I challenge him to explain it in terms that an ex managing director of equity derivatives could understand
The point is that people trade for reasons other than theoretical profit maximization. E.g. day traders flattening at EOD, or guys panic selling the low due to a margin call, or managers who must adhere to a restrictive mandate, or adjusting the book based on certain calendar dates. Just a few of countless examples.
No that is not the definition of an edge. I could have a 10% win rate lose on 90% of my trades and still have a bigger edge than you.
Assets are priced at the price of the asset at some time in the future, discounted back to the present. The future price of the asset is, of course, unknown, so that the current price is only an estimate of the future price. That forward estimate, and investor uncertainty around it, constitute an implied forward distribution (density) of the price. The discounting includes adjustment for risk as well as time-value (we often call this discount function the SDF or pricing kernel), so the shape of the implied forward density incorporates risk- aversion, trading constraints, etc... as well as any aggregate investor (the representative agent) mis-forecast of the probabilities. Any difference between that implied forward distro and the actual "perfect knowledge" forward distro is a potential edge. The size of the edge is the difference in local probability mass. We can back out what the implied distro would look like without risk adjustment if we know or can guess the SDF (Stochastic Discount Factor). This will tell us whether the edge we are looking at is a risk premium or stems from mistaken investor beliefs. To guess the SDF we will often assume CRRA (constant relative risk aversion) and a power (specifically log, which Kenneth Arrow called "a good first order approximation") utility. I realize this is not a very good explanation. To really understand my previous post you need a grounding in Asset Pricing theory. I recommend John Cochrane's book on the subject. He also has a free graduate level Canvas course on it. Or if that is too much work, you can find the video lectures on youtube: https://www.johnhcochrane.com/asset-pricing One college level calculus course is probably a minimum prerequisite for these lectures. For a quicker intro, the first part of Iqbal's FX book, recommended in another thread by @longandshort, is a good start.
Thanks for trying. Us third graders have trouble grasping "The discounting includes adjustment for risk as well as time-value (we often call this discount function the SDF or pricing kernel), so the shape of the implied forward density incorporates risk-aversion, trading constraints, etc... as well as any aggregate investor (the representative agent) mis-forecast of the probabilities." However I understood this explanation a little bit and the first one was way over my head. I find it easier to find stocks that are going up and buying them. Why over complicate something?
I never mentioned percentages, i sad "above random". A 10% win rate that catches profitable trades on average at say 20:1 reward to risk is above random, in that a 10% win rate by random chance would only average a RR of 9:1 (thereby only breaking even). A clearer example: A 2:1 reward to risk ratio breaks even at 33.3%. If a trader can average 2:1 RR with a 50% win rate, they are winning at almost 17% above random for this particular R:R