Optimal Asset Allocation Research Articles

Dynamic mean variance asset allocation: Tests for robustness

We consider a portfolio consisting of a risk-free bond and an equity index which follows a jump diffusion process. Parameters for the inflation-adjusted return of the stock index and the risk-free bond are determined by examining 89 years of data. The optimal dynamic asset allocation strategy for a long-term pre-commitment mean variance (MV) investor is determined by numerically solving a Hamilton–Jacobi–Bellman partial integro-differential equation. The MV strategy is mathematically equivalent to minimizing the quadratic shortfall of the target terminal wealth. We incorporate realistic constraints on the strategy: discrete rebalancing (yearly), maximum leverage, and no trading if insolvent. Extensive synthetic market tests and resampled backtests of historical data indicate that the multi-period MV strategy achieves approximately the same expected terminal wealth as a constant weight strategy, but with much smaller variance and probability of shortfall.

Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization

In this paper, we study the dual control approach for the optimal asset allocation problem in a continuous-time regime-switching market. We find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations. These bounds can be tightened with additional controls to the dual process. We suggest a Monte-Carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utility functions, including power, non-HARA and Yaari utilities. The latter two utilities are beyond the scope of any current methods available in finding the value function.

RISK MANAGEMENT OF FINANCIAL CRISES: AN OPTIMAL INVESTMENT STRATEGY WITH MULTIVARIATE JUMP-DIFFUSION MODELS

AbstractThis paper provides an optimal asset allocation strategy to enhance risk management performance in the face of a financial crisis; this strategy entails constructing a good asset model – a multivariate jump-diffusion (MJD) model which includes idiosyncratic and systematic jumps simultaneously – and choosing suitable asset allocations and objective functions for fund management. This study also provides the dependence structure for the MJD model. The empirical implementation demonstrates that the proposed MJD model provides more detailed information about the financial crisis, allowing fund managers to determine an appropriate asset allocation strategy that enhances investment performance during the crisis.

International portfolio optimisation with integrated currency overlay costs and constraints

International financial portfolios can be exposed to substantial risk from variations of the exchange rates between the countries in which they hold investments. Nonetheless, foreign exchange can both generate extra return as well as loss to a portfolio, hence rather than just being avoided, there are potential advantages to well-managed international portfolios. This paper introduces an optimisation model that manages currency exposure of a portfolio through a combination of foreign exchange forward contracts, thereby creating a “currency overlay” on top of asset allocation. Crucially, the hedging and transaction costs associated with holding forward contracts are taken into account in the portfolio risk and return calculations. This novel extension of previous overlay models improves the accuracy of the risk and return calculations of portfolios. Consequently, more accurate investment decisions are obtained through optimal asset allocation and hedging positions. Our experimental results show that inclusion of such costs significantly changes the optimal decisions. Furthermore, effects of constraints related to currency hedging are examined. It is shown that tighter constraints weaken the benefit of a currency overlay and that forward positions vary significantly across return targets. A larger currency overlay is advantageous at low and high return targets, whereas small overlay positions are observed at medium return targets. The resulting system can hence enhance intelligent expert decision support for financial managers.

Decision Theory Matters for Financial Advice

We show that the optimal asset allocation for an investor depends crucially on the decision theory with which the investor is modeled. For the same market data and the same client data different theories lead to different portfolios. The market data we consider is standard asset allocation data. The client data is determined by a standard risk profiling question and the theories we apply are mean–variance analysis, expected utility analysis and cumulative prospect theory. For testing the robustness of our results, we carry out the comparisons for alternative data sets and also for variants of the risk profiling question.

International diversification for portfolios of European fixed-income mutual funds

PurposeThe purpose of this paper is to study the scope for country diversification in international portfolios of mutual funds for the “core” EMU countries. The author uses a sample of daily returns for country indices of French, German and Italian funds to investigate the quest for international diversification. The author focuses on fixed-income mutual funds during the period of the financial market turmoil since 2007.Design/methodology/approachThe author compute optimal portfolio allocations from both unconstrained and constrained mean-variance frameworks that take as input the out-of-sample forecasts for the conditional mean, volatility and correlation of country-level indices for funds returns. The author also applies a portfolio allocation model based on utility maximization with learning about the time-varying conditional moments. The author compares the out-of-sample forecasting performance of 12 multivariate volatility models.FindingsThe author finds that there is a “core” EMU country also for the mutual fund industry: optimal portfolios allocate the largest portfolio weight to German funds, with Italian funds assigned a lower weight in comparison to French funds. This result is remarkably robust across competing forecasting models and optimal allocation strategies. It is also consistent with the findings from a utility-maximization model that incorporates learning about time-varying conditional moments.Originality/valueThis is the first study on optimal country-level diversification for a mutual fund investor focused on European countries in the fixed-income space for the turmoil period. The author uses a large array of econometric models that captures the salient features of a period characterized by large changes in volatility and correlation, and compare the performance of different optimal asset allocation models.

