All About Alpha has an interesting post discussing a brand new paper by Godfrey Cadogan titled: Trading Rules Over Fundamentals: A Stock Price Formula for High Frequency Trading, Bubbles and Crashes.

Cadogan writes:

In this paper we present a simple closed form stock price formula, which captures empirical regularities of high frequency trading (HFT), based on two factors: (1) exposure to hedge factor; and (2) hedge factor volatility. Thus, the parsimonious formula is not based on fundamental valuation. For applications, we first show that in tandem with a cost of carry model, it allows us to use exposure to and volatility of E-mini contracts to estimate dynamic hedge ratios, and mark-to-market capital gains on contracts. Second, we show that for given exposure to hedge factor, and suitable specification of hedge factor volatility, HFT stock price has a closed form double exponential representation.

All About Alpha is skeptical

As is often the case, though, the discussion can leave those of us outside the quant world confused: does the rendering of facts as a formula make them clearer, or does it just create a potentially misleading patina of precision?

Given Cadogan’s ambitious-sounding program, linking HFT, bubbles, and crashes all into one formula, one remarkable feature of the result is his formula’s extreme simplicity or, as Cadogan puts it, its “parsimony.” I was reminded of the warnings in Emanuel Derman’s recent book, Models.Behaving.Badly, that the “simple models” of finance economists have failed “to reflect the complex reality of the world around them,”

The paper, “Trading Rules Over Fundamentals: A Stock Price Formula for High Frequency Trading, Bubbles and Crashes,” was inspired by recent studies indicating that HFT accounts for 77 percent of the volume of trading in the UK and 70 percent in the US, and that it is concentrated in the most popular and liquid stocks, commodities, and currencies. Cadogan takes it as evident that “high frequency traders quest for alpha, and [that] their concomitant trade strategies are the driving forces behind short term stock price dynamics.”