Value Investing

Random Walk Part 2 – Does Any Asset Price Fit The Bell Curve?

Advisor Perspectives welcomes guest contributions. The views presented here do not necessarily represent those of Advisor Perspectives.

Get The Timeless Reading eBook in PDF

Get the entire 10-part series on Timeless Reading in PDF. Save it to your desktop, read it on your tablet, or email to your colleagues.

This is the second of my four-part empirical research into the fallacy of the random walk paradigm in investments. Part 1 focused on the failure of the random walk to depict the Dow Jones Industrial Average. In this article, I expand the study to include six diverse asset classes including large-caps (the S&P500), small-caps (the Russell 2000), emerging markets, gold, the dollar and the 10-year Treasury bond. Asset prices do not walk in tiny steps along an orderly bell curve, but often take giant leaps leaving chaotic turbulence behind.

What are the common features among seven widely diverse asset classes? Why are asset prices so hard to pin down by random walk or other analytical and descriptive models? What are the investment implications if asset returns do not fit the bell curves?

Part 3 will deal with its flaws in defining investment risk. Part 4 offers a new reward and risk framework alternative to the random walk paradigm. The new framework yields new insights on how to logically beat the S&P 500 total return.

Empirical evidence against the random walk model

In Part 1, I presented price return histograms of the Dow Jones Industrial Average from 1900 to 2016. In this paper, I extend the empirical research to six other assets. Detailed results are in the Appendix. Figure 1 summarizes the five-year return histograms (light blue bars) of seven asset classes – the DJIA from Part 1 and six other assets from the Appendix. No return histogram (light blue bar) has any resemblance to its corresponding random walk probability density functions PDF (dark blue curve). All random walk PDFs are unimodal (with a single central mean) with matching wings on both sides. All empirical distributions have multiple peaks with no central symmetry.

Asset Price Bell Curve

Common themes among different asset classes

  1. None of the return histograms of the seven asset classes follows the random walk bell curve for periods longer than one day. The longer the return periods, the less bell-shaped they become. Real world prices do not follow a random walk.
  2. Even for the one-day returns, all histograms show asymmetric fat tails. Random walk theorists have no explanation for them and treat them as anomalous statistical outliers.
  3. All return distributions of time horizons beyond one year do not have a single mean and a definable variance. Random walk's mean-variance paradigm does not reflect reality.
  4. Random walk's bell curve underestimates the probabilities of both large losses and gains beyond ± one standard deviation. This has dire consequences in risk management.
  5. It is standard practice to scale returns and volatilities in different time horizons by the number of trading days and by the square root of trading days, respectively. Data show that neither return nor the volatility follows such scaling rules.

By Theodore Wong, read the full article here.