Trading compared to Roulette

Being able to digest the following post numbers should help to set benchmarks/targets for how often the trader needs to be right, in order to overcome transaction costs, and to end up with a profit.

Roulette – 2.7% house edge

UK casinos offer the game of roulette – this being the game encompassing a wheel with 37 fields for a ball to land in.  18 of the fields are black, and 18 are red – finally there is one green field – the “zero” field.  With this game in the casino, the house has an edge of 2.7% over the player.  This means that on every wager the casino makes on a theoretical return of 2.7%.  In the long-run the actual return will run pretty darn close to that number.  Thus on a $100 bet the player is expected to lose $2.70.  On 10 bets of $100, the theoretical loss is 2.7% x ( 10 x $100) = $27.  Nobody goes to the casino expecting to make money playing roulette – betting progression systems on roulette do not work because each spin of the wheel is independent from the previous spin.  In the US, and in some European casinos, the roulette wheels mostly contain two green fields – a single 0 and a double 0.  In those games the house edge is 5.4%.

The only way that a player can beat the game of roulette (other than by cheating) is by discovering an physically imbalanced wheel, whereby some numbers come up more often than they should – the player will have a positive expectancy when placing bets on those numbers.  This occurs very rarely – wheels are checked on a very regular basis.  The second possibility for beating the game is to develop the skill of predicting the section of the wheel that the ball is likely to end up based on the way that the croupier rolls the ball and observing its path.

Finally, players that are able to beat the game in one of these two ways, need to be extremely good and appearing as losing players to the casinos.  Else they will be either tossed out onto the street by the casino personnel or kindly directed to play other games on the casino floor.

What is the “house edge” in the financial markets?  Answer: 3 to 15%+ in a random market

The edge depends on the level of transaction costs (bid-ask spread, commission, rollover charges) relative to the size of the trader’s stops and targets.

The transaction costs are the edge that a trader is up against.  If we assumed that price movements of a financial instrument are completely random – so a forex pair has the same probability of rallying 50 pips as it has to decline 50 pips, then a trader who trades (or bets) on these movements – will have a 50/50 of ending up with a win or 50/50 chance of a loss (ignoring scratch trades).  However when the trader wins, he will not win 50 pips, he will only win say 48.5 pips – because the pair will have a spread of 1.5 pips on a liquid pair such as EURUSD, AUDUSD or GBPUSD (if you have a decent broker, else the spread might be 3 or 4 pip).

Example.  GBPUSD is trading 1.6050.  The brokers has a bid of 1.60493 and an offer of 1.60508 (a spread of 1.5 pips).  If Cable rallies 50 pips, the bid/ask will be 1.60993-1.6108.  Thus a favorable movement of 50 pips leaves the trader with a profit of 48.5 pips (1.60993 less 1.60508).    If Cable declines 50 pips then the bid/ask will be 1.5993-1.60008.  Thus a unfavorable move of 50 pips leaves the trader with a loss of 51.5 pips (1.60508 less 1.5993).  Thus if things were completely random, the trader makes a theoretical loss of 1.5 pips (50% x +48.5  and 50% x -51.5) every time that he places the trade.  Thus with a good broker and 50 pips stop/target, the 1.5 pips represent 3% of the stop/target.  This is slightly more than the casino edge in single zero roulette.  If the trader goes for a tighter stop, let’s say 25 pips, then the edge doubles to 6% – for a 10 pip stop the edge rises to 15%.

Of course the traders do not believe that the price movements are random, else they would not trade to begin with.  Thus in order to overcome this edge, the trader needs to develop the skill of being able to predict price movements correctly more often than not.

To keep things simple, if a trader always losses 50 pips on losing trades and always wins 50 pips on winning trades, then the trader must be right 51.5% in order to obtain a theoretical expectancy of zero, or 53% of the time if using a 25 pip stop, or 57.5% of the time if using a 10 pip stop.  So this higher win rates are required, not in order to win, but just in order to offset the transaction costs – in other words to be a break-even trader.

So clearly the tighter the stops, the more accurate and correct the trader needs to be.  The bigger the stops the less impact the transaction costs make to the trader.  But bear in mind that if holding positions overnight, then the rollover/financing charge is also added to the transaction cost.  Yes I know the financing charge can sometimes go in the favour of the trader, but remember that the broker uses one rate if the trader gets the benefit, and a different rate if the broker receives the rollover amount (in other words, there is a spread inherent in the rollover charge!).

Yes this is keeping things very simple.  Things would also if the trader’s stop are not the same size as the trader’s targets, or if scratch trades, partial winners or partial losers are included.

If a trader wants to trade with an edge, i.e. bank a theoretical return every time that a trade is place, then the win rates need to obviously be higher yet again.  If the trader targeted an edge of 10% – meaning that for every $100 risked, a theoretical return of $10 is desired – the trader then needs a win rate of 56.7%% (if using a 50 pip stop), and a win rate of 63.25% (if using a 10 pip stop). A win rate of 63.25% means that out of 100 trades, the trader gets 63 winners, and 37 losers (or 1.7 winning trades for every losing trade, or roughly 5 winners for every 3 losers).

Thus,  what can a new trader expect?

So, let’s stay that a trader is learning and cannot predict that well – let’s just stay that he gets things correct 50% of the time – in other words the analysis is not helping him to increase his accuracy of predicting price movement.  Assume that his broker does not offer the sharpest spreads in the world, and that he ends up with a spread of 2.5 pips and on average uses 25 pip stops.  Thus the edge against him is….. yes, 10% – about 3.5 times more than the single-zero roulette game.  Let’s say that he risks 1% of his trading capital on each trade, and then puts on 300 trades over several months.  Based on the formula above, you would expect to the trader to have reduced his bankroll by approx 30% after 300 trades (theoretical loss of 0.1 per trade) even though he is right 50% of the time.  Interesting, no?

Anyways, I thought I will leave that as food for thought.  Good luck out there.

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6 Responses to Trading compared to Roulette

  1. James says:

    i think this is one of your best posts yet. Very very good and analytical

    i do think there is some basis for markets being 50/50 between random and predictable, the ratio perhaps varying a little.

    as a retail trader (and even investor) the cost of doing business is prohibitively high. i fairly objectively believe that almost all traders (and possibly investors as well) lose money. this is depressing.

    my not-so-controversal view is that non-institutions involved either make money selling systems, advice, trading services, chatrooms etc. i’ve had some not-so-good experiences on this. Even my experiences with the more legitimate players was mixed, they made some money as brokers and selling a (good) service, many of their clients did this on the side to their paid jobs.

    i saw first hand how some of the prop shops worked and i would say it would leave a nasty taste in the mouth. They too have a business to run and quite rightly are in it for themselves.

    even bank trading in FX (etc), is about volume, spreads and client services. i don’t think many banks make much from trading any more. Prop trading was basically collusion (as we now see in the press), skimming your clients. i know our FX teams just call up, get a price, not really care what it is and place transactions for 10,000’s over and over (this would back up some of the randomness theory)

    however, keep it up – but don’t put all your eggs in one basket, explore other business opportunities as well if possible and keep questioning everything as you do

    Liked by 1 person

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  3. David Eppel says:

    It’s why I trade options- the market makes the moves,not me, I need no predictive skills. http://optionsinvesting.co.uk/before-sharesthere-were-options/

    Like

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