Timing is Everything

Commentary by Dr. James McCann, Chief Scientist, Plotinus Asset Management

Investment is a precarious business. Parting with your hard-earned cash is hard enough but deciding when, and where, and how much to risk is a painful process. The value of an investment portfolio is defined by the price others will pay rather than its intrinsic worth. In the frenzied world of traders, buyers and sellers agree to disagree. A seller takes the view that the price will probably fall in the future and the buyer takes the contrary opinion. Yet somehow the traders agree on one thing: the price at which they trade. The deal is done and both move on to the next opportunity.

Investors have a more strategic view: setting targets and entrusting the tactics to their fund managers and traders, to deliver. Often the target is whether their ‘team’ finishes the season well placed, rather than whether it won the match last weekend. It’s a marathon not a sprint!

The problem of meeting an objective is as common in nature as it is in business. Indeed, all the laws of nature seem to magically follow such principles. Perhaps the most elegant form is expressed as Hamilton’s principle of stationary action. Sir William Rowan Hamilton was a legendary 19th-century Irish mathematician with precocious gifts. Home-schooled in Dublin by his uncle, an Anglican minister, he learnt Hebrew, Greek and Latin (of course) French and German (naturally) and Arabic, Persian, Hindi, Sanskrit were added by his early teens. He happened to have a natural gift for mathematics as well, and while still an undergraduate at Trinity College Dublin he was appointed Royal Astronomer of Ireland.

We consider the principles of optimisation in terms of yield and risk. There is a trade-off between hitting and missing the target, and timing when to dive in is crucial.

Hamilton’s principle is deceptively simple: any physical system in nature will move in such a way as to optimise the ‘action’. For example, suppose you are walking along a beach and you notice a young child in the sea waving their arms in distress. Your objective is to reach the child in the shortest possible time. You run faster than you swim. So while you are tempted to make a bee line for the target, you correctly choose to run along the beach until a point where it is optimal to dive in and swim to the rescue. A ray of light takes the same approach when passing from air through glass. The deviation from the straight line is known as refraction. Variations from this trajectory would cost extra time and would be inefficient. Light follows Fermat’s principle of least time (before his theorem) : an example of Hamilton’s principle.

Least Action

Financial markets are more complex than strong waves breaking on a beach. Moreover, sometimes one must be prepared to ride the waves rather than lose energy (and money) fighting through the surf. At the same time, big waves are unpredictable and dangerous: we don’t want to be sleeping with the fishes.

So how should this inform our investment decisions? As an investor, we don’t want complex solutions, just simple answers. For example, should I invest now or wait? Should I ‘drip feed’ my investment or go ‘all in’ ? Is now a good time to enter/exit the market? Is there an optimal way of investing my funds?

At Plotinus Asset Management, we consider the principles of optimisation in terms of yield and risk. There is a trade-off between hitting and missing the target, and timing when to dive in is crucial. Suppose, like Baywatch, we were allowed 10 ‘takes’ of the life-saving rescue. Then we might choose the most efficient path to the struggling swimmer. The AI within Plotinus has a similar approach to learning. It’s not trial and error, but rather rehearsal and training, that is rewarded. By simulating (and road testing) multiple scenarios in real-life, we find optimal pathways in the presence of uncertainty.

Hamilton’s legacy is far reaching. His variational principle outlived him into the 20th century where it underpins quantum theory, perhaps the crowning intellectual achievement of the 20th century!

September 2020

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