DOCSLIB.ORG

Application of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic Trading

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Application of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic Trading Journal of Mathematics and Statistics Original Research Paper Application of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic Trading Aldo Taranto and Shahjahan Khan School of Sciences, University of Southern Queensland, Australia Article history Abstract: Bi-directional Grid Constrained (BGC) Stochastic Processes Received: 23-11-2020 (BGCSP) become more constrained the further they drift away from the Revised: 01-03-2021 origin or time axis are examined here. As they drift further away from the Accepted: 05-03-2021 time axis, then the greater the likelihood of stopping, as if by two hidden reflective barriers. The theory of BGCSP is applied to a trading environment in Corresponding Author: Aldo Taranto which long and short trading is available. The stochastic differential equation of School of Sciences, University the Grid Trading Problem (GTP) is proposed, proved and its solution is of Southern Queensland, simulated to derive new findings that can lead to further research in this area Australia and the reduction of risk in portfolio management. Email: [email protected] Keyword: Grid Trading, Random Walks, Probability of Ruin, Stochastic Differential Equation, Bi-Directional Grids, Trending Grids, Mean Reversion Grids Introduction To visualize the impact of the BGC function Ψ(Xt,t) in (1.1), 1000 Itô diffusions were simulated both with Bi-directional Grid Constrained (BGC) Stochastic and without BGC, with zero drift coefficient µ and unit Processes (BGCSP) are described as Itô diffusions in diffusion coefficient σ, as shown in Fig. 1. which the further they drift from the origin or time axis, The zero drift in (a) is constrained in (b) the more it then the more they will be reflected back to the origin. deviates from the origin, causing the hidden reflective Definition 1.1. (SDE of BGC Stochastic Process) upper barrier and hidden reflective lower barrier to emerge, together with horizontal bands to form due to For a complete filtered probability space (Ω,,{}t0, the discretization effect of BGC. ℙ) and a BGC function Ψ(x): ℝ ℝ, x ∈ ℝ, then the BGCSP have applications by solving problems corresponding BGC Itô diffusion is defined as follows: involving the constraining of stochastic processes within two reflective barriers (often times hidden and not predefined) and that an event occurs when the barriers are dX fXtdtgXtdW t, t , t sgn Xt t , Xt t , , (1.1) hit. In the context of mathematical, quantitative (quant) and BGC computational finance and algorithmic trading, we define an application of BGCSP by the following definition. where, sgn[x] is defined in the usual sense as: Definition 1.2. [Bi-Directional] Grid Trading (BGT) BGT is the simultaneous placement of a Long and 1 ,x 0 Short trade at every grid width g level at, above and sgnxx 0 , 0, below the initial price rate R0 and the corresponding 1 ,x 0 taking profit of each trade at the nearest Take Profit level (also of width g) without any predetermined stop losses. This definition is illustrated in Fig. 2. and f(Xt,t), g(Xt,t) and Ψ(Xt,t) are convex functions. As the BGCSP evolves over time, it will collect (i.e., The drift function f(x): ℝ ℝ and the diffusion function close) many winning trades and also hold on to some losing g(x): ℝ ℝ, x ∈ ℝ, in the limit, they approach the typical trades, which should become profitable over time. It is constant expressions for the drift and diffusion coefficients: remarkable how such a simple trading strategy can generate profits most of the time due to frequent periods of low volatility (i.e., diffusion σ). However, when a strong trend limf x ,lim g x . (1.2) xx emerges, this strategy accumulates large losses and so the © 2021 Aldo Taranto and Shahjahan Khan. This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Aldo Taranto and Shahjahan Khan / Journal of Mathematics and Statistics 2021, Volume 17: 22.29 DOI: 10.3844/jmssp.2021.22.29 trades need to be closed down before they exceed the of magnitude, then the trading account can become ruined, account’s current capital or balance level. When the losing inducing a stopping time. We call this the Grid Trading trades grow too far in terms of either total count or in terms Problem (GTP). 