Spectral Analysis in Mathematical Finance: Intelligent Walk
Ahmet Duran
Department of Mathematics, University of Michigan
March 27, 2008

I will present a new method of profitable investment strategy for portfolio risk management. Moreover, we implement a rule based expert system for the real-time financial decision making process by using the power of spectral analysis.
This is joint work with my financial mathematics student Michael Bommarito (U of M).

Each day is broken into morning and afternoon sessions. There will be no exams, no homework, no grades, although attendance is mandatory in order to continue to Fall semester. This is a pass fail course. Pass-fail grade will be determined by attendance and participation.

Soft Skills: Total 8 sessions, four hours each:

• Interviewing skills (dress, preparation for frequently asked questions) (2 sessions),
• Presentation skills (powerpoint, public speaking), (2 sessions),
• Introduction to writing executive memos (1 session),
• Teamwork and Leadership in organizations (1 session),
• Multi cultural Business Etiquette (1 session)
• Resume preparation (1 session).

Computer programming courses: Total 22 sessions, four hours each.

• SAS (8 sessions),
• MATLAB (1 sessions),
• Excel (2 session),
• C++ (10 sessions),
• Visual basic (1 session)

Basic disciplinary fundamentals: Total 34 sessions, four hours each:

• Accounting (4 sessions), Cost accounting, managerial uses of accounting statements for decision making, control, planning and evaluation. Generally accepted accounting principals.
• Ethics and Law (2 sessions)
• Applied Economics (4 sessions),
• Probability and Statistics (4 sessions),
• Corporate Finance (8 sessions) cash flows, ratio analysis, proforma analysis, financial forecasting, time value of money, investment decision rules, cost of capital, capital budgeting.
• International Finance (4 sessions), interest rate parity, purchasing power parity, international Fisher relation, expectations hypothesis, world asset pricing models, management of international portfolios
• Math Review (8 sessions)

server1 # ipmitool sensor get "Ambient Temp"
Locating sensor record...
Sensor ID              : Ambient Temp (0x8)
 Entity ID             : 7.1
 Sensor Type (Analog)  : Temperature
 Sensor Reading        : 28 (+/- 1) degrees C
 Status                : ok
 Lower Non-Recoverable : na
 Lower Critical        : 3.000
 Lower Non-Critical    : 8.000
 Upper Non-Critical    : 42.000
 Upper Critical        : 47.000
 Upper Non-Recoverable : na
 Assertion Events      : 
 Assertions Enabled    : lnc- lcr- unc+ ucr+ 
 Deassertions Enabled  : lnc- lcr- unc+ ucr+ 

As volatility has increased over the past months, the ProShares Ultra ETFs have seen a dramatic increase in average dollar liquidity.  There are exactly 50 of these leveraged instruments at the moment, and they are listed below, sorted by age.

ETF	Age (sessions)
ProShares Ultra Dow30	407
ProShares Ultra MidCap400	407
ProShares Ultra S&P500	407
ProShares Ultra QQQ	406
ProShares UltraShort Dow30	392
ProShares UltraShort MidCap400	392
ProShares UltraShort QQQ	392
ProShares UltraShort S&P500	392
ProShares Ultra SmallCap600	258
ProShares UltraShort SmallCap600	258
ProShares UltraShort Russell2000	258
ProShares Ultra Russell2000	258
ProShares Ultra Oil & Gas	253
ProShares UltraShort Oil & Gas	253
ProShares Ultra Technology	253
ProShares UltraShort Health Care	253
ProShares Ultra Health Care	253
ProShares UltraShort Industrials	253
ProShares UltraShort Financials	253
ProShares UltraShort Real Estate	253
ProShares UltraShort Semiconductors	253
ProShares UltraShort Consumer Goods	253
ProShares Ultra Consumer Goods	253
ProShares Ultra Utilities	253
ProShares Ultra Semiconductors	253
ProShares Ultra Financials	253
ProShares UltraShort Technology	252
ProShares UltraShort Consumer Services	252
ProShares UltraShort Basic Materials	252
ProShares Ultra Consumer Services	252
ProShares Ultra Real Estate	252
ProShares Ultra Industrials	252
ProShares Ultra Russell1000 Growth	239
ProShares Ultra Russell2000 Growth	239
ProShares Ultra Russell MidCap Growth	239
ProShares UltraShort Utilities	225
ProShares UltraShort Russell1000 Value	208
ProShares UltraShort Russell MidCap Growth	201
ProShares UltraShort Russell2000 Value	201
ProShares UltraShort Russell MidCap Value	201
ProShares UltraShort Russell2000 Growth	201
ProShares Ultra Russell1000 Value	201
ProShares Ultra Russell2000 Value	201
ProShares Ultra Russell MidCap Value	201
ProShares Ultra Basic Materials	201
ProShares UltraShort Russell1000 Growth	198
ProShares UltraShort MSCI EAFE	68
ProShares UltraShort MSCI Emerging Market	63
ProShares UltraShort MSCI Japan	58
ProShares UltraShort FTSE/Xinhua China	58

