Due Diligence and the Fallacy of Risk-Adjusted Returns

A 2008 paper “How Unlucky is 25-Sigma”[1], describes an interview with Goldman Sach’s then-CFO David Viniar who referred to their flagship fund’s 27% loss in August 2007 as a “25 Sigma event”.  The paper goes on to analyze this statement and quickly shows that a 25-Sigma event would take place once in  1.309e+135 years, a number so large that the paper accurately describes this time frame as “being on par with Hell freezing over”.

Mr. Viniar’s estimate was off by more than the age of the universe.  Clearly, no measure of market risk (a.k.a. Sigma, or standard deviation of returns) could provide a clue into what happened.  What was missing?

The vast majority of investors measure and compare the quality of their investments by calculating risk-adjusted returns provided by any number of readily available ratios such as Sharpe, Sortino, and others.  The denominator in these ratios is always risk.  Risk, conveniently, is measured by calculating standard deviation of returns, an observable metric.    Even if Viniar exaggerated and the event that occurred was “only” a 15-Sigma event (27% monthly loss divided by the fund’s monthly standard deviation of ~1.8%) this would imply a one-in-1.308E+49 chance of such a loss, an equivalent of winning the Powerball lottery 5 times in a row[2]

The only logical conclusion is that the models that Goldman (and most other investors in 2007-2008) were using were inadequate.  The true risk could not be explained by volatility of historical returns.  Another source of risk creeped into their portfolio, resulting in a massive overallocation of risk capital.

Let’s reverse engineer the true risk that was embedded in Goldman’s portfolio at that time.  If we assume that a loss like this might occur once every 1,000 years (=12,000 months), this would have been an approximately 5-sigma event, implying the monthly standard deviation of 5.4%, triple the market risk implied by volatility of returns.    Assuming the frequency of such loss to be once every 100 years, the implied total risk would be 6.8%, almost quadruple the market risk.

Clearly, traditional measures of risk failed to predict the true size of the problem.  Proper due diligence could have uncovered the fat tail not visible through the lens of market analysis.

What was the source of that additional risk?  In Goldman’s case, it was something called “model risk”, or the likelihood that internally-developed investment models did not properly account for all aspects of complex investments.    In other cases, infrastructural risks such as a cyber-security breach, unauthorized cash movements, trade errors, or plain fraud, could decimate an investment that may otherwise seem relatively safe.

Estimating non-market risk must be a critical component of any investment analysis.  The challenge is that these risks are incredibly difficult to quantify ex ante.  Just like in the above example, we can only do this ex post, by which time it’s always too late.

One of the problems in quantifying non-market risk is that it does not have a clear scale or a standard measure.   Most investors who perform a thorough due diligence do so using their own proprietary metrics, and thus no standard measure is available for investors to use in estimating their true risk.

DDX blockchain protocol aims to change this.  With multiple participants sharing their findings in a trusted, secure distributed network, a quantifiable measure can potentially be established.  It will not be as clear cut or formulaic as standard deviation of returns.  But in a world where no measure exists at all, consensus-based risk metrics can help make risk management and capital allocation decisions a lot more efficient.

To learn about our project or apply to join the group of large financial institutions helping us with the development of the blockchain due diligence protocol, visit our website, https://ddx.exchange


[1] “How Unlucky is 25-Sigma?” By Kevin Dowd, John Cotter, Chris Humphrey and Margaret Woods, March 24 2008. Available at SSRN:https://papers.ssrn.com/abstract=1517146.

[2] Probability of winning a single Powerball lottery is 1 in 292 million according to an Allstate report.  Winning it 5 times in a row is (1/292 million)^5 or 4.7197E+43, slightly better odds than 15 sigma.

Blockchain: The Next Great Arbitrage Opportunity, Part 1.

