Kemkhadze, Nato (2004) Information and optimisation in investment and risk measurement. PhD thesis, University of Warwick.

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Abstract

The thesis explores applications of optimisation in investment management and risk
measurement. In investment management the information issues are largely concerned
with generating optimal forecasts. It is difficult to get inputs that have the properties
they are supposed to have. Thus optimisation is prone to 'Garbage In, Garbage Out', that
leads to substantial biases in portfolio selection, unless forecasts are adjusted suitably
for estimation error. We consider three case studies where we investigate the impact of
forecast error on portfolio performance and examine ways of adjusting for resulting bias.
Treynor and Black (1973) first tried to make the best possible use of the information
provided by security analysis based on Markovitz (1952) portfolio selection. They
established a relationship between the correlation of forecasts, the number of independent
securities available and the Sharpe ratio which can be obtained. Their analysis was based
on the assumption that the correlation between the forecasts and outcomes is known precisely.
In practice, given the low levels of correlation possible, an investor may believe
himself to have a different degree of correlation from what he actually has. Using two
different metrics we explore how the portfolio performance depends on both the anticipated
and realised correlation when these differ. One measure, the Sharpe ratio, captures
the efficiency loss, attributed to the change in reward for risk. The other measure, the
Generalised Sharpe Ratio (GSR), introduced by Hodges (1997), quantifies the reduction
in the welfare of a particular investor due to adopting an inappropriate risk profile. We
show that these two metrics, the Sharpe ratio and GSR, complement each other and in
combination provide a fair ranking of existing investment opportunities.
Using Bayesian adjustment is a popular way of dealing with estimation error in portfolio
selection. In a Bayesian implementation, we study how to use non-sample information
to infer optimal scaling of unknown forecasts of asset returns in the presence of uncertainty
about the quality of our information, and how the efficient use of information affects portfolio
decision. Optimal portfolios, derived under full use of information, differ strikingly
from those derived from the sample information only; the latter, unlike the former, are
highly affected by estimation error and favour several (up to ten) times larger holdings.
The impact of estimation error in a dynamic setting is particularly severe because of the
complexity of the setting in which it is necessary to have time varying forecasts. We take
Brennan, Schwartz and Lagnado's structure (1997) as a specific illustration of a generic
problem and investigate the bias in long-term portfolio selection models that comes from
optimisation with (unadjusted) parameters estimated from historical data. Using a Monte
Carlo simulation analysis, we quantify the degree of bias in the optimisation approach of
Brennan, Schwartz and Lagnado. We find that estimated parameters make an investor
believe in investment opportunities five times larger than they actually are. Also a mild real
time-variation in opportunities inflates wildly when measured with estimated parameters.
In the latter part of the thesis we look at slightly less straightforward optimisation
applications in risk measurement, which arise in reporting risk. We ask, what is the most
efficient way of complying with the rules? In other words, we investigate how to report
the smallest exposure within a rule. For this purpose we develop two optimal efficient
algorithms that calculate the minimal amount of the position risk required, to cover a
firm's open positions and obligations, as required by respective rules in the FSA (Financial
Securities Association) Handbook. Both algorithms lead to interesting generalisations.

Item Type:	Thesis (PhD)
Subjects:	H Social Sciences > HF Commerce H Social Sciences > HG Finance
Library of Congress Subject Headings (LCSH):	Investment analysis, Portfolio management , Mathematical optimization, Bayesian statistical decision theory, Financial risk management
Official Date:	April 2004
Dates:	Date Event April 2004 Submitted
Institution:	University of Warwick
Theses Department:	Warwick Business School
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hodges, Stewart D. ; Podinovski, Victor V.
Sponsors:	Overseas Research Students Fees Support Scheme ; University of Warwick
Extent:	ix, 223 leaves : illustrations
Language:	eng

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