Strategic Asset Allocation and Risk Budgeting for Insurers Under Solvency II

Solvency II is a new risk-based framework for setting the capital requirements of European insurance companies, in force since January 2016. The solvency capital requirement (SCR) is set such that the insurer can meet its obligations over the next 12 months with a probability of at least 99.5%. In this paper we derive expressions for an investment's marginal contribution to the solvency capital requirement, to provide insight in the risk allocation and the trade-off between return and marginal risk. In addition we derive the optimal strategic asset allocation for an insurer that maximizes the expected return on its own funds, subject to a limit on the SCR for market risk determined with the Solvency II standard formula. We then provide numerical examples to illustrate how the new framework for asset allocation and risk budgeting under Solvency II can be applied at a representative European life insurance company.

Sortino Ratio Based Portfolio Optimization Considering EVs and Renewable Energy in Microgrid Power Market

Portfolio optimization in finance is the optimal allocation of financial assets in different stocks, mutual funds, bonds, etc. to maximize the returns with risk tolerance. Sortino ratio is a measure for calculating risk adjusted return of investment portfolios. Here, it is adapted for power portfolio optimization in microgrid where total load demand (including losses) is optimally distributed to different microsources so that profit per unit risk of aggregator is maximized. The diminishment in profit (from energy and reserve markets) with reference to a target profit, for different levels of uncertainties in renewable energy and electric vehicles (EVs), is consolidated to find an estimate of risk. The profit relating to deterministic forecasted data of renewable energy and pre-dispatch information from the EV parking lots is considered as the risk free target profit. The reserve market is balanced using demand response, grid power purchase, EV discharging, and other dispatchable energy sources to compensate possible discrepancy between scheduled and actual dispatch. Stochastic weight tradeoff particle swarm optimization (SWT-PSO) is used to maximize the Sortino ratio subjected to constraints of a modified backward--forward sweep (BFS) power flow problem. The results are found to be better in terms of reduced financial risk and increased robustness to uncertainties.

The Application in the Portfolio of China's A-share Market with Fama-French Five-Factor Model and the Robust Median Covariance Matrix

In the traditional portfolio model, investors calculate the expected return of assets and the covariance matrix for optimal asset allocation. This paper divides market sentiment period into three states and selectes the securities in the Chinese stock market to construct portfolios. We implement both the Fama-French five-factor model and the robust median covariance matrix approach for predicting the expected return of the selected stocks and portfolio optimization respectively. Then we compare the performance of the portfolio constructed by the Fama-French three-factor model with that by the traditional covariance matrix in different market sentiment periods. The empirical results indicates that the performance of the portfolio constructed by the Fama-French five-factor model is more sensitive to the fluctuation of stock market sentiment, and that the robust median covariance matrix approach tends to have relatively stable portfolio return, while ineffective in the bull market. The main contribution of this paper is having empirically tested different model combinations in portfolio theory using the data of Chinese market where market sentiment has unique impact. To some extent, this paper provides a reference to the portfolio strategy.

Large‐Scale Portfolio Optimization Using Multiobjective Evolutionary Algorithms and Preselection Methods

Portfolio optimization problems involve selection of different assets to invest in order to maximize the overall return and minimize the overall risk simultaneously. The complexity of the optimal asset allocation problem increases with an increase in the number of assets available to select from for investing. The optimization problem becomes computationally challenging when there are more than a few hundreds of assets to select from. To reduce the complexity of large‐scale portfolio optimization, two asset preselection procedures that consider return and risk of individual asset and pairwise correlation to remove assets that may not potentially be selected into any portfolio are proposed in this paper. With these asset preselection methods, the number of assets considered to be included in a portfolio can be increased to thousands. To test the effectiveness of the proposed methods, a Normalized Multiobjective Evolutionary Algorithm based on Decomposition (NMOEA/D) algorithm and several other commonly used multiobjective evolutionary algorithms are applied and compared. Six experiments with different settings are carried out. The experimental results show that with the proposed methods the simulation time is reduced while return‐risk trade‐off performances are significantly improved. Meanwhile, the NMOEA/D is able to outperform other compared algorithms on all experiments according to the comparative analysis.

