Simplicity versus Complexity: What are the Limits of Structured Financial Products?
Once praised for allowing pre-defined payoff structures and ameliorating the risk of underlying assets, structured financial products were heavily criticized in the aftermath of the global financial crisis 2007-2009. Critics deemed these products as too opaque and complex for investors. However, after an initial decline, the sales volume of structured financial products is surging again. Based on this trend, can we argue that structured financial products are indeed simple enough for investors to understand them? Are these products nevertheless too complex and can they cause another financial turmoil? What are the limits of complexity? Do we need to differentiate between the products? This essay intends to shed light on these questions and determine the limits of the complexity of structured financial products by using CDOs as examples.
2. Complexity matters
Imagine a completely rational world. The rational agent has access to unlimited information, can process this information completely and can base his choices on readily available, accurate and quickly executable calculations. In this world the rational agent can always make informed decisions, rendering the concept of simplicity and complexity obsolete. However, Brunnermeier and Oehmke point out that in a world of bounded rationality, complexity does matter. The agent faces computational limitations, information asymmetry, time constraints and information overload. According to the authors, if the agent has no interest in gathering and evaluating information for highly complex products, hidden information may build up, which lead to sudden price adjustments when releasing the information. Agents might also make wrong choices due to lacking information or inaccurate models.1 This reasoning reveals that complexity matters in reality and imposes limits to our ability to understand certain financial products. In the following, some of these limits for structural financial products are outlined.
3. Risk and price determination
One prerequisite of understanding financial products is being able to determine their risks and prices. For pricing simple synthetic CDOs, one-factor Gaussian copula models are used. Due to their easy implementation and flexibility, these models are essential to practice.2 But these models face drawbacks as they cannot account for the ‘correlation smile’ and they imply parameters to be normally distributed.3 These simplifications have led to substantial mispricing during the financial crisis. Sophisticated and significantly more accurate pricing models, which use Student-t copulas and can account for extreme events, are available but their long computation time yet renders them impractical for daily use.4 For pricing more complicating cash flow CDOs, academic literature currently offers no solution but using Monte Carlo Simulation, which has substantial drawbacks.5 Hence, accurate pricing models are currently limited to simple CDOs (e.g. simple synthetic CDOs) as no accurate pricing model – even theoretical – is currently available for more complex CDOs (e.g. cash flow CDOs).
In assessing the default likelihood of CDOs, rating agencies rely on Monte Carlo simulation. But unless the CDOs are backed by corporate bonds, this approach suffers from approximation errors, whose magnitude is difficult to quantify.6 Coval, Jurek and Stafford have tested the sensitivity of expected payoffs of CDOs to changes in the default probability. While the senior and collateral tranche of CDOs seem reasonably robust, the mezzanine tranche appears to be sensitive to changes in the default probability. The sensitivity to default probabilities is magnified for CDO² (see Figure 1). According to the authors, a 2.5% increase in the default probability will change the credit rating for the mezzanine tranche from AAA to BBB- for CDO2.7 Given the approximation errors of Monte Carlo Simulation, an accurate cash flow prediction of higher-order CDOs seems to be well-nigh impossible.
Koebrugge’s proposed IPS algorithm can calculate rare default probabilities up to 10-13 and reveals the impact of the parameters T,s, r and r on these probabilities; hence, the model improves risk assessment compared to Monte Carlo Simulation. But he also acknowledged that it is still impossible to calculate the default probability of k out of d firms analytically.8 With accurate approximation models, like the IPS algorithm, it should be possible to assess the risk of simple synthetic CDOs reasonably. However, in assessing CDO2, CDO3… CDOn the payoff becomes so sensitive to the accuracy of default probabilities that the inherent model risk constitutes a limit in assessing the risk and payoffs of these products accurately, as even small errors can alter the payoff dramatically.
1. Accounting issues
Another prerequisite for our understanding of financial products is the product’s proper compliance with general accounting standards. SFAS 157 requires a financial product to be valued at its fair value. In accordance with paragraph 18, fair valuation of CDOs mainly relies on the market and/or the income approach. Relying on market prices was extremely problematic during the financial crisis as the market for CDOs almost dried out, which significantly distorted prices for CDOs. Unlike for other financial products, the availability of historic prices for comparison for CDOs is fairly limited. For very exotic CDOs the illiquid market limits or prohibits the applicability of market valuation. Relying on cash flow valuation is problematic as well. Ryan points out that CDOs exhibit skewed distributions for future cash flows and as a result, even the fair values of super senior tranches are less than implied by cash-flow valuation, if the underlying asset performs below a certain threshold. As other tranches are exposed to more risk, their option value may be even more important.9 Hence, current accounting standards are limited to market valuation of frequently traded, simple CDOs. Highly complex, exotic CDOs can currently not be adequately valued using market prices and their cash-flow valuation might be inaccurate.
2. Information disclosure and asymmetry
Aiming to maintain the integrity of financial markets, security regulation relies on information disclosure in many countries. Complexity can cause disclosure to fail and the resulting information failure can exacerbate the misalignment between firms and third parties.10 Beltran and Thomas point out that a CDO investor typically receives information on the RMBS, CMBS or ABS in his portfolio, but that the underlying of these instruments is not disclosed. According to the authors, this problem is further magnified by the non-static nature of the CDO’s portfolio, as the CDO manager can replace and add underlying instruments.11 Additionally, the computational complexity (default probability and correlation, waterfalls, etc.) limits the investor’s ability in using the available information to make sound decisions.
