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4,000 |
Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios
|
q-fin.PM
|
Markowitz (1952, 1959) laid down the ground-breaking work on the
mean-variance analysis. Under his framework, the theoretical optimal allocation
vector can be very different from the estimated one for large portfolios due to
the intrinsic difficulty of estimating a vast covariance matrix and return
vector. This can result in adverse performance in portfolio selected based on
empirical data due to the accumulation of estimation errors. We address this
problem by introducing the gross-exposure constrained mean-variance portfolio
selection. We show that with gross-exposure constraint the theoretical optimal
portfolios have similar performance to the empirically selected ones based on
estimated covariance matrices and there is no error accumulation effect from
estimation of vast covariance matrices. This gives theoretical justification to
the empirical results in Jagannathan and Ma (2003). We also show that the
no-short-sale portfolio is not diversified enough and can be improved by
allowing some short positions. As the constraint on short sales relaxes, the
number of selected assets varies from a small number to the total number of
stocks, when tracking portfolios or selecting assets. This achieves the optimal
sparse portfolio selection, which has close performance to the theoretical
optimal one. Among 1000 stocks, for example, we are able to identify all
optimal subsets of portfolios of different sizes, their associated allocation
vectors, and their estimated risks. The utility of our new approach is
illustrated by simulation and empirical studies on the 100 Fama-French
industrial portfolios and the 400 stocks randomly selected from Russell 3000.
|
finance
|
4,001 |
Evaluating the performance of adapting trading strategies with different memory lengths
|
q-fin.PM
|
We propose a prediction model based on the minority game in which traders
continuously evaluate a complete set of trading strategies with different
memory lengths using the strategies' past performance. Based on the chosen
trading strategy they determine their prediction of the movement for the
following time period of a single asset. We find empirically using stocks from
the S&P500 that our prediction model yields a high success rate of over 51.5%
and produces higher returns than a buy-and-hold strategy. Even when taking into
account trading costs we find that using the predictions will generate superior
investment portfolios.
|
finance
|
4,002 |
Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes
|
q-fin.PM
|
In this paper, we study the Kelly criterion in the continuous time framework
building on the work of E.O. Thorp and others. The existence of an optimal
strategy is proven in a general setting and the corresponding optimal wealth
process is found. A simple formula is provided for calculating the optimal
portfolio for a set of price processes satisfying some simple conditions.
Properties of the optimal investment strategy for assets governed by multiple
Ornstein-Uhlenbeck processes are studied. The paper ends with a short
discussion of the implications of these ideas for financial markets.
|
finance
|
4,003 |
La prime de risque dans un cadre international : le risque de change est-il apprécié ?
|
q-fin.PM
|
In this article, we investigate whether exchange rate risk is priced. We use
a multivariate GARCH-in-Mean specification and test alternative conditional
international CAPM versions. Our results support strongly the international
asset-pricing model that includes exchange rate risk for both developed and
emerging stock markets. However, there are important time and cross-country
variations in the relative size and dynamics of different risk premia.
|
finance
|
4,004 |
Jump-Diffusion Risk-Sensitive Asset Management
|
q-fin.PM
|
This paper considers a portfolio optimization problem in which asset prices
are represented by SDEs driven by Brownian motion and a Poisson random measure,
with drifts that are functions of an auxiliary diffusion 'factor' process. The
criterion, following earlier work by Bielecki, Pliska, Nagai and others, is
risk-sensitive optimization (equivalent to maximizing the expected growth rate
subject to a constraint on variance.) By using a change of measure technique
introduced by Kuroda and Nagai we show that the problem reduces to solving a
certain stochastic control problem in the factor process, which has no jumps.
The main result of the paper is that the Hamilton-Jacobi-Bellman equation for
this problem has a classical solution. The proof uses Bellman's "policy
improvement" method together with results on linear parabolic PDEs due to
Ladyzhenskaya et al.
|
finance
|
4,005 |
Continuous-Time Markowitz's Model with Transaction Costs
|
q-fin.PM
|
A continuous-time Markowitz's mean-variance portfolio selection problem is
studied in a market with one stock, one bond, and proportional transaction
costs. This is a singular stochastic control problem,inherently in a finite
time horizon. With a series of transformations, the problem is turned into a
so-called double obstacle problem, a well studied problem in physics and
partial differential equation literature, featuring two time-varying free
boundaries. The two boundaries, which define the buy, sell, and no-trade
regions, are proved to be smooth in time. This in turn characterizes the
optimal strategy, via a Skorokhod problem, as one that tries to keep a certain
adjusted bond-stock position within the no-trade region. Several features of
the optimal strategy are revealed that are remarkably different from its
no-transaction-cost counterpart. It is shown that there exists a critical
length in time, which is dependent on the stock excess return as well as the
transaction fees but independent of the investment target and the stock
volatility, so that an expected terminal return may not be achievable if the
planning horizon is shorter than that critical length (while in the absence of
transaction costs any expected return can be reached in an arbitrary period of
time). It is further demonstrated that anyone following the optimal strategy
should not buy the stock beyond the point when the time to maturity is shorter
than the aforementioned critical length. Moreover, the investor would be less
likely to buy the stock and more likely to sell the stock when the maturity
date is getting closer. These features, while consistent with the widely
accepted investment wisdom, suggest that the planning horizon is an integral
part of the investment opportunities.
|
finance
|
4,006 |
The premium of dynamic trading
|
q-fin.PM
|
It is well established that in a market with inclusion of a risk-free asset
the single-period mean-variance efficient frontier is a straight line tangent
to the risky region, a fact that is the very foundation of the classical CAPM.
In this paper, it is shown that in a continuous-time market where the risky
prices are described by Ito's processes and the investment opportunity set is
deterministic (albeit time-varying), any efficient portfolio must involve
allocation to the risk-free asset at any time. As a result, the dynamic
mean-variance efficient frontier, though still a straight line, is strictly
above the entire risky region. This in turn suggests a positive premium, in
terms of the Sharpe ratio of the efficient frontier, arising from the dynamic
trading. Another implication is that the inclusion of a risk-free asset boosts
the Sharpe ratio of the efficient frontier, which again contrasts sharply with
the single-period case.
|
finance
|
4,007 |
Global risk minimization in financial markets
|
q-fin.PM
|
Recurring international financial crises have adverse socioeconomic effects
and demand novel regulatory instruments or strategies for risk management and
market stabilization. However, the complex web of market interactions often
impedes rational decisions that would absolutely minimize the risk. Here we
show that, for any given expected return, investors can overcome this
complexity and globally minimize their financial risk in portfolio selection
models, which is mathematically equivalent to computing the ground state of
spin glass models in physics, provided the margin requirement remains below a
critical, empirically measurable value. For markets with centrally regulated
margin requirements, this result suggests a potentially stabilizing
intervention strategy.
|
finance
|
4,008 |
Optimal investment with inside information and parameter uncertainty
|
q-fin.PM
|
This paper has been withdrawn by the authors pending corrections.
|
finance
|
4,009 |
Mutual Fund Theorem for continuous time markets with random coefficients
|
q-fin.PM
|
We study the optimal investment problem for a continuous time incomplete
market model such that the risk-free rate, the appreciation rates and the
volatility of the stocks are all random; they are assumed to be independent
from the driving Brownian motion, and they are supposed to be currently
observable. It is shown that some weakened version of Mutual Fund Theorem holds
for this market for general class of utilities; more precisely, it is shown
that the supremum of expected utilities can be achieved on a sequence of
strategies with a certain distribution of risky assets that does not depend on
risk preferences described by different utilities.
|
finance
|
4,010 |
Existence of Shadow Prices in Finite Probability Spaces
|
q-fin.PM
|
A shadow price is a process lying within the bid/ask prices of a market with
proportional transaction costs, such that maximizing expected utility from
consumption in the frictionless market with this price process leads to the
same maximal utility as in the original market with transaction costs. For
finite probability spaces, this note provides an elementary proof for the
existence of such a shadow price.
|
finance
|
4,011 |
Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model
|
q-fin.PM
|
This paper considers a portfolio optimization problem in which asset prices
are represented by SDEs driven by Brownian motion and a Poisson random measure,
with drifts that are functions of an auxiliary diffusion factor process. The
criterion, following earlier work by Bielecki, Pliska, Nagai and others, is
risk-sensitive optimization (equivalent to maximizing the expected growth rate
subject to a constraint on variance.) By using a change of measure technique
introduced by Kuroda and Nagai we show that the problem reduces to solving a
certain stochastic control problem in the factor process, which has no jumps.
