Selecting a discrete portfolio

We study the problem of selecting an optimal portfolio out of a finite set of available assets. Assets are characterized by their expected returns and the covariance matrix, and investors are assumed to have a mean–variance utility, that is, their utility function is linear in the mean and variance of the portfolio they hold.When assets are negatively correlated, or even when a slightly more general condition is satisfied, we provide an algorithm for selecting an optimal portfolio. We illustrate the usefulness of this algorithm by some comparative statics result. When assets can be positively correlated, we deliver a negative result regarding the existence of useful algorithms for selecting an optimal portfolio.     

Lessons from naïve diversification about the risk-reward trade-off

Studies of naïve diversification show that average total portfolio risk declines asymptotically as number of stocks increases. Recent work shows that a significant amount of idiosyncratic risk remains, even for portfolios with large numbers of stocks. The corresponding shocks are non-trivial. For example, more than half of all equal-weighted portfolios with 100 stocks have better than a 16 percent chance of an annual shock at least as large as about half of the annualized mean excess return on the U.S. total stock market index over July 1963–June 2018. I perform a simulation analysis of portfolio reward-to-risk as well as the components of total portfolio risk. On average, investors do not appear to be rewarded for exposure to non-systematic risk. The cross-sectional distribution of the true Sharpe ratio rises and its dispersion shrinks significantly as the number of stocks in the portfolio increases, whereas the cross-sectional distribution of the true non-systematic risk falls and its dispersion shrinks significantly as the number of stocks in the portfolio increases. This pattern appears regardless of the true asset pricing model for generating security returns, the portfolio weighting method, or specification of security alphas.     

Distributional properties of portfolio weights

In this paper, we prove several distributional properties for optimal portfolio weights. The weights are estimated by replacing the parameters with the sample counterparts. All results for finite samples are made assuming normally distributed returns. We calculate the exact covariances for the weights obtained by the expected quadratic utility. Additionally we derive the multivariate density function of the global minimum variance portfolio and the univariate density of the tangency portfolio. We obtain the conditional density for the Sharpe ratio optimal weights and show that the expectations of the Sharpe ratio optimal weights do not exist. Moreover, we determine the asymptotic distributions of the estimated weights assuming that the returns follow a multivariate stationary Gaussian process.     

The economic benefits of market timing the style allocation of characteristic-based portfolios

Many exchange traded funds track simple characteristic-based equity portfolios such as the market capitalization, the fundamental value or the inverse volatility portfolio. This paper provides theoretical and empirical evidence for the economic benefits in exploiting the timing-gains that result from the time-varying relative performance of these characteristic-based portfolios. Under a factor model for expected returns, we show that this dynamic portfolio allocation can be efficient across the low-dimensional set of characteristic-based portfolios. We assess the out-of-sample performance on the S&P 100 universe over the period 1990–2013 and show gains in stability and significant positive risk-adjusted returns for the dynamic style portfolio. We conduct several robustness tests and extensions confirming the benefits of dynamic style allocation across characteristic-based portfolios.     

Assessing and valuing the nonlinear structure of hedge fund returns

Several studies have put forward that hedge fund returns exhibit a nonlinear relationship with equity market returns, captured either through constructed portfolios of traded options or piece‐wise linear regressions. This paper provides a statistical methodology to unveil such nonlinear features with respect to returns on benchmark risk portfolios. We estimate a portfolio of options that best approximates the returns of a given hedge fund, account for this search in the statistical testing of the nonlinearity, and provide a reliable test for a positive valuation of the fund. We find that not all fund categories exhibit significant nonlinearities, and that only a few strategies provide significant value to investors. Our methodology helps identify individual funds that provide value in an otherwise poorly performing category. Copyright © 2010 John Wiley & Sons, Ltd.     

Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options

We propose a criterion for portfolio selection, implied excess Sharpe ratio. The implied excess Sharpe ratio is intended as an excess Sharpe ratio (versus the underlying stock) that investors can expect to enjoy from portfolios that include options and is a useful ex ante indicator that can be easily calculated. There are a variety of ways to include options in a portfolio, but we theoretically show that the combination that produces the largest implied excess Sharpe ratio is the best way to maximize the short-term Sharpe ratio. The selection process uses implied excess Sharpe ratio, which is easily calculated from stock lending fees implied by stock prices and actual stock lending fee. It does not require historical simulation or prediction of share price average growth rates and is highly transparent as it can be easily reproduced (at a low calculation cost). Hence, the implied excess Sharpe ratio is a simple but effective tool for investors seeking returns in exchange for a certain amount of risk that want to use the options market efficiently. The short-term Sharpe ratio is not necessarily the only criterion, but is a rational benchmark of portfolio performance closely related to criteria such as the long-term Sharpe ratio and maximum drawdown. To examine the benefit of the concept, we construct an investment strategy that automatically selects from multiple candidate portfolios that are made up of combinations of Nikkei futures and Nikkei listed options the portfolio with the largest implied excess Sharpe ratio. Back-testing shows that this investment strategy performs well over the long term as well.     

Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-$t$ and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-$t$ copulas, are best at reducing the portfolio risk.     

Robust portfolio optimization

We address the problem of estimating risk-minimizing portfolios from a sample of historical returns, when the underlying distribution that generates returns exhibits departures from the standard Gaussian assumption. Specifically, we examine how the underlying estimation problem is influenced by marginal heavy tails, as modeled by the univariate Student-t distribution, and multivariate tail-dependence, as modeled by the copula of a multivariate Student-t distribution. We show that when such departures from normality are present, robust alternatives to the classical variance portfolio estimator have lower risk.     

The behavior of MENA oil and non-oil producing countries in international portfolio optimization

It is well documented in developed economies that portfolio investment across national borders brings benefits of increasing returns and/or reducing risk. Dividing MENA stock markets into two main groups (oil producing and non-oil producing countries), this study examines the potential role of each group in providing diversification benefits for international investors. In addition, the behavior of the long and the short-run Efficient Frontiers (EFs) constructed by each of the sub-groups and the combined MENA markets is explored. Multi-objective international portfolio models are proposed under Mean-Variance and Mean-Lower Partial Moment frameworks, and the Multiple Fitness Function Genetic Algorithm (MFFGA) is used to find the EFs of optimal portfolios. The findings indicate that the stock markets of oil producing countries can be considered as a potential avenue for international portfolio diversification for investors not only from the same countries but also from the other MENA markets. It was also found that international portfolios constructed from the combination of MENA equity markets are more stable compared to the portfolios of sub-group markets. Further, the findings indicate that the behavior of short-term EFs in the MENA region cannot be predicted by the behavior of long-term EFs.     

Rational plunging and the option value of sequential investment: The case of petroleum exploration

The potential to invest sequentially in related assets creates a tradeoff between diversification and concentration. Loading a portfolio with correlated assets has the potential to inflate variance, but also creates information spillovers and real options that may augment total return and mitigate variance. We examine this tradeoff in the context of petroleum exploration. Using a simple model of geological dependence, we show that the value of learning options creates incentives for investors to plunge into dependence; i.e., to assemble portfolios of highly correlated exploration prospects. Risk-neutral and risk-averse investors are distinguished not by the plunging phenomenon, but by the threshold level of dependence that triggers such behavior. Aversion to risk does not imply aversion to dependence. Indeed the potential to plunge should be larger for risk-averse investors than for risk-neutral investors. We test the empirical validity of our theory by examining bidding activity in petroleum lease sales. We find significant plunging behavior across a broad sample of oil companies. We also find that privately-held firms pursue even more concentrated (less diversified) prospect portfolios than publicly-held firms—which we attribute to risk aversion rather than size.     

Variance swaps,non-normality and macroeconomic and financial risks

This paper studies the determinants of the variance risk premium and discusses the hedging possibilities offered by variance swaps. We start by showing that the variance risk premium responds to changes in higher order moments of the distribution of market returns. But the uncertainty that determines the variance risk premium – the fear by investors to deviations from normality in returns – is also strongly related to a variety of macroeconomic and financial risks associated with default, employment growth, consumption growth, stock market and market illiquidity risks. We conclude that the variance risk premium reflects the market willingness to pay for hedging against these financial and macroeconomic sources of risk. An out-of-sample asset allocation exercise shows that the inclusion of the variance swap reduces the modified value-at-risk with respect to a portfolio holding exclusively the equity market portfolio.     

Is there a diversification “cost” of Shari’ah compliance? Empirical evidence from Malaysian equities

Islamic equity portfolios work with a smaller investment universe given the filtering of non-Shari’ah compliant stocks. It has been theoretically argued that this culminates in suboptimal portfolio diversification, which in turn adversely affects risk-adjusted returns. We offer empirical evidence that such a conceived portfolio diversification “penalty” is far from a foregone conclusion, at least empirically. Our results tend to indicate that Islamic portfolios are not invariably handicapped in terms of portfolio diversification. We also explored dimensions that may account for differences in the relative investment performance between Islamic and conventional portfolios, such as portfolio constraints, short selling and market conditions. We believe this paper is among the first to apply substantial empirical analysis specifically with respect to the portfolio diversification perspective on Islamic equity investments.     

Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models

We extend the recently introduced latent threshold dynamic models to include dependencies among the dynamic latent factors which underlie multivariate volatility. With an ability to induce time-varying sparsity in factor loadings, these models now also allow time-varying correlations among factors, which may be exploited in order to improve volatility forecasts. We couple multi-period, out-of-sample forecasting with portfolio analysis using standard and novel benchmark neutral portfolios. Detailed studies of stock index and FX time series include: multi-period, out-of-sample forecasting, statistical model comparisons, and portfolio performance testing using raw returns, risk-adjusted returns and portfolio volatility. We find uniform improvements on all measures relative to standard dynamic factor models. This is due to the parsimony of latent threshold models and their ability to exploit between-factor correlations so as to improve the characterization and prediction of volatility. These advances will be of interest to financial analysts, investors and practitioners, as well as to modeling researchers.     

