that 67% return per year is not sustainable. Although if you would ask a bunch of people: "is 1% return a week possible?" the majority could or might agree. The book "Thinking fast and slow" by Daniel Kahneman is a good read when it comes to behavioral finance and it touches perfectly upon this subject.

    What is leverage?

    Back on topic, the reason why most of my comrades blew up their account was due to the use of leverage. What is leverage? Leverage is using certain tools (financial products) to magnify a desirable outcome.

    Let's say you believe in the story of stock A. You have checked fundamentals and technical and you came to the conclusion, stock A is what you want! However you just graduated from university, have debts to pay and your entire cash pool is only 10.000$. Even though if this stock would rise 10% in 1 year (which is a great result) you would only get an extra 1000$ dollars. What if you could use a derivative which might magnify this return? The variety of options you could use is endless. The Netherlands offers sprinters/turbo's and speeders and in the United Kingdom CFDs are mostly used for these short term opportunities. These are derivatives with enormous amounts of leverage. If you are not allowed to trade any of these (for example if you would live in the USA) you could always try options. The underlying idea is the same, magnifying a certain outcome which you expect will happen!

    Theoretical example

    Let's have a random generated stock price for stock A.

    The value of the stock at month 1 is 100 dollars. You only buy 1 stock in the beginning of month 1. It ends after 121 months at the price of 144.55$. A return of 44.55% after almost 10 years, which is around 3.7% return a year. Not bad, but you would like to magnify this outcome. A leverage of let's say 16 would make this 3.7% return into 60% return a year right?


    Let's see what it looks like if we magnify the monthly outcomes by a factor 2, 4, 8 and 16.

    As depicted in the graph above, when using leverage (thus magnifying the outcome of a monthly result) you simply get 2x, 4x, 8x or 16x times the 1x monthly result. Cool right? Bam! Screw it, let's go for 16x times the leverage! I want this 60% return a year!


    Unfortunately the 16x leverage portfolio got blown out of the water and went on minus before the end of the period was reached. Ouch! Although it seems that 8 times the leverage is the best choice, the lowest value of the 8x leverage was 10.55$. This is an 89% loss out of the initial 100 dollars!

    Portfolio with leverage

    Lowest value in portfolio

    Loss in comparison to initial value
















    Would you sit still and not make a move in your portfolio when it shows -89%? Most likely you would not and sell everything far before that.

    Cost of loss

    I recommend for every starter on the stock market, no matter the amount of money they have to only invest little chunks of their portfolio rather than going on a 'all-out war'. The best argument to this advice is the cost of loss.

    Let's go back to the 100$ dollar initial investment. You buy a derivative and lose half of the value the first day. How long does it take for you to get back at where you were?

    The graph above depicts three scenarios all on the basis of a 100 dollar investment. One where you have a solid growth of 1.37% a week (3), one where you lose 50 dollars on the first day due to a wrong investment but you have a stronger growth of 2.8% (2) a week and you have scenario (1) where you lose 50 on the first day but you gain a similar growth per week of 1.37% a week.

    When you prevent severe losses of your portfolio (scenario 3) and gain a solid 1.37% a week you end up with 200 dollars in the end of the year. However if you have made the unfortunate mistake of betting the wrong horse (scenario 1) it takes you at least a year with the same return as scenario 3 to get back to at least a 100$ dollars. You ended up with nothing. And in comparison to scenario 3, you have lost the opportunity to gain a 100$ dollars. It takes you (scenario 2) at least 2.8% return a week to get back on track to the same value as not having lost the 50 dollars in the first week.

    This indicates the importance of shielding losses of your portfolio.

    So what do we know about % losses? One last test, a simple check…

    A simple check ...

    When a share is priced at a 100 dollars and it drops 5%, is that the same movement as a share priced at a 95 and increasing 5%? If not, which share moved the most in price value? You got that right? So what if a share is priced at 105 and drops to 100 or a share is priced at 105 and increases to 110. Which stock has the highest percentage change? I assume you can fill in questions like that within a flickering of a thought.

    I hear you say …

    Awesome, another nitwit which raises concern about the use of leverage within a portfolio! And a common second phrase could be: "I am aware of the leverage issue, therefore I only use 1/5th (or any other percentage) of my portfolio for derivative products!" However if one would use only 1/5th of its portfolio for leverage (and uses a leverage of 5) the overall leverage would still equal to just 1.


    Be aware of what you do from a statistical point of view. Loss of portfolio is very costly. It could cost you years before you recover from losses. From a statistical point of view it's always better to lose 5% rather than 25%. Playing with leverage is like playing with fire. Having a few candles in your house lit is awesome, but the moment the house is on fire you run to the exits and you'll be left with nothing. Double digit growth year after year is not sustainable. This has nothing to do with the fundamentals but it's purely a statement from a statistical point of view. A country (or company) can't grow 15% per annum nor should you take double digit leverage without overshooting it twice. I've read fundamental research reports (here and on other websites) with valuations which reach to the sky. I worry when I see people pour their entire life savings after having read reports like that. After every crash you read in the newspaper how investors sue the company they invested in as they "expected it would grow constantly" but unfortunately that wasn't the case. These people obviously will only lose more money due to litigation and attorney fees but a wise lesson can be learned out of all that.

    I'm not saying to liquidate all positions and stand on the sideline (I myself am long equity) but remain realistic. You know that feeling when you are drunk and you see everything in a different perspective? Beer goggles? That famous phrase a friend says: "I never went to bed with an ugly woman but I definitely woke up with plenty?" People lose their rationalism when they see their portfolio hit high levels of greed. Math's however are never wrong.

    Currently there is a lot of debate in regards of whether or not the stock market is overvalued. People getting more and more greedy and therefore some even try their luck with very high leveraged products. The more you get, the more you want right? This article shows that investors should tread cautiously with leverage. And that is where I stand!

    Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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  • Learner16
    , contributor
    Comments (253) | Send Message
    Thank you for the reminder, Mr Elderman. Being a learner, reading this article has been very useful to me.
    25 May, 06:03 PM Reply Like
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