## A Theorem of Winning and Losing

I just read the book Contrary Opinion by R. Earl Hadady. Aside from his point on bullish consensus, I found the following very interesting (I call it theorem of winning and losing). We all know that the majority lose trading futures. So, say 80% traders lose, and let T denote the total number of traders, NW the average number of contracts held by winning traders, and NL the average number of contracts held by losing traders, then the following equation holds:

0.2 * T * NW = 0.8 * T * NL

From the above we get: NW = 4 * NL

Which mean the average number of contracts by winning traders is 4 times the average number of contracts by losing traders.

If 90% traders lose, then we have

NW = 9 * NL

So, the theorem says the deep pocket traders have a natural advantage to win. It begs the question of how traders with not so deep pocket can survive and win. What are the good strategies? I wonder if this also implies that one may increase the chance of winning by not diversifying funds.

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