In the rougher seas of water: Hamilton, Hamilton, and… Hamilton.

In “The Wave: In Pursuit of the Rogues, Freaks, and Giants of the Ocean,” author Susan Casey describes the who’s and why’s of surfing tsunami-size waves. These killer waves have become more frequent and they hit with more punch than registered before. They do not only attract big-wave surfers, such as Laird Hamilton, or wannabe surfers (such as perhaps me), but also serious academic studies, and… investors. The science of waves is quite fascinating, and bears resemblance to mathematical finance – which is not that surprising considering that there is only so much (little) mathematics that can be straightforwardly analysed and applied. It may be a bigger surprise that one of my old teachers at University of California at San Diego, James Hamilton, albeit bearing very little physical resemblance to Laird, has written the gigantic “Time Series Analysis.” That book is as well known in the scientific econometric modelling community as are Laird’s accomplishments in riding gigantic ocean waves.

Standard models of mathematical finance and of waves usually assume some sort of stationarity and linearity. You may quite safely omit their precise definition here. (Stationarity: certain key statistical aspects of time series do not change over time; Linearity: a situation where the effects of impulses are easier to forecast as being linearly related to the impulse.) But you should not miss this: waves or stock prices do not succumb easily to mathematics. Rogue waves are almost impossible to predict. Likewise, stock market prices experience jumps that are in most practical purposes impossible to predict. One can predict that rogue waves (jumps) may exist, but it is not practically feasible to wait long for one laying on your surfboard in calm seas. A potential solution for Laird is to identify certain key characteristics that make a rogue wave more probable. James can help in that endeavour as one of the pioneers of regime switching models aiming to describe how environments change over time.

Only there are yet more problems. Not all rogue waves succumb to any known regime switching. Yes, rogue waves are more likely to happen in certain places on Earth where certain key characteristics (or dimensions, scientifically) happily meet. There are places on Earth that are reported to have a high concentration of shipwrecks in the history of seafaring; Bermuda Triangle and South Africa’s coast are two among the most famous. The Cape of Good Hope in South Africa is true to its name: you need good luck (hope) to get through. And who would not have heard of the mysterious gone-missing cases near the tropical paradise island of Bermuda where even solidly built aeroplanes disappear into thin air (or into deep waters, more exactly). However, both of these places have much traffic and face a larger tendency for wrecks. Forecasting rogue waves based on characteristics alone may lead to an identification problem of the true behaviour of oceans and the actual potential of waves.

What does any of the above have to do with investing? After all, Laird or James are not assets to own in legal terms, at least not nowadays. But connections exist. Consider, first, risk management: selling insurances to trans-ocean ships and deep-water oil rigs. But since insurance business is not particularly sexy to invest in at the moment of writing, and it does not fit into the story here anyhow, I have to postpone my thoughts on investing into assets directly related to the statistical Law of Large Numbers. So what makes me to write such a slippery introduction? Wave energy: wave energy that moves all surfers around the world every day, from the dark and cold coasts of Norway to the golden beaches of Australia. And yet it remains obscure. Should not this almost untapped and quite eco-friendly energy source be used more efficiently than it seems to be done now? Wave energy firms have popped up, such as AW-Energy in Finland, and they appear to be far from realising their true potential.

About two-thirds of the surface of Earth is under water. AW-Energy states that waves could potentially satisfy one tenth of the global electricity need and that “ocean waves are consistent and sea states can be accurately predicted more than 48 hours in advance.” In normal close-to-shore conditions, that is. AW-Energy’s “WaveRoller” technology operates best at depths of only approximately 8-20 meters. In deeper off-shore waters, waves become much less manageable and energy extraction more difficult. However, the National Ocean Service states the average ocean depth to be 4300 meters, and Mariana Trench, where James (not Hamilton) Cameron dived in with the DeepSea Challenger in March 2012, is gigantic 10,994 meters deep. It is not unreasonable to predict that there will be need for deep-water wave energy. Similar technology needs have been met and well solved in the energy sector by SeaDrill (among others), an offshore oil drilling company incorporated in – fittingly – Bermuda.

Wikipedia educates me that “Hamilton is the capital of the British Overseas Territory of Bermuda.” Hamilton appears to be synonymous for things related to waves on Earth. And waves are just becoming less manageable; much like at Bermuda Triangle. What other “Hamiltonians” may the future hold? This is a question any God-fearing and momentum (trend) believing trader should have in his (or her) mind right now. Where can be the conditions be any more extreme than on Earth? Well, in space they are. As an extreme case – which may be our future – consider the “sci-fi” movie Interstellar. Its main characters visit “Miller’s planet” where they are surprised by gigantic tidal waves caused by the close proximity to the Gargantua black-hole. In Miller’s planet, that proximity causes gravity to be so extreme that water is lumped into gigantic waves arriving at discrete times. Corollary: Should the Moon be any closer to Earth, our tidal waves would be bigger and that energy could be a more potent story.

This is all about gravity, really. Earth orbits the Sun. The Moon orbits Earth. Earth is in constant motion around its own axle. We can model the movement of heavenly bodies more accurately than some of the phenomena on our beloved Earth. Miller’s planet exemplifies the case of easily predictive power of a simple James’s regime switching model with only two separable states: calm and extreme. If so, Laird could forecast the next rogue wave with great precision. On Earth, however, clean states rarely exist, and when they seem to exist, they still take various forms; the states are approximations. Surely, using human technology to move the Moon closer to Earth seems like science fiction, so I pass on that possibility – for now. But it is interesting to learn that gravity is a wave, too. Physicists speak of “gravitational waves.” Should there be technology to take advantage of gravitational waves and its patent holding company would carry out an IPO with some Hamilton as its CEO, I would definitely go “ALL-IN.”

[Signed: 7/.V]

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