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The AMH is right about one thing: investors will exploit arbitrage opportunities until they no longer work.

Today’s obsession with indexation and passive investment vehicles is predicated on the belief that markets go up over time, and a well-diversified portfolio will “always” participate in that growth. This belief is, obviously, widely held – that if you ignore price movement, or price discovery at all for that matter, you can expect to achieve an implicitly-guaranteed growth rate over a long enough time horizon simply by participating. Said differently, the aggregate decision-making of corporate equity investors (the price-setters), after accounting for periods of abnormal liquidity mismatches (manifested via volatility), delivers an expected rate of return equal to the historical nominal trend rate. This belief is a derivative of efficient market hypotheses.

Moreover, this belief is essentially proposing the existence of a time/volatility arbitrage.

To be clear, I do believe volatility is not a legitimate risk for a portfolio with carefully-evaluated investments and appropriate liquidity accommodations, but let us ignore that for a moment. This will be a conversation about market structure and the existence of systemic risk, not portfolio construction.

If investors believe they can arbitrage volatility with time – that is, converting volatility into a risk-free profit by allotting a sufficient time horizon – the obvious next step is to apply leverage, as doing so would multiply the “risk free” profit.

It is, however, important to recognize “levered arbitrage” for what it is: the act of doubling down on the permanence of a riskless set of conditions. An arbitrage of course fails when those expectations are not met – that is, the expected hedge fails to hedge. While the intent of a levered arbitrage is of course to multiply the riskless return, if the riskless proposition were to become risky, the risk gets multiplied as well. Hence, when levered, a failed arbitrage develops risk suddenly and that risk emerges exponentially. It is for this reason levered arb trades gone bad unravel violently. We will come back this multiplicative effect in just a moment.

How does one leverage a time/volatility arbitrage?

One way to multiply time, in the absence of a wonder drug, is by selling Theta; volatility can be multiplied by purchasing call options, purchasing levered ETFs/ETNs, shorting bonds, or simply going out on margin. If scaled appropriately (to avoid a margin call), you theoretically just have to wait for the risk-free profits to multiply if time is truly a volatility arbitrage. Unsurprisingly, these types of strategies are exactly what we have seen gain traction via the explosion of buy-write and other systematic vol strategies, inflated call-buying activity, and debt-driven repurchase of corporate equity.

Observe:

Source: Created by author using data from Squeezemetrics

Source: Created by author using data from The OCC and Yahoo Finance

Source: Created by author using data from The OCC and Yahoo Finance.

The perverse reality is, however, whatever arbitrage may exist, if it is widely believed to produce a consistent, desired outcome, will be exploited until it is non-existent. The implications to this are serious. It is not volatility itself that is the risk; it is the initial belief that volatility may always be tolerated and investors failing to recognize if the sources of volatility have changed, thereby making it a systemic blind spot.

The thought progression is quite logical:

If all forms of arbitrage will be exploited until they no longer work, and if a statistically-significant share of capital markets participation is expression of a time/volatility arbitrage, the market itself eventually fails works. That is to say, volatility can no longer be arbitraged by time in the market. Since volatility is a product of liquidity mismatches, this can also be interpreted as time no longer reconciles mismatches between buyers and sellers.

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This thought progression also demonstrates the absurdity of efficient market hypotheses. If the market is believed to be efficient (it isn’t), and investors also perceive they can exploit that efficiency via an arbitrage (backwards logic as arbitrage implies inefficiency), the market structure itself would hence be exploited until it no longer works.

And it has been.

There is indeed evidence the volatility landscape has become increasingly engineered as a result. Consider the following chart, which applies Benford’s Law to realized S&P 500 volatility:Source: Created by author using S&P 500 price data from Yahoo Finance.

One may infer the higher lows suggests market efficiency is improving-i.e., the numerical dispersion of recorded daily volatility is progressively getting closer to its natural Benford-implied Slope. However, the observed lower highs and higher lows also suggests attempted manipulation of volatility conditions.

In fact, the Fed Funds Rate follows an eerily similar path:

Source: Created by author using S&P 500 price data from Yahoo Finance and fed funds data from the St Louis Fed.