80 60 20 40 10 20 0 X X 0 -20 -40 -10 -60 -20 -80 0 200 400 600 800 1000 0 200 400 600 800 1000 T T (a) (b) Fig. 1: Itô Diffusions with and without BGC R R T T 1 2 3 4 5 6 T = 6, W = 6, L = 21, P = -15 Fig. 2: Illustration of BGCSP in trading R = Rate, T = Time, W = Winning trades, L = Losing trades, P = Profit, E = Equity. (a) Horizontal blue lines represent when Long Trades occur and horizontal red lines represent when Short trades occur. The arrows represent the movement of the rate Rt over time t. (b) Dotted lines depict trades in profit and closed at their nearest Take Profit (TP). Solid lines depict trades that are held in loss until they reach their TP, closed down when loss becomes ‘too large’ or finally if an account is ruined 23 Aldo Taranto and Shahjahan Khan / Journal of Mathematics and Statistics 2021, Volume 17: 22.29 DOI: 10.3844/jmssp.2021.22.29 Literature Review n0, E00 E , n1, E E v v E , BGC stochastic processes are relatively new 1 0 0 n2, E E 2 v 3 v E v , (Taranto and Khan, 2020a-d). To the best of the authors’ 2 0 0 (3.1) knowledge, there is no additional formal academic nn 1 n t, E E vt v definition of BGC stochastic processes nor grid trading t 0 2 Wt available within all the references on the subject matter Lt (Mitchell, 2019; DuPloy, 2008; 2010; Harris, 1998; King, 2010; 2015; Markets, 2017; Work, 2018). These where, n is the grid level reached by the price Rt at secondary sources are not rigorous journal papers but time t. However, the markets do not trend indefinitely instead informal blog posts or software user manuals. and so Lt in (3.1) needs to be replaced with a Even if there were any academic worthey results found stochastic process. In a continuous time stochastic on grid trading, there is a general reluctance for traders framework t ∈ ℝ+, (3.1) becomes: to publish any trading innovation that will help other traders and potentially errode their own trading edge. dEt v Despite this, grid trading can be expressed vt dt n t n t 1, (3.2) Et 2 academically as a discrete form of the Dynamic Mean- Variance Hedging and Mean-Variance Potfolio where, E = E at t = 0 as an initial condition and adopting Optimization problem (Schweizer, 2010; Biagini et al., t 0 the simplest of 1-Dimensional Itô Diffusion processes: 2000; Thomson, 2005). There are many reasons why a firm would undertake a hedge, ranging from minimizing 1 the market risk of one of its client’s trades by trading in n t tt dt dW , (3.3) the opposite direction, through to minimizing the loss on g a wrong trade by correcting the new trade’s direction whilst keeping the old trade still open until a more noting that now we highlight that n is a function of t where: opportune time (Stulz, 2013). In the case of grid trading, it can be considered as a form of hedging of multiple µt is The drift (or direction) over time positions simultaneously over time, for the generation of σt is The diffusion (or volatility) over time, which trading profits whilst minimizing the total portfolio loss. are random and assumed independent of µt over time Wt is A Wiener Process (or Brownian motion) as dW dt with Methodology t t t (0,1) Derivation of Continuous Grid SDE We note that (3.2) is essentially a non-standard Geometric Brownian Motion (GBM). The reason why Theorem 3.1 we have not expressed it as a Arithmetic Brownian For a Bi-Directional grid trading constrained Itô Motion (ABM) is that we require the equity Itô diffusion process with a given grid width g, value ν per grid width, to be modelled as products of random factors and not drift (direction) µt and variance (risk) σt, then the change sums of random terms. GBM involves independently and in equity E over time t is: identically distributed ratios between successive factors. dW Furthermore, we require t 0, t as trading dE v v g E tt2.tg22 g dt dW t 22t t t Et 22 g g systems seek to exponentially compound E over time and an Et = 0 equates to ruin or bankruptcy. In fact, since Proof our drift and diffusion terms are non-constant over time, then our non-standard GBM is actually a form of a more In the discrete time framework t ∈ of Fig. 2, one generalised Itô Processes. Finally, we note that (3.2) does can see that the equity Et at any time t is comprised of the not appear at first glance to be a GBM as it does not exhibit initial equity E0, plus the sum of all the winning trades an explicit dWt term, even though it is implied due to (3.3). Wt, minus the sum of any losing trades Lt. We can Substituting (3.3) into (3.2) expands to: elaborate how the progression can evolve over time, in dE v 2 the worst case scenario of a strongly trending market, as t vt dt n t n t shown in Fig.
