Dynamic Portfolio Research Articles

Dynamic portfolio allocation in goals-based wealth management

We report a dynamic programming algorithm which, given a set of efficient (or even inefficient) portfolios, constructs an optimal portfolio trading strategy that maximizes the probability of attaining an investor’s specified target wealth at the end of a designated time horizon. Our algorithm also accommodates periodic infusions or withdrawals of cash with no degradation to the dynamic portfolio’s performance or runtime. We explore the sensitivity of the terminal wealth distribution to restricting the segment of the efficient frontier available to the investor. Since our algorithm’s optimal strategy can be on the efficient frontier and is driven by an investor’s wealth and goals, it soundly beats the performance of target date funds in attaining investors’ goals. These optimal goals-based wealth management strategies are useful for independent financial advisors to implement behavioral-based FinTech offerings and for robo-advisors.

Formulation of a Dynamic Portfolio With Stocks and Fixed-income Instruments in the Indonesian Capital Market

This research creates a crossed asset portfolio formulation dynamically with stocks and fixed-income instruments. This dynamic portfolio formulation did not require normally distributed data and accommodated the correlation among class assets which kept changing across time. This was based on the existing assumptions in the modern portfolio theory which were rarely found in the real world, for example, when stock return was normally distributed, the correlation among securities would be constant at all times. The data used in this research were LQ45 Index as a stock market proxy, S and P Indonesia Corporate Bond Index (representing the corporate bond market) and S and P Indonesia Government Bond Index data (representing the government bond market) during the period of June 4th, 2007 to April 11th, 2016. This research found that the dynamic portfolio of stock with either government or corporate bonds was able to reduce the level of risk significantly despite producing a lower rate of return, compared to the ones specifically invested in the stock market. Investors who believe in the principles of prudent investment may use this dynamic approach in shaping the portfolio with stocks and fixed-income instruments.

Dynamic Asset Allocation with Relative Wealth Concerns in Incomplete Markets

In dynamic portfolio choice problems, stochastic state variables such as stochastic volatility lead to adjustments of the optimal stock demand referred to as hedge terms or Merton-Breeden terms. By deriving an explicit solution in a multi-agent framework with a stochastic opportunity set, we show that relative wealth concerns give rise to new hedge terms beyond the ordinary ones. This is because the agents hedge against both exogenous changes in the state variable and endogenous decisions of the other agent. Depending on the parametrization of the model, these new terms can significantly change the investors' hedging demands. We also show that both heterogeneity in risk aversion or relative wealth concerns can have similar effects on the heterogeneity in portfolio decisions. Formally, we study a non-cooperative, non-zero sum stochastic differential game for which we prove a verification theorem in a setting with an unspanned state variable.

Dynamic portfolio choice with return predictability and transaction costs

We derive a closed-form solution to a continuous-time optimal portfolio selection problem with return predictability and transaction costs. Specifically, we assume that asset returns are predicted by stochastic signals, and that transaction costs are of quadratic form. The agent chooses a trading strategy to maximize the expected exponential utility of his terminal wealth. Our feedback trading strategy indicates that the agent should trade gradually toward a dynamic aim portfolio, which is a weighted sum of the expected future Merton portfolios. The agent’s aim portfolio converges to the Merton portfolio as time approaches the terminal date. Our analysis offers new insights to the existing literature. First, our optimal trading strategy is affected by the volatility of return-predicting factors, while such an effect is absent in Gârleanu and Pedersen (2016). Secondly, the agent invests more into the assets with more persistent signals and with less transaction costs.

Multi-period mean–variance portfolio optimization with management fees

Due to limited capital and limited information from stock market, some individual investors prefer to construct a portfolio of funds instead of stocks. But, there will be management fees paid to the fund managers during the investment, which are in general proportional to the net asset value of the funds. Motivated by this phenomena, this paper considers multi-period mean–variance portfolio optimization problem with proportional management fees. Using stochastic dynamic programming, we derive the semi-analytical optimal portfolio policy. Our result helps clarify the benefit and cost of adopting such dynamic portfolio policy with management fees.

