Risk MSc dissertation topic
Colin Rowat
Room220,J.G.Smith Building
University of Birmingham
Edgbaston B152TT
01214143754
www.socscistaff.bham.ac.uk/rowat
March8,2011
1.Diversification Meucci(2009)presents a recursive acceptance algorithm
for implementing diversified portfolios in the presence of transaction costs.1 This algorithm is a form of gr
eedy algorithm,which often performs well, but which may also perform arbitrarily badly(Bang-Jensen,Gutin,and Yeo,2004).
(a)can an example of poor performance be found?
(b)does the portfolio diversification problem belong to the class identi-
fied by Bang-Jensen et al.(2004)in which the greedy algorithm may
find the worst possible solution?
(c)what algorithms improve over greedy for relevant combinations of
run–time and accuracy?
(d)how do maximum diversification portfolios compare in performance
to minimum variance ones?
Meucci has not yet found such markets,but would be interested to hear of them.
Mansini and Pferschy(2004),which tests the greedy algorithm’s perfor-mance in the context of asset–backed securitisation(ABS),may provide
a good template to follow(see also Kellerer,Pferschy,and Pisinger(2004,
§15.5.1)for an overview).They model the ABS problem as one of choos-ing which illiquid assets to securitise in return for a liquid loan subject to being able to make interest payments,making it equivalent to a knapsack problem.They show that greedy can perform arbitrarily badly,and there-fore test a direct extension of greedy as well as one based on decomposing the problem into multiple knapsack problems.They show that each has relative performance of50%,a tight bound.Combining the two allows ac-curacy and speed to be traded offmoreflexibly.On data from an Italian bank,the algorithms performed well above their lower bounds.
1An updated version of his paper is available on SSRN,here.
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C.Rowat Risk dissertation topic
reaction paper to metaphor2.Endogenous risk Shin(2010)studies endogenous risk,noting that the
optimal behaviour of economic agents collectively determines the economic environment,including its level of riskiness.This gives rise to the concern (addressed directly in Chapter3)that widespread use of risk-management techniques like VaR may give rise to boom-and-bust cycles.This observa-tion has also been made elsewhere:
So-called risk management herding can take place,whereby in-
stitutions following similar(perhaps VaR-based)rules may all
be running for the same exit in times of crises,consequently
destabilizing an already precarious situation even further.This
herding phenomenon has been suggested in connection with the
1987crash and the events surrounding the1998LTCM crisis.
...In an article of12June1999,the Economist wrote that“at-
tempts to measure and put a price on risk infinancial markets
may actually be making them riskier”.(McNeil,Frey,and Em-
brechts,2005)
See Avinash Persaud’s1993‘Sending the Herd Offthe CliffEdge’for further background.
Endogenising risk seems to require consideration of general equilibrium finance(q.v.Cs´o ka,Herings,and K´o czy,2007).As Cs´o ka et al.(2007)is only able to derive GE measures of risk in extremely simple environments, they cannot currently be applied to real situations.When is this a prob-lem?In other words,when do a portfolio’s GE effects become significant?
When significant,how can they be approximated?
Can Shin’s metaphor of the Millennium Bridge be pushed further:do portfolios tend to become more homogeneous as a result of endogenous risk?How can one use Shin’s insights to trade ral equi-librium delta hedging models)?What is the more important criticism of VaR:that it is not coherent,or that–as typically used–it fails to consider endogenous risk?In thin markets,does it help to consider game theoret-ical interactions such as those considered in the microstructure literature (Kyle,1985,1989)?
3.Ambiguity.Finance tends to make the classical assumption of point
parameter estimates,allowing portfolio returns to be represented as a probability distribution.Risk or satisfaction measures are then defined over probability distributions,their axioms studied,and portfolios ranked.
More robust analysis may be conducted,typically by allowing the param-eter estimates to vary over some space.Is risk,however,too simple a framework?In other words,might there be advantages to considering ambiguity,which allows probability distributions over the uncertain pa-rameters from the outset?See Epstein and Schneider(2010)for a current survey of these issues.See also Weitzman(2007),which showed that uncertain parameter estimates can reverse well known puzzles such as the equity premium puzzle.Caballero and Krishnamurthy(2008)con-sider the link between(Knightian)uncertainty andflights to quality.2Do ambiguity-based measures satisfy coherence or spectral axioms?Do they 2See also Ang,Dong and Piazzesi’s No-arbitrage Taylor rules.
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C.Rowat Risk dissertation topic
have natural interpretations in terms of risk capital to be set against in-vestments?
4.Estimation risk.Attitudes towards risk have been well studied,allowing
complete ordering of portfolios’return distributions.However,“modeling the investor’s attitude toward estimation risk is an even harder than mod-eling his attitude toward risk”(Meucci,2005,0.403).Clearly,though, estimation risk is a significant consideration.Should there be a way of completely ordering portfolios subject to estimation risk?What is the relationship between estimation risk and ambiguity?
