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Author: Yuhong Xu Publisher: ISBN: Category : Languages : en Pages : 22
Book Description
In this paper I investigate financial markets with drift and volatility uncertainties. Appropriate definitions of arbitrage for super and sub-hedging strategies are presented such that the super and sub-hedging prices are reasonable. Especially the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty. The Profit&Loss (P&L for short) of super(sub)-hedging is derived to be in fact the penalty term K with finite-variance arising in the super(sub)-hedging strategy. The ask-bid spread is hence an accumulation of the superhedging P&L and the subhedging P&L.Asset allocation under constant absolute risk aversion (CARA) utility is investigated with ambiguous volatility and subjective risk premium. I show that ambiguity aversion of a rational individual decreases her market participation. The aggregate premium is computed explicitly which is decomposed into three parts. Opposite signs between the rates of ambiguity premium and risk premium demonstrate that a decrease in ambiguity premium on volatility gives rise to an increase in risk premium.Kelly criterion for the wealth process to reach a goal is also studied under such ambiguous market. Ambiguity of stock appreciation rate results in investors' withdraw from markets whereas in a single-priced market, investors always trade with the market if no short-sale constraints and no transaction cost.
Author: Yuhong Xu Publisher: ISBN: Category : Languages : en Pages : 22
Book Description
In this paper I investigate financial markets with drift and volatility uncertainties. Appropriate definitions of arbitrage for super and sub-hedging strategies are presented such that the super and sub-hedging prices are reasonable. Especially the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty. The Profit&Loss (P&L for short) of super(sub)-hedging is derived to be in fact the penalty term K with finite-variance arising in the super(sub)-hedging strategy. The ask-bid spread is hence an accumulation of the superhedging P&L and the subhedging P&L.Asset allocation under constant absolute risk aversion (CARA) utility is investigated with ambiguous volatility and subjective risk premium. I show that ambiguity aversion of a rational individual decreases her market participation. The aggregate premium is computed explicitly which is decomposed into three parts. Opposite signs between the rates of ambiguity premium and risk premium demonstrate that a decrease in ambiguity premium on volatility gives rise to an increase in risk premium.Kelly criterion for the wealth process to reach a goal is also studied under such ambiguous market. Ambiguity of stock appreciation rate results in investors' withdraw from markets whereas in a single-priced market, investors always trade with the market if no short-sale constraints and no transaction cost.
Author: Thomas Dangl Publisher: ISBN: Category : Languages : en Pages : 51
Book Description
We study the implications of predictability on the optimal asset allocation of ambiguity-averse long-term investors and analyze the term structure of the multivariate risk-return trade-off considering parameter uncertainty. We calibrate the model to real returns of US stocks, long-term bonds, cash, real estate, and gold using the term spread and the dividend-price ratio as additional predictive variables, and we show that over long horizons the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. The ambiguity-averse long-term investor optimally tilts her portfolio toward a seemingly inefficient portfolio, which shows maximum robustness against estimation errors.
Author: David Hirshleifer Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Ambiguity aversion alone does not explain the market nonparticipation puzzle. We show that in a rational expectations equilibrium model with a fund offering the risk-adjusted market portfolio (RAMP), ambiguity averse investors hold the fund and an information-based portfolio, and thus participate in all asset markets, directly or indirectly. This result follows from a new separation theorem which states that an investor's equilibrium portfolio can be decomposed into components, each matching the optimal portfolio based on only one information source (price versus private signal). Asset risk premia satisfy the CAPM with the fund as the pricing portfolio.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
This article takes a shrinkage approach to examine the empirical implications of aversion to model uncertainty. The shrinkage approach explicitly shows how predictive distributions incorporate data and prior beliefs. It enables us to solve the optimal portfolios for uncertainty-averse investors. Aversion to uncertainty about the capital asset pricing model leads investors to hold a portfolio that is not mean-variance efficient for any predictive distribution. However, mean-variance efficient portfolios corresponding to extremely strong beliefs in the Fama-French model are approximately optimal for uncertainty-averse investors. The empirical Bayes approach does not result in optimal portfolios for investors who are averse to model uncertainty.