The main result of the paper is to show that the risk-sensitive jump diffusion
problem can be fully characterized in terms of a parabolic
Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a
classical C^{1,2} solution.
|
finance
|
4,012 |
Rentes en cours de service : un nouveau critère d'allocation d'actif
|
q-fin.PM
|
The aim of this paper is to compare two asset allocation methods for a
pension scheme during the decumulation phase in the simplified portfolio
selection between a risky asset following a geometric Brownian motion and a
riskless asset. The two asset allocation criteria are the ruin probability of
the insurance company and the optimization of the economic capital. We first
solve the asset allocation problem with deterministic pension payments then
with stochastic mortality risk. We analyze the part of mortality risk in the
global risk of the company. Then we show the impact of the indexation of the
pensions to the inflation on the asset allocation.
|
finance
|
4,013 |
Risk Sensitive Investment Management with Affine Processes: a Viscosity Approach
|
q-fin.PM
|
In this paper, we extend the jump-diffusion model proposed by Davis and Lleo
to include jumps in asset prices as well as valuation factors. The criterion,
following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive
optimization (equivalent to maximizing the expected growth rate subject to a
constraint on variance.) In this setting, the Hamilton- Jacobi-Bellman equation
is a partial integro-differential PDE. The main result of the paper is to show
that the value function of the control problem is the unique viscosity solution
of the Hamilton-Jacobi-Bellman equation.
|
finance
|
4,014 |
Utility Maximization of an Indivisible Market with Transaction Costs
|
q-fin.PM
|
This work takes up the challenges of utility maximization problem when the
market is indivisible and the transaction costs are included. First there is a
so-called solvency region given by the minimum margin requirement in the
problem formulation. Then the associated utility maximization is formulated as
an optimal switching problem. The diffusion turns out to be degenerate and the
boundary of domain is an unbounded set. One no longer has the continuity of the
value function without posing further conditions due to the degeneracy and the
dependence of the random terminal time on the initial data. This paper provides
sufficient conditions under which the continuity of the value function is
obtained. The essence of our approach is to find a sequence of continuous
functions locally uniformly converging to the desired value function. Thanks to
continuity, the value function can be characterized by using the notion of
viscosity solution of certain quasi-variational inequality.
|
finance
|
4,015 |
Horizon dependence of utility optimizers in incomplete models
|
q-fin.PM
|
This paper studies the utility maximization problem with changing time
horizons in the incomplete Brownian setting. We first show that the primal
value function and the optimal terminal wealth are continuous with respect to
the time horizon $T$. Secondly, we exemplify that the expected utility stemming
from applying the $T$-horizon optimizer on a shorter time horizon $S$, $S < T$,
may not converge as $S\uparrow T$ to the $T$-horizon value. Finally, we provide
necessary and sufficient conditions preventing the existence of this
phenomenon.
|
finance
|
4,016 |
Transaction fees and optimal rebalancing in the growth-optimal portfolio
|
q-fin.PM
|
The growth-optimal portfolio optimization strategy pioneered by Kelly is
based on constant portfolio rebalancing which makes it sensitive to transaction
fees. We examine the effect of fees on an example of a risky asset with a
binary return distribution and show that the fees may give rise to an optimal
period of portfolio rebalancing. The optimal period is found analytically in
the case of lognormal returns. This result is consequently generalized and
numerically verified for broad return distributions and returns generated by a
GARCH process. Finally we study the case when investment is rebalanced only
partially and show that this strategy can improve the investment long-term
growth rate more than optimization of the rebalancing period.
|
finance
|
4,017 |
Fully Flexible Views: Theory and Practice
|
q-fin.PM
|
We propose a unified methodology to input non-linear views from any number of
users in fully general non-normal markets, and perform, among others,
stress-testing, scenario analysis, and ranking allocation. We walk the reader
through the theory and we detail an extremely efficient algorithm to easily
implement this methodology under fully general assumptions. As it turns out, no
repricing is ever necessary, hence the methodology can be readily applied to
books with complex derivatives. We also present an analytical solution, useful
for benchmarking, which per se generalizes notable previous results. Code
illustrating this methodology in practice is available at
http://www.mathworks.com/matlabcentral/fileexchange/21307
|
finance
|
4,018 |
Utility theory front to back - inferring utility from agents' choices
|
q-fin.PM
|
We pursue an inverse approach to utility theory and consumption & investment
problems. Instead of specifying an agent's utility function and deriving her
actions, we assume we observe her actions (i.e. her consumption and investment
strategies) and ask if it is possible to derive a utility function for which
the observed behaviour is optimal. We work in continuous time both in a
deterministic and stochastic setting. In the deterministic setup, we find that
there are infinitely many utility functions generating a given consumption
pattern. In the stochastic setting of the Black-Scholes complete market it
turns out that the consumption and investment strategies have to satisfy a
consistency condition (PDE) if they are to come from a classical utility
maximisation problem. We show further that important characteristics of the
agent such as her attitude towards risk (e.g. DARA) can be deduced directly
from her consumption/investment choices.
|
finance
|
4,019 |
Measuring Portfolio Diversification
|
q-fin.PM
|
In the market place, diversification reduces risk and provides protection
against extreme events by ensuring that one is not overly exposed to individual
occurrences. We argue that diversification is best measured by characteristics
of the combined portfolio of assets and introduce a measure based on the
information entropy of the probability distribution for the final portfolio
asset value. For Gaussian assets the measure is a logarithmic function of the
variance and combining independent Gaussian assets of equal variance adds an
amount to the diversification. The advantages of this measure include that it
naturally extends to any type of distribution and that it takes all moments
into account. Furthermore, it can be used in cases of undefined weights
(zero-cost assets) or moments. We present examples which apply this measure to
derivative overlays.
|
finance
|
4,020 |
Hedging of Game Options With the Presence of Transaction Costs
|
q-fin.PM
|
We study the problem of super-replication for game options under proportional
transaction costs. We consider a multidimensional continuous time model, in
which the discounted stock price process satisfies the conditional full support
property. We show that the super-replication price is the cheapest cost of a
trivial super-replication strategy. This result is an extension of previous
papers (see [3] and [7]) which considered only European options. In these
papers the authors showed that with the presence of proportional transaction
costs the super--replication price of a European option is given in terms of
the concave envelope of the payoff function. In the present work we prove that
for game options the super-replication price is given by a game variant analog
of the standard concave envelope term. The treatment of game options is more
complicated and requires additional tools. We combine the theory of consistent
price systems together with the theory of extended weak convergence which was
developed in [1]. The second theory is essential in dealing with hedging which
involves stopping times, like in the case of game options.
|
finance
|
4,021 |
Notional portfolios and normalized linear returns
|
q-fin.PM
|
The vector of periodic, compound returns of a typical investment portfolio is
almost never a convex combination of the return vectors of the securities in
the portfolio. As a result the ex post version of Harry Markowitz's "standard
mean-variance portfolio selection model" does not apply to compound return
data. We propose using notional portfolios and normalized linear returns to
remedy this problem.
|
finance
|
4,022 |
Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching
|
q-fin.PM
|
We consider a portfolio optimization problem in a defaultable market with
finitely-many economical regimes, where the investor can dynamically allocate
her wealth among a defaultable bond, a stock, and a money market account. The
market coefficients are assumed to depend on the market regime in place, which
is modeled by a finite state continuous time Markov process. We rigorously
deduce the dynamics of the defaultable bond price process in terms of a Markov
modulated stochastic differential equation. Then, by separating the utility
maximization problem into the pre-default and post-default scenarios, we deduce
two coupled Hamilton-Jacobi-Bellman equations for the post and pre-default
optimal value functions and show a novel verification theorem for their
solutions. We obtain explicit optimal investment strategies and value functions
for an investor with logarithmic utility. We finish with an economic analysis
in the case of a market with two regimes and homogenous transition rates, and
show the impact of the default intensities and loss rates on the optimal
strategies and value functions.
|
finance
|
4,023 |
Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption
|
q-fin.PM
|
We consider a problem of optimal investment with intermediate consumption in
the framework of an incomplete semimartingale model of a financial market. We
show that a necessary and sufficient condition for the validity of key
assertions of the theory is that the value functions of the primal and dual
problems are finite
|
finance
|
4,024 |
Constructing the Best Trading Strategy: A New General Framework
|
q-fin.PM
|
We introduce a new general framework for constructing the best trading
strategy for a given historical indicator. We construct the unique trading
strategy with the highest expected return. This optimal strategy may be
implemented directly, or its expected return may be used as a benchmark to
evaluate how far away from the optimal other proposed strategies for the given
indicators are. Separately, we also construct the unique trading strategy with
the highest information ratio. In the normal case, when the traded security
return is near zero, and for reasonable correlations, the performance
differences are economically insignificant. However, when the correlation
approaches one, the trading strategy with the highest expected return
approaches its maximum information ratio of 1.32 while the trading strategy
with the highest information ratio goes to infinity.
|
finance
|
4,025 |
Diversification Return, Portfolio Rebalancing, and the Commodity Return Puzzle
|
q-fin.PM
|
Diversification return is an incremental return earned by a rebalanced
portfolio of assets. The diversification return of a rebalanced portfolio is
often incorrectly ascribed to a reduction in variance. We argue that the
underlying source of the diversification return is the rebalancing, which
forces the investor to sell assets that have appreciated in relative value and
buy assets that have declined in relative value, as measured by their weights
in the portfolio. In contrast, the incremental return of a buy-and-hold
portfolio is driven by the fact that the assets that perform the best become a
greater fraction of the portfolio. We use these results to resolve two puzzles
associated with the Gorton and Rouwenhorst index of commodity futures, and
thereby obtain a clear understanding of the source of the return of that index.
Diversification return can be a significant source of return for any rebalanced
portfolio of volatile assets.
|
finance
|
4,026 |
Optimal investment with intermediate consumption and random endowment
|
q-fin.PM
|
We consider a problem of optimal investment with intermediate consumption and
random endowment in an incomplete semimartingale model of a financial market.
