Computing optimal rebalance frequency for log-optimal portfolios

Log-optimal investment portfolio is deemed to be impractical and cost-prohibitive due to inherent need for continuous rebalancing and significant overhead of trading cost. We study the question of how often a log-optimal portfolio should be rebalanced for any given finite investment horizon. We develop an analytical framework to compute the expected log of portfolio growth when a given discrete-time periodic rebalance frequency is used. For a certain class of portfolio assets, we compute the optimal rebalance frequency. We show that it is possible to improve investor log utility using this quasi-passive or hybrid rebalancing strategy. Simulation studies show that an investor shall gain significantly by rebalancing periodically in discrete time, overcoming the limitations of continuous rebalancing.     

Computing optimal rebalance frequency for log-optimal portfolios in linear time

The pure form of log-optimal investment strategies are often considered to be impractical due to the inherent need for continuous rebalancing. It is however possible to improve investor log utility by adopting a discrete-time periodic rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and approximate log-normality for a sum of log-normal random variables, we find that the optimum rebalance frequency is a piecewise continuous function of investment horizon. One can construct this rebalance strategy function, called the optimal rebalance frequency function, up to a specified investment horizon given a limited trajectory of the expected log of portfolio growth when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm.     

Who gains and who loses on stock markets? Risk preferences and timing matter

This paper uses an agent-based multi-asset model to examine the effect of risk preferences and optimal rebalancing frequency on performance measures while tracking profit and risk-adjusted return. We focus on the evolution of portfolios managed by heterogeneous mean-variance optimizers with a quadratic utility function under different market conditions. We show that patient and risk-averse agents are able to outperform aggressive risk-takers in the long-run. Our findings also suggest that the trading frequency determined by the optimal tolerance for the deviation from portfolio targets should be derived from a tradeoff between rebalancing benefits and rebalancing costs. In a relatively calm market, the absolute range of 6% to 8% and the complete-way back rebalancing technique outperforms others. During particular turbulent periods, however, none of the existing rebalancing techniques improves tax-adjusted profits and risk-adjusted returns simultaneously.     

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

We study the destabilizing effect of hedging strategies under Markovian dynamics with transaction costs. Once transaction costs are taken into account, continuous portfolio rehedging is no longer an optimal strategy. Using a non-optimizing (local in time) strategy for portfolio rebalancing, explicit dynamics for the price of the underlying asset are derived, focusing in particular on excess volatility and feedback effects of these portfolio insurance strategies. Moreover, it is shown how these latter depend on the heterogeneity of the insured payoffs. Finally, conditions are derived under which it may be still reasonable, from a practical viewpoint, to implement Black–Scholes strategies.     

Monetary policy and portfolio rebalancing: Evidence from European equity mutual funds

In this study, we provide empirical evidence on the portfolio rebalancing of European equity mutual funds following both conventional (CMP) and unconventional monetary policies (UMP). We use 1772 equity mutual funds’ portfolio holdings over the period 2002Q4–2016Q4. This level of granularity allows us to characterise the funds’ asset allocation in different portfolio dimensions: the size, style, currency, and domicile of the stocks, and managers’ preferred investment strategies. Using a panel fixed effect estimator, our results support the existence of portfolio rebalancing across equity categories following UMP. European equity mutual funds’ assets are, on average, reallocated towards mid-cap, and core stocks and developing economies, and shifted away from small-cap and value stocks and home as well as developed countries. Furthermore, mutual funds seem to concentrate on their preferred and historical investment strategies. These two results suggest that managers are more willing to invest in safer and familiar stocks following UMP announcements thereby decreasing the risk of asymmetry of information. We finally show that the funds size, returns volatility and expense ratio affect the strength of the rebalancing.     

