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|  | Aigner, P., S. Albrecht, G. Beyschlag, T. Friederich, M. Kalepky und R. Zagst |
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What Drives PE? Analyses of Success Factors for Private Equity Funds
Journal of Private Equity, Vol. 11, No. 4, 63-85
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| Kurzbeschreibung: |
This paper identifies key performance indicators for private equity funds by scrutinizing a data set of 358 funds holding an aggregate number of 7511 portfolio companies.
First, we show a high persistence of the top performing private equity fund managers.
Then, we explore the influence on fund performance measured by the internal rate of return and the public market equivalent of the following variables:
the stock market return, the GDP growth and the average interest rate all during a fund’s lifetime and in its vintage year,
the experience of the fund manager, the percentage of buyout deals and
the diversification across portfolio companies, industry sectors, regions and financing stages.
Furthermore, we demonstrate that successful general partners venture riskier investments than their less fortunate colleagues.
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| | Aigner, P., G. Beyschlag, T. Friederich, M. Kalepky und R. Zagst |
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Optimal Risk-Return Profiles for Portfolios including Stocks, Bonds, and Listed Private Equity
Submitted for publication
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| Kurzbeschreibung: |
Listed private equity (LPE) provides a liquid means for investors to consider
private equity in their portfolios. This paper presents a Markov-Switching
model which is able to capture the characteristics of the asset classes bonds,
stocks and LPE, and simulate multivariate return paths for this set of assets.
This study is based on return time series of the JP Morgan Global Govern-
ment Bond Index, the MSCI World Index, and the Listed Private Equity
Index LPX 50. Applying several risk measures and optimization frameworks
the question of the optimal fraction for an LPE investment is scrutinized.
Depending on the risk aversion of the investor, the optimal fraction of an
LPE investment in this study ranges between 0% for a very risk-averse in-
vestor, 6.2% - 15.2% for a moderately risky investor and 14.8% - 33.4% for
an investor willing to take high risks.enture riskier investments than their less fortunate colleagues.
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| | Antes, S., M. Ilg, B. Schmid und R. Zagst |
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Empirical Evaluation of Hybrid Defaultable Bond Pricing Models
Applied Mathematical Finance, Vol. 15, No. 3, 219-249
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| Kurzbeschreibung: |
We present a four-factor model (the extended model of Schmid and Zagst) for pricing credit risk related
instruments such as defaultable bonds or credit derivatives. It is a consequent advancement of our prior threefactor
model (see Schmid & Zagst (2000)). In addition to a firm-specific credit risk factor we include a new
systematic risk factor in form of the GDP growth rates. We set this new model in the context of other hybrid
defaultable bond pricing models and empirically compare it to specific
representatives. In analogy to Krishnan, Ritchken & Thomson (2005) we find that a model only based on firmspecific
variables is unable to capture changes in credit spreads completely. However, consistent to Krishnan et
al. (2005) we show that in our model market variables such as GDP growth rates, non-defaultable interest rates
and firm-specific variables together significantly influence credit spread levels and changes.
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| | Bernhardt, E., A. Kolbe und R. Zagst |
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Optimal Portfolios with Mortgage-Backed Securities
Submitted for Publication
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Preprint.pdf |
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| Kurzbeschreibung: |
In this paper we consider portfolio optimisation problems based on
simulated scenarios and extend their usual application by including
prepayment-sensitive fixed-rate agency mortgage-backed securities into
the universe of available assets. This has become feasible due to recent
closed-form approximation approaches for the pricing of MBS, which
have long been neglected in modern portfolio optimisation applications
due to the computational burden. In an empirical case study we show
that an optimal asset allocation strategy with MBS is indeed able to
substantially outperform strategies based on stocks and regular bonds
only.
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| | Cerny, A. und J. Kallsen |
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A Counterexample Concerning the Variance-Optimal Martingale Measure
Mathematical Finance, Vol. 18, 305-316
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| Kurzbeschreibung: |
The present note addresses an open question concerning a sufficient characterization
of the variance-optimal martingale measure. Denote by S the discounted price
process of an asset and suppose that Q* is an equivalent martingale measure whose
density is a multiple of 1 - φ · S(T) for some S-integrable process φ. We show that Q*
does not necessarily coincide with the variance-optimal martingale measure, not even
if φ · S is a uniformly integrable Q*-martingale.
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| | Cerny, A. und J. Kallsen |
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Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation
Mathematical Finance, Vol. 18, 473-492
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| Kurzbeschreibung: |
This paper solves the mean variance hedging problem in
Heston's model with a stochastic opportunity set moving systematically
with the volatility of stock returns. We allow for correlation between
stock returns and their volatility (so-called leverage effect).