We establish the key assertions of the utility maximization theory assuming
that both primal and dual value functions are finite in the interiors of their
domains as well as that random endowment at maturity can be dominated by the
terminal value of a self-financing wealth process. In order to facilitate
verification of these conditions, we present alternative, but equivalent
conditions, under which the conclusions of the theory hold.
|
finance
|
4,027 |
Suitability of using technical indicators as potential strategies within intelligent trading systems
|
q-fin.PM
|
The potential of machine learning to automate and control nonlinear, complex
systems is well established. These same techniques have always presented
potential for use in the investment arena, specifically for the managing of
equity portfolios. In this paper, the opportunity for such exploitation is
investigated through analysis of potential simple trading strategies that can
then be meshed together for the machine learning system to switch between. It
is the eligibility of these strategies that is being investigated in this
paper, rather than application. In order to accomplish this, the underlying
assumptions of each trading system are explored, and data is created in order
to evaluate the efficacy of these systems when trading on data with the
underlying patterns that they expect. The strategies are tested against a
buy-and-hold strategy to determine if the act of trading has actually produced
any worthwhile results, or are simply facets of the underlying prices. These
results are then used to produce targeted returns based upon either a desired
return or a desired risk, as both are required within the portfolio-management
industry. Results show a very viable opportunity for exploitation within the
aforementioned industry, with the Strategies performing well within their
narrow assumptions, and the intelligent system combining them to perform
without assumptions.
|
finance
|
4,028 |
Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model
|
q-fin.PM
|
A drawdown constraint forces the current wealth to remain above a given
function of its maximum to date. We consider the portfolio optimisation problem
of maximising the long-term growth rate of the expected utility of wealth
subject to a drawdown constraint, as in the original setup of Grossman and Zhou
(1993). We work in an abstract semimartingale financial market model with a
general class of utility functions and drawdown constraints. We solve the
problem by showing that it is in fact equivalent to an unconstrained problem
with a suitably modified utility function. Both the value function and the
optimal investment policy for the drawdown problem are given explicitly in
terms of their counterparts in the unconstrained problem.
|
finance
|
4,029 |
An analytical performance comparison of exchanged traded funds with index funds: 2002-2010
|
q-fin.PM
|
Exchange Traded Funds (ETFs) have been gaining increasing popularity in the
investment community as is evidenced by the high growth both in the number of
ETFs and their net assets since 2000. As ETFs are in nature similar to index
mutual funds, in this paper we examined if this growing demand for ETFs can be
explained through their outperformance as compared to index mutual funds. We
considered the population of all ETFs with inception dates prior to 2002 and
then for each ETF found all the passive index mutual funds that had the same
investment style as the selected ETF and had inception date prior to 2002.
Within each investment style we matched every ETF with all the passive index
funds in that investment style and compared the performances of the matched
pairs in terms of Sharp Ratios and risk adjusted buy and hold total returns for
the period 2002-2010. We then applied the Wilcoxon signed rank test to examine
if ETFs had better performances than index mutual funds during the sample
period. Out of the 230 paired matches of all the styles, ETFs outperformed
index mutual funds in 134 of the times in terms of Sharpe Ratio, however, the
test of the hypothesis showed no statistically significant difference between
ETFs and index funds performances in terms of Sharpe ratio. Out of the 230
paired matches of all the styles, ETFs outperformed index mutual funds in 125
of the times in terms of risk adjusted buy and hold total return, however, the
test of hypothesis showed no statistically significant difference between ETFs
and index funds performances in terms of risk adjusted buy and hold total
return. These findings indicate there is statistically no significant
difference between ETFs and passive index mutual funds performances at the fund
level and investors' choice between the two is related to product
characteristics and tax advantages.
|
finance
|
4,030 |
Multicurrency advisor based on the NSW model. Detailed description and perspectives
|
q-fin.PM
|
Flexible algorithm of multicurrency trade on Forex market has been built on
the grounds of non-linear stochastic wavelets (NSW) model. Probability of the
loss-free trade has been evaluated. Results of the algorithm's real-time
testing and issues of the algorithm's development are discussed.
|
finance
|
4,031 |
The Nature of Alpha
|
q-fin.PM
|
We suggest an empirical model of investment strategy returns which elucidates
the importance of non-Gaussian features, such as time-varying volatility,
asymmetry and fat tails, in explaining the level of expected returns.
Estimating the model on the (former) Lehman Brothers Hedge Fund Index data, we
demonstrate that the volatility compensation is a significant component of the
expected returns for most strategy styles, suggesting that many of these
strategies should be thought of as being `short vol'. We present some
fundamental and technical reasons why this should indeed be the case, and
suggest explanation for exception cases exhibiting `long vol' characteristics.
We conclude by drawing some lessons for hedge fund portfolio construction.
|
finance
|
4,032 |
On the game interpretation of a shadow price process in utility maximization problems under transaction costs
|
q-fin.PM
|
To any utility maximization problem under transaction costs one can assign a
frictionless model with a price process $S^*$, lying in the bid/ask price
interval $[\underline S, \bar{S}]$. Such process $S^*$ is called a \emph{shadow
price} if it provides the same optimal utility value as in the original model
with bid-ask spread.
We call $S^*$ a \emph{generalized shadow price} if the above property is true
for the \emph{relaxed} utility function in the frictionless model. This
relaxation is defined as the lower semicontinuous envelope of the original
utility, considered as a function on the set $[\underline S, \bar{S}]$,
equipped with some natural weak topology. We prove the existence of a
generalized shadow price under rather weak assumptions and mark its relation to
a saddle point of the trader/market zero-sum game, determined by the relaxed
utility function. The relation of the notion of a shadow price to its
generalization is illustrated by several examples. Also, we briefly discuss the
interpretation of shadow prices via Lagrange duality.
|
finance
|
4,033 |
Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs
|
q-fin.PM
|
We consider an agent who invests in a stock and a money market account with
the goal of maximizing the utility of his investment at the final time T in the
presence of a proportional transaction cost. The utility function considered is
power utility. We provide a heuristic and a rigorous derivation of the
asymptotic expansion of the value function in powers of transaction cost
parameter. We also obtain a "nearly optimal" strategy, whose utility
asymptotically matches the leading terms in the value function.
|
finance
|
4,034 |
Building portfolios of stocks in the São Paulo Stock Exchange using Random Matrix Theory
|
q-fin.PM
|
By using Random Matrix Theory, we build covariance matrices between stocks of
the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S\~ao Paulo) which
are cleaned of some of the noise due to the complex interactions between the
many stocks and the finiteness of available data. We also use a regression
model in order to remove the market effect due to the common movement of all
stocks. These two procedures are then used to build stock portfolios based on
Markowitz's theory, trying to obtain better predictions of future risk based on
past data. This is done for years of both low and high volatility of the
Brazilian stock market, from 2004 to 2010. The results show that the use of
regression to subtract the market effect on returns greatly increases the
accuracy of the prediction of risk, and that, although the cleaning of the
correlation matrix often leads to portfolios that better predict risks, in
periods of high volatility of the market this procedure may fail to do so.
|
finance
|
4,035 |
Optimal Trading with Linear Costs
|
q-fin.PM
|
We consider the problem of the optimal trading strategy in the presence of
linear costs, and with a strict cap on the allowed position in the market.
Using Bellman's backward recursion method, we show that the optimal strategy is
to switch between the maximum allowed long position and the maximum allowed
short position, whenever the predictor exceeds a threshold value, for which we
establish an exact equation. This equation can be solved explicitely in the
case of a discrete Ornstein-Uhlenbeck predictor. We discuss in detail the
dependence of this threshold value on the transaction costs. Finally, we
establish a strong connection between our problem and the case of a quadratic
risk penalty, where our threshold becomes the size of the optimal non-trading
band.
|
finance
|
4,036 |
Transaction Costs, Shadow Prices, and Duality in Discrete Time
|
q-fin.PM
|
For portfolio choice problems with proportional transaction costs, we discuss
whether or not there exists a "shadow price", i.e., a least favorable
frictionless market extension leading to the same optimal strategy and utility.
By means of an explicit counter-example, we show that shadow prices may fail
to exist even in seemingly perfectly benign situations, i.e., for a
log-investor trading in an arbitrage-free market with bounded prices and
arbitrarily small transaction costs.
We also clarify the connection between shadow prices and duality theory.
