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The Power Law

October 30, 2013

Essay. We’ve had inquiries from all over the world on “The Power Law“, [SF] = [P/E] × EPS, which is our description of a familiar relationship in “financial analysis” that is not only colourful but accurate in its relationship to the power concept in “physics”.

In physics, “power” is a binding form between work, energy, and heat in which [P] = [V] × I and the equation “power” P equals the “voltage” V times the “current” I is correct from microcircuits to nuclear generators; the equation is exact if the voltage and current are constant but most typically, the voltage is varying (such as 50 or 60 cycles per second) and we can provably measure its “force of action” not as an “average” (which is zero) but as the quadratic mean [V] of its amplitude and so instead of getting “power at this instant” we get [SF] which is the demonstrated power on average but is just as real as the “instantaneous” power because it demonstrates the properties of power that we expect to see and which can be verified by experiment; for example, “power” can be used to do “work” and we can measure the latter and begin to understand the meaning of “more power” and “less power” in terms of the “work” that it does.

Since V = I×R (the resistance) is also required and we expect that the “resistance” is the least variable element of our “circuit”, we can re-state the power law in a more effective form as [P] = [V]²×(1/R) and we can think of (1/R) as a measure of “transparency” or “risk aversion” in the sense of von Neumann-Morgenstern.

The Power Law

The Power Law

All of this is now so ordinary that most of us have forgotten how extraordinary it is. But having forgotten, should we now sell our house because the lights flicker?

If we are a speculator, the answer is yes because we don’t have time for maintenance. Maintenance costs time and money and we don’t want to spend any if we have some and the reason that we are “speculators” is that we don’t enough of one or the other or both.

As an investor, however, we have a different point of view. With respect to the diagram, we’re prepared to buy and hold any stock at $10 or $25 as long as its yield is above 2% (P/Es less than 50×), for example, because we know that government secured bonds are readily available at 2% and that return is guaranteed no matter how much the government earns or not, notwithstanding that the 2% figure might need to increase with increasing inflation and the lines at 2% and 5% could have an upwards slope, or even curvature, to them if we knew something about inflation and expected EPS or we could just talk about real returns, adjusted for inflation.

For me?

For me?
[P/E]<20x, you say?

We also know that yields above 8% or so (P/Es of 12× or less) are unlikely. After all, if we owned them, why would we sell them? Although we do know that it’s possible to work for them and there are also many investors – “value investors” – who think that they know so much about the future that they deserve them.

But if we have that modest goal firmly in mind – a goal that we share with the world’s biggest and most experienced investors – that still leaves a lot of room for the “lights to flicker”, that is, for the earnings per share EPS to falter, vary, decrease or increase according to the many factors that will affect a company’s earnings and for which we have hired its managers.

For example, if the EPS is declining then we don’t expect the share price to increase. But it might and if it does, we still have our 2% “bogey” as the sell point ($25) at which we take profits and sensibly move on to some other investment with a 5% or so apparent yield.

“Speculators”, however, despite all logic, will tend to think that the price will keep on rising (and sometimes it does) but tend to have no “sell point” in mind, absent the need for a new house that other investors are building for them.

On the other hand, if the EPS is declining, then the stock price might drop because some investors are responding to the decrease in earnings per share but not to the change in yield which could be increasing as the share price drops while they are trying to find buyers for the shares that they have. In principle, then, that’s a buying opportunity for the 5%’s at 8% (let’s say) and buying the stock might oppose the price decline and re-build the yield at 5% or better.


Oops! Maybe we overreacted?

Or it might not, in which case the price decline overwhelms the decrease in earnings per share – like a “short” circuit, so to speak – and pushes the instantaneous yield to spectacular levels at 10%, 20%, 50% and so on as the [P/E] multiple drops towards zero or even becomes negative.

And we would lose a lot of money were it not for our effective stop/loss or long puts because when there’s a sell-off (and there are suddenly a lot of houses on the market), the yield curve moves sharply to the left and “flips over” in an excess of supply over demand (until the power is restored).

Always On

The Power Is Always On
The Perpetual Bond

The “price of risk” [SF] = [V/N*] × N*/Share is also an example of the Power Law with the difference that the measure of “current” N*/Share is a provable measure of investor risk aversion and demonstrates the properties of the Power Law that we expect in investing because it can be shown to resolve the conflict between “risk seeking” and “risk averse” investors whose common object is to obtain a non-negative return and a hopeful non-negative real return; the effective difference between them is the need for liquidity which cannot be predicted from past stock prices and could also be affected by “surprise”.

Our topology is also quite different from the above chart but amounts to the same thing. The Power Law suggests that “investments” begin as “negative cash” (such as a start-up or failed investment that is “project financed”), through investment “work” and earnings and end in cash which has no earnings. The price of risk collapses (figuratively) the 2% and 5% lines into one, the same one, which is the price of risk. We do not buy or hold investments below the price of risk which we call (N); we buy on demonstrated plausible transitions from (N) to (B) above the price of risk; hold in (B) and sell on transitions from (B) to (N) absent profit-taking or price protection through the stop/loss price which could still be a buying opportunity if the stock price appears to be still above the price of risk. In the latter case, if we have a put option in force against our long position, we have the option of putting the stock or keeping the stock and selling the put.

Moreover, the power is always on which is why we call it the Perpetual Bond™ of the (B)-class companies in any market.

For more information and references, please see our recent Post, The RiskWerk Company Glossary.

And for more on what risk averse investing has done for us this year, please see our recent Posts on The S&P TSX “Hangdog” Market or The Wall Street Put or specialty markets such as The Dow Transports & Utilities or (B)(N) The Woods Are Burning, or for the real class actionLa Dolce Vita – Let’s Do Prada! and It’s For You, Dear on the smartphone business.

And for more stocks at high prices, The World’s Most Talked About Stocks or Earnings Don’t Matter – NASDAQ 100.


We are The RiskWerk Company and care not a jot for mutual funds, hedge funds, “alternative investments”, the “risk/reward equation” and every other unprovable artifact of investment lore. We have just one product

The Perpetual Bond
Alpha-smart with 100% Capital Safety and 100% Liquidity
With No Fees and No Loads on Capital

For more information on RiskWerk, please follow the Tags or Categories attached to this Letter or simply enter Search for additional references to any term that we have used. Related data may be obtained from us for free in a machine readable format by request to


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*.

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