Our contribution is threefold: using a new concept of opportunity-neutral
measure we present a simplified strategy for computing a candidate solution
in the correlated case. We then go on to show that this
candidate generates the true variance-optimal martingale measure; this
step seems to be partially missing in the literature. Finally, we derive
formulas for the hedging strategy and the hedging error.
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| | Escobar, M., B. Götz, L. Seco und R. Zagst |
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Pricing of a CDO Option on Stochastically Correlated Underlyings
Forthcoming in Quantitative Finance
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| Kurzbeschreibung: |
In this paper, we propose a method to price Collateralized debt obligations
(CDO) within Merton’s structural model on underlyings with
a stochastic mean-reverting covariance dependence. There are two key
elements in our development, first we reduce dimensionality and complexity
using principal component analysis on the assets’ covariance
matrix. Second, we approximate this continuous multidimensional
structure using a tree method. Trinomial-tree models can be developed
for both the principal components and the eigenvalues assuming
the eigenvectors constant over time and the eigenvalues stochastic.
Our method allows us to compute the joint default probabilities for k
defaults of stochastically correlated underlyings and the value of CDOs
in a fast manner, without having lost much accuracy. Furthermore we
provide a method based on moments to estimate the parameters of
the model.
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| | Höcht, S., K.H. Ng, C. Roesch und R. Zagst |
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Asset Liability Managment in Financial Planning
The Journal of Wealth Management, Vol.11, No. 2, 2008, 29-46.
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| Kurzbeschreibung: |
In this work we study several models that manage the asset and liability needs of an individual investor
in an integrated fashion. The models are tested using typical assets of household portfolios including real
estate for both, the case of stochastic and deterministic liabilities. Most of the investment models suggest
to heavily invest in real estate which is conforming with empirical research on the composition on household
portfolios. The performance results indicate that the models perform better for stochastic liabilities due to
the fact that assets and liabilities share common risk factors.
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| | Höcht, S., K.H. Ng, J. Wolf and R. Zagst |
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Optimal Portfolio Allocation with Asian Hedge Funds and Asian Reits
International Journal of Service Sciences, Vol. 1, No.1, 2008, 36-68.
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Preprint.pdf |
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| Kurzbeschreibung: |
During the past years, the institutional interest in investments into hedge funds and
real estate investment trusts has grown considerably. In this paper the benefits of investing in
these asset classes are analyzed by applying models that recognize higher-order moments or
the whole return distribution like the power-utility, Omega, and Score-value model. Trying to
obtain more general results than those we can find from historical data only, we modelled the
asset returns by Markov switching processes and did a Monte Carlo study. Within this design
we analyzed the optimal allocations to hedge funds and REITs statically and with monthly
reallocations based on data from Asian markets. Our main findings are that in the static case
the utility model and the Score model are dominant, whereas the mean-variance model
appears to be the model of first choice in the dynamic case. In both settings hedge funds are
the most dominant asset of the optimal portfolios. REITs are mainly used for diversification
and added at comparably lower rates.
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| | Hofert, M. und M. Scherer |
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CDO pricing with nested Archimedean copulas
Forthcoming in Quantitative Finance
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Preprint.pdf |
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| Kurzbeschreibung: |
Companies in the same industry sector are usually stronger correlated than firms in
different sectors, as they are similarly affected by macroeconomic effects, political
decisions, and consumer trends. In spite of many stock return models taking account
of this fact there are only a few credit default models taking it into consideration.
In this paper we present a default model based on nested Archimedean copulas
which is able to capture hierarchical dependence structures among the obligors in
a credit portfolio. Nested Archimedean copulas have a surprisingly simple and
intuitive interpretation. The dependence among all companies in the same sector
is described by an inner copula; the sectors are then coupled via an outer copula.
Consequently, our model implies a larger default correlation for companies in the
same industry sector compared to companies in different sectors. A calibration to
CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate
the fitting capability of our model. This portfolio consists of CDS on 125 companies
from six different industry sectors. It is therefore an excellent portfolio to compare
our generalized model to a traditional copula model of the same family, which does
not account for different sectors.
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| | Kallsen, J. |
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Option Pricing
In: T. Andersen, R. Davis, J. Kreiß und T. Mikosch, editors, Handbook of Financial Time Series. Springer, Berlin, 2008. To appear
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| Kurzbeschreibung: |
This paper reviews basic concepts of derivative pricing in finanicial
mathematics. We distinguish market prices and individual values of a potential
seller. We focus mainly on arbitrage theory. In addition, two hedging-based valuation
approaches are discussed. The first relies on quadratic hedging whereas the second
involves a first-order approximation to utility indifference prices.