Load more

Recommended publications
  • Lifecycle Goal Achievement of Portfolio Volatility Reduction?
    1 Life Cycle Goal Achievement or Portfolio Volatility Reduction? M A H Dempster*†, Dwayne Kloppers**1, Igor Osmolovskiy†2, Elena Medova*† and Philipp Ustinov† * University of Cambridge UK ** Alexander Forbes SA † Cambridge Systems Associates UK [email protected], [email protected], [email protected], [email protected], [email protected] Abstract This paper is concerned with the use of currently available technology to provide individuals, financial advisors and pension fund financial planners with detailed prospective financial plans tailored to an individual's financial goals and obligations. By taking account of all prospective cash flows of an individual, including servicing current liabilities, and simultaneously optimizing prospective spending, saving, asset allocation, tax, insurance, etc. using dynamic stochastic optimization, the paper addresses the question of the title by comparing the results of such a goal- based fully dynamic strategy with representative current best practices of the financial advisory industry. These include piecemeal fixed allocation portfolios for specific goals, target-date retirement funds and fixed real income post-retirement financial products, all using Markowitz mean variance optimization based on the very general goal of minimizing portfolio volatility for a specific portfolio expected return over a finite horizon. Making use of the same data and market calibrated Monte Carlo stochastic simulation for all the alternative portfolio strategies, we find that flexibility turns out to be of key importance to individuals for both portfolio and spending decisions. The performance of the adaptive dynamic goal-based portfolio strategy is found to be far superior to all the industry’s Markowitz-based approaches.
    [Show full text]
  • Credit Risk Measurement: Developments Over the Last 20 Years
    Journal of Banking & Finance 21 (1998) 1721±1742 Credit risk measurement: Developments over the last 20 years Edward I. Altman, Anthony Saunders * Salomon Brothers Center, Leonard Stern School of Business, New York University, 44 West 4th street, New York, NY 10012, USA Abstractz This paper traces developments in the credit risk measurement literature over the last 20 years. The paper is essentially divided into two parts. In the ®rst part the evolution of the literature on the credit-risk measurement of individual loans and portfolios of loans is traced by way of reference to articles appearing in relevant issues of the Journal of Banking and Finance and other publications. In the second part, a new approach built around a mortality risk framework to measuring the risk and returns on loans and bonds is presented. This model is shown to oer some promise in analyzing the risk-re- turn structures of portfolios of credit-risk exposed debt instruments. Ó 1998 Elsevier Science B.V. All rights reserved. JEL classi®cation: G21; G28 Keywords: Banking; Credit risk; Default 1. Introduction Credit risk measurement has evolved dramatically over the last 20 years in response to a number of secular forces that have made its measurement more * Corresponding author. Tel.: +1 212 998 0711; fax: +1 212 995 4220; e-mail: asaun- [email protected]. 0378-4266/97/$17.00 Ó 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 4 2 6 6 ( 9 7 ) 0 0 0 3 6 - 8 1722 E.I. Altman, A. Saunders / Journal of Banking & Finance 21 (1998) 1721±1742 important than ever before.