I was introduced to the concept of arbitrage at my first job on a convertible arb trading desk, 32 years ago.  Back then, arbitrage meant exactly what it was supposed to – a riskless opportunity to extract profits from a relative mispricing of multiple securities.  In plain English, when information is scarce, buyers and sellers tend to price similar assets inefficiently. That results in an opportunity where one could simultaneously buy and sell the same thing at different prices, generating a guaranteed profit.

This was free lunch.

The advent of trading technology, speed and transparency has virtually eliminated every arbitrage opportunity in the public securities markets.  Many fund managers retained the moniker “arbitrage” in describing their strategy. The nomenclature became more of a marketing tool to gather assets from gullible investors rather than a repeatable, robust investment strategy Proper arbitrage was then in turn labeled, “bona fide arbitrage”, as if to separate truth from fiction.  Being old-fashioned, I will drop the “bona fide” from the name – it’s either arbitrage, or it’s not.

Arbitrage breeds well when a number of conditions are present.  First, there has to be lots of participants in a marketplace. Second, the information available to these participants should be difficult to obtain and hard to analyze.  And third, the product being priced should not be homogenous. Arbitrage opportunities go back thousands of years, with coins-by-weight arbitrage in ancient Babylonia as an early example, and continue to appear regularly in different markets: bills of exchange arbitrage in 17th century Europe, geographical stock exchange arbitrage in the late 19th century in London and New York, and more recently, convertible arbitrage in the 1970’s and 80’s, and ETF and index arbitrage in the 90’s.  By and large, these opportunities for riskless profits are gone.

One thing we know for sure: technology is a great enemy of arbitrage.  Technology creates efficiency, equal access to information, and enough transparency to eliminate mispricing.  It democratizes inefficient markets, whether it’s paper money printing in Tang Dynasty China in 700 AD, advent of telegraph in late 1800’s, or the ubiquitous Bloomberg terminal in late 20th century.  

Over the past decade or so Internet 1.0 provided an amazing opportunity to address certain arbitrage opportunities by means of centralized marketplaces.  Amazon, Airbnb, Uber, OpenTable, Yelp – every one of these tech businesses seized on pricing and informational inefficiencies existing in specific markets, and as a result became multi-billion dollar behemoths.

Oddly, as some arbitrage opportunities are eliminated by certain technology applications, others continue to exist.  

Similarly to many previous opportunities, arbitrage can still be observed in ecosystems with scarce information, multiple participants, mutable and opaque pricing structures, and unequal access to the underlying asset.  Examples are numerous – money transfers for the unbanked, pricing of water resources in emerging economies, identity theft, voter fraud, and medical records systems, to name a few. Like it or not, these are all arbitrage opportunities that exist today (another question is whether capitalizing on some of these is entirely risk-free as they may actually carry a stiff prison sentence).  

In the past couple years, we have seen the emergence of a new technological revolution: blockchain.  For too many people this is a cool buzzword, usually preceded by words “I don’t understand the first thing about… “.  I’d imagine that most of us could easily replace the word “blockchain” in that quote with “cell phone technology”, “global positioning systems”, “telegraph”, “electricity”, or even “the printing press”.   Yet, all of the above acted as great arbitrage busters and provided massive rewards for those with the foresight to use these technologies toward elimination of specific arbitrage phenomena.

Much like revolutionary technologies of the past, blockchain’s main reason to exist and its main benefit is the elimination of specific economic arbitrage cases created by various human activities.  Nothing more, nothing less.  There are now millions of ideas of how to identify various arbitrage use cases and eliminate them, and thousands of applications attempting to experiment with this new technology.  Most of them will prove futile, as is often the case when mankind gets a shiny new toy.  Just like the telegraph and Internet 1.0, blockchain is not an answer to all problems of humanity.  It can, however, address certain specific arbitrage use cases very elegantly and efficiently.  Those who identify real-world, practical cases where meaningfully large arbitrage can be eliminated by blockchain applications, will reap massive rewards in the process.

In the follow up to this article, I will provide a specific numerical example of how one arbitrage opportunity which, shockingly, continues to exist in the investment world, expresses itself.  Stand by.