The wealth effects of portfolio rebalancing in emerging equity markets

This paper analyzes the wealth effects of alternative portfolio rebalancing strategies for equity investments in nine emerging markets for the period from 1976 to 1998. The choice of rebalancing intervals has a large effect on wealth accumulation and the geometric mean return. The difference between no rebalancing and semi-annual rebalancing is 5.87 percentage points per year. Surprisingly, semi-annual rebalancing, which was optimal for this data set, was also 2.62 percentage points per year better than monthly rebalancing. Positive first- and second-degree autocorrelation among the monthly returns appears to account for the decrease in returns for rebalancing more frequently than semi-annually.     

Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

We study the constant rebalancing strategy for multi-period portfolio optimization via conditional value-at-risk (CVaR) when there are nonlinear transaction costs. This problem is difficult to solve because of its nonconvexity. The nonlinear transaction costs and CVaR constraints make things worse; state-of-the-art nonlinear programming (NLP) solvers have trouble in reaching even locally optimal solutions. As a practical solution, we develop a local search algorithm in which linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the algorithm attains a good solution in a practical time. It is better than the revised version of an existing global optimization. We also assess the performance of the constant rebalancing strategy in comparison with the buy-and-hold strategy.     

Properties of the Margrabe Best-of-two strategy to tactical asset allocation

The Margrabe Best-of-two (MBo2) strategy is a rule-based dynamic investment solution for the two-asset allocation problem. Its typical implementation involves yearly rebalancing the portfolio weights to 50–50 between a low-risk and high-risk asset. It uses intra-year weight adjustments to chase the momentum of the best performing asset by replicating the Margrabe formula for the value of a European option to exchange an asset for another asset at year-end. In practice, this means that the Margrabe portfolio allocation benefits from the upside potential of the high-risk asset and the downside protection from the low-risk asset. The MBo2 allocation depends on the assets' prices, their return volatilities, and correlation, as well as the remaining time until year-end. In this paper, we derive analytical formulae and use simulations to provide insights into the sensitivity of the strategy's weights and performance to these input parameters. We also report the results of an extensive out-of-sample evaluation for the MBo2 strategy applied to the bond–equity, real estate–equity, and world equity–emerging market equity portfolio allocation problems.     

Portfolio rebalancing and the transmission of large-scale asset purchase programs: Evidence from the Euro area

The European Central Bank's large-scale asset purchase program targeted safe assets, but also aimed to impact prices of risky assets. The mechanism for this is the “portfolio rebalancing channel”, where financial institutions’ portfolio decisions impact financial prices more broadly. We examine this mechanism using cross-sectional heterogeneity in how the financial portfolios of different sectors of the European economy were affected around the purchase program. We find evidence of rebalancing. In vulnerable countries, where macroeconomic unbalances and relatively high risk premia remained, we document rebalancing towards riskier securities. In less vulnerable countries, based on granular information for large European banks, we document rebalancing toward bank loans.     

Risk parity portfolio optimization under a Markov regime-switching framework

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.     

Relative performance of dynamic portfolio insurance strategies: Australian evidence

This paper simulates the performance of synthetic put portfolio insurance and Constant Proportion Portfolio Insurance (CPPI) using Australian data for the period from 1992 to 2000. These strategies are implemented by trading in the index and bills and simulation is conducted across 18 scenarios. We find that while the CPPI dominates in scenarios using daily rebalancing, the synthetic put strategy delivers better outcomes when value based triggers are used. More importantly, although the two per cent market move trigger emerges as the optimal rebalancing choice, overall, neither strategy appears justifiable in terms of achieving downside protection or allowing upside gain.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints

We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of state variables. By suitably embedding the constrained problem in an appropriate family of unconstrained ones, we provide some equivalent optimality conditions for the indirect value function and optimal portfolio weights. These results simplify and help to solve the constrained optimal portfolio choice problem in jump-diffusion models. Finally, we apply our theoretical results to several examples, to examine the impact of no-short-selling and/or no-borrowing constraints on the performance of optimal portfolio strategies.     