Economic Slowdown and Housing Dynamics in China: A Tale of Two Investments by Firms

In the past decade, the Chinese economy has witnessed a great housing boom, accompanied by a slowdown in economic growth and an increase in firms' financial investment. The waning economic prospects lead to a surge in housing prices by stimulating firms' demand for financial (especially housing) assets. Motivated by these facts, we take an off-the-shelf dynamic New Keynesian model with novel modeling of firms' dynamic portfolio choice between physical and housing investment. Housing assets earn a positive return and can be used as collateral for the firm's external finances. A negative productivity shock decreases the relative return of production capital, which translates into a housing boom by increasing the firm's housing demand. A rise in house prices then generates competing effects on real investment: it not only raises the firm's leverage due to the collateral effect but also depresses the firm's demand for physical capital because of the crowding-out effect. After calibrating the model for the Chinese economy, our quantitative exercise suggests the former effect is dominated by the latter, which implies counter-cyclical housing prices. Among the policies used to stabilize the aggregate economy and housing markets, our counterfactual analysis implies that the capital subsidization policy targeting house prices performs better than other macroeconomic policies.

Cryptocurrency market contagion: Market uncertainty, market complexity, and dynamic portfolios

In this study, we employ a TVP-FAVAR connectedness approach in order to investigate the transmission mechanism in the cryptocurrency market. To this end, we concentrate on the top 9 cryptocurrencies by virtue of market capitalization and one market factor – based on 45 additional digital currencies – capturing the co-movements in the cryptocurrency market. The period of study spans between August 7, 2015 and May 31, 2018. We find that the dynamic total connectedness across several cryptocurrencies exhibits large dynamic variability ranging between 25% and 75%. In particular, periods of high (low) market uncertainty correspond to strong (weak) connectedness. We show that these results could be explained on the basis of increased market uncertainty that is associated with periods of highly volatile prices. In addition, despite the fact that Bitcoin still influences the cryptocurrency market substantially, we note that, recently, Ethereum has become the number one net transmitting cryptocurrency. We further note that the market gradually becomes more complex considering our connectedness approach and that this might be attributed to the unique characteristics and possibilities inherent in the technology of each cryptocurrency. A simplified application concentrating on bivariate portfolios is indicative of potential hedging opportunities using dynamic hedge ratios and dynamic portfolio weights.

An Extended Stochastic Goal Mixed Integer Programming for Optimal Portfolio Selection in the Amman Stock Exchange

This paper optimally solves the portfolio selection problem that consists of multi assets in a continuous time period to achieve the optimal trade-off between multi-objectives. In this paper, the Stochastic Goal Mixed Integer programming of Stoyan (2009) is extended. The empirical contributions of this research presented on extending the SGMIP model by adding information as a new factor that selects the portfolio elements. The information element used as a portfolio managing characteristics to see whether it is applicable for different problems. The data was collected on a daily basis for all the parameters of the individual stock. Brownian motion formula was used to predict the stock price in the future time period. SP framework used to capture numerous sources of uncertainty and to formulate the portfolio problem. The main challenge of this model is that it contains additional real-world objective and multi types of financial assets, which form a Mixed Integer Programming (MIP). This large-scale problem solved using Optimising Programming Language (OPL) and decomposition algorithm to improve the memory allocation and CPU time. A fascinating result was obtained from the portfolio algorithm design. The ESGMIP portfolio outperforms the Index portfolio return. Under uncertain environment, the availability of information rationalized the diversity when the dynamic portfolio invested in one financial instrument (stocks), and tend to be diversifiable when invested in more than one financial instrument (stock and bond). This work presents a novel extended SGMIP model to reach an optimal solution.

Fine-Tuning Private Equity Replication Using Textual Analysis

In this article, the authors use textual analysis to create an investable, dynamic portfolio to mimic the factor characteristics of private equity. First, using textual analysis, they identify firms taken private by those firms in the 10-year period ending June 2018. Second, they use a multifactor model to measure the cross-sectional factor exposures of firms immediately prior to the announcement that they were being acquired by a private equity firm. Finally, they use holdings-based optimization to build a liquid, investible, long-only portfolio that dynamically mimics the factor characteristics of the portfolio of stocks that were taken private. Practitioner applications include interim beta solutions for investors (including venture capital and private equity firms) seeking to deploy excess cash, mitigate underfunding risk, and manage capital calls.

Importance sampling in stochastic optimization: An application to intertemporal portfolio choice

In this paper, we propose an approach to construct an analytical approximation of the zero-variance importance sampling distribution. We show specifically how this can be designed for the classic intertemporal portfolio choice problem with proportional transaction costs and constant relative risk aversion preferences. We compare the method to standard variance reduction techniques in single-period optimization and multi-stage stochastic programming formulations of the problem. The numerical experiments show that the method produces significant improvements in solution quality. In the single-period setting, the number of scenarios can be reduced by a factor of 400 with maintained solution quality compared to the best standard method; Latin hypercube sampling. Using importance sampling in multi-stage formulations, the gaps between lower and upper bound estimates are reduced by a factor of 26-500 with maintained scenario tree size. On a higher level, we consider analytical approximations of the zero-variance importance sampling distribution to be a promising method to improve solution quality in stochastic optimization.

