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The Investing Constants

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Investing isn’t like mathematics or 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 of the circumference of a circle to its diameter. 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.


Pythagoras’ constant, often referred to as root 2 (√2), is the number that when multiplied by itself equals 2. In geometry (following the Pythagorean theorem), the square root of 2 represents the length of the hypotenuse (longest side) in a right-angled triangle where the other two sides have a length of 1.

The concept was used in the building of pavements and designing of atriums in ancient Rome. The square root of 2 is also found in music, photographic lenses and astronomy and is actually the basis for standardized paper sizes in most of the world (Lichtenberg’s ratio: longer sides are √2 times larger than shorter sides).

There is no Pythagoras’ constant in investing.


The golden ratio (φ), also known as the golden mean or golden section, is found where the sum of two quantities (e.g., 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.

Does the lack of a mathematical constant make investing an impossible task? No, it just means you can’t approach the markets in the same way you would a problem in math or physics. There is no one “right” answer — no precision and certainly no holy grail.

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

  • No big reward comes without risk.
  • The longer your holding period, the higher your odds of success.
  • All else is never equal.
  • Every time is different.
  • Price targets are pointless.
  • Forecasts are foolish.
  • Cycles and trends exist but that doesn’t mean they’re easy to predict or navigate.
  • Concentration is the fastest way to build wealth and the fastest way to destroy it.
  • The only certainty is uncertainty.
  • Time is more valuable than money.
  • Saving is more important than investing.
  • Lower fee beats higher fee on average.
  • Passive beats active on average.
  • Simple beats complex on average.
  • Lower frequency beats higher frequency on average.
  • Volatility and sentiment are mean reverting at extremes.
  • If it seems too good to be true, it is.
  • Ego is the enemy.
  • No one rings a bell at the top or bottom.
  • The portfolio and plan you can stick with is the only one that matters.
  • Diversification is the best protection against our inability to predict the future.
  • Controlling your emotions (e.g., fear and greed) is the most important thing.

While these quasi-constants don’t leave investors with a single solution, that’s by design. For there can’t be one answer when we’re dealing with a 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? At what interest rate?
  • How much loss can you tolerate before selling in a panic or losing sleep at night?

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

This commentary is provided for general information purposes only, should not be construed as investment, tax or legal advice, and does not constitute an attorney/client relationship. Past performance of any market results is no assurance of future performance. The information contained herein has been obtained from sources deemed reliable but is not guaranteed.


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