This could suggest lower rates “improve” market structure efficiency by forcing volatility to its Benford-implied (read: natural) distribution. However, one must consider the second-order effect:

If government intervention-via collateral inflation-is required to force capital markets toward its “natural” volatility profile, market structure is forced to a “natural” state in an unnatural way. This is, in a sense, a manufactured ecosystem disruption-and the control mechanism naturally absolves as rates approach the zero bound.

In fact, there is a case to be made that lower rates’ interaction with leverage and collateral values temporarily suppresses volatility, but it ultimately has a destabilizing impact on the market. Observe the following chart, which demonstrates lower rates have a noteworthy correlation with skewness of the S&P 500:

Source: Created by author using S&P 500 daily price data from Yahoo Finance and daily federal funds rate data from fred.stlouisfed.org

Moreover, it appears there may even be a predictive relationship. Observe the improved fit when the fed funds rate is lagged 4.5 years:

Source: Created by author using S&P 500 daily price data from Yahoo Finance and daily federal funds rate data from the St. Louis Fed.

Overlaying the skew measure with kurtosis implies the tails are getting both longer and fatter – i.e., more frequent negative return events and larger negative return events:

Source: Created by author using S&P 500 price data from Yahoo Finance.

While one could dismiss these concerns by musing “markets are adaptive”, the reality is that markets are notorious for crowding and trend-following, and over time they have displayed increasing homogeneity:

Source: Logica Capital Advisers, LLC

Source: Logica Capital Advisers, LLC

As such, it would not be unusual to see a disrupted ecosystem undergo a dynamic reversionary process in search of equilibrium. Mean reversion is a very real thing, and artificial volatility compression would ultimately be expected to result in aggressive volatility expansion-conditions which I believe we are seeing evidenced even now

Consider the following two charts, the first of which illustrates the annualized volatility per cumulative trades conducted over the period…

Source: Created by author using S&P 500 price data from Yahoo Finance and volume data from The OCC.

…and the other, which samples 100 day cumulative volatility and evaluates what percentage of the cumulative volatility can be attributed to only 25% of the trading days. One may observe that an increasing percentage of the cumulative 100 day volatility can be attributed to only one quarter of the trading days in the rolling sample, which supports the thesis of vol compression/vol expansion pattern:

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Source: Created by author using S&P 500 daily price data from Yahoo Finance.

The factors that allow arbitrage conditions to persist are cost and barriers to entry. If costs wipe out arbitrage profit, or if barriers to entry make execution of the arbitrage unfeasible, the arbitrage conditions can persist endlessly.

What have we done though? We have virtually eliminated trading costs and fees, we have increased leverage limits and inflated collateral values, we have removed price discovery and vilified active management, we have glorified price-agnostic, systematic allocation of capital via passive vehicles, and we have reduced settlement times and increased the speed of information transmission. The barriers that, arguably, may have permitted perpetual time arbitrage to exist have evaporated, and the supply of risk that was permitted to multiply is now left unhedged.

Traditionally, equity market volatility is a product of the trading liquidity available through the stock market and mismatches in seeking to exploit that liquidity. That is, if the aggregate demand for liquidity is greater than the aggregate demand for equity purchases, liquidity mismatches force prices down. Said differently, investors may be willing to give away more equity for less currency. This should be fairly intuitive; in fact, this is true of any asset class, really.

What happens historically when leverage combined with arb trades blow up? The pressure for liquidity is magnified, and investors exchange even more treasuries for less cash (LTCM), they exchange even more JPY for less USD (1990s), even more real estate for less currency (2008), etc. “Lower prices” is just another way of saying “less stuff per unit of currency”

So what happens if a time/volatility arbitrage blows up? More volatility and more time are exchanged for less currency.

Do not misinterpret that as implied volatility gets cheaper. Rather, realized volatility does. That is far from ideal; remember, “half price” is another way of saying “double per dollar”.

