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Re #1. Yes and no. It is not exactly that I am looking to shorten the remainder. That I could simply do with rounding to whatever precision I want.
Perhaps a side note in finance and trading would hint at my intention behind the question.
I offer 3 points:
1. In machine learning (ML) EP Chan is one of the better experts. (there is a webinar of his here at FIO). He started at IBM labs in ML for speak recognition. His colleges went off to Renaissance Tech and are now billionaires along with the founder Jim Simmons. He also went into finance first with Goldman (?) and then on his own with a small hedge fund. In a talk (he has 17 years experience) he posed the question: "I have applied ML to trading and with all my knowledge and the success of my colleagues I thought I would have great success. How it work out? - I did not make money with ML." (rough quote)
He had ASSUMED that with all his knowledge and tools and experience and other resources he would make money.
2. Ed Thorpe is a giant - well known mathematician (writing How to beat the Casino) and created the blackjack card counting system. He has run a fund with great success (average 19%/yr) and had only 3 (?) down months in 19(?) years which is equivalent (according to Jack Schwager of picking one atom at random from all the atoms on the surface of the earth.) Both Thrope and Chan refer often to the Kelly formula for position sizing. The formula ASSUMES that, that is it relies on, the returns being a)known and b)Gaussian for the formula to work. The market and the returns are NOT Gaussian. The most widely used formula relies upon a false ASSUMPTION
3. Dr. Marcos López de Prado, another giant in the industry, who ran a quant fund with 138 billion under management, speaks of how the MVO portfolio optimization which is used by funds representing trillions under management is deeply flawed, unstable with only 10% of back data removed, and only fits applies past correlations of at least 5 years which are not reasonable based on the insatiability of the market. The Fund managers ASSUME MVO is the correct tool for portfolio optimization - a totally incorrect assumption. De Prado has also shown that selection bias can create a sharp ratio of 3 or more on a random number series (where there is no edge) with enough trails and quotes his colleague Dr. Tom Harvey that most financial conclusions in academic work are false.
