The problem with 'edge' in trading is that you don't know you have one. The casinos know they have an edge because it is set in stone mathematically, but in trading you can only quantify your edge after the fact. You have an edge if you can consistently make money trading, and you obviously don't have one when you're losing money. The problem with that is that there might be more reasons to you losing money then not having an edge, which makes it even harder to quantify your edge. Even if you do think you have an edge, it might change or go away since the market is dynamic while the casinos edge is constant and never goes away.
I believe you can indeed know that you possess an edge. Casinos know they have an edge and as you said mathmatically, they have their edge- but psychology wise- traders can have their edge. As Casinos know their are only 52 cards in the deck, good traders know that fear and greed of other traders will come into play. If a trader learns to read the other players moves- it most certainly gives you an edge. Knowing how the masses move, how they tend to think and the overriding emotions of fear and greed in the marketplace- they are a distinct advantage over someone who is unaware of what really drives the markets.
if you pick a few indicators and use them over and over you will notice correlations between the indicator and the markets reaction to it,that doesn't mean you will always know what the market is doing,but occassionally the market will follow your assumption based on that indicator and you will profit from it. One trader who gives a heads up on his trades and why he takes them uses the macd and 5 or 6 times a day he will take a few points out of the market. He uses divergence when the macd is making a mountain above zero and then a second smalller mountain . When the market is trending up and the mountains are going down he feels confident in selling it when the 2,3 and 5 minute chart lines are crossing over,that gives him an edge,the other thing he does is hold steadfast to a 2 or 3 point stop rule,if he gets stopped out and he still likes the trade he will reenter,but he never takes a big loss,i admire his discipline. That doesn't always set up but when it does he takes advantage of that edge
i've never seen his trading platform but he watches several time frames,he uses a weekly to get a trend and then reduces it to a daily ,hourly,30 min,10,5 ,3 ,2 min,i use different indicators,his was just easy to explain, if you put 4 charts of the es on your screen all using different time frames with the same macd indicator,it should be easy to watch
I think trading edge derives from market makers. A market maker buys on the bid and sells on the offer, the spread is roughly his edge. My friend is an option market maker. In this case, he sits on a relatively wide bid/ask spread and a customer hits his bid with an order -- he instantly hedges that position by trading an appropriate amount of stock to offset this position. The difference is therefore, the fact that he sold on the bid -- a price he has calculated to be a discount to the cost of hedging. In regular market making, your edge is less tangible. A casino knows his edge because the game has mathematical properties where 'past does in fact equal future.' In regular trading, you never know if future will be different than the past -- so any mathematical model may be optimized to one set of past rules -- where a new set of rules may have instead been created. That said, there is much literature on this subject in portfolio management. Instead of 'edge' --- you think of 'reward/risk'. Reward and risk are estimated and ratios are created to summarize/describe different strategies. Many different strategies have proven to be uncorrelated over time such that 'reward/risk' on average can be estimated with reasonable accuracy for a properly diversified portfolio.
My definition of Trading Edge 'When one is consistent part of one's own Trading System' System are as good as the weakest link within it & most of the time I find myself as the weakest link The period I could maintain Edge is limited (< 40 minutes Ave) and hence split trading sessions 2 to 3 times a day to play with it
edge and risk management are the ONLY ingredients to be net positive. Simple as that. One sentence. No bullshxt. No Jack Hershey.
My own definition of a trading edge is a mixture of technical skills and psychology. 1. Knowing yourself ie identifying your strengths and weaknesses; 2. A logical and flexible trading method(s) suited to your own personality and written down; 3. Intelligent position sizing; 4. Maximising profits as much as possible; 5. Minimising losses and risk as much as possible; 6. Discipline to follow your trading plan; and 7. Patience to wait for the very best setups. Should lead to a trading edge ie positive expectancy.
To me an edge in trading is the sum total of what you do that beats the monkey throwing darts at a dart board. Of course this doesn't need to be backtested, you can forward test what your doing purely discretionary but you may not realize you have no edge until you blow up. I soppose the same thing goes for backtesting too in that you may not find out that your "edge" was just data snooping bias and that you didn't account for enough variables until you blow up.