Volatility is the square root of time and fat tails, a guest commentary by Russ Certo

Author: David R. Kotok, Post Date: April 24, 2015

Russ Certo of Brean Capital has penned a superb research note which is copied below and also posted (with full permission) as a guest commentary on Cumberland’s website. Here is the link so readers worldwide may load it directly from their various devices.


Russ is Managing Director, Rates Trading, Brean Capital, LLC, 1345 Avenue of the Americas, New York, NY 10105-0302, Tel: (212) 702-6643.

Readers may note that this is a technical essay and it is thought provoking for the professional in the money management and/or for those skilled in the monetary policy arena. We thank Russ and his colleague, Peter Tchir, for allowing us to share their effort with our clients, friends and readers worldwide. Please enjoy what is probably better printed and read leisurely during the weekend. David Kotok

Guest commentary by Russ Certo follows.

The trio of macro-prudential policy, the onset and evolution of shadow banking , and the nebulous concept of financial stability may have become a toxic cocktail which can be instrumental in moving forward the Federal Reserve’s timeline for lift-off zero bound rates. The intuition here is stooped in concepts of volatility and how market structure evolution may contribute or detract from asset volatility. Please bear with me with the following pros.

Volatility is the square root of time.

For price making a random walk, variance is proportional to time.
Standard deviation is the square root of variance and therefore it is proportional to the square root of time.
Volatility is standard deviation and therefore it is proportional to the square root of time.
Volatility formula


In modern portfolio theory one standard deviation from the mean accounts for 68% confidence interval of all activity and observations within the mean distribution. Two standard deviations account for 95% of occurrences. Three standard deviations account for 99% of activity relative to the mean in a given probability outcome.

Fortunately or unfortunately, there are many asset price occurrences and events globally which occur outside the mean and with far greater frequency than typical option pricing theory suggests. Ironically, outlier events outside the mean can be sown by the seeds of persistent LACK of volatility. This can be a challenge in a zero interest rate policy world.

Annualized Standard Deviation

Unlike implied volatility – which belongs to option pricing theory and is a forward-looking estimate based on a market consensus – regular volatility looks backward. Specifically, it is the annualized standard deviation of historical returns. For the sake of bond trading there are approximately 252 trading days a year which is the time series used to derive daily volatility of interest rates. But these normal bell curve distributions have been repressed by vagaries of central bank policy.

There are limitations to capital asset pricing theory (CAPM) and one is that regular volatility looks BACKWARD. In fact, we know a few acquaintances that think typical option pricing theory is limited in its capacity and that FAT tails occur much more frequently than a normal distribution bell curve would suggest. To some there is a wall at the end of that fat tail with black swans perched atop in far greater frequency than option pricing theory academically suggests.

Allow me the license of some theoretical equations to serve for relevant discussion to markets and policy today. These are conceptual.

Financial repression times time equals volatility

Financial repression times time is an input to the inverse of financial stability

Macro-prudential policy times time is an input that can contribute to volatility

Macro-prudential policy times time+ financial repression times time equals volatility squared.

We all realize that during period of low volatility, market participants are incented to reach for alpha in a variety of expressions. Sometimes investors go down in credit quality to gain enhanced yield. Others execute buy-right strategies to augment performance whereby one owns an asset and writes a call on that asset to take in premium which enhances return. Others simply write naked options on assets. Some increase leverage or increase exposures to an asset class to achieve desired performance. Others simply become lulled to sleep and miss-allocate resources. So much for sharp ratios, a risk adjusted return, the average return earned in EXCESS of the risk-free rate per unit of VOLATILITY or TOTAL RISK.

These concepts of risk allocation or miss-allocation have historically led to consequent periods of great volatility spikes and deleveraging. The basic premise and inference here is that these bouts or tails occur at greater frequency than the inputs imbedded in our statistical pricing models.

These periods of selling volatility or miss-allocated resource absorption chasing alpha for performance enhancement and portfolio boosting can endure for EXTENDED periods of time. The classic unwinds of these allocations are of epic fare and proportion; tulip manias, alchemists, Mississippi Company, South Sea Company bubbles, modern prophesies, fortune-telling, great orators, dot.com bubbles, housing bubbles, Alt-A at par, national delusions, peculiar follies and other miss-guided exercises which tend to unravel at meteoric pace. Negative interest rates across large swaths of global rate structure come to mind at the moment. Buy volatility. Extraordinary Popular Delusions and the Madness of Crowds http://books.google.com/books?id=xeHsAgAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false.

What I would like to talk about is the marriage of three timely, prescient, and inter-related topics noted above which are encased with an understanding of how volatility can be catalyst: Macro-prudential policy, shadow banking formation and market structure and financial stability.


This is an all-encompassing topic and is defined by the IMF is “protecting the whole.” “Keeping individual financial institutions sound is not enough. A broader approach is needed to safeguard the financial system and mitigate risks to systemic stability. To reduce the cost to society and the economy from a disruption in financial services that underpin the workings of financial markets—such as the provision of credit, but also of insurance and payment and settlement services.” (FSB/IMF/BIS, 2009; IMF 2011a).

