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Nuts & Bolts: Risk Reduction vs Portfolio Size

I was just re-reading a chapter on risk in a trading book I bought a few years ago, and came across an interesting observation:

The reduction in risk of a portfolio is proportional to the number of stocks in that portfolio.

Not exactly page one news for most traders/investors.  But here’s the more interesting part:

Portfolio Risk has a non linear relationship to Portfolio Size roughly equivalent to 1/sqrt(N).

According to the book, if you start with one stock in your portfolio and add one additional stock, your risk drops by 30%, a very significant change. With a portfolio of 3 stocks, it drops by 43%, and with 4 stocks, by 50%. But you start to get diminishing returns above 4 stocks, as can be seen by this table from the book:

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Martingale Madness

At least once in their lifetime, every trader has been tempted by the seductive lure of the high win percentages and “easy” profits offered by Martingale money management (doubling/averaging down).

Its all nonsense of course, and every time I think about revisiting the Martingale, I force myself to take a look at the equity curve of a particular ES strategy on C2:

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