Modeling common volatility characteristics and dynamic risk premia in European equity markets

The paper applies a Factor-GARCH model to evaluate the impact of the market portfolio, as a single common dynamic risk factor, on conditional volatility and risk premia for the returns on size-based equity portfolios of three major European markets; France, Germany and the United Kingdom. The results show that for the size-based portfolios the factor loading for the dynamic market factor is significant and positive but the association between the risk premia and the conditional market volatility is weak. However, the dynamic market factor is shown to explain common characteristics in the conditional variance such as asymmetry and persistence. This finding is consistent across markets and portfolio sizes.     

The economic value of patent portfolios

Patent holders may choose to protect innovations with single patents or to develop portfolios of multiple, related patents. We propose a decision‐making model in which patent holders allocate resources to either expanding the number of related patents or investing in higher value of patents in the portfolio. We estimate the derived value equation using portfolio value data from an inventor survey at the level of individual inventions rather than the firm as a whole. We find that investments in individual inventions exhibit diminishing returns, and that a good part of the value of a portfolio depends on adding new patented inventions. Also, while diminishing returns to individual inventions are stable across subsamples, the returns to portfolio size vary between complex and discrete industries, and between inventions that are science‐based or driven by customer information. When firms seek to strengthen appropriability, the returns to an increase of portfolio size are not different from the sample average. Thus, a higher number of inventions in a portfolio may reflect both stronger appropriability via patents and genuine creation of value.     

Homeownership and mixed-asset portfolio allocations

Homeownership represents both a consumption and an investment decision for individuals. Considering the investment benefits of the home, we estimate the total returns and risk associated with the investment in single-family homes. Then, using a mean–variance utility function, we consider the impact of homeownership and mortgage loan financing on the optimal asset allocation decisions of individuals and contrast this with advice that does not include the home as part of the portfolio. While optimal portfolio weights are dependant upon both the degree of risk aversion of the individual investor and the relative importance of the home in the overall net worth picture, we show that, in general, the higher the home-to-net worth ratio, the higher the optimal portfolio allocation to stock. For most investors, including the home in the optimization decision leads to higher allocations to risky stock than suggested by traditional advice that ignores the home.     

A test for the weights of the global minimum variance portfolio in an elliptical model

In this paper we consider the weights of the global minimum variance portfolio (GMVP). The returns are assumed to follow a matrix elliptically contoured distribution, i.e., the returns are assumed to be neither independent nor normally distributed. A test for the general linear hypothesis is given. The distribution of the test statistic is derived under the null and the alternative hypothesis. It turns out that its distribution is invariant with respect to the type of the matrix elliptical distribution, i.e., the stochastic properties of the GMVP do not depend either on the mean vector or on the distributional assumptions imposed on asset returns. In an empirical study we analyze an international diversified portfolio.     

Takeover prediction using forecast combinations

The ability to identify likely takeover targets at an early stage should provide investors with valuable information, enabling them to profit by investing in potential target firms. In this paper we contribute to the takeover forecasting literature by suggesting the combination of probability forecasts as an alternative method of improving the forecast accuracy in takeover prediction and realizing improved economic returns from portfolios made up of predicted targets. Forecasts from several non-linear forecasting models, such as logistic and neural network models and a combination of them, are used to determine the methodology that best reduces the out-of-sample misclassification error. We draw two general conclusions from our results. First, the forecast combination method outperforms the single models, and should therefore be used to improve the accuracy of takeover target predictions. Second, we demonstrate that an investment in a portfolio of the combined predicted targets results in significant abnormal returns being made by an investor, in the order of up to double the market benchmark return when using a portfolio of manageable size.     

Do High‐Frequency Data Improve High‐Dimensional Portfolio Allocations?

This paper addresses the debate about the usefulness of high‐frequency (HF) data in large‐scale portfolio allocation. We construct global minimum variance portfolios based on the constituents of the S&P 500. HF‐based covariance matrix predictions are obtained by applying a blocked realized kernel estimator, different smoothing windows, various regularization methods and two forecasting models. We show that HF‐based predictions yield a significantly lower portfolio volatility than methods employing daily returns. Particularly during the 2008 financial crisis, these performance gains hold over longer horizons than previous studies have shown, translating into substantial utility gains for an investor with pronounced risk aversion. Copyright © 2013 John Wiley & Sons, Ltd.     

Time and frequency connectedness and portfolio diversification between cryptocurrencies and renewable energy stock markets during COVID-19

The assessment of the time and frequency connectedness between cryptocurrencies and renewable energy stock markets is of key interest for portfolio diversification. In this paper, we utilize weekly data from 07 August 2015 to 26 March 2021 to document the dynamics and portfolio diversification from a fresh cryptocurrencies-renewable energy perspective. Our time-frequency domain spillovers results reveal that renewable energy stocks are the main spillover contributors in the connectedness system and the short-run spillovers dominate their long-run counterparts. Furthermore, investors can gain more profits through short-run transactions in our portfolio design and we can optimize portfolios by investing a large portion in cryptocurrencies. A fascinating fact is that the COVID-19 pandemic can reverse the effectiveness of our hedging strategy.