A Time-Series Model of Stock Returns with a Positive Short-Term Correlation and a Negative Long-Term Correlation

We study portfolio stock return behavior that exhibits both a positive autocorrelation over short horizons and a negative autocorrelation over long horizons. These autocorrelations are more significant in small size portfolios. Among various forms of temporary components in stock prices, an AR(2) component is the simplest model compatible with this pattern of returns, which yields an ARMA(2,2) model of stock returns. We show that the significance of this model is that it requires the presence of feedback trading, which is a form of irrational trades, and the market's slow adjustment to the market fundamentals, which is consistent with recent modelings of stock prices. We find that the variation of the temporary component becomes greater as the firm size gets smaller. This implies that the deviation from the market fundamentals is larger in small size portfolios than in large size portfolios.     

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.     

Moments of multivariate regime switching with application to risk-return trade-off

We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.     

Time and frequency dynamics of connectedness and hedging performance in global stock markets: Bitcoin versus conventional hedges

Some studies have revealed the hedging ability of Bitcoin against stock markets, but the knowledge of how it compares with other hedges is in its infancy. This paper presents the first study on time-frequency domain connectedness and hedging among five hedges (Bitcoin, crude oil, commodities, gold and the U.S. dollar (USD) index) and four stock indices (developed markets ex U.S., emerging markets ex China, U.S. and China). We find that the connectedness between hedges and stock markets varies by time across time horizons. Specifically, the connectedness between Bitcoin and stock indices is the smallest among all hedges, especially for the short horizon. Gold and USD are isolated from other markets at longer horizons. The hedging ratio, optimal portfolio weights and hedging effectiveness also vary across investment horizons. For short-term investment, gold has better hedging effectiveness, especially for emerging stock markets and the U.S. stock market. For median- and long-term investment, USD has better performance, especially for developed markets ex U.S. and emerging stock markets. Additionally, although Bitcoin has good hedging properties, it has high volatility compared with other hedging assets. In other words, if Bitcoin is included in a portfolio, investors should pay attention to its wide variation. These empirical findings highlight the important role that gold and USD play in hedging against global stock markets.     

Short Positions in the First Principal Component Portfolio

Insurance companies and pension plans typically hold well-diversified equity portfolios. These institutions are also often restricted from taking short positions. The diversification requirement operates on the portfolio level, while the short sale constraint is at the individual security level. We examine an investment strategy that exposes a tension between these two requirements. This strategy uses the first principal component to construct the portfolio and by design meets the first requirement. Empirical portfolios based on the first principal component do an excellent job of capturing market exposure and minimizing diversifiable risk. However, in practice such portfolios sometimes contain a few short positions. So this strategy does not always meet the second requirement. We examine which features of stock returns give rise to short positions when a portfolio is based on the first principal component, and we are able to identify the characteristics of the stocks that are responsible for the short positions. These stocks tend to have negative correlations with the majority of other stocks. In contrast such stocks would typically be held long in a Markowitz portfolio. We discuss and explain this puzzle.     

Portfolio Diversification Benefits at Different Investment Horizons During the Arab Uprisings: Turkish Perspectives Based on MGARCH–DCC and Wavelet Approaches

This study is an initial attempt at investigating the extent to which portfolio diversification benefits at different investment horizons are available to a Turkish investor from investment in MENA countries exposed to the Arab spring based on MGARCH-DCC and Wavelet techniques on daily data spanning from 2005 to 2015. The findings tend to suggest that the Turkish investors may not benefit from investment in Egypt for almost all investment horizons but may have moderate benefits from Lebanon up to the investment horizons of 32–64 days and longer. However, Turkish investors may benefit from Oman excepting the longer investment horizons. In the long run, all stock holding periods exceeding 32 days have minimal benefits for portfolio diversification.     

Investment Horizon and Composition of Optimal Portofolio: International Evidence

Little attention has been paid in the literature to the impact of different investment horizons on the portfolio compositiondespite its importance to portfolio managers. One exception isthe study by Gunthorpe and Levy (1994) on the U.S. stock market.Our paper extends the same study to the stock markets of Japan,Hong Kong and Korea. Using 40 individual stocks in each market,our results support those of Gunthorpe and Levy (1994) in thatthe composition of an optimal portfolio depends heavily on theinvestment horizon. When the investment horizon lengthens, theproportion of defensive stocks becomes larger while that ofaggressive stocks becomes smaller.     