Whereas dual minimizers need not lead to shadow prices in the above "global"
sense, we show that they always correspond to a "local" version.
|
finance
|
4,037 |
Life Insurance Purchasing to Maximize Utility of Household Consumption
|
q-fin.PM
|
We determine the optimal amount of life insurance for a household of two wage
earners. We consider the simple case of exponential utility, thereby removing
wealth as a factor in buying life insurance, while retaining the relationship
among life insurance, income, and the probability of dying and thus losing that
income. For insurance purchased via a single premium or premium payable
continuously, we explicitly determine the optimal death benefit. We show that
if the premium is determined to target a specific probability of loss per
policy, then the rates of consumption are identical under single premium or
continuously payable premium. Thus, not only is equivalence of consumption
achieved for the households under the two premium schemes, it is also obtained
for the insurance company in the sense of equivalence of loss probabilities.
|
finance
|
4,038 |
Stability of the exponential utility maximization problem with respect to preferences
|
q-fin.PM
|
This paper studies stability of the exponential utility maximization when
there are small variations on agent's utility function. Two settings are
considered. First, in a general semimartingale model where random endowments
are present, a sequence of utilities defined on R converges to the exponential
utility. Under a uniform condition on their marginal utilities, convergence of
value functions, optimal payoffs and optimal investment strategies are
obtained, their rate of convergence are also determined. Stability of
utility-based pricing is studied as an application. Second, a sequence of
utilities defined on R_+ converges to the exponential utility after shifting
and scaling. Their associated optimal strategies, after appropriate scaling,
converge to the optimal strategy for the exponential hedging problem. This
complements Theorem 3.2 in \textit{M. Nutz, Probab. Theory Relat. Fields, 152,
2012}, which establishes the convergence for a sequence of power utilities.
|
finance
|
4,039 |
The Long Neglected Critically Leveraged Portfolio
|
q-fin.PM
|
We show that the efficient frontier for a portfolio in which short positions
precisely offset the long ones is composed of a pair of straight lines through
the origin of the risk-return plane. This unique but important case has been
overlooked because the original formulation of the mean-variance model by
Markowitz as well as all its subsequent elaborations have implicitly excluded
it by using portfolio weights rather than actual amounts allocated to
individual assets. We also elucidate the properties of portfolios where short
positions dominate the long ones, a case which has similarly been obscured by
the adoption of portfolio weights.
|
finance
|
4,040 |
Can Metropolitan Housing Risk be Diversified? A Cautionary Tale from the Recent Boom and Bust
|
q-fin.PM
|
Geographic diversification is fundamental to risk mitigation among investors
and insurers of housing, mortgages, and mortgage-related derivatives. To
characterize diversification potential, we provide estimates of integration,
spatial correlation, and contagion among US metropolitan housing markets.
Results reveal a high and increasing level of integration among US markets over
the decade of the 2000s, especially in California. We apply integration results
to assess the risk of alternative housing investment portfolios. Portfolio
simulation indicates reduced diversification potential and increased risk in
the wake of estimated increases in metropolitan housing market integration.
Research findings provide new insights regarding the synchronous
non-performance of geographically-disparate MBS investments during the late
2000s.
|
finance
|
4,041 |
Diffusion-based models for financial markets without martingale measures
|
q-fin.PM
|
We consider a general class of diffusion-based models and show that, even in
the absence of an Equivalent Local Martingale Measure, the financial market may
still be viable, in the sense that strong forms of arbitrage are excluded and
portfolio optimisation problems can be meaningfully solved. Relying partly on
the recent literature, we provide necessary and sufficient conditions for
market viability in terms of the market price of risk process and martingale
deflators. Regardless of the existence of a martingale measure, we show that
the financial market may still be complete and contingent claims can be valued
under the original (real-world) probability measure, provided we use as
numeraire the Growth-Optimal Portfolio.
|
finance
|
4,042 |
Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process
|
q-fin.PM
|
We consider the problem of optimizing the expected logarithmic utility of the
value of a portfolio in a binomial model with proportional transaction costs
with a long time horizon. By duality methods, we can find expressions for the
boundaries of the no-trade-region and the asymptotic optimal growth rate, which
can be made explicit for small transaction costs. Here we find that, contrary
to the classical results in continuous time, the size of the no-trade-region as
well as the asymptotic growth rate depend analytically on the level of
transaction costs, implying a linear first order effect of perturbations of
(small) transaction costs. We obtain the asymptotic expansion by an almost
explicit construction of the shadow price process.
|
finance
|
4,043 |
Maximising Survival, Growth, and Goal Reaching Under Borrowing Constraints
|
q-fin.PM
|
In this paper, we consider three problems related to survival, growth, and
goal reaching maximization of an investment portfolio with proportional net
cash flow. We solve the problems in a market constrained due to borrowing
prohibition. To solve the problems, we first construct an auxiliary market and
then apply the dynamic programming approach. Via our solutions, an alternative
approach is introduced in order to solve the problems defined under an
auxiliary market.
|
finance
|
4,044 |
Portfolio Choice in Markets with Contagion
|
q-fin.PM
|
We consider the problem of optimal investment and consumption in a class of
multidimensional jump-diffusion models in which asset prices are subject to
mutually exciting jump processes. This captures a type of contagion where each
downward jump in an asset's price results in increased likelihood of further
jumps, both in that asset and in the other assets. We solve in closed-form the
dynamic consumption-investment problem of a log-utility investor in such a
contagion model, prove a theorem verifying its optimality and discuss features
of the solution, including flight-to-quality. The exponential and power utility
investors are also considered: in these cases, the optimal strategy can be
characterized as a distortion of the strategy of a corresponding non-contagion
investor.
|
finance
|
4,045 |
The Merton Problem with a Drawdown Constraint on Consumption
|
q-fin.PM
|
In this paper, we work in the framework of the Merton problem but we impose a
drawdown constraint on the consumption process. This means that consumption can
never fall below a fixed proportion of the running maximum of past consumption.
In terms of economic motivation, this constraint represents a type of habit
formation where the investor is reluctant to let his standard of living fall
too far from the maximum standard achieved to date. We use techniques from
stochastic optimal control and duality theory to obtain our candidate value
function and optimal controls, which are then verified.
|
finance
|
4,046 |
Impact of time illiquidity in a mixed market without full observation
|
q-fin.PM
|
We study a problem of optimal investment/consumption over an infinite horizon
in a market consisting of two possibly correlated assets: one liquid and one
illiquid. The liquid asset is observed and can be traded continuously, while
the illiquid one can be traded only at discrete random times corresponding to
the jumps of a Poisson process with intensity $\lambda$, is observed at the
trading dates, and is partially observed between two different trading dates.
The problem is a nonstandard mixed discrete/continuous optimal control problem
which we face by the dynamic programming approach. When the utility has a
general form we prove that the value function is the unique viscosity solution
of the HJB equation and, assuming sufficient regularity of the value function,
we give a verification theorem that describes the optimal investment strategies
for the illiquid asset. In the case of power utility, we prove the regularity
of the value function needed to apply the verification theorem, providing the
complete theoretical solution of the problem. This allows us to perform
numerical simulation, so to analyze the impact of time illiquidity in this
mixed market and how this impact is affected by the degree of observation.
|
finance
|
4,047 |
Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets
|
q-fin.PM
|
We study a problem of optimal investment/consumption over an infinite horizon
in a market consisting of a liquid and an illiquid asset. The liquid asset is
observed and can be traded continuously, while the illiquid one can only be
traded and observed at discrete random times corresponding to the jumps of a
Poisson process. The problem is a nonstandard mixed discrete/continuous optimal
control problem which we face by the dynamic programming approach. The main aim
of the paper is to prove that the value function is the unique viscosity
solution of an associated HJB equation. We then use such result to build a
numerical algorithm allowing to approximate the value function and so to
measure the cost of illiquidity.
|
finance
|
4,048 |
Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage
|
q-fin.PM
|
The theory of functionally generated portfolios (FGPs) is an aspect of the
continuous-time, continuous-path Stochastic Portfolio Theory of Robert
Fernholz. FGPs have been formulated to yield a master equation - a description
of their return relative to a passive (buy-and-hold) benchmark portfolio
serving as the num\'eraire. This description has proven to be analytically very
useful, as it is both pathwise and free of stochastic integrals. Here we
generalize the class of FGPs in several ways: (1) the num\'eraire may be any
strictly positive wealth process, not necessarily the market portfolio or even
a passive portfolio; (2) generating functions may be stochastically dynamic,
adjusting to changing market conditions through an auxiliary continuous-path
stochastic argument of finite variation. These generalizations do not forfeit
the important tractability properties of the associated master equation. We
show how these generalizations can be usefully applied to scenario analysis,
statistical arbitrage, portfolio risk immunization, and the theory of mirror
portfolios.
|
finance
|
4,049 |
Smooth Value Function with Applications in Wealth-CVaR Efficient Portfolio and Turnpike Property
|
q-fin.PM
|
In this paper we continue the study of Bian-Miao-Zheng (2011) and extend the
results there to a more general class of utility functions which may be bounded
and non-strictly-concave and show that there is a classical solution to the HJB
equation with the dual control method. We then apply the results to study the
efficient frontier of wealth and conditional VaR (CVaR) problem and the
turnpike property problem. For the former we construct explicitly the optimal
control and discuss the choice of the optimal threadshold level and illustrate
that the wealth and the CVaR are positively correlated. For the latter we give
a simple proof to the turnpike property of the optimal policy of long-run
investors and generalize the results of Huang-Zariphopoulou (1999).
|
finance
|
4,050 |
Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact
|
q-fin.PM
|
In this paper we discuss the optimal liquidation over a finite time horizon
until the exit time. The drift and diffusion terms of the asset price are
general functions depending on all variables including control and market
regime. There is also a local nonlinear transaction cost associated to the
liquidation. The model deals with both the permanent impact and the temporary
impact in a regime switching framework. The problem can be solved with the
dynamic programming principle. The optimal value function is the unique
continuous viscosity solution to the HJB equation and can be computed with the
finite difference method.
|
finance
|
4,051 |
Gambling in contests with regret
|
q-fin.PM
|
This paper discusses the gambling contest introduced in Seel & Strack
(Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the
Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of
adding a penalty associated with failure to follow a winning strategy.
