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.     

Time Diversification,Safety-First and Risk

The purpose of this article is to demonstrate the effect of investment time horizon on the choice of risky assets in a portfolio when the investor in question is optimizing a Safety-First (downside risk-aversion) utility function. It is shown, under standard assumptions, that although shortfall risk decreases exponentially with investment time horizon, the portfolio asset allocation proportions remain invariant. In fact, in some instances, the optimal allocation will not even depend on the drift of the underlying assets. Thus, we extend the classical results of Samuelson and Merton, derived under conventional utility assumptions, to an individual optimizing an A.D. Roy Safety-First objective; a discontinuous utility function that has been extolled as conforming to observed investor behaviour. A numerical example is provided.     

Speculative trading preferences of retail investor birth cohorts

This study examines the effect of investor birth cohorts on speculative investment preferences. Using retail trading and portfolio data from Finland over two decades, we find that individuals who have experienced desirable macro-economic and social conditions during adolescence, such as high gross domestic product (GDP) growth and low divorce rates, are more likely to invest in speculative stocks. A positive relation is found between the proportion of speculative-prone cohorts in the stock market and returns of stocks of lottery nature. We provide new evidence on the adverse effect of speculative investments, finding that cohorts with higher speculative investment weights on their portfolios achieve lower absolute and risk-adjusted returns. We also provide support for earlier research that identifies a positive association between recent portfolio performance and the propensity to invest in speculative stocks.     

On equity market inefficiency during the COVID-19 pandemic

We show that during the weeks following the initiation of the COVID-19 pandemic, the United States equity market was inefficient. This is demonstrated by showing that utility maximizing agents over the time period ranging from mid-February to late March 2020 can generate statistically significant profits by utilizing only historical price and virus related data to forecast future equity ETF returns. We generalize Merton’s optimal portfolio problem using a novel method based upon a likelihood ratio in order to construct a dynamic trading strategy for utility maximizing agents. These strategies are shown to have statistically significant profitability and strong risk and performance statistics during the COVID-19 time-frame.     

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.     

Tax management strategies with multiple risky assets

We study the consumption-portfolio problem in a setting with capital gain taxes and multiple risky stocks to understand how short selling influences portfolio choice with a shorting-the-box restriction. Our analysis uncovers a novel trading flexibility strategy whereby, to minimize future tax-induced trading costs, the investor optimally shorts one of the stocks (or equivalently, buys put options) even when no stock has an embedded gain. Alternatively, an imperfect form of shorting the box can reduce aggregate equity exposure ex post. Given these two short selling strategies, it is common for an unconstrained investor to short some equity while a constrained investor holds a positive investment in all stocks. With no shorting, the benefit of trading separately in multiple stocks is not economically significant.     

Does long-term disequilibrium in stock price predict future returns?

We propose a trading strategy based on error correction term (ECT), the residuals from the cointegration relation between the levels of security and the market portfolio. We find that buying stocks in the top 10 % ECT and selling stocks in the bottom 10 % ECT generates 1.09 % a month for 6-month holding period over 1965–2005. The monthly return increases to 1.57 % when the above trading strategy is applied to stocks with insignificant cointegration with the market portfolio. This profit is robust to three and four factor models. Moreover, this profit is neither driven by small and illiquid stocks nor is the result of any inherent positive serial correlation.     

Small caps in international equity portfolios: the effects of variance risk

We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e., display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary, small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns.      

Responsible investment in the Chinese stock market

This paper provides insights into the current development of responsible investment in the Chinese stock market. We find that responsible investment can bring portfolio benefits to investors, and institutional investors have a holding preference for stocks in responsible investment indexes. By using a national air pollution proxy, we find that investors’ pessimistic mood on days with heavy air pollution has a negative influence on the stock return of A-shares, while stocks in responsible investment indexes display improved performance over the same time period. We use aggregated trading data to study the trading preference of Chinese retail investors on days when they are influenced by air pollution, and find that their total trading ratio shows a negative influence for both A-shares and responsible investment indexes. Moreover, there is more seller-initiated trading of the whole sample but more buyer-initiated trading of stocks in responsible investment indexes on air pollution days. This finding is consistent with the different stock return performances of these two samples. Our finding extends the studies of responsible investment to emerging markets and presents new evidence about the influence of environmental factors on trading behavior and return performance.     