Author: Hui Chen Publisher: ISBN: Category : Languages : en Pages : 46
Book Description
We study an investor's optimal consumption and portfolio choice problem when he is confronted with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor's aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. This effect is especially strong when the submodel with a low Bayesian probability delivers a much smaller continuation value. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor's stock allocation to decrease sharply given a small doubt of return predictability, even though the predictive variable is large. Adopting the Bayesian strategy can lead to sizable welfare costs for an ambiguity-averse investor, especially when he has a strong prior of return predictability.
Author: Yacine Aït-Sahalia Publisher: ISBN: Category : Languages : en Pages :
Book Description
We analyze an environment where the uncertainty in the equity market return and its volatility are both stochastic, and may be potentially disconnected. We solve a representative investor's optimal asset allocation and derive the resulting conditional equity premium and risk-free rate in equilibrium. Our empirical analysis shows that the equity premium appears to be earned for facing uncertainty, especially high uncertainty that is disconnected from lower volatility, rather than for facing volatility as traditionally assumed. Incorporating the possibility of a disconnect between volatility and uncertainty significantly improves portfolio performance, over and above the performance obtained by conditioning on volatility only.
Author: Valery Polkovnichenko Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
Testing portfolio alpha against a linear factor model can be interpreted as a mean-variance efficiency test of the optimal portfolio of factors. For ambiguity neutral investor, adding active portfolio with statistically significant alpha always implies efficiency gain relative to the optimal portfolio of factors. In contrast, for ambiguity averse investor, the efficiency gain must be above a threshold which depends on the uncertainty about the factors' and active portfolio's expected returns. Building on the theoretical framework developed in Garlappi, Uppal and Wang (2007), we propose a new method to test portfolio efficiency relative to a factor model by using asset exclusion conditions from the optimal portfolio of the ambiguity averse investor. The asset exclusion threshold is an F-statistic that is non-redundant with significance of alpha under the ambiguity-neutral test. Active portfolios with statistically significant alpha but weak efficiency gain may be excluded from the optimal portfolio. We apply this criterion empirically to screen active portfolios ("anomalies'') and find that some anomalies do not pass our exclusion test under statistically reasonable ambiguity about their expected return.
Author: Hyunjong Jin Publisher: ISBN: Category : Languages : en Pages : 58
Book Description
The classical mean-variance model, proposed by Harry Markowitz in 1952, has been one of the most powerful tools in the field of portfolio optimization. In this model, parameters are estimated by their sample counterparts. However, this leads to estimation risk, which the model completely ignores. In addition, the mean-variance model fails to incorporate behavioral aspects of investment decisions. To remedy the problem, the notion of ambiguity aversion has been addressed by several papers where investors acknowledge uncertainty in the estimation of mean returns. We extend the idea to the variances and correlation coefficient of the portfolio, and study their impact. The performance of the portfolio is measured in terms of its Sharpe ratio. We consider different cases where one parameter is assumed to be perfectly estimated by the sample counterpart whereas the other parameters introduce ambiguity, and vice versa, and investigate which parameter has what impact on the performance of the portfolio.
Author: Qian Lin Publisher: ISBN: Category : Languages : en Pages :
Book Description
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.
Author: Yuki Shigeta Publisher: ISBN: Category : Languages : en Pages : 58
Book Description
This study examines the practical performance of the multiple priors optimal portfolio based on the mean-variance preference. The multiple priors optimal portfolio is designed to be robust to model uncertainty, also known as ambiguity. A back test finds two properties: the multiple priors optimal portfolio tends to be efficient when the number of assets is large and it has fewer turnovers than the mean-variance-efficient portfolios. Furthermore, the presented simulation shows that the multiple priors optimal portfolio outperforms the others when the number of assets is large and number of observations to form a portfolio is small.
Author: Yuhong Xu
Author: Yuhong Xu
Author: Thomas Dangl
Author: David Hirshleifer
Author: 
Author: Hui Chen
Author: Yacine Aït-Sahalia
Author: Valery Polkovnichenko
Author: Hyunjong Jin
Author: Qian Lin
Author: Yuki Shigeta