Long-Term Asset Allocation under Time-Varying Investment Opportunities: Optimal Portfolios with Parameter and Model Uncertainty

We study the implications of predictability on the optimal asset allocation of ambiguity averse long-term investors. We analyze the term structure of the multivariate risk-return trade-off in a VAR model under full consideration of parameter uncertainty, and we decompose the predictive covariance along different sources of risk/uncertainty. We calibrate the model to real returns of US stocks, US long-term government bonds, cash, real-estate and gold using term spread and dividend yields as additional predictive variables. While over short periods the model-implied conditional covariance structure of asset-class returns determines the optimal allocation, we find that over longer horizons the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. As a consequence, the ambiguity averse long-term investor tilts her portfolio not simply toward the global minimum-variance portfolio but shrinks portfolio weights toward a seemingly inefficient portfolio which shows maximum robustness against estimation errors. Most interestingly, we find that even though time diversification of stock returns vanishes after consideration of estimation errors, real long-term bond returns are even more affected, making stocks an important asset class for the ambiguity averse long-term investor.

Asset Allocation Strategy under Rate of Return, Rate of Inflation and Credit Spread Rate in Finite-Time Horizon

The global financial crisis has given a very tremendous financial market chaos in the world. Beside the reason that it caused mostly by the bubble economic, it also caused by the ignorance of default risk from bond derivatives such as CDO, CDS and SWAP. Those portfolio of bond ignored the risk of the low rating bonds, which gives a very high risk of having default. This research aims to find an optimal solution for dynamic portfolio in finite-time horizon under defaultable assets. Defaultable assets mean that the assets has a chance to be liquidated in a finite time horizon, e.g stock and corporate bond. The assets that will be used here are limited to the equity, corporate bond and money account. In this study, beside for having the risk of default, the investor will also consider the risk of market such as inflation into her investment. The indirect utility function will be used as the reference for investment decision. Further the asset allocation will be obtained by maximizing the total expected discounted utility in the time span during the investment is executed.To determine the financial defaulty assets, there are two methods that can be used, namely the reduced form and the structural methods. The first method is more applicable because the assets price can be linked with the market risk and credit risk and the latter method. The interest rate and the rate of inflation will be allowed as a representation of market risk, while the credit spread will be used as a representation of credit risk. Furthermore, the dynamic of asset prices can be derived analytically by using Ito Calculus in the form of the movement of the three risk factors above.The dynamic process of investor wealth will be derived from the dynamics of asset prices and budget constraints, which will be linked with portfolio composition. This problem will be solved using the stochastic dynamic programming method. Depending on the chosen utility function, the optimal solution of the portfolio composition can be found explicitly in the form of feedback control. The closed form solution will give the proportion of wealth between bond and money account. Furthermore, the composition of the portfolio will be given as the result. The complicated equation of bond pricing will follow recovery market value (RMV) methods. The finding model is later simulated with different possible values of the parameters. The result shows that the optimal asset allocation will depend on various parameters such as correlation between the risks, the chosen utility function and also recovery rate.

Optimal Asset Allocation and Benefit Outgo Policies of the DC Pension Plan During the Decumulation Phase

In this paper, we study the optimal dynamic asset allocation and benefit outgo policies of the DC pension plan with index-linked target during the decumulation phase. The pension management controls the asset allocation to minimize the deviations between the actual benefit outgo and the pre-set target with index-linked property. Using stochastic maximum principle and HJB methods, we establish the optimal proportions allocated in the risky and risk-free assets separately and the optimal benefit outgo policy. We also study the impacts of the fund wealth, target pension-salary replacement rate, the expected return of the risky asset, and the expected growth rate of the average salary on the optimal policies.

Managing ambiguity in asset allocation

This paper is about the issue of input parameter uncertainty in portfolio optimization in a discrete setting with finite states (such as the case in a world with different macroeconomic regimes). In such a setting, being unable to assign reliable point estimates to the probabilities (or frequencies) of the states creates the ambiguity. We first describe how this ambiguity can be modeled probabilistically. Then, we show how this added uncertainty can be dealt with in optimal asset allocation problems. In simple-yet-realistic example applications we demonstrate that without sacrificing much of the upside, ambiguity managed portfolios may enhance the uniformity of returns across different states when compared to portfolios constructed by traditional methods. We stress that a key conclusion to be taken from these methods builds the case for insurance-like and potentially negative-yielding investments such as bonds and commodities so as to hedge the unforeseeable macrouncertainties for a smoother portfolio performance. Finally, we offer a variety of problem domains in which ambiguity management can be nested including macroeconomic scenario-based asset allocation, investing with regime-switching models, momentum investing, and risk-based investing.