The Seel & Strack model consists of $n$-agents each of whom privately
observes a transient diffusion process and chooses when to stop it. The player
with the highest stopped value wins the contest, and each player's objective is
to maximise their probability of winning the contest. We give a new derivation
of the results of Seel & Strack based on a Lagrangian approach. Moreover, we
consider an extension of the problem in which in the case when an agent is
penalised when their strategy is suboptimal, in the sense that they do not win
the contest, but there existed an alternative strategy which would have
resulted in victory.
|
finance
|
4,052 |
Value-Based Inventory Management
|
q-fin.PM
|
The basic financial purpose of a firm is to maximize its value. An inventory
management system should also contribute to realization of this basic aim. Many
current asset management models currently found in financial management
literature were constructed with the assumption of book profit maximization as
basic aim. However these models could lack what relates to another aim, i.e.,
maximization of enterprise value. This article presents a modified value-based
inventory management model.
|
finance
|
4,053 |
Theory of Performance Participation Strategies
|
q-fin.PM
|
The purpose of this article is to introduce, analyze and compare two
performance participation methods based on a portfolio consisting of two risky
assets: Option-Based Performance Participation (OBPP) and Constant Proportion
Performance Participation (CPPP). By generalizing the provided guarantee to a
participation in the performance of a second risky underlying, the new
strategies allow to cope with well-known problems associated with standard
portfolio insurance methods, like e.g. the CPPI cash lock-in. This is
especially an issue in times of market crisis. However, the minimum guaranteed
portfolio value at the end of the investment horizon is not deterministic
anymore, but subject to systematic risk instead. With respect to the comparison
of the two strategies, various criteria are applied such as comparison of
terminal payoffs and payoff distributions. General analytical expressions for
all moments of both performance participation strategies as well as standard
OBPI and CPPI are derived. Furthermore, dynamic hedging properties are
examined, in particular classical delta hedging.
|
finance
|
4,054 |
Optimal investment and price dependence in a semi-static market
|
q-fin.PM
|
This paper studies the problem of maximizing expected utility from terminal
wealth in a semi-static market composed of derivative securities, which we
assume can be traded only at time zero, and of stocks, which can be traded
continuously in time and are modeled as locally-bounded semi-martingales.
Using a general utility function defined on the positive real line, we first
study existence and uniqueness of the solution, and then we consider the
dependence of the outputs of the utility maximization problem on the price of
the derivatives, investigating not only stability but also differentiability,
monotonicity, convexity and limiting properties.
|
finance
|
4,055 |
Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach
|
q-fin.PM
|
This paper investigates optimal portfolio strategies in a market where the
drift is driven by an unobserved Markov chain. Information on the state of this
chain is obtained from stock prices and expert opinions in the form of signals
at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl.
Finance, 15, No. 1, we use stochastic filtering to transform the original
problem into an optimization problem under full information where the state
variable is the filter for the Markov chain. The dynamic programming equation
for this problem is studied with viscosity-solution techniques and with
regularization arguments.
|
finance
|
4,056 |
Dynamic Credit Investment in Partially Observed Markets
|
q-fin.PM
|
We consider the problem of maximizing expected utility for a power investor
who can allocate his wealth in a stock, a defaultable security, and a money
market account. The dynamics of these security prices are governed by geometric
Brownian motions modulated by a hidden continuous time finite state Markov
chain. We reduce the partially observed stochastic control problem to a
complete observation risk sensitive control problem via the filtered regime
switching probabilities. We separate the latter into pre-default and
post-default dynamic optimization subproblems, and obtain two coupled
Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove
existence and uniqueness of a globally bounded classical solution to each HJB
equation, and give the corresponding verification theorem. We provide a
numerical analysis showing that the investor increases his holdings in stock as
the filter probability of being in high growth regimes increases, and decreases
his credit risk exposure when the filter probability of being in high default
risk regimes gets larger.
|
finance
|
4,057 |
A liability tracking approach to long term management of pension funds
|
q-fin.PM
|
We propose a long term portfolio management method which takes into account a
liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian)
control problem framework and then the optimal portfolio strategy hedges the
liability by directly tracking a benchmark process which represents the
liability. Two numerical results using empirical data published by Japanese
organizations are served: simulations tracking an artificial liability and an
estimated liability of Japanese organization. The latter one demonstrates that
our optimal portfolio strategy can hedge his or her liability.
|
finance
|
4,058 |
Optimal initiation of a GLWB in a variable annuity: no arbitrage approach
|
q-fin.PM
|
This paper offers a financial economic perspective on the optimal time (and
age) at which the owner of a Variable Annuity (VA) policy with a Guaranteed
Living Withdrawal Benefit (GLWB) rider should initiate guaranteed lifetime
income payments. We abstract from utility, bequest and consumption preference
issues by treating the VA as liquid and tradable. This allows us to use an
American option pricing framework to derive a so-called optimal initiation
region. Our main practical finding is that given current design parameters in
which volatility (asset allocation) is restricted to less than 20%, while
guaranteed payout rates (GPR) as well as bonus (roll-up) rates are less than
5%, GLWBs that are in-the-money should be turned on by the late 50s and
certainly the early 60s. The exception to the rule is when a non-constant GPR
is about to increase (soon) to a higher age band, in which case the optimal
policy is to wait until the new GPR is hit and then initiate immediately. Also,
to offer a different perspective, we invert the model and solve for the bonus
(roll-up) rate that is required to justify delaying initiation at any age. We
find that the required bonus is quite high and more than what is currently
promised by existing products. Our methodology and results should be of
interest to researchers as well as to the individuals that collectively have
over \$1 USD trillion in aggregate invested in these products. We conclude by
suggesting that much of the non-initiation at older age is irrational (which
obviously benefits the insurance industry.)
|
finance
|
4,059 |
On the Dividend Strategies with Non-Exponential Discounting
|
q-fin.PM
|
In this paper, we study the dividend strategies for a shareholder with
non-constant discount rate in a diffusion risk model. We assume that the
dividends can only be paid at a bounded rate and restrict ourselves to the
Markov strategies. This is a time inconsistent control problem. The extended
HJB equation is given and the verification theorem is proved for a general
discount function. Considering the pseudo-exponential discount functions (Type
I and Type II), we get the equilibrium dividend strategies and the equilibrium
value functions by solving the extended HJB equations.
|
finance
|
4,060 |
Optimal portfolios of a long-term investor with floor or drawdown constraints
|
q-fin.PM
|
We study the portfolio selection problem of a long-run investor who is
maximising the asymptotic growth rate of her expected utility. We show that,
somewhat surprisingly, it is essentially not affected by introduction of a
floor constraint which requires the wealth process to dominate a given
benchmark at all times. We further study the notion of long-run optimality of
wealth processes via convergence of finite horizon value functions to the
asymptotic optimal value. We characterise long-run optimality under floor and
drawdown constraints.
|
finance
|
4,061 |
Robust Portfolios and Weak Incentives in Long-Run Investments
|
q-fin.PM
|
When the planning horizon is long, and the safe asset grows indefinitely,
isoelastic portfolios are nearly optimal for investors who are close to
isoelastic for high wealth, and not too risk averse for low wealth. We prove
this result in a general arbitrage-free, frictionless, semimartingale model. As
a consequence, optimal portfolios are robust to the perturbations in
preferences induced by common option compensation schemes, and such incentives
are weaker when their horizon is longer. Robust option incentives are possible,
but require several, arbitrarily large exercise prices, and are not always
convex.
|
finance
|
4,062 |
Hedging and Leveraging: Principal Portfolios of the Capital Asset Pricing Model
|
q-fin.PM
|
The principal portfolios of the standard Capital Asset Pricing Model (CAPM)
are analyzed and found to have remarkable hedging and leveraging properties.
Principal portfolios implement a recasting of any correlated asset set of N
risky securities into an equivalent but uncorrelated set when short sales are
allowed. While a determination of principal portfolios in general requires a
detailed knowledge of the covariance matrix for the asset set, the rather
simple structure of CAPM permits an accurate solution for any reasonably large
asset set that reveals interesting universal properties. Thus for an asset set
of size N, we find a market-aligned portfolio, corresponding to the market
portfolio of CAPM, as well as N-1 market-orthogonal portfolios which are market
neutral and strongly leveraged. These results provide new insight into the
return-volatility structure of CAPM, and demonstrate the effect of unbridled
leveraging on volatility.
|
finance
|
4,063 |
Portfolio Optimization in R
|
q-fin.PM
|
We consider the problem of finding the efficient frontier associated with the
risk-return portfolio optimization model. We derive the analytical expression
of the efficient frontier for a portfolio of N risky assets, and for the case
when a risk-free asset is added to the model. Also, we provide an R
implementation, and we discuss in detail a numerical example of a portfolio of
several risky common stocks.
|
finance
|
4,064 |
Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem
|
q-fin.PM
|
In this paper we propose and analyze a method based on the Riccati
transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation
arising from the stochastic dynamic optimal allocation problem. We show how the
fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a
quasi-linear parabolic equation whose diffusion function is obtained as the
value function of certain parametric convex optimization problem. Although the
diffusion function need not be sufficiently smooth, we are able to prove
existence, uniqueness and derive useful bounds of classical H\"older smooth
solutions. We furthermore construct a fully implicit iterative numerical scheme
based on finite volume approximation of the governing equation. A numerical
solution is compared to a semi-explicit traveling wave solution by means of the
convergence ratio of the method. We compute optimal strategies for a portfolio
investment problem motivated by the German DAX 30 Index as an example of
application of the method.
|
finance
|
4,065 |
Asset Allocation under the Basel Accord Risk Measures
|
q-fin.PM
|
Financial institutions are currently required to meet more stringent capital
requirements than they were before the recent financial crisis; in particular,
the capital requirement for a large bank's trading book under the Basel 2.5
Accord more than doubles that under the Basel II Accord. The significant
increase in capital requirements renders it necessary for banks to take into
account the constraint of capital requirement when they make asset allocation
decisions. In this paper, we propose a new asset allocation model that
incorporates the regulatory capital requirements under both the Basel 2.5
Accord, which is currently in effect, and the Basel III Accord, which was
recently proposed and is currently under discussion. We propose an unified
algorithm based on the alternating direction augmented Lagrangian method to
solve the model; we also establish the first-order optimality of the limit
points of the sequence generated by the algorithm under some mild conditions.
