The Surprising Effect of Small Edges

Imagine you have a trading method which trades the GLOBEX west Texas crude oil contract (ticker:CL).  This is a futures contract that represents 1000 barrels of crude oil.  At current oil prices, the contract has a value of about $100,000.  Price for CL is specified in dollars per barrel, and the tick is one cent per barrel, or $10 for the contract.  Now, let’s say this method has very simple trade management – once a trade is entered, a stop loss order is placed 10 ticks away from the entry price, and a limit order to exit is placed 10 ticks the other direction.  These orders are set up as a “one cancels all” or OCA group, meaning that if one of the two exit orders executes, the other is canceled.

This is a very simple type of trade setup, and is common for very short term trades.  In this example once you enter a trade (assume a 1 contract position) you should get one of two resuls:

  1. You win $100 minus fees
  2. You lose $100 plus fees + slippage

Fees in this example are simply your transaction fees.  Slippage is the cost associated with stop orders executing at a price worse than the trigger price, which they can do since they trigger market orders.  For now, let’s assume that the round trip transaction fees for 1 contract of CL are $4 (my broker charges $4.01 for some strange reason) and that slippage is zero.  The slippage assumption is unrealistic and I’ll address it in a subsequent post, but for now I want to get at a different aspect of the situation.  I want to know:

How often do you have to place your trade in the right direction in order to make good money here?

Luckily, the math for this is easy.  Assign a probability P that your trade is a winner.  For readability sake I’ll write these in percent – 50% would mean that half the trades hit the profit target and half stopped out for a loss.  But for arithmetic purposes we need to represent that as P=0.5 since probabilities range 0 to 1.  Now, what I want to do is calculate our expectation for the trade as a function of P.  Expectation is simply the result you expect to get for one trade if you did a large number and averaged the outcomes.  Some trading literature will term it “expectancy” instead – same thing.  The formula for expectation is

The sum across all possible outcomes of P(outcome)*result in dollars

P(outcome) is simply the probability that you get a given outcome.  All the P(outcomes) should add up to one since every trade should produce some result.  Now, I’ll re-name P from earlier to P(win) – the probability that you win 10 ticks minus fees.  And I’ll coin P(loss) = 1 – P(win) as the probability that you lose ten ticks plus fees.  Since the trade management for this trade is so simple, there are only two possible outcomes and the relationship between them is easy to understand.  Now, the formula for our expectation is as folows:

Expectation = P(win)*($96) + P(loss)*(-$104)

note: P(loss) = 1 – P(win)

Now I’ve gone and computed a table of some expectations for various values of P(win):

Win percentage P(win) Expectation on $100 bet, $4 fees Results from 250 trades per year Simple Annual Return on $10,000 Performance Bond Approximate years to double your money assuming full compounding
45% -$14.00 -$3,500.00 -35% N/A
50% -$4.00 -$1,000.00 -10% N/A
52% $0.00 $0.00 0% N/A
54% $4.00 $1,000.00 10% 7.2
56% $8.00 $2,000.00 20% 3.6
58% $12.00 $3,000.00 30% 2.4
60% $16.00 $4,000.00 40% 1.8
62% $20.00 $5,000.00 50% 1.4
64% $24.00 $6,000.00 60% 1.2
66% $28.00 $7,000.00 70% 1.0

The second column is the per-trade expectation.  These values may seem small – anywhere from negative to just less than $30 in profit per trade.  But my mission here is to convince you these results are much more dramatic than they appear, which is the purpose of the rest of the table.  Remember these are very short term trades – typically CL will move 10 ticks one way or the other within a couple of minutes.  So it’s not unreasonable, depending on how exactly the trading method found its trades, that you could take several such trades per day.  Perhaps even 10s of trades.  But let’s assume on average your method finds one such trade per day, 250 trading days a year.  The second column then represents your yearly profit per contract.  Again, these numbers don’t appear very spectacular in the context of $100,000 of capital for one contract.  But futures contracts don’t require you to put up the full value of the contract in order to take a position – right now the CL contract requires you put up $8,100 of capital as a performance bond.  For simplicity sake, we’ll assume you have $10,000 in your trading account per contract as a pad.  Note that this makes you maximum win or loss 1% of your account value.  So while these trades are very heavily leveraged, their effect on the account is small because the profit target and stop loss are so close to the entry price.

The results from the third column are more interesting in the context of a $10,000 capital requirement.   Earning $2,000 on $100,000 isn’t very attractive but earning $2,000 on $10,000 is pretty good.  That’s what the fourth column represents in the form of annual return.

I want to stop for a second and talk about what constitutes good results in trading.  It’s easy to get a very distorted view.  This distortion comes from two sources, exceptional results and exceptional risks.  Yes, there are some traders who manage to string together triple digit returns on equity year after year.  But they’re incredibly rare, and they seem to be becoming rarer as time goes on – probably because the game is getting harder.  But what’s a “typical” result?  Well, most money managers of all stripes underperform the broader market (assume the broader market is the S&P 500 for simplicity)  And S&P returned roughly 0% over the last 10 years.  Of course, “most money managers” includes a lot of clowns who don’t deserve to be touching other people’s money.  It’s a sad fact that the best trading talent ends up captive to prop and bank desks, not trading outside managed money.  And those desks target about a 20% return on capital – if they could make that year in, year out they would be happy.  The fifth column shows why: as your return on capital passes 20%, the time it takes to double your capital by trading starts dropping basically to nothing.  It’s stupid to talk about the magic of compounding interest in a savings account yielding 0.5%, but for the capital of a trading desk yielding 30% the compounding becomes a pretty huge deal.

Similarly, it’s possible to achieve very high aparent rates of return by taking a very small number of huge bets and getting lucky.  Such “performance”, as you might guess, is not sustainable.  Imagine a totally unskilled trader who found a way to bet his entire account balance on a coin flip.  Heads he doubles his money, tails he’s broke.  There’s no edge here obviously (expectation: +$0) but there’s a lot of variance.  That said, If a trader takes this gamble and wins, he’ll have a +100% year.  That doesn’t mean you’d want to have him manage your money though – point being small samples can turn lucky fools into apparent winners for a while.  Don’t be tricked into thinking your trading needs to match those kinds of results – they’re a mirage achieved by taking outsized risks.

All that said, I’m going to denote 20% annual return as the point where really good things start to happen for a trader.  With those kinds of results you can solicit money to manage assuming you can prove your track record.  Or if you prefer to trade your own account then over the course of a lifetime you could make yourself very wealthy.  Basically, past that point it’s all goodness.  Now, I want to hop back to column one and see how accurate your predictions need to be to achieve that 20% annual return: 56% right.

No, seriously, 56%.  You can actually build a highly profitable trading career off being right 6% more frequently than you would be if you guessed randomly.  This is a very different concept from being “right” in a general information, business or education context.  56% right is a failing grade on a test.  If a website gave you correct information 56% of the time, you’d consider it highly unreliable.  But 56% right in trading can make you a millionaire if you can get enough money bet on your thin edge.

There’s huge difficulty associated with this, because the human mind is not built to track small edges.  In fact, our innate desire to find patterns and simplify tends to obscure them.  It’s very hard to just look at a sequence of trades and tell if they’re 50% winners or 56%.  The difference is just over one extra trade in twenty going your way.  But 50% is losing money and 56% is highly profitable.  The only tool I know of to tell those two situations apart is statistical analysis, which is why I feel such analysis is essentially necessary to achieve profitable trading.  For now though I just want to get you thinking about how much power there is in a small edge.

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