“The failure of an individual institution can create systemic risk when it impairs the ability of other institutions to continue to provide financial services to the economy. Usually only a large institution that is heavily connected to many other institutions can cause such spillovers that its failure threatens systemic stability. These spillovers can occur through one or more of four channels of contagion:

• direct exposure of other financial institutions to the stricken institution;

• fire sales of assets by the stricken institution that cause the value of all similar assets to decline, forcing other institutions to take losses on the assets they hold;

• reliance of other financial institutions on the continued provision of financial services, such as credit, insurance, and payment services, by the stricken institution; and

• increases in funding costs and runs on other institutions in the wake of the failure of the systemic institution”


One could or should look at the pursuit of macro-prudential policy as a sort of parallel regulatory exercise of the likes of Glass-Steagall, which separated the activities of commercial and investment banks. Only the late macro-prudential regulatory arena isn’t centrally legislated per se. In fact, it is decentralized regulation in a variety of forms.

One can broadly consider Basil III, Dodd Frank, risk based capital standards, haircut capital, leverage reduction, floating rate NAV money market reform, evolution of monetary tools tested and available at the Federal Reserve, litigation, stress tests, derivative and repo reform, central clearing houses and much more as representative of macro-prudential policy geared toward making the financial system safer by neutering a bevy of systemically relevant financial institutions.

Without validating or invalidating the integrity and effectiveness of such reforms, both explicit, implicit, and tacit capital, legal, and operative strictures have been placed on financial institutions intended to ring-fence a variety of real or perceived organizational behaviors which are deemed to put the greater financial system at risk. The collective and aggregate ring-fencing of SYSTEMICALLY RELEVANT institutions appears to have reduced some leverage, proprietary, and service aspects of banking and dealer models, and now asset manager, fund, and other capital company models.

Some specific examples follow along with a discussion of how these behaviors have altered the protocols in the financial market landscape. These “altered” protocols are ultimately passed along to clients in terms of various frictions of quality and quantity of service and price of service.

Primary Dealers/Banks/ & Boutique Financial Institutions: Some banks and financial intermediaries are charging clients for funding in a variety of capacities both in extension of balance sheet and in business protocols. Financing of client positions is prioritized with a business premium embedded in decision. In other instances, total dealer repurchase exposure has shrunk and is shrinking. Dealers are trading LESS volume in the over the counter and cash securities markets across multiple product lines. There is less balance sheet deployment and usage in secondary security positioning for house franchise or client service commitment. These are merely a few topical examples of adverse OR desired prudential impacts on intermediary models.

Further, there are additional facilities in the broad framework of macro-prudential arena that have been created, intended or not, which bypass traditional banking/dealer activities. For instance, the Federal Reserve has tested and used in various capacities its overnight Reverse Repo Facility (RRP) and its Term Deposit Facility (TDF) which INCLUDES additional counterparties like asset managers and money market institutions which qualify based on capitalization, commitment and other factors.

This is a departure and augmentation of the traditional market piping of bi-lateral Open Market Operations with the Federal Reserve which were traditionally inclusive and unique to PRIMARY dealers. This decentralization of funding counterparties has also reduced the volume and impact of dealers in financing markets with clients as these facilities have been inclusive of other genre of management firms WHILE increasing the Federal Reserve as an active repo counterparty as a percentage of total counterparty exposure. These are tools which have effectively allowed for diminished total participation of traditional repo and financial dealing with traditional cadre of players which, in turn, is passed along the financial market food chain of diminishing utility.

In other arenas, the Bank of England estimated the impact on collateral markets of macro-prudential policy to exceed $800 billion dollars. This was an estimate years ago but still evolving today which aspired to quantify how much of high quality assets would be required and applied for risk-based capital standards. The obvious storehouse asset of cash or marketable securities, U.S. Treasury securities, have compressed more than 50 basis points in market structure as a result of the implementation of these globally aligned reforms. I rhetorically ask, will this gobbling up of collateral for macro-prudential considerations spurn negative rates in U.S. money markets? I cuff envelope analysis and imperfectly suspect the collateral impacts of cumulative risk based capital requirements have and will exceed several trillion notional par value worldwide.

Not to stray from point, I think a very interesting linkage is that the collateral required for banks in macro-prudential regulatory reform HAPPENS to be held within global central banking balance sheets at the moment and is rolling into the front end of capital and money market curves. The Federal Reserve alone has approximately $1.3 trillion in collateral scheduled to roll off or mature between early 2006 and 2022.

In other prudential related areas, actual and perceived litigation has likely impacted dealer’s behavior in a variety of lending, trading, and commitment of balance sheet usage. The changing dynamic has increased the challenges of assigning INTELLECTUAL and CAPITAL resources to any specific strategic product line or business unit, which again, ultimately serves consumers/clients. Oh, the fun of assigning a return on equity to a business line for your reporting line (boss) and to dedicate resources across the product spectrum of distressed, emerging markets, Equities, HY, IG, ABS, MBS, Rates, Loans, FX, Commodities and more.

It may be a chore to allocate resources above in light of the dynamic of elevated asset prices globally due to central bank quantitative easing duly coupling your VAR decisions for asset growth across your products lines in the coming fiscal year? What rate of growth would YOU assign to those businesses and then how would you respectively allocate your precious capital which is definitely shrinking and yet not possibly known?

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