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| | Kallsen, J. und J. Muhle-Karbe |
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Exponentially affine martingales, affine measure changes and exponential moments of affine processes
Forthcoming in Stochastic Processes and their Applications
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Preprint.pdf |
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| Kurzbeschreibung: |
We consider local martingales of exponential form M = E(X) or exp (X) where X
denotes one component of a multivariate affine process. We give a weak sufficient criterion
for M to be a true martingale. As a first application, we derive a simple sufficient
condition for absolute continuity of the laws of two given affine processes. As a second
application, we study whether the exponential moments of an affine process solve a
generalized Riccati equation.
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| | Kallsen, J. und J. Muhle-Karbe |
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On Using Shadow Prices in Portfolio Optimization with Transaction Costs
Forthcoming in The Annals of Applied Probability
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Preprint.pdf |
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| Kurzbeschreibung: |
In frictionless markets, utility maximization problems are typically solved either by
stochastic control or by martingale methods. Beginning with the seminal paper of Davis
and Norman, stochastic control theory has been used to solve various problems of
this type in the presence of proportional transaction costs. Martingale methods, on the
other hand, have so far only been used to derive general structural results. These apply
the duality theory for frictionless markets typically to a fictious shadow price process
lying within the bid-ask bounds of the real price process.
In this paper we show that this dual approach can actually be used for both deriving
a candidate solution and verification in Merton’s problem with logarithmic utility and
proportional transaction costs. In particular, the shadow price process is determined
explicitly.
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| | Kallsen, J. und J. Muhle-Karbe |
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Utility maximization in affine stochastic volatility models
Forthcoming in The International Journal of Theoretical and Applied Finance
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Preprint.pdf |
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| Kurzbeschreibung: |
We consider the classical problem of maximizing expected utility from terminal
wealth. With the help of a martingale criterion explicit solutions are derived for power
utility in a number of affine stochastic volatility models.
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| | Kallsen, J. und B. Vesenmayer |
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COGARCH as a Continuous-Time Limit of GARCH(1,1)
Stochastic Processes and their Applications, Vol. 119, 74-98
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| Kurzbeschreibung: |
COGARCH is an extension of the GARCH time series concept to continuous time,
which has been suggested by Klüppelberg, Lindner, Maller (2004). We show that any
COGARCH process can be represented as the limit in law of a sequence of GARCH(1,1)
processes. As a by-product we derive the infinitesimal generator of the bivariate Markov
process representation of COGARCH.
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| | Kolbe, A. und R. Zagst |
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A Hybrid-Form Model for the Prepayment-Risk-Neutral Valuation of Mortgage-Backed Securities
International Journal of Theoretical and Applied Finance, Vol. 11, Issue 6 (Sept. 2008), p. 635-656.
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| Kurzbeschreibung: |
In this paper we present a prepayment-risk-neutral valuation model for fixed-rate Mortgage-Backed Securities.
Our model is based on intensity models as used in credit-risk modelling and extends existing models for
individual mortgage contracts in a proportional hazard framework. The general economic environment
is explicitly accounted for in the prepayment process by an additional factor which we fit to the quarterly
GDP growth rate in the US. In our risk-neutral setting we account for both the fears of refinancing
understatement and turnover overstatement which sometimes result in higher option-adjusted spreads (OAS)
for premiums and discounts respectively. We apply our prepayment-risk-neutral pricing approach to a sample of
generic 30yr GNMA MBS pass-throughs from 1996 to 2006. Our empirical results indicate that the
GDP growth factor adds explanatory power to the model.
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| | Kraus, J. und R. Zagst |
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Stochastic Dominance of Portfolio Insurance Strategies - OBPI versus CPPI
Submitted for publication
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Preprint.pdf |
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| Kurzbeschreibung: |
The purpose of this article is to analyze and compare two standard portfolio insurance methods:
Option-based Portfolio Insurance (OBPI) and Constant Proportion Portfolio Insurance (CPPI). Various stochastic dominance
criteria up to third order are considered. We derive parameter conditions implying the second- and third-order stochastic
dominance of the CPPI strategy. In particular, restrictions on the CPPI multiplier resulting from the spread between the
(usually higher) implied volatility and the empirical volatility are analyzed.