Together these issues not only undermine effective information disclosure but also create information asymmetry, which results in lemon costs. Arora, Barak, Brunnermeier and Ge prove that using exponential time computation, the CDO buyer can verify whether was properly constructed and insulate against asymmetric information; however, using real world polynomial computation, this is not possible. The authors prove that lemon costs for binary CDOs (senior tranche of a simple CDO) will be larger than for a derivative-free security and that these costs are maximized for CDO2.12 As outlined in this paragraph, information disclosure issues and information asymmetry pose a problem to the prudential use of CDOs under real world constraints. However, Schwarcz outlines a feasible solution to the problem by proposing that the CDO issuer could be required to retain a proportion of the lowest-ranked security tranche that is sold.13
Recent criticisms on the complexity of structured financial products, in particular CDOs, were and are not unfounded. The preceding analysis outlined three important reasons: failure to model risks and prices accurately, issues in determining the fair value and asymmetric information. Simultaneously the analysis revealed a need to differentiate in criticizing CDOs (this holds as well for criticizing other structured financial products). For some CDOs (e.g. simple synthetic CDOs), model predictions are reasonably robust, fair valuation is possible and information asymmetry is resolvable. However, this reasoning does not hold for more complex CDOs (e.g. CDO2). Especially the current inability to accurately calculate their highly sensitive cash flows constitutes a limit for the near, foreseeable future. Due to the cash flow risk, higher-order CDO may even cause another financial turmoil, if traded excessively and imprudently.
In the more distant future, things might change considerably. Much progress in the evaluation of CDOs has been made since their first issue in 1987 and their genuine emergence one decade later. With the emerging field of Financial Engineering, more complex and highly accurate models might be developed that allow for precise determination of risks, cash flows and fair valuation. Highly specialized investors and sellers and strict disclosure rules might minimize information asymmetry. But speculating about distant future limits is not only beyond the scope of this paper but also requires overcoming the current limits beforehand.
- Koebrugge, J 2011, ‘Estimating default probabilities for CDO’s: a regime switching model’, Dissertation for the Master Applied Mathematics, University of Twente, Enschede, viewed 13 November 2012, <essay.utwente.nl/59806/>
- Ryan, S 2008, ‘Fair Value Accounting: Understanding The Issues Raised By The Credit Crunch’, paper for the Council of Institutional Investors, viewed 14 November 2012, <http://www.ifrs.org/Current-Projects/IASB-Projects/Amendments-to-IFRS-7-...
- Schwarcz, S 2011, ‘Information asymmetry and information failure: disclosure problems in complex financial markets’, in W Sun, J Stewart & D Pollard, Corporate Governance and the Global Financial Crisis: International Perspectives, Cambridge University press, Cambridge, viewed 17 November 2012, <books.google.nl>
- Beltran, D & Thomas, C 2010, ‘Could Asymmetric Information Alone Have Caused the Collapse of Private-Label Securitization?’, International Finance Discussion Papers, Number 1010, viewed 17 November 2012, < http://www.federalreserve.gov/pubs/ifdp/2010/1010/ifdp1010.pdf>
- Arora, S, Barak, B, Brunnermeier, M & Ge, R 2012, ‘Computational Complexity and Information Asymmetry in Financial Products’, Working Paper, 5 February 2012, viewed 17 November 2012, < http://www.cs.princeton.edu/~rongge/derivativelatest.pdf> Schwarcz, S, op. cit.
- Brunnermeier, M & Oehmke, M 2009, ‘Complexity in Financial Markets’, viewed 15 November 2012, <http://www.princeton.edu/~markus/research/papers/Complexity.pdf>
- Meng, C & Sengupta, A n.d., ‘CDO Tranche Sensitivities In The Gaussian Copula Model’, viewed 13 November 2012, <https://www.math.lsu.edu/~sengupta/papers/MengSenguptaTranche08.pdf>
- Lüschner, A 2005, ‘Synthetic CDO pricing using the double normal inverse Gaussian copula with stochastic factor loadings’, Diploma Thesis, ETH Zurich and University of Zurich, viewed 17 November 2012, <http://www.javaquant.net/papers/annelisluescher.pdf>
- Kalemanova, A, Schmid, B & Werner, R 2005, ‘The Normal inverse Gaussian distribution for synthetic CDO pricing’, Working Paper risklab germany GmbH, viewed 13 November 2012, <http://www.risklab.com/Dokumente/wp/wp%2005-03%20Kalemanova%20et%20all%2... >
- Gallagher, D, Gleeson, J, Kenyon, C & Lichters, R 2009, ‘Valuation of a Cashflow CDO Without Monte Carlo Simulation’, Working Paper Series, viewed 13 November 2012, <http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1473737>
- Fender, I, Tarashev, N & Zhu, H 2008, ‘Credit fundamentals, ratings and value-at-risk: CDOs versus corporate exposures’, BIS Quaterly Review, March, pp. 87-101, viewed 13 November 2012, <http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1473651>
- Coval, J, Jurek, J & Stafford, E 2009, ‘The Economics of Structured Finance’, Journal of Economic Perspectives, vol.23, no.1, pp. 3-25, viewed 13 November 2012, <http://dss.ucsd.edu/~grondina/pdfs/CovalJurekStafford_structfinance.pdf>