The “Edge” in Trading That Comes From Understanding Math

WORD COUNT: About 1800
READ TIME: 8-10 Minutes

What’s the most important facet of trading? There’s quite a bit of controversy over what makes a successful trader. In my study of the lives of GREAT traders, I’ve found that each one had a vastly different philosophy about:

what kinds of issues to trade…
what kind of entry/exit signals to use…
the ideal holding period…
the target return…
what constitutes good fundamentals…
…or even if fundamentals have anything to do with trading.

To many, fundamental analysis is the “holy” grail. Finding and picking the right stocks is the bread and butter of analysts and value traders. The assumption is that we can know something that no one else knows… yet… and that the rest of the market will catch up with our deep wisdom later and buy the stock that was undervalued.

Kind of arrogant.

Others believe that the most important part of trading is technical analysis: the assumption here is that the future can be known by the past. By looking at a chart’s pattern, one can predict what the future will be… and buy and sell accordingly.

Kinda spooky.

I’d like to talk with you today about the one way I know to trade with a definite mathematical edge.

Say we completely strip away the fundamental and technical aspects of trading by making EVERYONE play the exact same ‘market’… the same win/loss record and payouts…

…is it possible to expect better or worse results based on something entirely different?

The following principle is the most important, and most overlooked, facet of trading. Period.

Knowing the most important facet of trading, you might expect to have an edge over other traders that don’t understand it, right? The edge I’m talking about is evident in the RadioActive Trading foundational principle F.I.S.T. (Force Ideal Sized Trades).

Consider this: you have a game that gives you a 60% chance of winning, with an even-money payout. That is, you make a dollar for every dollar you bet when you win, and lose what’s on the table the other 40% of the time. You start with $1,000 and have an hour to play.

Did you know that in a test with forty subjects, every one of which held Ph.D’s… only TWO were able to take that game and make money with it?

It’s true. Google “Ralph Vince” sometime and look up this experiment.

Intelligent people + winning game does NOT necessarily = money.
Do the math: statistically, 95% (38 out of 40) of these Ph.D’s LOST money even when given a game with a winning edge. That’s because none of those PhD.’s had a degree in probability or statistics. 😉

What do you think the difference was between the two players that won, and the thirty-eight that lost money? They had the same “market” to play… the same chances, the same payouts. But they had VASTLY different results. The only difference between the winning and losing players was HOW MUCH each of them put AT RISK when they played.

Let’s say that the record went like this for the first ten trades:

1)   LOSS
2)   LOSS
3)   WIN
4)   LOSS
5)   WIN
6)   WIN
7)   WIN
8)   LOSS
9)   WIN
10) WIN

That’s 60% winners, right? Six wins and four losses out of ten plays. Okay…let’s look at three different ways to play this game:

Arbitrarily (the way MOST folks play the market),
Arithmetically (a better way for sure), and
Logarithmically (this is the IDEAL… and most underused way to go):

In the example above, thirty-eight of forty subjects LOST money, even though they were given a winning game: 60% winning trades with an even-money payout. I’m willing to ‘bet’ that the thirty-eight losing players bet Arbitrarily.

That is, they had no plan for HOW MUCH to put into any one trade. They knew that they would be right 60% of the time, and so automatically assumed that they were going to win. That nearsighted view, coupled with overconfidence and and no understanding of the laws of probability, coupled to take them out of the game. Some even went BROKE.

Let’s make up some imaginary characters: Arbitrary Albert, Arithmetic Andy, and Larry Logarithm. We’ll take the exact same win-loss record, with the exact same payouts, and see what different results they may achieve with their particular approach to money management.

MANY traders approach the money management portion of their trading with an on-the-fly method, adjusting their amounts AT RISK as the trading unfolds. Most are Arbitrary traders. Here’s how Arbitrary Albert’s thought process might have gone, with the win/loss record above:

“Hmmm…. I have $1,000 bucks… if I bet it ALL, I have a 40% chance of losing everything on the first play. SO, I better not go that high. Let’s just try about, er, 25%. I’ll bet $250.”

1) LOSS!