    [Show full text]
  • The New Diversification: Open Your Eyes to Alternatives a Conversation
    THE NEW DIVERSIFICATION: OPEN YOUR EYES TO ALTERNATIVES A CONVERSATION WITH PROFESSOR GECZY, PH.D During the credit crisis, many investors discovered to their unfortunate surprise that their portfolios were not nearly as protected from downside risk as they thought and that their traditional notion of “diversification” failed their expectations. As part of our efforts to provide investors with Dr. Christopher Geczy perspective on how to implement what BlackRock terms Academic Director of the Wharton Wealth “The New Diversification,” we sat down for a discussion with Management Initiative Professor Christopher Geczy. & Adjunct Associate Professor of Finance Highlights include: at The Wharton School } Modern Portfolio Theory did not fail during the credit crisis—portfolio construction did. Many investors did not have exposure to enough different asset classes. } Investors should consider incorporating a much wider range of strategies and assets as part of their core investment strategy. } T he notion of “alternative” investing is often misunderstood. Gaining access to different types of investments is an approach that almost everyone should employ, and many strategies are now available to a broad range of individuals. Dr. Geczy teaches investment management and co-created the first full course on hedge funds at The Wharton School. He also teaches a number of executive education courses and has taught AIMR/CFA-Institute-accredited professional Risk Management courses through the University of Chicago’s Graduate School of Business. He has a B.A. in Economics from the University of Pennsylvania and a Ph.D. in Finance and Economics from the Graduate School of Business at the University of Chicago.
    [Show full text]
  • Gambler's Ruin Problem and Bi-Directional Grid Constrained Trading and Investment Strategies
    “Gambler’s ruin problem and bi-directional grid constrained trading and investment strategies” Aldo Taranto https://orcid.org/0000-0001-6763-4997 AUTHORS Shahjahan Khan https://orcid.org/0000-0002-0446-086X Aldo Taranto and Shahjahan Khan (2020). Gambler’s ruin problem and bi- ARTICLE INFO directional grid constrained trading and investment strategies. Investment Management and Financial Innovations, 17(3), 54-66. doi:10.21511/imfi.17(3).2020.05 DOI http://dx.doi.org/10.21511/imfi.17(3).2020.05 RELEASED ON Friday, 14 August 2020 RECEIVED ON Wednesday, 24 June 2020 ACCEPTED ON Monday, 27 July 2020 LICENSE This work is licensed under a Creative Commons Attribution 4.0 International License JOURNAL "Investment Management and Financial Innovations" ISSN PRINT 1810-4967 ISSN ONLINE 1812-9358 PUBLISHER LLC “Consulting Publishing Company “Business Perspectives” FOUNDER LLC “Consulting Publishing Company “Business Perspectives” NUMBER OF REFERENCES NUMBER OF FIGURES NUMBER OF TABLES 35 9 0 © The author(s) 2020. This publication is an open access article. businessperspectives.org Investment Management and Financial Innovations, Volume 17, Issue 3, 2020 Aldo Taranto (Australia), Shahjahan Khan (Australia) Gambler’s ruin problem BUSINESS PERSPECTIVES and bi-directional grid LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, constrained trading Sumy, 40022, Ukraine www.businessperspectives.org and investment strategies Abstract Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically until now, are relatively new in the world of financial markets and have the ability to out-perform many other trading algorithms in the short term but will almost surely ruin an investment account in the long term.
    [Show full text]
  • ERM-INV Model Solutions Fall 2014
    ERM-INV Model Solutions Fall 2014 1. Learning Objectives: 5. The candidate will understand the concept of economic capital, risk measures in capital assessment and techniques to allocate the cost of risks within business units. Learning Outcomes: (5a) Describe the concepts of measures of value and capital requirements (for example, EVA, embedded value, economic capital, regulatory measures, and accounting measures) and demonstrate their uses in the risk management and corporate decision-making processes. Sources: Understanding ORSA before Implementing It – Shapella and Stein Commentary on Question: In general, candidates performed well on this question, demonstrating adequate knowledge of ORSA requirements and ERM practices. Most of the candidates understood the benefits to Humber’s risk management - part (b) - and many received full credit. Many candidates performed better in part (a) than in part (c). Solution: (a) Explain how Humber will need to adjust its current ERM practices in order to comply with the new ORSA requirements. Commentary on Question: The following list of three adjustments is an example of what would receive full credit for part (a). Some candidates stated the need to document but spent too much time providing details of the perfect or ideal ERM practice, rather than spending that time on explaining other adjustments that would be required. Some candidates stated that Humber would need to develop an economic capital model; however, an EC model is not an ORSA requirement, so an absolute statement to that effect did not receive credit. Candidates could receive credit for stating that Humber could look into developing an EC model. ERM-INV Fall 2014 Solutions Page 1 1.