Financial contagion in the laboratory: The cross-market rebalancing channel

We present the results of the first experimental study of financial markets contagion. We develop a model of financial contagion amenable to be tested in the laboratory. In the model, contagion happens because of cross-market rebalancing, a channel for transmission of shocks across markets first studied by Kodres and Pritsker (2002). Theory predicts that, because of portfolio rebalancing, a negative shock in one market transmits itself to the others, as investors adjust their portfolio allocations. The theory is supported by the experimental results. The price observed in the laboratory is close to that predicted by theory, and strong contagion effects are observed. The results are robust across different market structures. Moreover, as theory predicts, lower asymmetric information in a (“developed”) financial market increases the contagion effects in (“emerging”) markets.     

Performance evaluation of portfolio insurance strategies using stochastic dominance criteria

This paper evaluates the performance of the stop-loss, synthetic put and constant proportion portfolio insurance techniques based on a block-bootstrap simulation. We consider not only traditional performance measures, but also some recently developed measures that capture the non-normality of the return distribution (value-at-risk, expected shortfall, and the Omega measure). We compare them to the more comprehensive stochastic dominance criteria. The impact of changing the rebalancing frequency and level of capital protection is examined. We find that, even though a buy-and-hold strategy generates higher average excess returns, it does not stochastically dominate the portfolio insurance strategies, nor vice versa. Our results indicate that a 100% floor value should be preferred to lower floor values and that daily-rebalanced synthetic put and CPPI strategies dominate their counterparts with less frequent rebalancing.     

Consumption smoothing and portfolio rebalancing: The effects of adjustment costs

A household's response to income and return shocks depends on the costs of portfolio adjustment. In particular, the extent of portfolio rebalancing and consumption smoothing are influenced by the presence of non-convex portfolio adjustment costs. Suppose bonds can be adjusted costlessly while adjustments to stock accounts entail adjustment costs. Due to these portfolio adjustment costs, the household demands both stocks and bonds. A household can buffer some income fluctuations without incurring adjustment costs and engage in costly portfolio rebalancing less frequently. Using the estimated preference parameters and portfolio adjustment costs, the response to income and return shocks is nonlinear and reflects the interaction of portfolio rebalancing and consumption smoothing.     

Can Investors Profit from the Prophets? Security Analyst Recommendations and Stock Returns

We document that purchasing (selling short) stocks with the most (least) favorable consensus recommendations, in conjunction with daily portfolio rebalancing and a timely response to recommendation changes, yield annual abnormal gross returns greater than four percent. Less frequent portfolio rebalancing or a delay in reacting to recommendation changes diminishes these returns; however, they remain significant for the least favorably rated stocks. We also show that high trading levels are required to capture the excess returns generated by the strategies analyzed, entailing substantial transactions costs and leading to abnormal net returns for these strategies that are not reliably greater than zero.     

New Evidence on Optimal Asset Allocation

Brocato and Steed (1998) showed that portfolio rebalancing based on NBER business cycle turning points substantially improves in‐sample Markowitz efficiency. In a similar vein, we investigate potential improvements from rebalancing based on turning points in the monetary cycle. We find that the monetary cycle has greater influence than the business cycle on the variance/covariance structure of multiple asset classes. Furthermore, we find substantial improvements in in‐sample efficiency beyond a buy‐and‐hold strategy and the business‐cycle approach. Importantly, our indicator of monetary cycle turning points has a practical advantage over NBER business cycle turning points, in that it relies only on ex ante information. In out‐of‐sample tests, we continue to find superior portfolio performance after transactions costs using the monetary cycle to time portfolio rebalancing.     

Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20-year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor's horizon and rebalancing frequency.     

New evidence on the impact of size and taxation on the seasonality of UK equity returns

The paper investigates the extent to which capital gains taxation and the portfolio rebalancing hypothesis may account for the seasonality of UK equity returns. The empirical results show that in small firm portfolios during the period of capital gains taxation, April but not January seasonality is consistent with the tax-loss selling hypothesis. The January seasonality, which is detected even before the introduction of capital gains taxation, is also consistent with the portfolio rebalancing hypothesis until the 1980s, when such seasonality becomes increasingly insignificant.