Let’s look at the stock market in the most basic terms. Let’s forget for a moment about dividends and buybacks and mergers and acquisitions, people who buy and hold stocks for years on end, and frequent traders who buy and sell based on technical analysis. Let’s just consider the large majority of stock pickers, most of them institutional. These folks buy and sell stocks based on whether they expect the stock’s price will go up or down. They’re looking for alpha. (Strictly defined, alpha is a risk-adjusted performance measure, but loosely defined, it's the amount by which your returns are better than the market’s.)

So let’s ask the most basic question of all: what makes a stock’s price go up or down relative to the market?

A stock’s price goes up when investors are buying it and goes down when they’re selling. So a stock’s price is based purely on investor sentiment, and it changes when that sentiment changes. And what will cause that sentiment to change?

There are a huge number of answers, but they can be broken down into five things, more or less:

- news about the company that, in investors’ opinion, changes the company’s prospects
- speculation and/or rumors about the company’s prospects
- actual earnings/revenue performance that is higher or lower than expected
- expectations that the price will rise or fall because of a future change in investor sentiment
- expectations that the company will grow enough to attract additional investors, or will decline enough to make current investors sell.

In other words, stock market investing is an *expectations game*. A stock’s price rises and falls based not on the *value *(defined as net assets plus discounted future cash flows) of the company but on the *expectation *that that value will change. That’s why for years Amazon and Facebook commanded high prices while the companies were losing millions of dollars—investors *expected *their earnings to grow. And a very profitable and rapidly growing company whose growth rate slows will find its stock price falling—not because it’s doing badly or is losing value, but because it’s failing to meet expectations.

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I have a theory about this. It's my own; it's not in any books I've read. It's still under development, and further research is necessary. I'd be grateful for any comments about it.

In mathematical terms, the graph of a stock’s price does not correspond to the graph of a company’s value, but approximates the second derivative of that graph. (The graph of a company's value, as defined above, is necessarily an imaginary construct since that value is impossible to determine and very difficult to estimate, but I'm positing its potential existence as a kind of thought experiment.) The derivative of a graph depicts the rate of change, or the slope, of that graph; the second derivative is the slope of the first derivative. So if you had a graph depicting the value of a company, the first derivative would depict the growth or decline of that value, and the second would depict its acceleration or deceleration. To get a rough picture of a company’s real value over time you could do worse than taking the second antiderivative of the graph of its stock price. This is, of course, a drastic oversimplification, as growth is not the only thing that investors pay attention to, and it doesn't take into account the vagaries of false and unmet expectations. But it illustrates the general idea of the relationship of stock prices to a company’s value.

My theory is opposed to the more conventional wisdom that price = value + noise. No calculus is required there.

There is a paradox here, not unlike Zeno’s paradox: investors are focused not just on change, but on the expectation of future change, and on whether that expectation is too high or low, which involves the expectation of a future change in expectations, which should probably take into account the expectation of a future change in expectation of a future change in expectation, etc. In mathematical terms, you’re looking at a combination of the first derivative of the imaginary value chart, the second derivative, the third derivative, and so on.

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I am a largely quantitative investor, and an amateur one at that. I cannot pretend to predict news about a company, nor speculation about it. I cannot predict the sentiment of other investors either. I am not a financial analyst, nor will I ever hope to have the acumen, experience, or skills of one. Where, then, is my edge?

There are hundreds of companies that are not heavily followed by financial analysts, or who are covered by only a few, or to which most investors simply aren’t paying very heavy attention. These are low-volume stocks. Big investors don’t like them because it takes more effort and more money to buy and sell and investigate them; and because they’re usually smaller, they’re considered riskier. You look up these companies on Google News and you find almost nothing about them. Very few people write about them, even at Seeking Alpha (a website that specializes in the financials of small public companies). About all you can go on is their financial statements. The price of these stocks is less likely to be influenced by news and rumors than that of high-volume stocks.

So this is where I hope to have an edge. This is where the metrics that I use are, I believe, most likely to uncover underestimated companies: companies that will *outperform* the few expectations of other investors.

Certain financial metrics are so widely used that they can give me no advantage over other investors: price to book value, for instance, or price to trailing-twelve-month earnings, or EV to EBITDA, or return on equity. I don’t use those.

There are others that have become *overused *to the extent that one sees a reaction against them. For example, because stock prices are tied solely to expectations, very high year-on-year growth in revenue or earnings will often result in a reaction of disappointment to the next earnings statement. The company’s unsustainable growth rate has already been factored into its price; the company may be very healthy and keep growing, but at a slightly lower rate, so its price will decline. This is the second derivative—deceleration—in action.

There are still plenty of financial metrics that many investors don’t pay much attention to but make a big difference to a company’s future performance. These give investors like me an edge. I’ll write about some of them in future posts.

And these are the metrics that are key to my method of beating the market: to invest in those companies most likely to beat expectations.

My ten largest holdings right now: LNTH, FONR, APT, EMMS, PCMI, GSOL, BLBD, DGICA, ABCD, FSI

YTD CAGR: 39%