The Constants

Investing is not mathematics. Investing is not physics. There are no fundamental laws that govern the markets and dictate their every move. There are no constants, universal in nature, to help you solve for the perfect portfolio.


Archimedes’ constant, also known as Pi (π), is the ratio between the circumference and the diameter of a circle. You probably remember using it in grade school to calculate the area of a circle with a radius of r (πr2) or the surface area of a sphere (4πr2). It has many other applications in higher math and physics.

There is no Pi in investing.


Euler’s number, also known as the exponential growth constant (e), is the base of the natural logarithm. That likely means nothing to you but the term “compound interest” may be more familiar. Euler’s number is the representation of continuous compounding. Calculating the growth of $1 over a year, we find the following, assuming a 100% interest rate:

  • $1 compounded monthly is equal to (1+ (1/12))^12 = $2.61
  • $1 compounded weekly is equal to (1+ (1/52))^52 = $2.69.
  • $1 compounded daily is equal to (1+ (1/365))^36 = $2.71.
  • $1 compounded hourly is equal to (1+ (1/8,760))^8,760 = $2.71812669161742

As the time period (n) gets bigger and bigger, the compounding equation (1 + (1/n))^n approaches a limit of e. Exponential growth is found in many areas, including the number of microorganisms in a culture, a nuclear chain reaction, and processing power of computers.

There is no exponential growth constant in investing.


The golden ratio (φ), also known as the golden mean or golden section, is found where the sum of two quantities (ex: two lines, a and b) divided by the larger (a) is equal to the ratio of the larger (a) divided by the smaller (b).

(a+b)/(a) = (a)/(b) = 1.61803…

The ratio is found in geometry (pentagonal symmetry), architecture (Parthenon), nature (leaves and branches along the stems of plants), and even music (833 cents scale).

There is no golden ratio in investing.

The Constants

Does the lack of a constant mean you should not invest? No, it just means you shouldn’t approach the markets in the same way you would a problem in math or physics. There is no “right” answer, no precision, and certainly no holy grail.

Instead, the only constants in investing are generalities, probabilities, rules of thumb:

While these quasi-constants don’t leave investors with a single solution, that is by design. For there cannot be one when we’re dealing with problem with multiple questions…

  • How much money do you want/need?
  • What do you plan on doing with that money?
  • When do you plan on doing it?
  • How stable are your current and future sources of income?
  • How much do you have saved in case of an emergency?
  • Do you have any debt and at what interest rate?
  • How much loss can you tolerate before selling in a panic or losing sleep at night?

Everyone has a different answer to these questions and the answers are forever changing. There is no constant in life just as there is no constant in markets. And that’s ok, so long as it means we’re forever growing, learning, and adapting. Constants in math and physics are essential; constants in life are extraneous.


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This writing is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation regarding any securities transaction, or as an offer to provide advisory or other services by Pension Partners, LLC in any jurisdiction in which such offer, solicitation, purchase or sale would be unlawful under the securities laws of such jurisdiction. The information contained in this writing should not be construed as financial or investment advice on any subject matter. Pension Partners, LLC expressly disclaims all liability in respect to actions taken based on any or all of the information on this writing.



Charlie Bilello is the Director of Research at Pension Partners, LLC, an investment advisor that manages mutual funds and separate accounts. He is the co-author of four award-winning research papers on market anomalies and investing. Mr. Bilello is responsible for strategy development, investment research and communicating the firm’s investment themes and portfolio positioning to clients. Prior to joining Pension Partners, he was the Managing Member of Momentum Global Advisors and previously held positions as a Credit, Equity and Hedge Fund Analyst at billion dollar alternative investment firms.

Mr. Bilello holds a J.D. and M.B.A. in Finance and Accounting from Fordham University and a B.A. in Economics from Binghamton University. He is a Chartered Market Technician (CMT) and a Member of the Market Technicians Association. Mr. Bilello also holds the Certified Public Accountant (CPA) certificate.

You can follow Charlie on twitter here.

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