Tuesday, 13 August 2019

Tidal Forces & Financial Markets

There's a pattern & predictability to tides that make them easy to forecast. But, on very long timescales, that doesn't mean they are constant by any measure. At a celestial level, the amount of force produced depends on the mass of the objects involved, the distance, the eccentricity of the orbits, and the radius of the bodies - for starters. The push & pull that's observed in financial markets is analogous: different assets exhibit similar ebb & flow as correlations oscillate. Trough to crest to trough to crest...
Since the Earth is about 80 times more massive than the Moon, with a radius about 4 times greater, the tidal force per unit mass of the Earth on the Moon is about 20 times stronger than that of the Moon on the Earth. Thus, while the extent of the tidal force on Earth is limited to the observance of tides, the extent of the force on the Moon is to lock its rotational period - which is why we will only ever see about 59% of the Moon in the night sky (the other 9% being due to other, very slight, perturbations in inclination known as libration).

Our neighbor, exhibiting both longitudinal & latitudinal libration - simulated view over 1 month.
The tidal force felt by the Earth has caused not just the effects on coastal regions with which we're well-acquainted, it's also caused the length of the terrestrial day to increase by about 2 hours in the past 600 million years as torque is exerted due to unequal distribution of gravitational effects. This would, in an otherwise closed system, continue until the Moon & the Earth were tidally locked: the rotational period of the Earth would match the orbital period of the Moon, causing our familiar satellite to remain fixed in the same position in the sky & days to lengthen to months.
Two views of the Seven Sisters, near Eastbourne.
But, unfortunately, this won't come to pass - because this is literally a three-body problem & the endgame will be dictated by the Sun. Well before tidal locking can come to pass, the expansion of the Sun as its life-cycle comes to a close will cause a drag to be exerted on tidal acceleration. As the Sun transitions to a red giant, the atmospheric drag created will cause the Moon's orbit to rapidly decay.

The pull of the Earth's gravity will take hold & spin the Moon ever-closer. At this point, our pock-marked solar companion will be a mass of craters that takes up a quarter of the sky - until it reaches an orbital distance of just under 11,500 miles, versus its currently observed 238,856 mi. At this point, an event of cataclysmic proportions takes place to end the life of our celestial partner.

At this point, the gravity holding the Moon together will be exceeded by the tidal forces which act to pull it apart. In an event made even more awesome by the vast swath of the sky taken up by the Moon, it will be torn apart in a monumental seizure that displaces a Saturn-like ring around the Earth.

That's short lived, however - in all likelihood the smaller fragments will begin raining down on the planet in a meteor shower a million times over. Life at this point will be long gone already, but shortly thereafter the Earth itself will be consumed by the expanding Sun, a final coda on the planet that's been home to the entirety of human existence.

Death by Moon, "Oblivion".
The force which today we see as just the predictably casual ebb & flow of oceans, ultimately becomes that which dictates the destruction of the Moon in a global hailstorm of fire.

The evolution of a microscopic relationship that pushes & pulls before ultimately transforming into a cataclysm of epic proportions is analogous beyond the life-cycle of our nearest & dearest celestial neighbor. The inherent instability of such a system is a classical example of the n-body problem, for which there is no general analytical solution. Except in very special cases, the motion of the bodies involved is generally non-repeating.

An example of a very special three-body solution, with an exceptionally small domain of stability.
Atmospheric instability is an example of one such system, so are financial markets. There may be a constant observable "gravitational pull" between two entities or asset classes, but there's no closed-form solution that's arbitrage-free. Hence, diversification is seen as a virtue & correlations, except in times of extreme stress, carry a certain predictability - waxing & waning between intertwined assets.

At extremes, however, this tug of war begets system stress. Rising correlations are not always a harbinger of market drawdowns, but recent observational evidence does seem to suggest an observed rise in correlations may indeed be caused by herd-like behavior that accompanies generalized, directional activity. When global equity markets key off only a few inputs (or, one), this leads to systemic instability, especially when these inputs have high realized volatility. Recent examples include the Turkish Lira in the fall of 2018, or the Chinese Yuan now.

Measures of cross-asset correlations on a micro-level have increased to exceptionally high levels. Hourly correlations between equities, fixed income, commodities & currencies are at their highest levels since last December's collapse in risk assets, sitting at well north of 90% for key relationships. US equity markets, gold, CNH & rates are now intertwined on an hourly basis in excess of 95%. That's not a good thing when a single spark could cause a large move in any one.

Avg Hourly Correlation (rolling 24-hour lookback) for SPX vs CNH, Gold, FFF0.
However, it could be a very good thing if you had an idea of the predictable range one asset class might follow. That's rarely the case, however, unless one or more external forces are allowed to dictate prices. In the case of the rates market, due to the intervention of the Federal Reserve, this is the current reality.

Below is a histogram that shows the distribution of market-implied policy action in 2019, in basis points. At one extreme is 0, the amount of time the market has anticipated no action by the Federal Reserve this year. At the other extreme is -100, or the amount of time the market has judged the Federal Reserve likely to enact 4 cuts of 25bps each (or 2 cuts of 50bps, etc).

In the middle is -50, the amount of the time the market has anticipated the Fed will cut just twice this year. Interestingly, the shape of the distribution forms around two anticipated outcomes. One which groups loosely around only one cut this year, another grouped around the implication of three cuts this year. Oddly enough, there's very little middle-ground that's covered. This effect is captured by the ongoing debate between "mid-cycle adjustment" and a more traditional turn in the business cycle that necessitates successive Fed action. 

Currently, we sit at the far right of the histogram - about 3.5 cuts total priced for 2019 (or an additional 2.5 following July's action). It's conceivable that we could return very easily to the -75 region within the next week or so as the Damoclean threat of tariffs is delayed. That very region was exactly where we sat when equities last tested the highs, SPX at 3000. 

It's not at all clear, however, that further reduction in the number of cuts priced this year will yield much in the way of price appreciation for equities. Bouncing back to the lower gravitational well of only one cut this year (which we've already realized) would mean removing further stimulative effects from policymakers this year. While the threat of tariffs remain & the economic slowdown that has galvanized policymakers from Frankfurt to Auckland persists, risk assets still thirst for additional easing to maintain their current altitude.

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