“Stock prices” are a new kind of data. To be more precise in this mathematically inclined monologue, we must first think of the “stock price” as a datum or object to be defined and, possibly,  “stock prices” for one company, many, or all, if that is possible, as instances or observables of the datum “stock price”.

For example, if we are given a basket of numbers, with or without decimal fractions, is there any way that we might know that these are “stock prices” ? And if so, could we then further distinguish them with a “signature” such as “\$” or “£” or “€” or “¥” or is there also a “cultural” or” societal element” that we must account for before doing so?

That is not an idle question. There is no capitalist hegemony (or one size fits all) among the cultures and nations of the world – consider Europe at the present time – and one would think that with some clarity in these matters – some foundational work – we might obtain a kind of Principia Economica and a metalanguage with possibly Gödelian outcomes that actually defines the field and what we’re talking about that is, in fact, provably correct – that logical arguments with verified data could lead to logical conclusions that are, in fact, correct and can be verified as such.

We begin by asserting something about the properties of stock prices that is something other than their values which we know minutely but don’t really know why they are what they are or why they change so frequently.

Property 1: “All stock prices begin and end at zero.” (Goetze 2009)

Property 2: “There is a  price of risk (for equities as well as bonds) and it is the least stock price at which a company is likeable.” (Goetze 2009).

Stock prices begin at zero or a small par value when issued from a company’s treasury stock and the price is eventually determined only by what people (including the company itself) are willing to pay for it, at issue and subsequently. They also end at zero through a company failure or bankruptcy, or by acquisition in which case the “stock price” is effectively carried into the new owner’s company which, too, must eventually end in failure, bankruptcy or acquisition (even if it takes one hundred or more years to do so – time is not of the essence).

The second property is a little more complicated because the term “likeable” appears to be undefined, although the existence of the (or a) “price of risk” might easily be inferred by thinking about the company itself buying in or selling out its own stock from treasury shares and how much of that it can do before investors refuse to sell what they already own or buy the stock at the current or offered price. That is, they want, on due deliberation, a higher price if the company is buying and a lower price if the company is selling.

On the other hand, we are familiar with the “price of risk” and have used it frequently in these Letters and have also given many examples of it (please see, for example, these Letters and the Dow Jones Industrial Companies or NASDAQ 100 – (B)(N) There And Done That, June 2012).

Property 3: “All investment (including the purchase of stocks) is just and only the purchase of risk, and, like anything else that we might want to purchase, we ought to know the price of it, that is, we ought to know the price of risk.” (Goetze 2009)

In the context of risk aversion – as risk averse investors we want to keep our money and obtain a hopeful (but not necessarily guaranteed) return above the rate of inflation – we can define “likeability” opportunistically, in a way that suits our purpose.

Property 4: “However we define ‘likeability’ – and investors will have different opinions – we require that portfolios of such companies deemed ‘likeable’ in our market of interest, should tend not to lose in value, and that the contra portfolio in the same market should tend not to gain in value.” (Goetze 2009)

In the examples below (Exhibit 1 and 2), we have made that distinction in a “basket” of stock prices (17,500 of them) gathered in the S&P 500 companies over a ten year period (2000-2009).

The test is not quite “blind” because we know that these are stock prices and each price is tagged by a company name and the year-quarter in which that price obtained, SP=SP(Company, Year-Quarter), but otherwise there is nothing special about these prices – they are not systematically minimums,  maximums, medians or averages, for example – all that we know is that the stock was bought and sold at that price during that year-quarter regardless of whatever other price the stock had or subsequently obtained.

If SP=SP(company, quarter) is a stock price in the basket and SP1 is the stock price drawn from the previous quarter for the same company, then the coloured threads (some of which are pink) show the path of such collections of log(SP/SP1) as long as SP1 was a (B) or (N) – that is, either SP1 exceeded the price of risk (SF1) at that time and was therefore a (B), or was below the price of risk (SF1) at that time and was therefore an (N).

In order to squeeze all of this information into a small and colourful space, we scaled the x-axis uniformly as -½ log(b) to the base (a) = -½ log(b)/log(a) where (b) is the product of all the positive returns (SP/SP1, SP>SP1) in any quarter (and is therefore greater than one), and the base (a) is the product of all the negative returns (SP/SP1, SP<SP1) in any quarter  (and is therefore less than one).

Exhibit 1: Bond-like Behaviour Above the Price of Risk – SP>SF

Log(SP/SP1) if SP>SF.

The instances of price increase, quarter over quarter (SP/SP1), over price decrease (SP/SP1), were better than 2:1 in this example, based on all of the companies of the S&P 500, and the center of mass is greater then zero, that is, it is positive and up and to the right, in the first quadrant, and it is obvious that the quarterly changes are significantly different in size, direction, and volatility from the ones in the chart below, in the same family of stocks. Note that the y-axis is substantially in the range [-0.5, 1.0] as opposed to [-1.0, 0.5] in the chart below and that the x-axis range is not as fiercely truncated.

Exhibit 2: Equity-like Behaviour Below the Price of Risk – SP<SF

Log(SP/SP1) if SP<SF.

The instances of price increase (SP/SP1), quarter over quarter, over price decrease (SP/SP1), were about even, and the center of mass is less than zero, that is, negative, down and to the left, with a markedly increased volatility (as measured by distance on the x-axis and size on the y-axis), and with a higher reward (or loss) potential, if we’re right (or wrong), and willing to place our bets against the risk seekers, volatility players, and market makers, banks, and brokers who also rely on micro-arbitrage profits in agency and transaction costs in making their decisions.

The actual numbers are as follows:

Price Increase       Price Decrease            Ratio

(B) SP>SF                  4,728                          2,290            2.06

(N) SP<SF                  5,515                          5,025            1.10

And that’s all that one really needs to know – that the house odds on the portfolio (B) SP>SF, which is we (who want to keep our houses) are 2 to 1 and in the “volatility range” (N) SP<SF are 1 to 1.

Disclaimer

Investing in the bond and stock markets has become a highly regulated and litigious industry but despite that, there remains only one effective rule and that is caveat emptor or “buyer beware”.

Nothing that we say should be construed by any person as advice or a recommendation to buy, sell, hold or avoid the common stock or bonds of any public company at any time for any purpose. That is the law and we fully support and respect that law and regulation in every jurisdiction without exception and without qualification to the best of our knowledge and ability.

We can only tell you what we do and why we do it or have done it and we know nothing at all about the future or the future of stock prices of any company nor why they are what they are, now.

The author retains all copyrights to his works in this blog and on this website. The Perpetual Bond®™ is a registered trademark and patented technology of The RiskWerk Company and RiskWerk Limited (“Company”) . The Canada Pension Bond®™ and The Medina Bond®™ are registered trademarks or trademarks of the Company as are the words and phrases “Alpha-smart”, “100% Capital Safety”, “100% Liquidity”,  ”price of risk”, “risk price”, and the symbols “(B)” , “(N)” and N*.