Analysing dynamic linkages and hedging strategies between Islamic and conventional sector equity indexes

ABSTRACTThis study analyses the dynamic spillovers across 10 Dow Jones Islamic and conventional sector index pairs. Using various multivariate GARCH models, the results show significant time-varying conditional correlations for all the pairs. Moreover, there is evidence that the conditional correlations for all the sector pairs, except those of the Telecommunication and Utilities sectors, increase after the onset of the global financial crisis (GFC), suggesting non-subsiding risks, contagion effects and gradual greater financial linkages. The Islamic sectors’ risk exposure can be effectively hedged over time in diversified portfolios containing conventional sector stocks. These results provide several practical implications for portfolio managers and policymakers in regard to optimal asset allocations, portfolio risk management and the diversification benefits among these markets.

Landmark buildings and diversification opportunities in the residential market

PurposeThis article aims to analyze the performance and risk of landmark building in the housing sector and to evaluate their usefulness for a diversification strategy.Design/methodology/approachAfter comparing summary statistics on the performance of landmark building with respect to other types of housing investments, the article evaluates their usefulness for a diversification strategy. The role of landmark buildings is studied using the modern portfolio theory and evaluating the role of this type of asset in the optimal asset allocation. The analysis is performed considering both the risk/return trade-off in a one-year and a multiple-year time horizon.FindingsThe results show that a landmark building can be a good investment opportunity, especially for high-risk/return investors. A not perfect correlation of the returns of this asset class with other types of housing investments implies the existence of a minimum investment in this asset class for almost all portfolios on the efficient frontier. Results are robust with respect to the length of the investment time horizon.Originality/valueThe article presents a unique analysis of intra-housing market diversification opportunities focusing on the role of landmark building in the portfolio construction. Empirical evidence supports the hypothesis that real estate investors can take advantage of investing in landmark buildings in the residential sector as well because there are no reasons to limit such investments to trophy buildings in the office and commercial sectors.

The quantification of type-2 prudence in asset allocation by the trustees of a retirement fund

AbstractIn this paper, consideration is given to the normative use of expected-utility theory for the purposes of asset allocation by the trustees of retirement funds. A distinction is drawn between “type-1 prudence”, which relates to deliberate conservatism on the part of actuaries in the setting of assumptions and the determination of model parameters, and “type-2 prudence”, which relates to the risk aversion of the trustees. The intention of the research was to quantify type-2 prudence for the purposes of asset allocation, both for defined-contribution (DC) and defined-benefit (DB) funds. The authors propose new definitions of the objective variables used as the argument of the utility function: one for DC funds and another for DB funds. A new class of utility functions, referred to as the “weighted average relative risk aversion” class is proposed. Practicalities of implementation are discussed. Illustrative results of the application of the method are presented, and it is shown that the proposed approach resolves the paradox of counter-intuitive results found in the literature regarding the sensitivity of the optimal asset allocation to the funding level of a DB fund.

Pure higher-order effects in the portfolio choice model

This paper examines the effects of higher-order risk attitudes and statistical moments on the optimal allocation of risky assets within the standard portfolio choice model. We derive the expressions for the optimal proportion of wealth invested in the risky asset to show they are functions of portfolio returns third- and fourth-order moments as well as on the investor’s risk preferences of prudence and temperance. We illustrate the relative importance that the introduction of those higher-order effects have in the decision of expected utility maximizers using data for the US.

Modelling optimal asset allocation when households experience health shocks

Health status is an important factor in household portfolio decision-making. We develop a theoretical framework to model how households make optimal asset allocation decisions in response to health risks. Our two- and three-asset models both suggest that the maximum utility is derived when households allocate a majority of their assets to human capital. When households experience acute illness shocks, their welfare and portfolio values reduce, and they need to increase their investment in human capital. When an expensive health catastrophe befalls member(s) of households, the optimal decision for asset-rich households is to undertake medical treatment, whereas for asset-poor households it is to forgo treatment. Asset-poor households in particular require public financial assistance to enable them to invest in human capital.

Optimal Granularity for Portfolio Choice

Many optimization-based portfolio rules fail to beat the simple 1/N rule out-of-sample because of parameter uncertainty. In this paper we suggest a grouping strategy in which we first form groups of equally weighted stocks and then optimize over the resulting groups only. In a simplified setting we show analytically how to optimize the trade-off between drawbacks from parameter uncertainty and drawbacks from deviating from the overall optimal asset allocation. We illustrate that the optimal group size depends on the volatility of the assets, on the number of observations and on how much the optimal asset allocation differs from 1/N. Out of sample back-tests confirm the validity of our grouping strategy empirically.