    [Show full text]
  • Breaking Bad Better Call Hedge Funds?
    Research HEDGE FUND MONITOR | 2nd Quarter 2020 Breaking Bad Better Call Hedge Funds? KEY ELEMENTS In the wake of COVID-19’s impact on markets, potential investors in hedge funds have a handful of opportunities they can consider. In the current environment, hedge funds will be more likely to earn positive alpha, especially where central banks are not controlling the markets. Before considering these options, institutional investors must undertake a self-assessment to manage the two often-understated risks of hedge fund investing: implementation risk and decision risk. “The murky economic outlook will spur the need for price discovery in every trade, a more hospitable environment for less-constrained strategies like hedge funds.” Jim McKee Callan’s Hedge Fund Research Group Chemistry is the study of matter, but I prefer to see it as the study of change… It’s growth, then decay, then transformation. —Bryan Cranston, as Walter White in “Breaking Bad” After the longest recovery on record, the U.S. economy experienced an “unprecedented” event last quar- ter: Contagion risk from COVID-19 quickly exposed a fragile financial system. Without the grease of credit, the wheels of markets quickly stopped turning. Following trillions of dollars in government intervention, faith in equity and credit markets was restored. Sort of. While the world scrambles to ameliorate the pandemic’s devastation, institutional investors have devel- oped a renewed appreciation of prudent measures to both protect and grow their capital. Since that dual objective is the mission of hedge funds, it is appropriate to revisit how they are positioned to potentially help investors.
    [Show full text]
  • Bi-Directional Grid Absorption Barrier Constrained Stochastic Processes with Applications in Finance & Investment
    Risk Governance & Control: Financial Markets & Institutions / Volume 10, Issue 3, 2020 BI-DIRECTIONAL GRID ABSORPTION BARRIER CONSTRAINED STOCHASTIC PROCESSES WITH APPLICATIONS IN FINANCE & INVESTMENT Aldo Taranto *, Shahjahan Khan ** * Corresponding author, Faculty of Health, Engineering and Sciences, University of Southern Queensland, Australia Contact details: University of Southern Queensland, Toowoomba, QLD 4350, Australia ** Faculty of Health, Engineering and Sciences, University of Southern Queensland, Australia Abstract How to cite this paper: Taranto, A., & Whilst the gambler’s ruin problem (GRP) is based on martingales Khan, S. (2020). Bi-directional grid absorption barrier constrained stochastic and the established probability theory proves that the GRP is processes with applications in finance & a doomed strategy, this research details how the semimartingale investment. Risk Governance and framework is required for the grid trading problem (GTP) of Control: Financial Markets & Institutions, financial markets, especially foreign exchange (FX) markets. As 10(3), 20-33. http://doi.org/10.22495/rgcv10i3p2 banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater Copyright © 2020 The Authors automation of the hedging process and help forecast which hedge This work is licensed under a Creative scenarios to avoid. Two theorems are adapted from GRP to GTP and Commons Attribution 4.0 International prove that grid trading, whilst still subject to the risk of ruin, has License (CC BY 4.0). the ability to generate significantly more profitable returns in https://creativecommons.org/licenses/ the short term. This is also supported by extensive simulation and by/4.0/ distributional analysis. We introduce two absorption barriers, one ISSN Online: 2077-4303 at zero balance (ruin) and one at a specified profit target.