Dynamic portfolio allocation with time-varying jump risk

Abstract This paper solves the dynamic portfolio allocation problem with account of time-varying jump risk. We find that both the initial jump intensity as a state variable and the jump dynamics including the average jump intensity and jump persistence are important for the investor’s optimal portfolio decision. The risk-averse investor can benefit from the optimal dynamic strategy instead of the myopic strategy. The out-of-sample results show that compared with the no-jump model, constant-jump model or the equal weighted portfolio, the dynamic portfolio with account of time-varying jump risk can produce better performance, and is more preferred by the risk-averse investor.

Horizon-unbiased Investment with Ambiguity

In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that the market risk premium and the utility risk premium jointly determine the investors' trading direction and the worst-case scenarios of the risky asset's mean return and volatility. The closed-form formulas for the optimal investment strategies are given in the special settings of the CRRA preference.

Dynamic Portfolio Optimization with Looping Contagion Risk

In this paper, we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies, and the default of the company induces immediate drops in the stock prices of the surviving companies. We prove that the value function is the unique viscosity solution of the Hamilton--Jacobi--Bellman equation. We also perform some numerical tests to compare and analyze the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process.

Machine Learning With Kernels for Portfolio Valuation and Risk Management

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.

A consistent investment strategy

This paper introduces a consistent performance strategy (CPS), which, if followed, leads to a portfolio having consistently positive returns over time and exhibiting a steady upward trend. This strategy is inspired by moving average trading rules in classical technical analysis and is shown to be optimal in a modern dynamic portfolio choice framework. We illustrate our strategy via both simulation (model) and walk- forward testing (market data).

A Dynamic Model of Strategic Allocation of Sovereign Wealth Funds

This article draws on stylized facts to build a dynamic portfolio allocation model of sovereign wealth funds (SWF). We show that a traditional dynamic Merton allocation model allows for the stylized evidence that, on the one hand, the shares of monetary assets in such funds grow with the risk aversion of the state-investor in time, and on the other hand, these funds include the presence or absence of hedge funds correlated to the financial situation. One weakness of this model is its prediction of a lower risk/riskier asset ratio for sovereign stabilization funds and generational savings sovereign funds. This result contradicts the stylized fact of a lower risk/riskier asset ratio in stabilization funds than in generational savings funds. A dynamic model inspired by the theoretical framework of Bajeux-Besnainou et al. [1] is compatible with all the stylized facts.

Tracking VIX with VIX Futures: Portfolio Construction and Performance

We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and a simulation study is performed to understand the properties exhibited by the strategy. In addition, comparing to the volatility ETN, VXX, we find that our dynamic strategy has a superior tracking performance.

Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ($CVaRD$) based Sharpe ratio for measuring risk-adjusted performance of a dynamic portfolio. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index and we evaluate and analyze the dependence of the $CVaRD$-based Sharpe ratio on the utility function and the associated risk aversion level.

Convex Incentives and Liquidity Premia

We show that convexity in investors' preferences can significantly amplify the effect of transaction costs on the liquidity premia of stocks. This result is derived from the dynamic portfolio problem of fund managers who engage in risk-shifting to capture year-end bonuses, but is robust to other sources of convexity such as loss aversion or status concerns. The larger premia compensate primarily for the lower bonuses resulting from the suboptimal implementation of risk-shifting strategies. Using data on actively-managed mutual funds, we provide empirical support for the novel predictions of our model.

An Incremental-Hybrid-Yager’s Entropy Model for Dynamic Portfolio Selection with Fuzzy Variable

To settle down the resolutional uncertainty in optimum portfolio strategy, this paper addresses an incremental-hybrid-Yager’s entropy model to newly describe the relationship between return and risk. Different from the traditional multiperiod portfolio, we design the ratio threshold to divide asset price into different time interval and use state instead of time point to model the dynamic portfolio process. In addition, fuzzy variables are utilized to represent prices of assets, while historical data based on Markov chain is exploited to estimate membership functions of fuzzy prices. At last, a compromised genetic algorithm is designed, and the numerical example shows that the proposed model achieves solid returns compared against the mean-variance model and Markov chain Monte Carlo method.