Normal versus Cauchy Distribution - Trend-followers as traders against normalcy

I want to fit the world into normality, yet it could be a Cauchy distribution and have properties that exhibit extreme risk, tails. The Cauchy or Lorenz is stable and has a probability density function that can be expressed analytically like the normal distribution, but as some would say, it is pathological with extreme oddities. The tails of the distribution are heavy, show slow decay, and can go to infinity. There are other heavy tailed distributions, but the Cauchy is the extreme.

The distribution of returns in financial markets is critical issue for risk management and performance. Life is easy if the world can be described as normal. The central limit holds, behavior is symmetric, and the moments of the distribution are measurable. Even if the distribution is not symmetric, if the moments of the distribution are measurable, an investor can calculate mean, standard deviation, skew, and kurtosis. 

However, there are some distributions that are not well-behaved. The Cauchy distribution looks fairly normal but is actually the evil cousin of the normal distribution. It is more peaked, and does not dampen in the tails of the distribution. Hence, the mean and standard deviation cannot be calculated. Anything is possible in a Cauchy world, and it is not measurable.

What does this mean for a trend-follower? If you believe the world is not normal and may exhibit fat tails like the Cauchy distribution, you will want to hold a large portfolio of assets awaiting the chances that a fat-tailed event will occur. With the Cauchy, the center of the distribution will be very peaked and the general returns will be close to zero, yet evidence suggests that non-normality is a reality, fat tails do occur. To capture these heavy tail returns, the trend investor has to hold positions in long-term trends even if it seems odd under the assumption of normality. 

Because there is a higher likelihood that some assets will move to the extremes and those moves may not be capped, the divergent trend-follower holds a well-diversified portfolio and waits to exploit these big moves. Their implicit assumption is that a non-normal world with fat tails will generate outside returns much greater than anything likely in a normal world. Expect and trade (hold the trend) for these heavy tails. A belief in heavy tails is an underlying assumption for many trend-followers.