    [Show full text]
  • “Gambler's Ruin Problem and Bi-Directional Grid Constrained Trading and Investment Strategies”
    “Gambler’s ruin problem and bi-directional grid constrained trading and investment strategies” Aldo Taranto https://orcid.org/0000-0001-6763-4997 AUTHORS Shahjahan Khan https://orcid.org/0000-0002-0446-086X Aldo Taranto and Shahjahan Khan (2020). Gambler’s ruin problem and bi- ARTICLE INFO directional grid constrained trading and investment strategies. Investment Management and Financial Innovations, 17(3), 54-66. doi:10.21511/imfi.17(3).2020.05 DOI http://dx.doi.org/10.21511/imfi.17(3).2020.05 RELEASED ON Friday, 14 August 2020 RECEIVED ON Wednesday, 24 June 2020 ACCEPTED ON Monday, 27 July 2020 LICENSE This work is licensed under a Creative Commons Attribution 4.0 International License JOURNAL "Investment Management and Financial Innovations" ISSN PRINT 1810-4967 ISSN ONLINE 1812-9358 PUBLISHER LLC “Consulting Publishing Company “Business Perspectives” FOUNDER LLC “Consulting Publishing Company “Business Perspectives” NUMBER OF REFERENCES NUMBER OF FIGURES NUMBER OF TABLES 35 9 0 © The author(s) 2021. This publication is an open access article. businessperspectives.org Investment Management and Financial Innovations, Volume 17, Issue 3, 2020 Aldo Taranto (Australia), Shahjahan Khan (Australia) Gambler’s ruin problem BUSINESS PERSPECTIVES and bi-directional grid LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, constrained trading Sumy, 40022, Ukraine www.businessperspectives.org and investment strategies Abstract Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically until now, are relatively new in the world of financial markets and have the ability to out-perform many other trading algorithms in the short term but will almost surely ruin an investment account in the long term.
    [Show full text]
  • Six Trends That Will Determine the Future of Global Non-Life Reinsurance Authors
    £ € 01011 $ 01001 Y 10010 01010 S £ This time is different Six trends that will determine the future of global non-life reinsurance Authors Clive Buesnel Insurance Leader – UK +44 (0)20 7303 3247 [email protected] Neal Baumann Global Insurance Leader +1 212 618 4105 [email protected] Kurt Mitzner Insurance Leader – Germany +49 21187 722656 [email protected] Peter Evans Insurance Research Leader – UK +44 (0)20 7303 0010 [email protected] Will Wilson UK Insurance Regulation & Advisory +44 (0)20 7007 7088 [email protected] Gaurav Narula Insurance Research – UK +1 678 299 5112 [email protected] Contact details of our insurance leaders across the world can be found at the end of this report. Discover more insurance insights and analysis like this at deloitte.co.uk/Insurance This time is different | Six trends that will determine the future of global non-life reinsurance Contents Foreword 02 Executive summary 03 Part one: Future trends 05 Part two: Future scenarios 35 Conclusion 40 Endnotes 41 Contacts 42 01 This time is different | Six trends that will determine the future of global non-life reinsurance Foreword The global non-life reinsurance industry has consistently delivered high returns, weathered storms both natural and financial, and innovated the way in which risk is identified, analysed and controlled. Yet, for an industry built on forecasting In this report Deloitte’s leading reinsurance We would like to thank those who took and preparing for the unexpected, we tend specialists have focussed on developing a part in our research. We look forward to to overestimate the speed and scale at deeper understanding of the trends that your feedback on the report and welcome which we change.
