Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

Follow the leader: Index tracking with factor models

We propose a new methodology to select a subset of assets for (partial) index replication, based on the latest research on factor models of large dimensions. Our method selects a set of leader stocks that fully captures the factor structure of the index to be replicated. Our selection methodology is consistent as the sample size and the number of assets jointly approach infinity. Monte Carlo experiments show that our estimated index replica tracks the underlying index with relatively small tracking errors in finite samples. We show the applicability of the method by tracking the S&P 500 equally weighed index and the MSCI USA Small Cap index with promising out-of-sample performance. Our method can be easily adapted for synthetic index replication, and to incorporate measures of liquidity or transaction cost.     

Cardinality versus q-norm constraints for index tracking

Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating portfolio. In this paper, we propose an alternative based on imposing a constraint on the q-norm (0?<?q?<?1) of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimization viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimization problems. The empirical analysis of real-world financial data allows us to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.     

Portfolio frontiers with restrictions to tracking error volatility and value at risk

Asset managers are often given the task of restricting their activity by keeping both the value at risk (VaR) and the tracking error volatility (TEV) under control. However, these constraints may be impossible to satisfy simultaneously because VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performance and produces a wide variety of scenarios in the risk-return space. The aim of this paper is to analyse various interactions between portfolio frontiers when risk managers impose joint restrictions upon TEV and VaR. Specifically, we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available. Finally, we introduce a new portfolio frontier.     

Index tracking through deep latent representation learning

We consider the problem of index tracking whose goal is to construct a portfolio that minimizes the tracking error between the returns of a benchmark index and the tracking portfolio. This problem carries significant importance in financial economics as the tracking portfolio represents a parsimonious index that facilitates a practical means to trade the benchmark index. For this reason, extensive studies from various optimization and machine learning-based approaches have ensued. In this paper, we solve this problem through the latest developments from deep learning. Specifically, we associate a deep latent representation of asset returns, obtained through a stacked autoencoder, with the benchmark index's return to identify the assets for inclusion in the tracking portfolio. Empirical results indicate that to improve the performance of previously proposed deep learning-based index tracking, the deep latent representation needs to be learned in a strictly hierarchical manner and the relationship between the returns of the index and the assets should be quantified by statistical measures. Various deep learning-based strategies have been tested for the stock market indices of the S&P 500, FTSE 100 and HSI, and it is shown that our proposed methodology generates the best index tracking performance.     

Optimizing a portfolio of mean-reverting assets with transaction costs via a feedforward neural network

Optimizing a portfolio of mean-reverting assets under transaction costs and a finite horizon is severely constrained by the curse of high dimensionality. To overcome the exponential barrier, we develop an efficient, scalable algorithm by employing a feedforward neural network. A novel concept is to apply HJB equations as an advanced start for the neural network. Empirical tests with several practical examples, including a portfolio of 48 correlated pair trades over 50 time steps, show the advantages of the approach in a high-dimensional setting. We conjecture that other financial optimization problems are amenable to similar approaches.     

An optimal investment model with Markov-driven volatilities

We consider a multi-stock market model. The processes of stock prices are governed by stochastic differential equations with stock return rates and volatilities driven by a finite-state Markov process. Each volatility is also disturbed by a Brownian motion; more exactly, it follows a Markov-driven Ornstein–Uhlenbeck process. Investors can observe the stock prices only. Both the underlying Brownian motion and the Markov process are unobservable. We study a discretized version, which is a discrete-time hidden Markov process. The objective is to control trading at each time step to maximize an expected utility function of terminal wealth. Exploiting dynamic programming techniques, we derive an approximate optimal trading strategy that results in an expected utility function close to the optimal value function. Necessary filtering and forecasting techniques are developed to compute the near-optimal trading strategy.     

Optimal insurance contract and coverage levels under loss aversion utility preference

This study develops an optimal insurance contract endogenously and determines the optimal coverage levels with respect to deductible insurance, upper-limit insurance, and proportional coinsurance, and, by assuming that the insured has an S-shaped loss aversion utility, the insured would retain the enormous losses entirely. The representative optimal insurance form is the truncated deductible insurance, where the insured retains all losses once losses exceed a critical level and adopts a particular deductible otherwise. Additionally, the effects of the optimal coverage levels are also examined with respect to benchmark wealth and loss aversion coefficient. Moreover, the efficiencies among various insurances are compared via numerical analysis by assuming that the loss obeys a uniform or log-normal distribution. In addition to optimal insurance, deductible insurance is the most efficient if the benchmark wealth is small and upper-limit insurance if large. In the case of a uniform distribution that has an upper bound, deductible insurance and optimal insurance coincide if benchmark wealth is small. Conversely, deductible insurance is never optimal for an unbounded loss such as a log-normal distribution.     

Asset allocation in markets with contagion: The interplay between volatilities,jump intensities,and correlations

We study the impact of financial contagion on the dynamic asset allocation problem of a CRRA investor facing an incomplete market with two risky assets. We apply a Markov chain regime-switching framework with state-dependent jump intensities, diffusion volatilities and diffusion correlations. The key model feature that a switch to the bad contagion regime is triggered by a loss in one of the risky assets allows for the implementation of a hedging demand against contagion risk. Moreover, a state-dependent diffusion correlation combined with heterogeneity in jump intensities and volatilities can, e.g., generate a flight to quality effect upon a systemic jump.