If you are having trouble following that, recall that volatility and equity prices have an inverse relationship; if you sell index futures on lower implied vol readings you profit from conditions in the future that support higher realized vol (prices go lower), and you benefit from buying futures if conditions in the future support lower realized vol (prices rise).

In the past, stocks, bonds, and currencies have all experienced intense price volatility when crowded trades came undone. That is, the supply/demand dynamics of the crowded trade swiftly changed, and the desire to enter the trade was replaced with sudden demand for liquidity; investors were willing to give up more of their crowded assets for less of their base currency. Without fail, assets overshoot to the downside and eventually are priced well below their intrinsic value. Sometimes the assets actually collapse to the point of failure.

The dynamics of a volatility trade are no different; when crowded enough, it, too, will experience intense volatility (volatility of volatility in this case) and liquidity will deteriorate.

Source: Created by author using S&P 500 price data from Yahoo Finance and volume data from The OCC.

Consequently, there are two issues which arise:

Firstly, if equity markets are the instrument used to express a time/volatility arbitrage, the volatility penalty towards equities is multiplied if the arbitrage fails to hold. In other words, realized volatility will cause stocks to trade lower for traditional reasons (demand for liquidation – i.e., selling stocks because they’re stocks), and they will also trade lower because they are no longer viable instruments to express an arbitrage trade.

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To understand this dynamic, it is useful to consider owning equities as an exchange rate – “Currency/Equity.” In the initial transaction, an investor exchanges currency for equity as a pass-through instrument, and equity ownership is an expression of the Time/Volatility exchange rate. A successful trade would involve time depreciating relative to realized volatility, and that result passes through to the Currency/Equity exchange rate (Currency depreciates relative to Equity). In an unsuccessful trade, however, time would depreciate relative to realized volatility (resulting in more vol per unit of time), which ultimately passes through to the investor as Equity depreciating relative to Currency.

This leads to the second issue: if volatility is multiplied by volatility, the penalty to the equity market would hence exhibit negative convexity (volatility multiplied by volatility is variance, and variance exhibits convexity). In other words, the equity risk premium would exponentially increase with the passage of time. Said differently, the expected return on equity would exponentially decay with the passage of time. Those conditions undoubtedly violate risk control assumptions of any fund – especially those running a levered strategy that implicitly attempts to exploit time/volatility arb. And of this sort, there are many (pension funds are chronic offenders).

How does that work? I am glad you asked. If a time/volatility arbitrage fails, that failure can manifest via either leg of the arbitrage: either by a compression in time – i.e., prices move abnormally fast…

Source: Created by author using data from Squeezemetrics.

Source: Created by author using data from Squeezemetrics.

…or an expansion in the volatility of volatility:

Source: Created by author using S&P 500 price data from Yahoo Finance.

Source: Created by author using S&P 500 price data from Yahoo Finance.

The latter is particularly dangerous, because equity indices can tolerate a traditional -50% drawdown (price volatility derived from liquidity imbalances), but if volatility experiences a -50% “drawdown” (i.e., double the volatility per dollar), that is a -100% penalty applied to equities.

Do I think major equity indices will reach zero? No. Do I think we could get closer than anyone believes (relative to today’s values)? For the reasons I just outlined, I feel it is prudent not to rule it out.

In my view, a “market” where capital flows and derivatives become determinants of price (look no further than the recent “Nasdaq Whale” incident) is not a market at all; that is to say, it is not a mechanism where buyers and sellers of corporate equity are expressing opinions of “fair value,” but rather it is a mechanism that allows participants to gamble on directionality.

If you buy into the thesis I have outlined here, the best advice I can offer is to avoid strategies tied to major market indexes, avoid large cap/high-float names that are exposed to price distortion as a function of broken capital market flow dynamics, and focus on low-float, high-quality enterprises that are ineligible for index inclusion or have limited index representation.

If my thesis proves true, I also believe a radical drawdown would prompt investors to confront the extent of bifurcation in today’s financial markets, ultimately proving to be a bullish tailwind for international equities, value equities, and commodities.

Or, perhaps this commentary will turn to be an esoteric thought exercise with no practical application.

Only “time” will tell.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.



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