The algorithm is simple and easy to implement; each step of the algorithm
consists of solving convex quadratic programming or one-dimensional
subproblems. Numerical experiments on simulated and real market data show that
the algorithm compares favorably with other existing methods, especially in
cases in which the model is non-convex.
|
finance
|
4,066 |
Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains
|
q-fin.PM
|
This paper examines an optimal investment problem in a continuous-time
(essentially) complete financial market with a finite horizon. We deal with an
investor who behaves consistently with principles of Cumulative Prospect
Theory, and whose utility function on gains is bounded above. The
well-posedness of the optimisation problem is trivial, and a necessary
condition for the existence of an optimal trading strategy is derived. This
condition requires that the investor's probability distortion function on
losses does not tend to 0 near 0 faster than a given rate, which is determined
by the utility function. Under additional assumptions, we show that this
condition is indeed the borderline for attainability, in the sense that for
slower convergence of the distortion function there does exist an optimal
portfolio.
|
finance
|
4,067 |
Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach
|
q-fin.PM
|
We consider an investor with constant absolute risk aversion who trades a
risky asset with general Ito dynamics, in the presence of small proportional
transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the
leading-order optimal trading policy and the associated welfare impact of
transaction costs. In the present paper, we carry out a convex duality approach
facilitated by the concept of shadow price processes in order to verify the
main results of Kallsen and Muhle-Karbe under well-defined regularity
conditions.
|
finance
|
4,068 |
Asymptotic analysis for Merton's problem with transaction costs in power utility case
|
q-fin.PM
|
We revisit the optimal investment and consumption problem with proportional
transaction costs. We prove that both the value function and the slopes of the
lines demarcating the no-trading region are analytic functions of cube root of
the transaction cost parameter. Also, we can explicitly calculate the
coefficients of the fractional power series expansions of the value function
and the no-trading region.
|
finance
|
4,069 |
Seven Sins in Portfolio Optimization
|
q-fin.PM
|
Although modern portfolio theory has been in existence for over 60 years,
fund managers often struggle to get its models to produce reliable portfolio
allocations without strongly constraining the decision vector by tight bands of
strategic allocation targets. The two main root causes to this problem are
inadequate parameter estimation and numerical artifacts. When both obstacles
are overcome, portfolio models yield excellent allocations. In this paper,
which is primarily aimed at practitioners, we discuss the most common mistakes
in setting up portfolio models and in solving them algorithmically.
|
finance
|
4,070 |
The Kelly growth optimal strategy with a stop-loss rule
|
q-fin.PM
|
From the Hamilton-Jacobi-Bellman equation for the value function we derive a
non-linear partial differential equation for the optimal portfolio strategy
(the dynamic control). The equation is general in the sense that it does not
depend on the terminal utility and provides additional analytical insight for
some optimal investment problems with known solutions. Furthermore, when
boundary conditions for the optimal strategy can be established independently,
it is considerably simpler than the HJB to solve numerically. Using this method
we calculate the Kelly growth optimal strategy subject to a periodically reset
stop-loss rule.
|
finance
|
4,071 |
Time--consistent investment under model uncertainty: the robust forward criteria
|
q-fin.PM
|
We combine forward investment performance processes and ambiguity averse
portfolio selection. We introduce the notion of robust forward criteria which
addresses the issues of ambiguity in model specification and in preferences and
investment horizon specification. It describes the evolution of time-consistent
ambiguity averse preferences.
We first focus on establishing dual characterizations of the robust forward
criteria. This offers various advantages as the dual problem amounts to a
search for an infimum whereas the primal problem features a saddle-point. Our
approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We
then study in detail non-volatile criteria. In particular, we solve explicitly
the example of an investor who starts with a logarithmic utility and applies a
quadratic penalty function. The investor builds a dynamical estimate of the
market price of risk $\hat \lambda$ and updates her stochastic utility in
accordance with the so-perceived elapsed market opportunities. We show that
this leads to a time-consistent optimal investment policy given by a fractional
Kelly strategy associated with $\hat \lambda$. The leverage is proportional to
the investor's confidence in her estimate $\hat \lambda$.
|
finance
|
4,072 |
A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios
|
q-fin.PM
|
In this paper we propose a cyclical coordinate descent (CCD) algorithm for
solving high dimensional risk parity problems. We show that this algorithm
converges and is very fast even with large covariance matrices (n > 500).
Comparison with existing algorithms also shows that it is one of the most
efficient algorithms.
|
finance
|
4,073 |
A New Characterization of Comonotonicity and its Application in Behavioral Finance
|
q-fin.PM
|
It is well-known that an $\mathbb{R}$-valued random vector $(X_1, X_2,
\cdots, X_n)$ is comonotonic if and only if $(X_1, X_2, \cdots, X_n)$ and
$(Q_1(U), Q_2(U),\cdots, Q_n(U))$ coincide \emph{in distribution}, for
\emph{any} random variable $U$ uniformly distributed on the unit interval
$(0,1)$, where $Q_k(\cdot)$ are the quantile functions of $X_k$, $k=1,2,\cdots,
n$. It is natural to ask whether $(X_1, X_2, \cdots, X_n)$ and $(Q_1(U),
Q_2(U),\cdots, Q_n(U))$ can coincide \emph{almost surely} for \emph{some}
special $U$. In this paper, we give a positive answer to this question by
construction. We then apply this result to a general behavioral investment
model with a law-invariant preference measure and develop a universal framework
to link the problem to its quantile formulation. We show that any optimal
investment output should be anti-comonotonic with the market pricing kernel.
Unlike previous studies, our approach avoids making the assumption that the
pricing kernel is atomless, and consequently, we overcome one of the major
difficulties encountered when one considers behavioral economic equilibrium
models in which the pricing kernel is a yet-to-be-determined unknown random
variable. The method is applicable to many other models such as risk sharing
model.
|
finance
|
4,074 |
Optimal Strategies for a Long-Term Static Investor
|
q-fin.PM
|
The optimal strategies for a long-term static investor are studied. Given a
portfolio of a stock and a bond, we derive the optimal allocation of the
capitols to maximize the expected long-term growth rate of a utility function
of the wealth. When the bond has constant interest rate, three models for the
underlying stock price processes are studied: Heston model, 3/2 model and jump
diffusion model. We also study the optimal strategies for a portfolio in which
the stock price process follows a Black-Scholes model and the bond process has
a Vasicek interest rate that is correlated to the stock price.
|
finance
|
4,075 |
Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals
|
q-fin.PM
|
Motivated by recent axiomatic developments, we study the risk- and
ambiguity-averse investment problem where trading takes place over a fixed
finite horizon and terminal payoffs are evaluated according to a criterion
defined in terms of a quasiconcave utility functional. We extend to the present
setting certain existence and duality results established for the so-called
variational preferences by Schied (2007). The results are proven by building on
existing results for the classical utility maximization problem.
|
finance
|
4,076 |
Credit Portfolio Management in a Turning Rates Environment
|
q-fin.PM
|
We give a detailed account of correlations between credit sector/quality and
treasury curve factors, using the robust framework of the Barclays POINT Global
Risk Model. Consistent with earlier studies, we find a strong negative
correlation between sector spreads and rate shifts. However, we also observe
that the correlations between spreads and Treasury twists reversed recently,
which is likely attributable to the Fed's ongoing quantitative easing. We also
find that short-term effective durations in the banking industry are now
significantly lower than historical patterns would indicate. Our findings are
relevant for credit portfolio managers contemplating the impact of rising
interest rates and steepening Treasury curve on corporate bond portfolios.
|
finance
|
4,077 |
Optimal Investment with Transaction Costs and Stochastic Volatility
|
q-fin.PM
|
Two major financial market complexities are transaction costs and uncertain
volatility, and we analyze their joint impact on the problem of portfolio
optimization. When volatility is constant, the transaction costs optimal
investment problem has a long history, especially in the use of asymptotic
approximations when the cost is small. Under stochastic volatility, but with no
transaction costs, the Merton problem under general utility functions can also
be analyzed with asymptotic methods. Here, we look at the long-run growth rate
problem when both complexities are present, using separation of time scales
approximations. This leads to perturbation analysis of an eigenvalue problem.
