Statistics for finance in a post crisis world
July 19, 2012
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I made a presentation on “Statistics for finance in a post crisis world” at the Sixth Statistics Day Conference organized by the Reserve Bank of India on July 17, 2012. Bullet points from my slides are given below.
Example: US Flash Crash
- The Flash Crash refers to unusual price movements in the US stock market on May 6, 2010
- Market index dropped by over 5% in the space of less than five minutes only to bounce back in the next five minutes.
- The crash was even worse in individual stocks. For example, Accenture fell from $30 to $0.01 in the space of seven seconds and then snapped back to the old level within two minutes.
- The joint study by the US SEC and the CFTC collected hundreds of millions of records comprising an estimated five to ten terabytes of information.
- The study however ended up aggregating the data into one minute intervals (and sometimes fifteen minute intervals) when the interesting events were happening at millisecond time frames.
- Big data became ordinary data by discarding data!
- And then analysis of the Flash Crash could use traditional methods.
Big Data in Finance
- Financial markets are the major source of big data. The US data feed company, Nanex, provides quote by quote data for US financial markets:
- 4.5 million quotes per second
- 8 billion quotes per trading day
- Trade repositories for OTC derivative markets will also create large databases.
- In traditional banking, massive amounts of data is available in core banking systems and is potentially available to regulators who by and large are not equipped to use it.
- Some experts are recommending that financial entities must provide disclosures with “gigabyte richness” (Hu, Henry T.C., “Too Complex to Depict? Innovation, ‘Pure Information,’ and the SEC Disclosure Paradigm”, Texas Law Review, Vol. 90, No. 7, 2012)
Shadow Banking and Hidden Credit
- Shadow banking has been estimated to be very large in the developed world – comparable in size to regular banking.
- These forms of shadow banking are not very prevalent in emerging markets like India, but there are other forms of credit that are beneath the radar of official statistics.
- During 2008, there were concerns in India about:
- Suppliers’ credit and buyers’ credit (hidden short term foreign currency corporate debt).
- Pledge of shares by promoters(hidden credit to the corporate sector/promoters)
- Today gold loans may be becoming a large hidden source of credit to the household sector
- Partly unsecured personal loans (inadequate or overvalued or undermargined gold collateral).
- Some recent estimates suggest that Chinese corporate sector has hidden dollar debt of $800 billion!
Hidden credit: the data challenge
- Data is hidden because somebody wants to hide it.
- Often credit hides in the shadows to evade regulation.
- Regulating one part of shadow banking only drives the activity somewhere else – even more underground.
- How can regulator collect data unobtrusively without driving the activity underground?
- Collect data through some industry association?
- Collect data from other elements of the chain?
- Use random sampling with anonymized data collection?
- Use econometric models for estimation?
- During a crisis, policy makers try to protect the banks and strategic non bank entities while letting other businesses to fend for themselves.
- Examples of this during 2008 include Korea and Russia.
- From this point of view, it is important to monitor the liabilities of the protected core – on balance sheet and off balance sheet, explicit and implicit.
- This is not easy. For example, consider the SIVs and ABCP conduits of banks in the US during the crisis.
- Indian banks have large operations outside India:
- Large derivative books
- Maturity mismatches and liquidity risk
- Credit link notes linked to Indian corporates
- Indian corporate sector has increasingly opaque off balance sheet structures outside India.
- During periods of stress, hidden risks constitute a vulnerability that can lead to unanticipated defaults that put strain on the banking system.
- This vulnerability can also put constraints on policy makers:
- Policy makers may be reluctant to crystallize losses for entities that are economically important.
- Vulnerable entities may be politically powerful and may be able to successfully lobby against economic policy measures that will materialize the hidden risk.
- For example, foreign exchange risk in the corporate sector may force policy makers to a suboptimal defence of the currency.
Hidden Foreign Exchange Risks
- Best known source of foreign exchange risk is unhedged foreign borrowing by the corporate sector.
