Asset Liability and Portfolio Management
Long/Short Strategies with Index Futures Portfolios
Diploma Thesis in "Mathematical Finance", Oxford (2006)
Long/short equity strategies are long known in the financial community.
This dissertation shows how to extend this concept to another financial
instrument class: stock index futures. It resumes briefly some proper-
ties of stock indices and index futures and defines the tradable portfolio.
Based on an intraday market data analysis, it shows that the Ornstein-
Uhlenbeck process is an appropriate model to describe the evolution of
such long/short futures portfolios. It also sketches a possible technical
design of a pairs trading tool. It presents some arguments how to pa-
rameterize it, and outlooks to some extensions of the strategy as cross
hedging for index options.
Universal portfolios
Master Thesis in "Mathematical Finance", Oxford (2004)
The starting point of our investigations is given by facts known from the literature.
The so-called best constant rebalanced portfolio strategy is often considered as a portfolio
strategy for long term multi-period investments. Since it is only computable in
hindsight, the universal portfolio strategy is chosen as a strategy to approximate its
wealth. This strategy possesses some surprising theoretical properties. Both strategies
depend only on the data of previous asset returns and do not depend on underlying
statistical assumptions. Our aim is "to value" the universal portfolio strategy.
To enlarge the known results that are based on the comparisons of universal portfolios
vs. best constant rebalanced strategies, some further suitable strategies should
be considered. The chosen strategies are very simple. On the one hand, we consider
uniformly chosen constant rebalanced portfolios. On the other hand, we take a look
at some portfolios chosen according to simple multi-period models which are based
on the well-known mean-variance approach for one-period investments. As for the
universal portfolio, there are no assumptions corresponding to the price processes.
Historical data are only used for very simple estimations of the parameters needed
for computing the simple strategies. The comparisons are done by some sort of worst
case analyses, i.e. we consider lower resp. upper bounds on the wealth obtained by
those strategies and we take a look at the so-called competitive ratio. Since the
method for valuation of the performance of investment strategies is usually not only
the worst market case, we use real market data for numerical experiments and finalize
our considerations with some numerical results based on different data sets.
Optimal Portfolios with Bounded Risks
Master Thesis in "Mathematical Finance", Oxford (2003)
Our focus in this thesis is on the portfolio selection of a trader subject to a risk limit
specified in terms of variance or Value-at-Risk (VaR).
First, we consider a Markowitz type portfolio problem founded on a mean-variance
analysis. Due to the prohibition of short selling, we employ a simplex based algorithm,
namely Wolfe's method, to compute for any feasible level of expected return the
portfolio of minimum risk.
Next, we present a generalisation of the mean-variance analysis to continuoustime.
The method consists of maximising expected terminal wealth using the martingale
approach. All formulas needed to implement the method are derived and
a comparison with the traditional portfolio selection as introduced by Markowitz is
provided.
We then consider a continuous-time model of optimal portfolio choice subject to
VaR limits. In a Black-Scholes setting the stochastic control approach is employed to
maximise the expected terminal wealth under the constraint of an upper bound for
the VaR. As an application, we compare the risk exposure of a trader subject to the
VaR limit with that of an unconstraint one.
Finally, we generalise the previous optimisation problem to a Black-Scholes setting
with jumps. All formulas needed to implement the method are derived. Since an
analytical solution is not available, we provide a finite-differences based algorithm to
compute the quantities of interest.
Portfolio Theory and Market Fluctuations
Master Thesis in "Mathematical Finance", Oxford (2002)
Evaluating Hedging Strategies in Asset Liability Management
Diploma Thesis in "Mathematical Finance", Oxford (2000)
The following thesis is a literature review on evaluating interest rate hedging strategies in asset liability management (ALM). ALM manages the interest rate risk at the total bank level and is long-term oriented.
The thesis outlines the framework for evaluating hedging strategies by the resulting risk/return profile of the bank. The steps involved are defining the target account and the time horizon of interest, identifying the contributing cashflows and linking them to the relevant interest rates, simulating interest rate paths and valuing the target account for each of them, calculating the expected target account value and its risk and summarizing the risk/return profile by some risk-adjusted return measure.
Emphasis is put on long-term simulations of interest rates. The problem with simulating an interest rate model over long time is that a small error in the drift leads to a big error in the final interest rate probability distribution. We therefore look into an alternative approach proposed in the literature, for which the final distribution (or several distributions at several time horizons simultaneously) is imposed and interest rate paths are simulated by Brownian Bridges.