The price of shelter - Downside risk reduction with precious metals

Investor aversion to extreme losses may motivate them to seek out investments perceived to function as a safe haven during times of crisis. In this study, we consider the potential for precious metals to mitigate downside risk when combined with equities, and evaluate the impact on portfolio risk-adjusted returns. Each of gold, silver and platinum are found to contribute to downside risk reduction at short horizons, but diversification into silver and platinum may result in increased long horizon portfolio risk. The price of sheltering an equity portfolio from downside risk is a relative reduction in portfolio risk-adjusted returns. Variance and kurtosis properties of precious metals are identified as marginal contributors to downside risk reduction. Futures markets on precious metals are also shown to present an interesting and viable diversification alternative to physical metals.     

Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis

This paper investigates the portfolio optimization under investor’s sentiment states of Hidden Markov model and over a different time horizon during the period 2004–2016. To compare the efficient portfolios of the Islamic and the conventional stock indexes, we have employed two approaches: the Bayesian and Markowitz mean-variance. Our findings reveal that the Bayesian efficient frontier of Islamic and conventional stock portfolios is affected by the investor’s sentiment state and the time horizon. Our findings also indicate that the investor’s sentiment regimes change the Islamic and the conventional optimal diversified portfolios.Moreover, the results show that the potential diversification benefits seem to be more important when using the Bayesian approach than when applying the Markowitz approach. This finding is valid for the bearish, depressed, bullish and calm states in Islamic stock markets. However, the diversification of potential portfolios is significant only for the bullish and the bubble states in the conventional financial markets.The findings of the study provided additional evidence for investors to exploit googling investor sentiment states to evaluate the portfolio performance and make an optimal portfolio allocation.     

Does a Held-to-Maturity Strategy Impede Effective Portfolio Diversification for Islamic Bond (Sukuk) Portfolios? A Multi-Scale Continuous Wavelet Correlation Analysis

There is a critical gap in the literature in studying the portfolio diversification opportunities available to sukuk investors and evaluating these in light of held-to-maturity strategies usually adopted by these investors. This article has made an initial attempt to study the portfolio diversification strategies for sukuk portfolios across heterogeneous investment horizons. Our findings critically indicate that returns between local currency sukuk in different markets generally have low levels of correlations across different investor holding periods, thus enabling both short and long-run portfolio diversification benefits. However, in contrast, international currency sukuk issued in different markets exhibits high levels of correlations in the longer-term investor holding periods. Also, in the domestic market context, returns on different classes of domestic sukuk are found to exhibit strong correlations in the longer-holding periods. Our findings critically highlight the feasibility of held-to-maturity sukuk investment strategies from a portfolio diversification perspective.     

Conditional portfolio allocation: Does aggregate market liquidity matter?

This paper investigates how aggregate liquidity influences optimal portfolio allocations across various US characteristic portfolios. We consider short-term allocation problems, with single and multiple risky assets, and use the nonparametric approach of Brandt (1999) to directly express optimal portfolio weights as functions of aggregate liquidity shocks. We find, first, that the effect of aggregate liquidity is positive and decreasing with the investment horizon. Second, at daily and weekly horizons, this effect is weaker on allocations in large stocks and gets stronger as we move toward small stocks, regardless of the other stock characteristics, suggesting that liquidity is the main concern of very short-term investors. Third, conditional allocations in risky assets decrease and exhibit shifts toward more liquid assets as aggregate liquidity worsens. Overall, conditioning on aggregate liquidity yields empirical results that are consistent with the so-called flight-to-safety and flight-to-liquidity episodes. Finally, we propose a simple tactical investment strategy and show how aggregate liquidity information can be exploited to enhance the out-of-sample performance of long-term strategies.     

Nonlinear mean reversion in stock prices

This paper provides new evidence on the time-series predictability of stock market returns by introducing a test of nonlinear mean reversion. The performance of extreme daily returns is evaluated in terms of their power to predict short- and long-horizon returns on various stock market indices and size portfolios. The paper shows that the speed of mean reversion is significantly higher during the large falls of the market. The parameter estimates indicate a negative and significant relation between the monthly portfolio returns and the extreme daily returns observed over the past one to eight months. Specifically, in a quarter in which the minimum daily return is −2% the expected excess return is 37 basis points higher than in a month in which the minimum return is only −1%. This result holds for the value-weighted and equal-weighted stock market indices and for each of the size decile portfolios. The findings are also robust to different sample periods, different indices, and investment horizons.     