5.Liquidity
•for a reading list,see LongstaffAER September2009,which cites–
inter alia–Acharya and Pedersen in2005J.Financial Economics
•Meucci:Liquidity risk is a very important topic.The simplest ap-
proach is a convolution of each security P&L pdf with a Gaussian as
wide as the bid-ask spread.The most refined approaches account for
multivariate market impact.
•Limited cognition and the market reaction to liquidity shocks:Limit
orders and algorithmic trading(Bruno Biais and Pierre-Olivier Weill)
6.Birmingham online portfolio optimiser
•to my knowledge,no existing open source online portfolio optimiser
•take daily price feed either from free source,Thomson ONE Banker,
etc.and output optimal portfolio
•track performance,inc.v benchmark
•write in what language?R?Java?
•what open source alternatives already hrough Quantlib,
Akutan)?
•is Meucci’s“Factors on Demand”paper(2010)relevant?
7.discounting the past
•if use simple RiskMetrics approach,howfit discount parameter?
•otherwise,does it make sense to use a subordinated time parameter,
to account for market activity?(q.v.Huth&Abergel,The Times
Change,2009)
8.statistical arbitrage opportunities on less developed stock markets?
9.do tools from algebraic geometry(implemented ,Magma,Singular,
FriCAS,Macaulay2)allow improvements relative to the approximations computed using linear algebra MATLAB)?
10.Derivatives design Arora,Barak,Brunnermeier,and Ge(2009)respond
to the standard argument that derivatives can reduce costs of informa-tional asymmetries by allowing informed parties to securitise their assets and sell the less informationally sensitive elements of their c
ashflow to less informed parties.They show that
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C.Rowat Risk dissertation topic
designers offinancial products can rely on computational in-
tractability to disguise their information via suitable“cherry
picking.”They can generate extra profits from this hidden in-
formation,far beyond what would be possible in a fully rational
setting.
Furthermore,this‘cherry picking’can occur even under securitisation, which typically has the originator retain the most junior tranches that bear thefirst losses.The authors show this by comparing‘tampered’derivatives to‘untampered’ones,and demonstrating that the problem of distinguishing between them is equivalent to the planted dense subgraph problem.
(a)can good tests be developed for‘tampered’derivatives?
(b)what policy implications arise from this analysis?3
< Brunnermeier and Sannikov’s ESWC2010presentation? References
Sanjeev Arora,Boaz Barak,Markus Brunnermeier,and Rong Ge.Computa-tional complexity and information asymmetry infinancial products.mimeo, 19October2009.
Jørgen Bang-Jensen,Gregory Gutin,and Anders Yeo.When the greedy algo-rithm fails.Discrete Optimization,1(2):121–127,November2004.
Ricardo J Caballero and Arvind Krishnamurthy.Collective risk management in aflight to quality episode.Journal of Finance,63(5):2195–2229,October 2008.
P´e ter Cs´o ka,P.Jean-Jacques Herings,and L´a szl´o´A.K´o czy.Coherent mea-sures of risk from a general equilibrium perspective.Journal of Banking and Finance,31(8):2517–2534,August2007.
Larry G.Epstein and Martin Schneider.Ambiguity and asset markets.Annual Review of Financial Economics,2:315–346,December2010.
Hans Kellerer,Ulrich Pferschy,and David Pisinger.Knapsack Problems. Springer-Verlag,2004.
Albert S.Kyle.Continuous auctions and insider trading.Econometrica,53(6): 1315–1335,November1985.
Albert S.Kyle.Informed speculation with imperfect competition.Review of Economic Studies,56(3):317–356,July1989.
Renata Mansini and Ulrich Pferschy.Securitization offinancial assets:Approxi-mation in theory and practice.Computational Optimization and Applications, 29(2):147–171,November2004.
3The SEC’s fraud charges against Goldman Sachs in April2010seem to be much more simply motivated.
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C.Rowat Risk dissertation topic Alexander J.McNeil,R¨u diger Frey,and Paul Embrechts.Quantitative Risk Management:Concepts,Techniques,and Tools.Princeton Series in Finance. Princeton University Press,2005.
Attilio Meucci.Risk and Asset Allocation.Springer Finance.Springer,2005. Attilio Meucci.Managing diversification.Risk,22(5):74–79,May2009.
Hyun Song Shin.Risk and liquidity.Clarendon Lectures in Finance.Oxford University Press,Oxford,2010.
Martin L.Weitzman.Subjective expectations and asset-return puzzles.Amer-ican Economic Review,97(4):1102–1130,September2007.
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