Predictability and diversification benefits of investing in commodity and currency futures

We re-examine diversification benefits of investing in commodities and currencies by considering a risk-averse investor with mean-variance preferences who exploits the possibility of predictable time variation in asset return means, variances, and covariances. We implement unconditional and conditional efficient portfolio strategies designed to exploit this predictability, together with more traditional and/or ad hoc ones yet hitherto relatively unexplored in this context (including the equally weighted, fixed weight, volatility timing, and reward-to-risk timing strategies). We find that, for all portfolio strategies, commodities and currencies do not improve the investment opportunity set of the investor with an existing portfolio of stocks, bonds and T-bills, and an investment horizon of one month. Our findings, which reverse the conclusions of previous studies that focus on static portfolio strategies, are robust across several performance metrics.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

Are investors consistent in their trading strategies? An examination of individual investor-level data

While it has been demonstrated that momentum or contrarian trading strategies can be profitable in a range of institutional settings, less evidence is available concerning the actual trading strategies investors adopt. Standard definitions of momentum or contrarian trading strategies imply that a given investor applies the same strategy to both their buy and sell trades, which need not be the case. Using investor-level, transaction-based data from China, where tax effects are neutral, we examine investors' buy-sell decisions separately to investigate how past returns impact differentially on the trading strategies investors adopt when buying and selling stock. After controlling for a wide range of stock characteristics, extreme price changes and portfolio value, a clear asymmetry in trading is observed; with investors displaying momentum behavior when buying stocks, but contrarian behavior when selling stocks. This asymmetry in behavior is not driven purely by reactions to stock characteristics or extreme stocks. We discuss behavioral and cultural explanations for our findings.     

Earning the right premium on the right factor in portfolio planning

The optimal portfolio as well as the utility from trading stocks and derivatives depends on the risk factors and on their market prices of risk. We analyze this dependence for a CRRA investor in models with stochastic volatility, jumps in the stock price, and jumps in volatility. We find that the compartment of the total variance into diffusion risk and jump risk has a small impact on the utility in an incomplete market only. In contrast, the decomposition of the equity risk premium into a diffusion component and a jump risk component and the compartment of the latter into its various elements has a huge impact on the utility in a complete market. The more extreme the market prices of risk, i.e. the more they deviate from their equilibrium values, the larger the utility of the investor. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced.     

Time Diversification: Empirical Tests

This paper investigates the relationship between the performance of equity and the length of the investment horizon used by investors. We examine optimal portfolio time diversification and two definitions of ex ante time diversification. Using almost two centuries of US and UK data we find some support for the hypothesis that equity represents a significantly better investment over long investment horizons than over short investment horizons. Where this result holds, the likely explanation is mean-aversion in fixed-income asset returns. However, these results are sensitive to changes in investor risk preference, changes in utility function specification, changes in the sample period used, changes in investor constraints, and the definition of time diversification adopted. They also differ between the US and UK markets.     

Are paper winners gamblers? Evidence from Australian retail investors

This study examines stock market gambling using a comprehensive set of investor characteristics and past portfolio performance measures. We find that retail investors overinvest in ‘lottery stocks’, stocks with gambling‐like properties. Significant portfolio underperformance is the result of gambling through lottery stocks. Investors are more likely to gamble following recent portfolio paper gains, regardless of realised performance, providing new evidence that paper gains trigger a house money effect. Investors trading greater values or holding more stocks, and older and female investors, are less likely to invest in lottery stocks.     

An encyclopedia for stock markets? Wikipedia searches and stock returns

We present empirical evidence that collective investor behavior can be inferred from large-scale Wikipedia search data for individual-level stocks. Drawing upon Shannon transfer entropy, a model-free measure that considers any kind of statistical dependence between two time series, we quantify the statistical information flow between daily company-specific Wikipedia searches and stock returns for a sample of 447 stocks from 2008 to 2017. The resulting stock-wise measures on information transmission are then used as a signal within a hypothetical trading strategy. The results evidence the predictive power of Wikipedia searches and are in line with the previously documented notion of buying pressure revealed by online investor attention and the trading patterns of retail investors.     

Portfolio implications of systemic crises

Systemic crises can have grave consequences for investors in international equity markets, because they cause the risk-return trade-off to deteriorate severely for a longer period. We propose a novel approach to include the possibility of systemic crises in asset allocation decisions. By combining regime switching models with Merton [Merton, R.C., 1969. Lifetime portfolio selection under uncertainty: The continuous time case. Review of Economics and Statistics 51, 247–257]-style portfolio construction, our approach captures persistence of crises much better than existing models. Our analysis shows that incorporating systemic crises greatly affects asset allocation decisions, while the costs of ignoring them is substantial. For an expected utility maximizing US investor, who can invest globally these costs range from 1.13% per year of his initial wealth when he has no prior information on the likelihood of a crisis, to over 3% per month if a crisis occurs with almost certainty. If a crisis is taken into account, the investor allocates less to risky assets, and particularly less to the crisis prone emerging markets.