The Diversification Effects of Initial Public Offerings

Abstract:  A firm's stock becomes publicly tradable through an initial public offering (IPO). This study suggests a portfolio diversification perspective to explore IPOs. We examine whether investors can gain diversification benefits by adding an IPO portfolio to a set of benchmark portfolios sorted by firm size and book-to-market ratio. Using US IPOs from 1980-2002, we find that adding a value-weighted IPO portfolio does lead to a statistically and economically significant enlargement of the investment opportunity set for investors relative to investing solely in a set of benchmark portfolios. Specifically, the Sharpe ratio of the tangency portfolio increases by 5.50% on average after including IPO stocks. Furthermore, IPOs associated with prestigious lead underwriters are the main source of this augmentation of the mean-variance investment opportunity set. Finally, our study implies that issuing IPO exchange traded funds or similar products can provide diversification gains to investors.     

Do IPO index portfolios improve the investment opportunities for mean–variance investors?

We set out in this study to examine whether investors can improve their investment opportunity sets through the addition of an IPO index portfolio into various sets of benchmark portfolios. Using the IPOX indices from the years 1980–2006, we find that adding an IPO index portfolio does lead to a statistically significant enlargement of the investment opportunity set for investors. Our empirical findings are robust, demonstrating that there is scope for the further development of financial products relating to IPO stocks, since investors can gain diversification benefits through investing in such IPO-related products.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.     

Bonds versus stocks: Investors’ age and risk taking

It has become increasingly popular to advise investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the well-known decision rules such as mean–variance or stochastic dominance rules are unable to explain this common practice. Almost stochastic dominance (ASD) and almost mean–variance (AMV) approaches are used to examine the dominance of stock and bond portfolios. ASD and AMV rules unambiguously support the popular practice of advising higher stock to bond ratio for long investment horizons. Hence, we provide an explanation to the practitioners’ recommendation within the expected utility paradigm.     

Block bootstrap methods and the choice of stocks for the long run

Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the ‘time diversification’. In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two methods of bias reduction. We show that an improper use of a block bootstrap method usually causes underestimation of the risk of a portfolio whose returns are independent over time and overestimation of the risk of a portfolio whose returns are mean-reverting.     

Nonsynchronous Security Trading and Market Index Autocorrelation

The theoretical portfolio autocorrelation due solely to nonsynchronous trading is estimated from a derived model. This estimated level is found to be substantially less than that observed empirically. The theoretical and empirical relationship between portfolio size and autocorrelation also is investigated. The results of this study suggest that other price-adjustment delay factors in addition to nonsynchronous trading cause the high autocorrelations present in daily returns on stock index portfolios.     

The Role of the Investment Horizon in Optimal Portfolio Sequencing (An Intuitive Demonstration in Discrete Time)

This paper examines the role played by the investor's investment horizon in the choice of optimal portfolios. A complete discrete-time, multiperiod, portfolio model is presented with a choice criterion that is consistent with the traditional utility approach but which is more amenable to a multiperiod environment. It is shown that investors should choose progressively less risky single-period portfolios as their investment horizons grow shorter, even if they do not become more risk averse. This result holds both in the presence and in the absence of a riskless asset. The results are consistent with empirical evidence and the financial planning practice of moving investors into progressively less risky portfolios as they grow older.     

Impact of financial market uncertainty and macroeconomic factors on stock–bond correlation in emerging markets

This paper examines the impact of global financial market uncertainty and domestic macroeconomic factors on stock–bond correlation in emerging markets. In particular, by applying the wavelet analysis approach, we are able to examine stock–bond correlations over different time horizons in ten emerging markets. We find that stock–bond correlation patterns vary significantly between the time horizons. In particular, the correlation in short horizon changes the sign rapidly showing sustainable negative episodes while the correlation in long horizon stays positive most of the time. The most important factor influencing stock–bond correlation in short horizon is the monetary policy stance, while the factors with the greatest long-term impact are inflation and stock market uncertainty. Finally, global stock market uncertainty plays a more significant role than global bond market uncertainty in explaining stock–bond correlations in emerging markets.