You're confusing accounting lol.
Imagine your balance sheet with A = L+E. On your asset side you have cash and investments. If you have $100 of cash and buy $100 worth of stocks, nothing to your net worth changes. Your -100 to cash is +100 to investments. Your L+E remains the same, at 100...
A simple way to understand edge is as the reason why you think you will make money on a trade. The fact that many people do not have such a reason partially explains why Ken Griffen is so rich.
Slippage and TC is the distance between your fill and your arrival price. Just because someone gets a fill close to their arrival price doesn't mean they have an edge in the direction of where the underlying is going, hence an execution edge is "delta neutral." E.g. just because I am a small...
Developing edge takes dedication, research, and commitment. You can embark on that path by reading my thread Elite Trader School | Elite Trader to first build knowledge on the market, and then narrow on your style, market, or sector.
Alpha = something that pays you with excess returns
Edge = your workflow that gets you that alpha
Simplistic example:
There doesn't seem to be much alpha in distressed stocks (Is there alpha in distressed stocks? (U.S. evidence) (alphagenstrategies.com)). However, you have a strategy where if...
Edges are tied to alphas. Things like momentum are beta, as in they’re broad characteristics of a stock or group of stock. You can have an edge in beta timing, but the more useful it is the more likely it gets discovered by others too. When everyone knows about it, then the price already...