“Ah, shoot. Well, I still have $750 left. And, if I bet another $250 there’s about a 50/50 chance that I’ll make it right back. Y’know, it’s actually BETTER than 50/50 because Ralph told me I’d have 60% winners, and since I’ve had one loser already, chances must be better, right? Okay, let’s go $250 again.”

2) LOSS!

“DRAT! Well, nuts. I only have $500 now. If I bet $250 again I’ll be down 75%… and I COULD lose the one after that too and go completely bust. Better play it safe. Let’s say only $100 this time.”

3)  WIN!

“Hmm, figures. I bet only $100 and now I win. Two losses and one win, eh? I’m probably due for another win. Put me down for the $250 again…”

4) LOSS!

“CRIKEY! Okay, now I HAVE to be conservative because I’ve lost so much. (SIGH) Okay, $100 it is.”

5) WIN!

“Oh good, I won something. I’m not ready to bet a lot again though, let’s go $100”

6) WIN!

“That’s two in a row! Getting some of that money back. (Whew!) Well, after two losses in a row I’m afraid to bet too much. Seems like it might be time for another losing trade. Now let’s see… I’ll bet $50. That way if I lose, I don’t lose too much.”

7) WIN!

“Awww. I can’t believe that I’m disappointed that I WON. I just wish I had bet more. Huh. Ralph said I would win 60% of the time. I’ll bet $100 again, because the $50 I bet just now and won MAKES $100, so that’s not really a big risk, is it?”

8) LOSS!

“MAN! Okay, I’m not getting faked out again. I’m going to just bet $100 every single time. Over a long enough period of time, I think that guarantees I’ll make money, right?

9) WIN!

“There we go. Okay, I’m sticking to my guns. Just $100 bet and that’s what I’ll keep doing.”

10) WIN!

“Good! Won again. Okay, let’s count up how much I’ve made so far… Hey, WHAT THE…?”

The arbitrary better, the one that bets according to a dialogue like this in his own brain, is unlikely to make it. Even with a winning game, he cheats himself with his lack of a plan. In this example, the record reads:

BALANCE          BET AMOUNT          WIN/LOSS          NEW
$1000              $250                     -$250                  $750
$  750              $250                     -$250                  $500
$  500              $100                     +$100                 $600
$  600              $250                     -$250                  $350
$  350              $100                     +$100                 $450
$  450              $100                     +$100                 $550
$  550              $  50                     +$  50                 $600
$  600              $100                     -$100                 $500
$  500              $100                     +$100                 $600
$  600              $100                     +$100                 $700

End Balance: $700, loss of 30%.

As you can see, Arbitrary Albert was faced with a winning game… 60% winners paying out even money… yet because of his lack of discipline and foresight he ended up with a 30% loss. It had nothing to do with the “market” he was trading, and everything to do with  his money management strategy… or lack thereof.

Let’s leave Arbitrary Albert’s mental and emotional  gymnastics… and instead go to Arithmetic Andy’s logic.

Arithmetic Andy knows he’s got a 60% chance of winning EACH time the game is played (probability is not affected by past games). Andy decides to bet a fixed amount each time. Since it’s unlikely that he’ll have five losses in a row… though it is possible… Andy sets the amount per trade at $200. He figures he has a very low probability of going bust but is also betting the maximum amount he’s willing to risk.

Arithmetic Andy is following a disciplined system, so there’s not a lot of mental/emotional dialogue between plays. Check out the results of HIS plan:

BALANCE          BET AMOUNT          WIN/LOSS          NEW
$1000              $200                     -$200                  $800
$  800              $200                     -$200                  $600
$  600              $200                     +$200                 $800
$  800              $200                     -$200                  $600
$  600              $200                     +$200                 $800
$  800              $200                     +$200                 $1000
$1000              $200                     +$200                 $1200
$1200              $200                     -$200                 $1000
$1000              $200                     +$200                 $1200
$1200              $200                     +$200                 $1400

Ending Balance: $1400, a 40% gain!

Arithmetic Andy knows that over enough iterations of the game he will make money, so long as he doesn’t go broke by risking too much. This amount was a good amount to risk on each play, given the parameters of risk, reward, and probability of a payout.

