2,147 research outputs found
Robust Portfolios and Weak Incentives in Long-Run Investments
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
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
CAPM and APT-like models with risk measures.
The paper deals with optimal portfolio choice problems when risk levels are given by coherent risk mea sures, expectation bounded risk measures or general deviations. Both static and dynamic pricing models may be involved. Unbounded problems are characterized by new notions such as (strong) compatibility between prices and risks. Surprisingly, the lack of bounded optimal risk and/or return levels arises for important pricing models (Black and Scholes) and risk measures (VaR, CVaR, absolute deviation, etc.). Bounded problems present a Market Price of Risk and generate a pair of benchmarks. From these bench marks we introduce APT and CAPM like analyses, in the sense that the level of correlation between every available security and some economic factors explains the security expected return. The risk level non correlated with these factors has no influence on any return, despite the fact that we are dealing with risk functions beyond the standard deviation.Risk measure; Compatibility between prices and risks; Efficient portfolio; APT and CAPM-like models;
Long time asymptotics for optimal investment
This survey reviews portfolio selection problem for long-term horizon. We
consider two objectives: (i) maximize the probability for outperforming a
target growth rate of wealth process (ii) minimize the probability of falling
below a target growth rate. We study the asymptotic behavior of these criteria
formulated as large deviations control pro\-blems, that we solve by duality
method leading to ergodic risk-sensitive portfolio optimization problems.
Special emphasis is placed on linear factor models where explicit solutions are
obtained
Growth-optimal portfolios under transaction costs
This paper studies a portfolio optimization problem in a discrete-time
Markovian model of a financial market, in which asset price dynamics depend on
an external process of economic factors. There are transaction costs with a
structure that covers, in particular, the case of fixed plus proportional
costs. We prove that there exists a self-financing trading strategy maximizing
the average growth rate of the portfolio wealth. We show that this strategy has
a Markovian form. Our result is obtained by large deviations estimates on
empirical measures of the price process and by a generalization of the
vanishing discount method to discontinuous transition operators.Comment: 32 page
Efficient and robust estimation for financial returns: an approach based on q-entropy
We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvàt-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and effciency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.q-entropy; robust estimation; power-divergence; financial returns
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