- But mishedged currency exposures are as important as unhedged exposures:
- The exotic currency derivatives disaster of 2008.
- Similar problem in Korea at the same time was euphemistically described as “overhedging”
- Currency risks are also embedded in commodity prices:
- During the last year or so, global gold prices have fallen while domestic prices have remained stable or even risen. Leveraged gold buyers have accumulated a large currency exposure.
Hidden Interest Rate Risk: Household Sector
- The Indian household sector today has a large interest rate exposure through floating rate home loans.
- At some point, this could become a constraint on monetary policy.
- There is a need to quantify the impact of interest rate reset on the distribution of household debt service ratios.
- Extreme example of this problem was the ERM crisis of 1992. Swedish interest rate defence of the krona had such a big impact on mortgage payments that the Prime Minister called an “all party” meeting to discuss monetary policy!
Only Traded Prices are Real
- Consider two different kinds of “prices”
- Prices at which actual trades have happened (for example, the weighted average call rate)
- Price at which people claim that they can trade or could have traded (LIBOR or MIBOR)
- During the last few decades, very large credit and derivative markets have come to rely on the second kind of price which we now know is more fiction than reality.
- This problem is present in many other markets as well. For example, practically all crude oil transactions (both physical and derivative) rely on polled prices reported by agencies like Platt.
- It is necessary to wean these markets away from polled prices and use actual traded prices wherever possible.
- A decade after the Enron collapse, Enronic accounting is alive and well and not just in the private sector.
- Some of the sovereign debt problem in Europe is due to falsified public debt data.
- Much of the data in financial institution balance sheets is widely believed to be unreliable:
- Enronic off-balance sheet liabilities like the SIVs and ABCPs
- Level 3 assets (or “marked to myth”) assets
- Banking book assets which are badly impaired but are carried at book value.
- Statisticians need to approach certain kinds of financial data with deep distrust.
- This requires a change of mindset.
- Mainstream statistics discards outliers and works with the remaining nice data.
- Sometimes the outliers are the data and the rest is just noise.
- Nice data is often the result of fraudulent smoothing.
- Using the right statistical tools, we may be able to ferret out the fraud.
- Statistical analysis has an important role in design of markets and benchmarks.
The Gaussian Distribution
- The Gaussian distribution is to be found everywhere in nature, but it is rarely found in finance.
- Most financial asset prices are closer to Student-t with 4-10 degrees of freedom.
- The really bad distributions (for example, the distribution of default losses in a large credit portfolio) have almost pathological levels of skewness and kurtosis.
- The multivariate Gaussian is even rarer as relationships between variables usually exhibit strong tail dependence.
- Non Gaussian copulas are therefore needed in addition to non Gaussian univariate distributions.
Non Gaussian Copulas and Marginals
- The marginal distribution determines the thickness of the tail
- The copula determines the tail dependence – whether large losses on one asset are accompanied by large losses on other assets
Low tail dependence
High tail dependence
Low tail dependence
High tail dependence
Very high risk
Gaussian Copulas and CDOs
- CDO pricing before the crisis and even today is based on the Gaussian copula
- This model required unrealistically high correlations to fit the observed prices of the senior and super-senior tranche of a CDO (the correlation skew).
- Even that was sometimes insufficient. There were situations in which no correlations could be found to match observed market prices.
- The paper by Donald MacKenzie and Taylor Spears describes how banks ended up using the Gaussian copula to price CDOs though the quants themselves were unhappy with the model. ‘The Formula That Killed Wall Street’? The Gaussian Copula and the Material Cultures of Modelling, June 2012.
The Way Forward
Simpler finance, maybe. Complex statistics, surely.
- The global financial crisis has led to calls for simplifying finance. This has not happened so far, and it is doubtful whether it will happen anytime soon.
- What is clear is that financial statistics will become a lot more complex:
- Terabyte and potentially petabyte data
- Indirect statistical estimates of the shadow financial sector
- Forensic statistical analysis
- Pervasive use of non Gaussian distributions and copulas