We find the first term in the asymptotic expansion in the time scale parameter,
of the optimal long-term growth rate, and of the optimal strategy, for fixed
small transaction costs.
|
finance
|
4,078 |
Dynamic Mean-LPM and Mean-CVaR Portfolio Optimization in Continuous-time
|
q-fin.PM
|
Instead of controlling "symmetric" risks measured by central moments of
investment return or terminal wealth, more and more portfolio models have
shifted their focus to manage "asymmetric" downside risks that the investment
return is below certain threshold. Among the existing downside risk measures,
the lower-partial moments (LPM) and conditional value-at-risk (CVaR) are
probably most promising. In this paper we investigate the dynamic mean-LPM and
mean-CVaR portfolio optimization problems in continuous-time, while the current
literature has only witnessed their static versions. Our contributions are
two-fold, in both building up tractable formulations and deriving corresponding
analytical solutions. By imposing a limit funding level on the terminal wealth,
we conquer the ill-posedness exhibited in the class of mean-downside risk
portfolio models. The limit funding level not only enables us to solve both
dynamic mean-LPM and mean-CVaR portfolio optimization problems, but also offers
a flexibility to tame the aggressiveness of the portfolio policies generated
from such mean - downside risk models. More specifically, for a general market
setting, we prove the existence and uniqueness of the Lagrangian multiplies,
which is a key step in applying the martingale approach, and establish a
theoretical foundation for developing efficient numerical solution approaches.
Moreover, for situations where the opportunity set of the market setting is
deterministic, we derive analytical portfolio policies for both dynamic
mean-LPM and mean-CVaR formulations.
|
finance
|
4,079 |
Purchasing Life Insurance to Reach a Bequest Goal
|
q-fin.PM
|
We determine how an individual can use life insurance to meet a bequest goal.
We assume that the individual's consumption is met by an income, such as a
pension, life annuity, or Social Security. Then, we consider the wealth that
the individual wants to devote towards heirs (separate from any wealth related
to the afore-mentioned income) and find the optimal strategy for buying life
insurance to maximize the probability of reaching a given bequest goal. We
consider life insurance purchased by a single premium, with and without cash
value available. We also consider irreversible and reversible life insurance
purchased by a continuously paid premium; one can view the latter as
(instantaneous) term life insurance.
|
finance
|
4,080 |
Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift
|
q-fin.PM
|
This paper investigates optimal portfolio strategies in a financial market
where the drift of the stock returns is driven by an unobserved Gaussian mean
reverting process. Information on this process is obtained from observing stock
returns and expert opinions. The latter provide at discrete time points an
unbiased estimate of the current state of the drift. Nevertheless, the drift
can only be observed partially and the best estimate is given by the
conditional expectation given the available information, i.e., by the filter.
We provide the filter equations in the model with expert opinion and derive in
detail properties of the conditional variance. For an investor who maximizes
expected logarithmic utility of his portfolio, we derive the optimal strategy
explicitly in different settings for the available information. The optimal
expected utility, the value function of the control problem, depends on the
conditional variance. The bounds and asymptotic results for the conditional
variances are used to derive bounds and asymptotic properties for the value
functions. The results are illustrated with numerical examples.
|
finance
|
4,081 |
Introduction to Risk Parity and Budgeting
|
q-fin.PM
|
Although portfolio management didn't change much during the 40 years after
the seminal works of Markowitz and Sharpe, the development of risk budgeting
techniques marked an important milestone in the deepening of the relationship
between risk and asset management. Risk parity then became a popular financial
model of investment after the global financial crisis in 2008. Today, pension
funds and institutional investors are using this approach in the development of
smart indexing and the redefinition of long-term investment policies.
Introduction to Risk Parity and Budgeting provides an up-to-date treatment of
this alternative method to Markowitz optimization. It builds financial exposure
to equities and commodities, considers credit risk in the management of bond
portfolios, and designs long-term investment policy.
This book contains the solutions of tutorial exercices which are included in
Introduction to Risk Parity and Budgeting.
|
finance
|
4,082 |
Momentum Strategies with L1 Filter
|
q-fin.PM
|
In this article, we discuss various implementation of L1 filtering in order
to detect some properties of noisy signals. This filter consists of using a L1
penalty condition in order to obtain the filtered signal composed by a set of
straight trends or steps. This penalty condition, which determines the number
of breaks, is implemented in a constrained least square problem and is
represented by a regularization parameter ? which is estimated by a
cross-validation procedure. Financial time series are usually characterized by
a long-term trend (called the global trend) and some short-term trends (which
are named local trends). A combination of these two time scales can form a
simple model describing the process of a global trend process with some
mean-reverting properties. Explicit applications to momentum strategies are
also discussed in detail with appropriate uses of the trend configurations.
|
finance
|
4,083 |
Utility maximization in the large markets
|
q-fin.PM
|
In the large financial market, which is described by a model with countably
many traded assets, we formulate the problem of the expected utility
maximization. Assuming that the preferences of an economic agent are modeled
with a stochastic utility and that the consumption occurs according to a
stochastic clock, we obtain the "usual" conclusions of the utility maximization
theory. We also give a characterization of the value function in the large
market in terms of a sequence of the value functions in the finite-dimensional
models.
|
finance
|
4,084 |
A Note on the Quantile Formulation
|
q-fin.PM
|
Many investment models in discrete or continuous-time settings boil down to
maximizing an objective of the quantile function of the decision variable. This
quantile optimization problem is known as the quantile formulation of the
original investment problem. Under certain monotonicity assumptions, several
schemes to solve such quantile optimization problems have been proposed in the
literature. In this paper, we propose a change-of-variable and relaxation
method to solve the quantile optimization problems without using the calculus
of variations or making any monotonicity assumptions. The method is
demonstrated through a portfolio choice problem under rank-dependent utility
theory (RDUT). We show that this problem is equivalent to a classical Merton's
portfolio choice problem under expected utility theory with the same utility
function but a different pricing kernel explicitly determined by the given
pricing kernel and probability weighting function. With this result, the
feasibility, well-posedness, attainability and uniqueness issues for the
portfolio choice problem under RDUT are solved. It is also shown that solving
functional optimization problems may reduce to solving probabilistic
optimization problems. The method is applicable to general models with
law-invariant preference measures including portfolio choice models under
cumulative prospect theory (CPT) or RDUT, Yaari's dual model, Lopes' SP/A
model, and optimal stopping models under CPT or RDUT.
|
finance
|
4,085 |
Is It Possible to OD on Alpha?
|
q-fin.PM
|
It is well known that combining multiple hedge fund alpha streams yields
diversification benefits to the resultant portfolio. Additionally, crossing
trades between different alpha streams reduces transaction costs. As the number
of alpha streams increases, the relative turnover of the portfolio decreases as
more trades are crossed. However, we argue, under reasonable assumptions, that
as the number of alphas increases, the turnover does not decrease indefinitely;
instead, the turnover approaches a non-vanishing limit related to the
correlation structure of the portfolio's alphas. We also point out that, more
generally, computational simplifications can arise when the number of alphas is
large.
|
finance
|
4,086 |
Signal-wise performance attribution for constrained portfolio optimisation
|
q-fin.PM
|
Performance analysis, from the external point of view of a client who would
only have access to returns and holdings of a fund, evolved towards exact
attribution made in the context of portfolio optimisation, which is the
internal point of view of a manager controlling all the parameters of this
optimisation. Attribution is exact, that-is-to-say no residual "interaction"
term remains, and various contributions to the optimal portfolio can be
identified: predictive signals, constraints, benchmark. However constraints are
identified as a separate portfolio and attribution for each signal that are
used to predict future returns thus corresponds to unconstrained signal
portfolios. We propose a novel attribution method that put predictive signals
at the core of attribution and allows to include the effect of constraints in
portfolios attributed to every signal. We show how this can be applied to
various trading models and portfolio optimisation frameworks and explain what
kind of insights such an attribution provides.
|
finance
|
4,087 |
An Optimal Consumption-Investment Model with Constraint on Consumption
|
q-fin.PM
|
A continuous-time consumption-investment model with constraint is considered
for a small investor whose decisions are the consumption rate and the
allocation of wealth to a risk-free and a risky asset with logarithmic Brownian
motion fluctuations. The consumption rate is subject to an upper bound
constraint which linearly depends on the investor's wealth and bankruptcy is
prohibited. The investor's objective is to maximize total expected discounted
utility of consumption over an infinite trading horizon. It is shown that the
value function is (second order) smooth everywhere but a unique possibility of
(known) exception point and the optimal consumption-investment strategy is
provided in a closed feedback form of wealth, which in contrast to the existing
work does not involve the value function. According to this model, an investor
should take the same optimal investment strategy as in Merton's model
regardless his financial situation. By contrast, the optimal consumption
strategy does depend on the investor's financial situation: he should use a
similar consumption strategy as in Merton's model when he is in a bad
situation, and consume as much as possible when he is in a good situation.
|
finance
|
4,088 |
Optimal investment under behavioural criteria -- a dual approach
|
q-fin.PM
|
We consider a discrete-time, generically incomplete market model and a
behavioural investor with power-like utility and distortion functions. The
existence of optimal strategies in this setting has been shown in a previous
paper under certain conditions on the parameters of these power functions.
In the present paper we prove the existence of optimal strategies under a
different set of conditions on the parameters, identical to the ones which were
shown to be necessary and sufficient in the Black-Scholes model.