I've taken the product of the close and the volume for the 46 funds that have traded at least 150 sessions and averaged their daily cross-section.  The following is a chart of this average dollar liquidity over the past  150 sessions in blue, with a 20-session moving average in red.  The trend quite clearly indicates that not all market volatility is bad for ETFs.

Venture Shares of the Dutch East India Company
Larry Neal
University of Illinois at Urbana-Champaign
Research Associate, NBER

The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government. The calibration of the CAT bond is based on the estimation of the intensity rate that describes the earthquake process from the two sides of the contract, the reinsurance and the capital markets, and from the historical data. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. Since other variables can affect the value of the losses caused by earthquakes, e.g. magnitude, depth, city impact, etc., we also derive the price of a hypothetical modeled-index (zero) coupon CAT bond for earthquakes, which is based on a compound doubly stochastic Poisson pricing methodology. In essence, this hybrid trigger combines modeled loss and index trigger types, trying to reduce basis risk borne by the sponsor while still preserving a non-indemnity trigger mechanism. Our results indicate that the (zero) coupon CAT bond price increases as the threshold level increases, but decreases as the expiration time increases. Due to the quality of the data, the results show that the expected loss is considerably more important for the valuation of the CAT bond than the entire distribution of losses.

rates: infinitesimal generator matrix G such that g_ij = rate of transition from i to j, g_ii = sum_{i=/=j} g_ij

1: ctmch()
2: Prgm
3: (eigVc(rates^T))^T[1]->u
4: (abs(w)/rowNorm(w))^T->v
5: Disp v
6: EndPrgm

• Relevant standards include, but are not limited to, transmission protocols, data models, database structures and elements, identifiers, and classification structures

• While members of the industry are competitors, the adoption of standards typically will not significantly undermine the commercial position of any firm vis-à-vis its competitors.

• Monitor standards environment, identify and educate the membership on emerging issues and needs


• Manage the development of FISD member consensus positions on standards-related issues and promote those positions in the appropriate forums


• Must have member consensus – may be difficult


• Facilitate FISD member participation in the standard setting processes, directly and indirectly through the FISD staff


• FISD staff can put in the leg work that members may not be able to commit.


• Individual members’ opinions can be represented even when there is no “FISD Consensus”


• Members can leverage FISD to learn about the latest developments in standard-setting processes and get their views exposed in the appropriate forums.


• In certain instances, a member may participate in standards processes directly as FISD’s representative. This needs to be approved by the committee participating in this standard or the SPA-AC.


• Any member serving in such capacity would need to be willing to meet certain requirements:


• Clear delineation of personal/corporate positions from FISD-consensus positions


• Regular, impartial communication with other interested members, facilitated by FISD .staff, regarding the activities within the standards process.


• Member responsible for their own travel and hotel costs.


• Provide knowledgeable and neutral staff resources for standards development within non-FISD standards organizations that could not be provided by any one member


• Standards body if necessary and feasible


• Existing standards and standards bodies may not be meeting a specific need of FISD membership


• In general, FISD should not seek to be a standards body or a Maintenance Agency


• Resources (both at the FISD and SIIA) and competencies not ideal for actively managing a standard


• Resources drained away from other FISD activities


• Conflicts of interest – FISD agenda may tend to favor the standard that it manages, or be perceived as such


• Prior to taking on any Standards Body responsibilities, FISD membership must have an explicit consensus (as voiced through the FISD Executive Committee) that it is necessary, appropriate and feasible for FISD to serve as a Standards Body. There should be member consensus that…


• FISD has the long-term resources to fully support the standard.