    [Show full text]
  • Does Community and Environmental Responsibility Affect Firm Risk? Evidence from UK Panel Data 1994-2006
    This is a repository copy of Does Community and Environmental Responsibility Affect Firm Risk? Evidence from UK Panel Data 1994-2006. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/11230/ Monograph: Toms, S., Anderson, K. orcid.org/0000-0002-6557-422X and Salama, A. (2009) Does Community and Environmental Responsibility Affect Firm Risk? Evidence from UK Panel Data 1994-2006. Working Paper. Department of Management Studies, University of York Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ promoting access to White Rose research papers Universities of Leeds, Sheffield and York http://eprints.whiterose.ac.uk/ White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/ 11230 Working Paper Toms, S, Anderson, K, Salama, A (2009) Does Community and Environmental ResponsibilityAffect Firm Risk? Evidence from UK Panel Data 1994-2006 Working paper number 49. White Rose Research Online [email protected] University of York The York Management School Working Paper No.
    [Show full text]
  • Modeling Fund and Portfolio Risk: a Bi-Modal Approach to Analyzing Risk in Turbulent Markets
    Modeling Fund and Portfolio Risk: A bi-modal Approach to Analyzing Risk in Turbulent Markets Iordanis Karagiannidis And D. Sykes Wilford Forthcoming in the Review of Financial Economics ABSTRACT Following the financial crisis of 2008, it has been argued that Value at Risk (VaR), and risk analysis in general, failed to alert risk managers of the turbulence on the horizon. This is a misguided view that should not have come as a surprise because many widely circulated academic papers and discussions suggested, well before the crisis, that simple VaR results could easily be misinterpreted if the circumstances for its proper use are not fully understood. This paper addresses some ways in which VaR concepts may be applied more effectively. Non-standard Monte Carlo simulations are utilized. Whereas standard mean-variance defined methodologies using Monte Carlo analysis may not capture how “fat” a lower tail may actually be, a bi-modal switching structure between assumed normal periods and possible turbulent economic periods may help resolve the problem. Lower boundaries (worst case paths) of the different (normal versus bi-modal) processes are mapped to illustrate implied riskiness of portfolios if turbulence occurs. The analysis implies that no mechanical risk analysis is sufficiently divorced from a judgment call about possible market disruptions; however, a bi-modal approach allows quantification of said judgment in conjunction with empirical observations from history. JEL Classification: G11, G12, G13, G17 Key Words: Risk Analysis, Monte Carlo, Portfolio Diversification, Commodity Futures 1 Modeling Fund and Portfolio Risk: A bi-modal Approach to Analyzing Turbulence in Markets Iordanis Karagiannidis And D.
    [Show full text]
  • Insurance-Linked Securities WHITEPAPER AUGUST 2020
    Insurance-linked Securities WHITEPAPER AUGUST 2020 Insurance-linked securities (“ILS”) is an asset class that generally derives its CONTRIBUTORS return and risk from property damage insurance contracts related to natural Colin Bebee, CFA Frank Benham, CFA, CAIA catastrophes (e.g., earthquakes, hurricanes, etc.). In this class, investors provide insurance-related, at-risk capital in exchange for pre-defined premium payments. Investors assume the role of an insurer, as the underlying risk sources are insurance policies and/or derivatives that are analogous to insurance policies. The archetype of ILS is natural catastrophe property reinsurance where investors effectively assume insurance policies from the original insurers of global property damage that stem from natural perils. ILS generally provides a moderate level of return whose risk sources are completely unrelated to the traditional capital markets. This type of investment provides a unique source of uncorrelated and economically intuitive returns that are typically absent from most investment portfolios. Moreover, ILS has the potential to provide societal benefits by lowering the cost of insurance for end policyholders and diluting the risk of ruin for the most susceptible companies and regions. For institutional investors that are willing to accept the complexity, modest returns, and relatively small market size, we believe that ILS, and in particular natural catastrophe property insurance/reinsurance, can benefit a total portfolio when included as an illiquid diversifying strategy. Key takeaways → Insurance is one of the world’s oldest commercial activities, and ILS/reinsurance offers institutional investors the ability to participate in this endeavor via the capital markets. → Reinsurance is best described as insurance for insurance companies.
    [Show full text]