Although there exists no natural dual problem for optimisation under
behavioural criteria (due to the lack of concavity), we will rely on techniques
based on the usual duality between attainable contingent claims and equivalent
martingale measures.
|
finance
|
4,089 |
Optimal Portfolio Problem Using Entropic Value at Risk: When the Underlying Distribution is Non-Elliptical
|
q-fin.PM
|
This paper is devoted to study the optimal portfolio problem. Harry
Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of
finance. In modern portfolio theory, we typically find asset returns that are
modeled by a random variable with an elliptical distribution and the notion of
portfolio risk is described by an appropriate risk measure. In this paper, we
propose new stochastic models for the asset returns that are based on Jumps-
Diffusion (J-D) distributions. This family of distributions are more compatible
with stylized features of asset returns. On the other hand, in the past
decades, we find attempts in the literature to use well-known risk measures,
such as Value at Risk and Expected Shortfall, in this context. Unfortunately,
one drawback with these previous approaches is that no explicit formulas are
available and numerical approximations are used to solve the optimization
problem. In this paper, we propose to use a new coherent risk measure,
so-called, Entropic Value at Risk(EVaR), in the optimization problem. For
certain models, including a jump-diffusion distribution, this risk measure
yields an explicit formula for the objective function so that the optimization
problem can be solved without resorting to numerical approximations.
|
finance
|
4,090 |
Active extension portfolio optimization with non-convex risk measures using metaheuristics
|
q-fin.PM
|
We consider the optimization of active extension portfolios. For this
purpose, the optimization problem is rewritten as a stochastic programming
model and solved using a clever multi-start local search heuristic, which turns
out to provide stable solutions. The heuristic solutions are compared to
optimization results of convex optimization solvers where applicable.
Furthermore, the approach is applied to solve problems with non-convex risk
measures, most notably to minimize Value-at-Risk. Numerical results using data
from both the Dow Jones Industrial Average as well as the DAX 30 are shown.
|
finance
|
4,091 |
Portfolio optimization in the case of an asset with a given liquidation time distribution
|
q-fin.PM
|
Management of the portfolios containing low liquidity assets is a tedious
problem. The buyer proposes the price that can differ greatly from the paper
value estimated by the seller, the seller, on the other hand, can not liquidate
his portfolio instantly and waits for a more favorable offer. To minimize
losses in this case we need to develop new methods. One of the steps moving the
theory towards practical needs is to take into account the time lag of the
liquidation of an illiquid asset. This task became especially significant for
the practitioners in the time of the global financial crises. Working in the
Merton's optimal consumption framework with continuous time we consider an
optimization problem for a portfolio with an illiquid, a risky and a risk-free
asset. While a standard Black-Scholes market describes the liquid part of the
investment the illiquid asset is sold at a random moment with prescribed
liquidation time distribution. In the moment of liquidation it generates
additional liquid wealth dependent on illiquid assets paper value. The investor
has the logarithmic utility function as a limit case of a HARA-type utility.
Different distributions of the liquidation time of the illiquid asset are under
consideration - a classical exponential distribution and Weibull distribution
that is more practically relevant. Under certain conditions we show the
existence of the viscosity solution in both cases. Applying numerical methods
we compare classical Merton's strategies and the optimal consumption-allocation
strategies for portfolios with different liquidation-time distributions of an
illiquid asset.
|
finance
|
4,092 |
Risk-sensitive investment in a finite-factor model
|
q-fin.PM
|
A new jump diffusion regime-switching model is introduced, which allows for
linking jumps in asset prices with regime changes. We prove the existence and
uniqueness of the solution to the risk-sensitive asset management criterion
maximisation problem in this setting. We provide an ODE for the optimal value
function, which may be efficiently solved numerically. Relevant probability
measure changes are discussed in the appendix. The approach of Klebaner and
Lipster (2014) is used to prove the martingale property of the relevant density
processes.
|
finance
|
4,093 |
Mean-Reversion and Optimization
|
q-fin.PM
|
The purpose of these notes is to provide a systematic quantitative framework
- in what is intended to be a "pedagogical" fashion - for discussing
mean-reversion and optimization. We start with pair trading and add complexity
by following the sequence "mean-reversion via demeaning -> regression ->
weighted regression -> (constrained) optimization -> factor models". We discuss
in detail how to do mean-reversion based on this approach, including common
pitfalls encountered in practical applications, such as the difference between
maximizing the Sharpe ratio and minimizing an objective function when trading
costs are included. We also discuss explicit algorithms for optimization with
linear costs, constraints and bounds.
|
finance
|
4,094 |
Bounds on Portfolio Quality
|
q-fin.PM
|
The signal-noise ratio of a portfolio of p assets, its expected return
divided by its risk, is couched as an estimation problem on the sphere. When
the portfolio is built using noisy data, the expected value of the signal-noise
ratio is bounded from above via a Cramer-Rao bound, for the case of Gaussian
returns. The bound holds for `biased' estimators, thus there appears to be no
bias-variance tradeoff for the problem of maximizing the signal-noise ratio. An
approximate distribution of the signal-noise ratio for the Markowitz portfolio
is given, and shown to be fairly accurate via Monte Carlo simulations, for
Gaussian returns as well as more exotic returns distributions. These findings
imply that if the maximal population signal-noise ratio grows slower than the
universe size to the 1/4 power, there may be no diversification benefit, rather
expected signal-noise ratio can decrease with additional assets. As a practical
matter, this may explain why the Markowitz portfolio is typically applied to
small asset universes. Finally, the theorem is expanded to cover more general
models of returns and trading schemes, including the conditional expectation
case where mean returns are linear in some observable features, subspace
constraints (i.e., dimensionality reduction), and hedging constraints.
|
finance
|
4,095 |
An expansion in the model space in the context of utility maximization
|
q-fin.PM
|
In the framework of an incomplete financial market where the stock price
dynamics are modeled by a continuous semimartingale (not necessarily Markovian)
an explicit second-order expansion formula for the power investor's value
function - seen as a function of the underlying market price of risk process -
is provided. This allows us to provide first-order approximations of the
optimal primal and dual controls. Two specific calibrated numerical examples
illustrating the accuracy of the method are also given.
|
finance
|
4,096 |
Dynamic Investment Portfolio Optimization under Constraints in the Financial Market with Regime Switching using Model Predictive Control
|
q-fin.PM
|
In this work, we consider the optimal portfolio selection problem under hard
constraints on trading volume amounts when the dynamics of the risky asset
returns are governed by a discrete-time approximation of the Markov-modulated
geometric Brownian motion. The states of Markov chain are interpreted as the
states of an economy. The problem is stated as a dynamic tracking problem of a
reference portfolio with desired return. We propose to use the model predictive
control (MPC) methodology in order to obtain feedback trading strategies. Our
approach is tested on a set of a real data from the radically different
financial markets: the Russian Stock Exchange MICEX, the New York Stock
Exchange and the Foreign Exchange Market (FOREX).
|
finance
|
4,097 |
Portfolio Optimization in the Financial Market with Correlated Returns under Constraints, Transaction Costs and Different Rates for Borrowing and Lending
|
q-fin.PM
|
In this work, we consider the optimal portfolio selection problem under hard
constraints on trading amounts, transaction costs and different rates for
borrowing and lending when the risky asset returns are serially correlated. No
assumptions about the correlation structure between different time points or
about the distribution of the asset returns are needed. The problem is stated
as a dynamic tracking problem of a reference portfolio with desired return. Our
approach is tested on a set of a real data from Russian Stock Exchange MICEX.
|
finance
|
4,098 |
Optimal Allocation of Trend Following Strategies
|
q-fin.PM
|
We consider a portfolio allocation problem for trend following (TF)
strategies on multiple correlated assets. Under simplifying assumptions of a
Gaussian market and linear TF strategies, we derive analytical formulas for the
mean and variance of the portfolio return. We construct then the optimal
portfolio that maximizes risk-adjusted return by accounting for inter-asset
correlations. The dynamic allocation problem for $n$ assets is shown to be
equivalent to the classical static allocation problem for $n^2$ virtual assets
that include lead-lag corrections in positions of TF strategies. The respective
roles of asset auto-correlations and inter-asset correlations are investigated
in depth for the two-asset case and a sector model. In contrast to the
principle of diversification suggesting to treat uncorrelated assets, we show
that inter-asset correlations allow one to estimate apparent trends more
reliably and to adjust the TF positions more efficiently. If properly accounted
for, inter-asset correlations are not deteriorative but beneficial for
portfolio management that can open new profit opportunities for trend
followers.
|
finance
|
4,099 |
Optimising Credit Portfolio Using a Quadratic Nonlinear Projection Method
|
q-fin.PM
|
A novel optimisation framework through quadratic nonlinear projection is
introduced for credit portfolio when the portfolio risk is measured by
Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search
toward the optimal portfolio state is conducted by a series of single-step
optimisations under the local constraints described in the multi-dimensional
constraint parameter space as functions of the total amount of portfolio
adjustment. Each single-step optimisation is approximated by the first-order
variation of the weight increments with respect to the total amount of
portfolio adjustment and is solved in the form of locally exact formula
formulated in the general Lagrange multiplier method. Our method can deal with
optimisation for general nonlinear objective functions, such as the
return-to-risk ratio maximisation or the diversification index, as well as the
risk minimisation or the return maximisation.
|
finance
|
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