**The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson**

The Misbehavior of Markets is often cited in lists of great books every serious investor should read. Richard Hudson is the inventor of fractal geometry; which he applied to many fields including finance. He provides compelling evidence against using traditional models of portfolio theory and market behavior. We believe this a must read for believers in the efficient market hypothesis, although we are not completely convinced of his view that market prices follow a fractal process.

Here are our key takeaways. Words in brackets denote our reflections.

Modern Portfolio Theory (MPT) is based on weak foundation made up of three pillars. 1) The Efficient Market Hypothesis (EMH), led by Eugene Fama who asserts that price incorporates all relevant information. 2) The construction of "Efficient Portfolios", led by Harry Markowitz who believed that one can mathematically construct a return maximizing portfolio for a given level of historical volatility. 3) Defining "Risk" as a function of correlation to the market (Beta), led by William Sharpe.

These foundations are weak because: 1) EMH cannot be proven or disproven, but it stands to reason that there need to be market inefficiencies in order to incentivize the existence of market arbitrage. 2) Volatility is a poor measure of risk. 3) Sharpe constructed the capital asset pricing model (CAPM) which assumes that risk equals volatility and prices follow normal distributions. Real market data reveal these assumptions to be false.

Markets, and the global financial system, are more risky than most realize because of the widespread acceptance of MPT. Failing to account for weak foundations of MPT can make positions more vulnerable.

Prices are discontinuous. This is another reason markets are more risky than commonly understood. [Price charts would probably be more accurately constructed using dots instead of lines because the lines conceal the fact that prices jump and crash.]

Provides some empirical evidence to support the view that market prices follow a fractal. A fractal is a pattern that repeats itself regardless of the scale. In the case of market prices, a price chart scaled out to a yearly frequency will be indistinguishable from a chart at a minute frequency. [The author is the inventor of fractal geometry so we are a bit skeptical of this his thesis that,

*“The very heart of finance is fractal.”*]Argues that successful market timing requires recognizing when regimes are changing. Market behavior tends to cluster. Big moves occur within clusters of similar small moves. Only fractals succeed in capturing the reality of the markets.

Volatility is more predictable than price. The implication here seems to be that a successful market timing model would more appropriately attempt to model “clusters” in terms of price volatility rather than predicting price directly.

The fractal nature of markets is one reason bubbles will always exist. If a price doubles, than the price can double again. The term “intrinsic value” does not actually exist. The “fundamental” factors that determine “intrinsic value”, such as cash flow, are too small in comparison to non-observable factors to be the driving force behind price.

Technical market “patterns” are meaningless…unless derives from fractal geometry. The author recommends testing this theory by taking any price chart, removing the time axis label, and asking someone to guess the timeframe.

Our favorite quote:

*“It is the Hippocratic Oath to ‘do no harm.’ In finance, I believe the conventional models *[MPT]* and their more recent ‘fixes’ *[Gaussian copulas, use of normal distributions, continuous prices]* violate that oath. They are not merely wrong; they are dangerously wrong.”*