Hello fellow traders,

I have been a part of the Twitter trading community for some time now and I am grateful to all the traders providing useful info via blogs and thought I should return the favor. Much thanks to all the guys providing great free content to help retail traders find an edge. That is why I have decided to create this blog, to give back and talk about a subject that I dont see many guys talking about, yet is incredibly important.

First a short background about myself: 
I am fairly new to day trading with about 1 year of experience, but I am not at all new to the concept of a market and identifying edges in order to maximize bankroll growth. I have successfully handicapped sports markets for over a decade and decided to transition over to stocks once I saw the kind of opportunities that exist, specifically in small caps. My entire system for handicapping sports was using math, primarily statistics and probabilities in order to identify positive expectation wagers in the markets and optimize wager size relative to bankroll in order to maximize expected growth. I feel as though these concepts are comparable when it comes to trading.

For those without a strong math background, the algebra below can get a bit tricky. Not to worry, its more important to understand the concepts than the actual math. I have included a Google Sheets link below with all the math formulas set so you can put your numbers in and everything is calculated automatically.

Lets get right into it:
What is an edge? We hear this term all the time but what does it mean mathematically? How can we calculate it and IF our system has an edge how much of our bankroll should we risk in order to maximize growth?

Edge = (Profit Ratio+1)(Win Probability%)-1
For example if you wager Black in roulette your profit ratio is 1 to 1, and the win probability is 47.36% (18/38). Therefore you can calculate your edge as follows:
Edge = (1+1)(47.36%)-1 = -5.26%
 
This results in a negative edge, meaning you will lose money on average every time you place this wager, obviously not a good strategy. However in the stock market you CAN find edges and be profitable long term.
Lets say for example you have tracked a system of yours for some time and have a large sample of data that shows you are profitable. Your system produces a 2 to 1 profit ratio and you win on average 60% of the time when using a 20% profit target and 10% stop loss. Your edge with this system is
Edge = (2+1)(60%)-1 = 80%
 
This is a great system producing a strong edge of 80%. With an edge this high should you risk your entire bankroll on every trade? Even leverage your account in order to maximize growth perhaps? NO! A common mistake is risking too much on a single trade, because no matter how good your system is, there IS a % amount risked that will guarantee you go broke! How can we calculate the appropriate stake for our system?
Stake% = (Win Probability% * (Profit Ratio + 1)–1)/((Profit Ratio + 1)–1)
Stake% = (.60*(2+1)-1)/((2+1)-1)
Stake% = 40%
So for this system we should risk 40% of our bankroll on each trade. This calculation is from the Kelly Criterion which is a calculus derived formula that is designed to maximize bankroll growth via optimized stake sizes. The stake calculation will result in a Full Kelly risk amount (1.0 Kelly Size), some people prefer fractional Kelly stakes in order to reduce volatility however they will sacrifice some returns. See the graph below.
As you can see risking either less or more than Full Kelly is not optimal, however risking less is acceptable for those looking to reduce volatility and have less swings in their bankroll size at the cost of returns. Risking too much is never a good idea however most people will lean towards that, I have found myself guilty of that also. In our minds we think more risk = more return, but you have to train yourself to think mathematically, always do what is optimal for your bankroll. LESS is MORE!
The important thing to realize is that no matter how strong your edge is, there is a specific % of your bankroll you should risk each time in order to maximize your growth exponentially. That is calculated as follows:
Expected Growth (EG) = (1 + (O-1) * S)p * (1 – S)1-p – 1
EG = (1 + ((2+1)-1) * .40).60 * (1 – .40)1-.60 – 1
EG = 16%

O = Profit Ratio+1
P = Win Probability%
S = Stake% of Bankroll

That means on average your bankroll will grow by 16% per trade with this system. No other stake size will result in a higher EG%, risking more than this amount will increase volatility and decrease returns.

When developing a system and deciding what % stop loss and profit target to use, be sure to consider this KEY point. Not all edges are the same!

Example:
Our system above produces an 80% edge with a 60% win rate (20% Profit target and 10% Stop loss). Lets say you have also tracked your system when using a 10% Profit target and 10% Stop loss and it also produces an 80% edge but your win rate is 90%.

Which system should you follow in order to maximize growth? Both systems produce the same 80% edge so they must be equal, right?

The expected growth for the 90% win rate system is 44.5%, a massive improvement from the 16% produced by the previous example. The reason for this is the compounding factor. Expected growth is ALWAYS higher for systems with a higher win probability because you will be able to reinvest your winnings and grow your bankroll exponentially via compounding. Even though the edge is the same, the expected growth can differ greatly. Sometimes you should even sacrifice edge in order to win at a higher rate. This goes against the general advice of cutting losers quickly and having positive profit ratios, but in most cases that will not result in optimized bankroll growth. Mathematically speaking it is more favorable to have profit ratios LESS than 1, in order to maximize win% and expected growth. Use the power of compounding in your favor in order to grow your bankroll.

We traders spend hours constantly trying to find an edge in the markets, but that is only half the battle, knowing which edges are the most valuable and how to take advantage of them optimally will take your trading to another level and give you more confidence than ever. Even a 5% edge is enough to grow your account exponentially with compounding, it all comes down to consistency and that is where most traders and sports bettors fail. Keep emotions out of it, think in terms of mathematics and everything becomes so very simple and clear that you CAN profit long term. Have a clear, well defined system and follow it religiously and watch your bankroll grow.

I have created a Google Sheets file with all of the calculations above, just type in your data and it will calculate all of the key numbers.

https://docs.google.com/spreadsheets/d/1jWOosTftcxuqmcPE8IbzrcyGJYykIye3OeYAFSZHkyQ/edit?usp=sharing

Best of luck to all my fellow traders,
Kris Verma