A respectable minority of the brightest investors are no friends of the classical recommendations to diversify and differentiate one's investments -- they prefer, in Mark Twain's (or maybe Andrew Carnegie's, check that link;-) great phrasing, to practice and preach the injunction "Put all your eggs in the one basket and --- WATCH THAT BASKET."
I disagree, because I consider avoiding losses to be somewhat more important than achieving gains -- a very widespread preference, actually more extreme in most people (and maybe most monkeys), known as loss aversion.
Suppose that through your thorough, careful research you've identified two promising micro-caps, in any or both of which you could invest. Each, you assess, uncorrelated from each other, has two chances in three of doubling its market price at your time-horizon of interest -- and, alas, one chance in three of going bust (because that's the way life IS -- no matter how good a small, starting-up business, adverse winds still have a substantial chance to scupper it).
Assuming your probability estimate is accurate, your mathematical expectation for each dollar you invest is to get 4/3 dollars, $1.33, so (if your time-horizon is short enough;-) any of them is a good investment, and an equally good one net of loss aversion considerations. Your expectation doesn't change whether you put all your available-for-this-investment money into a single one, or spread it around the two of them.
However, if you focus all your money on a single one, your probability of loss is 33%. If you split it between the two businesses, if one succeeds and one fails, having split your money 50-50 between them, you'll break even (no loss, no gain) -- so you end up with a loss only if both fails, 11%. Your chance of a _gain_ is also similarly reduced (since the expectation is left the same by any kind of differentiation, if you're reducing your chance of loss you must also be reducing your chance of gain!-), but if you have any level (no matter how small) of loss aversion, then with expectation being constant you will prefer the mix with a lower risk of loss (even though inevitably that means a lower best-case chance).
In a nutshell, this is the case for differentiation -- and while the numbers change, their overall import doesn't even if you're considering investments of a very different nature (say with only a 5% chance of losing all your money and a proportionally reduced chance of doubling, or a more continuous distribution of possible gains and losses, and so forth). Diversification (spreading investment around diverse asset classes &c) has a similar mathematical basis, though focused on more strategic overall-markets consideration rather than firm-specific ones.
If you're supremely over-confident that you're a genius, or inherently blessed by Lady Luck, you'll be scoffing at this, and "go for all the marbles" nevertheless -- good luck, and Lady bless. Me, as Jefferson (or somebody else, but I like Jefferson for this one), I'm a firm believer in Luck, and I've found that, the harder I work, the luckier I get; so, the hard work of picking and choosing my stocks and carefully diversifying my investments is part of the ritual propitiations to Signora Fortuna that I've found out in the course of a long and lucky life work very well for me!
I doubt any high-rollers, go-for-all-the-marbles types are wasting time reading this blog (what with all the penny stocks, exotic commodity plays, and abstruse options strategies just waiting for their blessedly-lucky attentions!-) -- if anything, I suspect my readers may be shaking their heads and sadly wondering why I waste so much energy rather than just buying low-cost, S&P500 index funds for maximum differentiation.
Well, a personal compound annualized performance (over many recent years, including dividends but not any options or shorting possibilities) of +12.2%, vs the S&P 500's annualized +1.7 over the same span of years and with identical constraints, has a little bit to do with it... but part of it is, in Charlie Munger's great, recent words, what amounts ultimately to a philosophical, or maybe religious, core belief: "I like understanding what works and what doesn't in human systems. To me that's not optional; that's a moral obligation. If you're capable of understanding the world, you have a moral obligation to become rational.". I feel very much that way, too.
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