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| | Poeschik, M. und R. Zagst |
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Inverse Portfolio Optimization under Constraints
The Journal of Asset Management, Vol. 9, 239-253
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| Kurzbeschreibung: |
The purpose of this paper is to present results on inverse optimization
in the case of portfolios that have been optimized under constraints. Inverse
optimization yields implied views that represent investors’ expectations
on market performance. While literature mainly considers the unconstrained
case, we will focus on views that can be derived from constrained portfolios.
The implied views are derived in the form of spreads representing the loss of
explanatory power with an increasing number of constraints. Applying the
Black Litterman model allows the incorporation of the derived views as an
additional source of information within the further asset allocation process.
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| | Scherer, M. und R. Zagst |
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Modeling and pricing credit derivatives
Submitted for publication
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| Kurzbeschreibung: |
Credit derivatives often show an appealing risk-return profile for
investors. They allow for an enhancement of portfolio returns, but also offer
high potential for risk diversification, due to the correlation structure of
their returns to those of traditional asset classes. Beside corporate bonds, we
therefore review popular credit derivatives and present a mathematical definition
of their payoff structures. To actually price credit derivatives, we discuss
the most important models and theoretical developments of the past years.
Structural-default models assume that the dynamics of the firm’s asset value
over time can be described as a stochastic process and that the defaultable
security can be regarded as a contingent claim on this value. Intensity-based
models do not consider the relation between default and asset value in an
explicit way. They rather specify the default process exogenously and model
default as the stopping time of some given hazard-rate process. While reduced-form
models have attractive properties, their main drawback is the missing
link between economic fundamentals and corporate defaults. Hybrid models
try to overcome this shortfall and combine the advantages of structural and
intensity-based models. Correlated changes in revenues and costs of different
companies usually influence the default probability of these firms. We will thus
present different approaches for the modeling of joint defaults and give some
algorithms to show how these approaches can be implemented for the pricing
of portfolio-credit derivatives.
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| | Scheuenstuhl, G. und R. Zagst |
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Integrated Portfolio Management with Options
European Journal of Operations Research, 185, 1477-1500
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| Kurzbeschreibung: |
In this paper we examine the problem of managing portfolios consisting of both, stocks and options. For
the simultaneous optimization of stock and option positions we base our analysis on the generally accepted
mean–variance framework. First, we analyze the effects of options on the mean–variance efficient frontier if they
are considered as separate investment alternatives. Due to the resulting asymmetric portfolio return distribution
mean–variance analysis will be not sufficient to identify optimal optioned portfolios. Additional investor
preferences which are expressed in terms of shortfall constraints allow a more detailed portfolio specification.
Under a mean–variance and shortfall preference structure we then derive optioned portfolios with a maximum
expected return. To circumvent the technical optimization problems arising from stochastic constraints we use an
approximation of the return distribution and develop economically meaningful conditions under which the complex
optimization problem can be transformed into a linear problem being comparably easy to solve. Empirical results
based on both, empirical market data and Monte Carlo simulations, illustrate the portfolio optimization procedure
with options.
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| | Schmitt, C. und R. Zagst |
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VaR and Risk Measures
In: Melnick E. und B. Everitt (Eds), Encyclopedia of Quantitative Risk Assessment and Analysis, 1823-1830, John Wiley, Chichester, UK
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| Kurzbeschreibung: |
In this article, we present different ways of measuring and quantifying risk. We discuss the theoretical
background of several risk measures and illustrate their potentials and limitations. Giving a historical overview, we
start with the Variance and Lower Partial Moments and present the concepts of Shortfall Probability and Expected
Shortfall. The main focus of this article is the Value at Risk, one of the most important risk measures in the
financial services industry. We analyze different calculation methods which use historical data or simulations.
Finally, we discuss the concept of Coherence which is a set of requirements a suitable risk measure should meet.
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| | Schöttle, K., R. Werner und R. Zagst |
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Comparison and robustification of Bayes and Black-Litterman models
Submitted for publication
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| Kurzbeschreibung: |
For determining an optimal portfolio allocation, parameters representing
the underlying market – characterized by expected asset returns and the covariance
matrix – are needed. Traditionally, these point estimates for the parameters are obtained
from historical data samples, but as experts often have strong opinions about
(some of) these values, approaches to combine sample information and experts’ views
are sought for. The focus of this paper is on the two most popular of these frameworks
– the Black-Litterman model and the Bayes approach. We will prove that – from the
point of traditional portfolio optimization – the Black-Litterman is just a special case of
the Bayes approach. In contrast to this, we will show that the extensions of both models
to the robust portfolio framework yield two rather different robustified optimization
problems.
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