• Consideration should be given to both expected costs and revenues that might be associated with management of the standard


• Alternatively, there should be an explicit termination date after which support for the standard would be either: (1) spun off as a stand-alone organization, (2) discontinued, or (3) transferred to another organization.


• There is no other body willing and qualified to manage the standard


• There is a critical industry need for the standard


• Management of the standard does not conflict with any other key FISD roles and responsibilities




]]> http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038662 http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038662 Markets Sat, 02 Feb 2008 20:21:06 -0500 The Future of United States Securities Regulation in an Age of Technological Uncertainty

The evolution of information technology will determine the future structure of the world's financial markets. A nuanced appreciation of technology and its implications for financial markets is herefore essential to the design of a successful, modern securities regulation regime. Although the SEC currently ranks as among the most successful federal agencies in responding to changes in information technology, its ability to stay abreast of new developments is open to question. The agency appears to lack an adequate number of staff that are adept in more advanced implications of information technology. It also has no articulated technology strategy.

This paper expands on the need to develop a technology strategy and provides five distinct examples of initiatives that could emerge from a more affirmative approach to information technology. These examples suggest: (1) a software-based open architecture redesign of EDGAR; (2) a more aggressive role for the SEC in the definition of financial XML and its integration into the disclosure regime; (3) the use of an open API structure to resolve market fragmentation issues generated by the emergence of ECNs and other novel marketplaces; (4) the application of Internet technology to provide individualized trading risk measures that could be responsive to the agency's concerns regarding suitability; and (5) the application of on-line authentication techniques to reduce the risk of "counterfeit" disclosures, such as those which adversely affected Emulex's and Pairgain's stock prices.


]]> http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038661 http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038661 Markets Sat, 02 Feb 2008 20:16:17 -0500 Cyclostationarity: Half a century of research

Abstract

In this paper, a concise survey of the literature on cyclostationarity is presented and includes an extensive bibliography. The literature in all languages, in which a substantial amount of research has been published, is included. Seminal contributions are identified as such. Citations are classified into 22 categories and listed in chronological order. Both stochastic and nonstochastic approaches for signal analysis are treated. In the former, which is the classical one, signals are modelled as realizations of stochastic processes. In the latter, signals are modelled as single functions of time and statistical functions are defined through infinite-time averages instead of ensemble averages. Applications of cyclostationarity in communications, signal processing, and many other research areas are considered.

]]> http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038660 http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038660 Mathematics Sat, 02 Feb 2008 17:43:17 -0500 http://sciencepolicy.colorado.edu/admin/publication_files/resource-2476-2008.02.pdf

Abstract: After more than two decades of relatively little Atlantic hurricane activity, the past decade saw heightened hurricane activity and more than $150 billion in damage in 2004 and 2005. This paper normalizes mainland U.S. hurricane damage from 1900–2005 to 2005 values using two methodologies. A normalization provides an estimate of the damage that would occur if storms from the past made landfall under another year’s societal conditions. Our methods use changes in inflation and wealth at the national level and changes in population and housing units at the coastal county level. Across both normalization methods, there is no remaining trend of increasing absolute damage in the data set, which follows the lack of trends in landfall frequency or intensity observed over the twentieth century. The 1970s and 1980s were notable because of the extremely low amounts of damage compared to other decades. The decade 1996–2005 has the second most damage among the past 11 decades, with only the decade 1926–1935 surpassing its costs. Over the 106 years of record, the average annual normalized damage in the continental United States is about $10 billion under both methods. The most damaging single storm is the 1926 Great Miami storm, with $140–157 billion of normalized damage: the most damaging years are 1926 and 2005. Of the total damage, about 85% is accounted for by the intense hurricanes Saffir-Simpson categories 3, 4, and 5, yet these have comprised only 24% of the U.S. landfalling tropical cyclones. Unless action is taken to address the growing concentration of people and properties in coastal areas where hurricanes strike, damage will increase, and by a great deal, as more and wealthier people increasingly inhabit these coastal locations.

]]> http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038659 http://mblog.lib.umich.edu/~mjbommar/archives/2008/02/index.html#038659 Mathematics Sat, 02 Feb 2008 17:38:53 -0500