So what could be better? Well, here’s the REAL edge: learning to adjust the strategy on the fly much like Arbitrary Albert… but doing so with a set of predefined rules like Arithmetic Andy used. Enter Logarithm Larry.

Logarithm Larry wants to INCREASE his exposure during winning runs, while DECREASING his exposure to the market during losing streaks. Here’s how he’ll do it:

By betting an ideal percent of his account every time, Larry will adjust accordingly when he is winning and also adjust accordingly while he is losing. Each bet is determined not by the perceived “chances” affected by the bet before it, but by the solid results left behind by each previous move.

Clear as mud? NAW. Larry is just going to bet 20% of whatever his balance is, because logarithmically it offers the best exponential growth over time. Let’s see how THAT idea plays out after ten trades:

$1000              $200                     -$200                  $  800
$  800              $160                     -$200                  $  640
$  640              $128                     +$128                 $  768
$  768              $154                     -$154                  $  614
$  614              $123                    +$123                  $  737
$  737              $148                     +$148                 $  885
$  885              $177                     +$177                 $1062
$1062              $212                     -$212                 $  850
$ 850              $170                    +$170                   $1020
$1020              $204                     +$204                 $1224

Ending Balance: $1224, a 22.4% gain!

Now, at first blush that may seem to be less than the gain that Arithmetic Andy got. Andy got a 40% gain by betting a fixed amount, while Logarithm Larry got only 22.4%.

Hold the phone, you may be saying. WHY would I want to seek out a logarithmic system instead of the better paying fixed bet? Stay tuned to find out.

If Andy keeps up his pattern of strictly betting $200, he will make money with this system for the rest of his life. However, he will be limited by the fact that he can only make a fixed dollar amount per winning trade. He will NEVER make more than $200 on a winner, and will probably never think to bet any more than that because his system is rewarding him with predictable returns.

This is where a deeper understanding of math comes in handy. Arithmetic Andy may seem to be beating Logarithm Larry early on… and he does at first… but remember this is only a sample of ten trades.

Andy sure knows his Arithmetic. Every ten trades or so, Andy will have $400 more dollars. Check the equation… (6 winners X $200) – (4 losers X $200) = $400.

After the same ten trades, Larry will be ahead by 22.4%, while Andy will be up 40% from the $1000 that they each started with. It appears as though Andy is beating Larry’s pants off. But WAIT… as they say. There’s more.

Over a long enough time horizon, things begin to change. While Andy’s money management method brings him a predictable $400 every ten trades, Larry’s technique takes the exact same win/loss/reward conditions and converts it to a reliable 22.4% gain.

The difference between the two is that one account increases in a linear way, while the other increase is exponential.

After 100 trades, Arithmetic Andy’s account is up $4000 because his method returns $400 every ten trades. In contrast, Logarithm Larry has an account size of about $7547 due to the magic of compound interest!

Let’s review: Arbitrary Albert, Arithmetic Andy, and Logarithm Larry all found the same opportunity… a trading system with a 60% chance of winning and a 1:1 payout… but they all have very different end results.

As long as Albert keeps betting all over the board, he will keep losing. And sadly, this is how MOST traders handle their accounts because they overestimate the importance of picking stocks and timing trades, while underestimating the importance of money management. Though Albert has a winning setup, his arbitrary method of betting will keep working against him as he bets too large on losing plays.

Andy indeed has a wining system, but it actually returns less and less percent-wise as time goes by.

The best play for the long term is to adjust the amount risked in each trade to the present value of the stake. That’s Larry’s way to go. Stay tuned for more math and trading in this blog…

Comments? Bring ’em on!

Happy Trading,


About Kurt Frankenberg

Kurt Frankenberg is an author and speaker about entrepreneurship, martial arts, and trading the stock and options markets. One of several "Biznesses" he founded as a teen, The Freedom School of Martial Arts, has been in continuous operation since 1986. Kurt lives in Colorado Springs with his wife Sabrina, German Shepherd Jovi, and his ninja cat Tabi.