Optimal Portfolio Weights Research Articles

Optimal Portfolio Selection: Comparison of Different Methods Based on Real Life Financial Data

In this thesis, our goal is to select optimal portfolios using several portfolio optimization models that are: the original Markowitz’ Mean Variance Optimization models and its variations and compare their performance based on the portfolio risks (standard deviations) for the same given level of expected rate of returns. We also compare their performance to that of equally weighted portfolio. A portfolio is created from 10 stocks selected from Nigeria Stocks Exchange, from Jan., 1, 2019 to Dec., 31, 2019. We find the optimal portfolio weights which help us to calculate the portfolio real rate of returns in Excel using the historical data for a period of one year. We made our comparison of the methods based on the standard deviation and real rate of returns and it turns out that MVO with Risk Adjusted Return with risk aversion coefficient λ=0.01 produces the best results, followed by MVO with short position, however for easier computation Mean Absolute Deviation Optimization model is preferable and as expected, they all outperform equally weighted portfolio.

Dynamic correlation and volatility spillovers across Chinese stock and commodity futures markets

AbstractThis paper examines the return links and volatility transmission between Chinese stock and commodity futures markets and draws implications for portfolio risk management. To these ends, we consider three vector autoregression‐multivariate generalized autoregressive conditional heteroskedasticity‐class models with which to model volatilities and conditional correlations between Chinese stock and three commodity futures markets. Our empirical results reveal evidence of return linkage and volatility transmission between the Chinese stock and commodity futures markets. We also analyse optimal portfolio weights and hedging ratios between s1tock–commodity pairs. Finally, we assess implications for mixed commodity–stock portfolios and find strong evidence of hedging effectiveness and downside risk reductions.

Portfolio management and dependencies among precious metal markets: Evidence from a Copula quantile-on-quantile approach

This study examines the dependence structure among four major precious metal markets: gold, palladium, platinum, and silver. Using the novel Copula Quantile-on-Quantile Regression (C-QQR) approach of Sim (2016), we show that precious metals share a systemic relationship despite their different demand-supply interplays, applications, and the macroeconomic factors, which influence their values. Our results also suggest that correlations among markets do not remain constant over time. Furthermore, we identify the quantiles of returns for two metals where maximum benefits of negative correlations can be obtained to enhance portfolio diversification. This knowledge provides an opportunity for hedgers to decide when they should avoid going long or short on a particular metal. Finally, we find that our approach determines optimal portfolio weights that can reduce risk in metals markets more efficiently than traditional, conditional covariance-based approaches.

Analisis Portofolio Investasi dengan Metode Multi Objektif

In the formation of an efficient portfolio, many methods can be used. Of course with its own assumptions and advantages. In the process, reasonable investor assumptions tend to be risk averse. Investors who are risk averse are investors who, when faced with two investments with the same expected return, will choose an investment with a lower risk level. If an investor has several efficient portfolio choices, then the most optimal portfolio will be chosen. Optimal portfolio with mean-variance efficient portfolio criteria, investors only invest in risky assets. Investors do not include risk free assets in their portfolios. Mean-variance efficient portfolio is defined as a portfolio that has a minimum variance among all possible portfolio that can be formed, at the mean level of the same expected return. The mean variant method of the two constraints can be used as a basis in determining the optimal portfolio weight by minimizing the risk of portfolio return with two constraints. In this article the problem referred to is symbolized by lamda and beta. With this two-constraint method, the results obtained are more detailed so that they can describe the results of a sharper analysis for an investor.

Correlation and spillover effects between the US and international banking sectors: New evidence and implications for risk management

This paper quantitatively examines return transmission and volatility spillovers between banking sector stocks in the US and eight other countries by applying our newly extended VAR-DCC-MEGARCH-M model with asymmetric spillovers and Student-t or skew-t errors. Our investigations clarify almost unidirectional stock return transmission from the US banking sector to all other eight international banking sectors. In addition, we also uncover bidirectional volatility spillovers between the US and other eight international banking sector stocks, which are all tied to the leverage effect. Moreover, using the dynamic conditional variances and covariances from our extended model, we derive the time-varying optimal hedge ratios and optimal portfolio weights. These analyses reveal that, except for such extraordinary periods as during financial crises, we can hedge the US banking sector stocks with other international banking sector stocks, and that well-balanced portfolios of the US and other banking sector stocks are optimal. Furthermore, additional analysis using gold, silver, and platinum futures reveals that we can hedge international banking sector stocks with precious metal futures highly effectively, and that well-balanced portfolios of banking stocks and precious metals are optimal. Based on the results from our analyses, this paper derives many significant interpretations and implications for financial and systemic risk management.

Optimal portfolio choices using financial leverage

AbstractThis paper investigates the role of leverage in determining the investor's optimal asset allocation over multiperiod investment horizons. To do this, we allow investors to lever their financial position by borrowing from credit markets. GMM methods are used to estimate and test the optimal portfolio weights and individual's optimal choice of financial leverage. These optimal choices are assumed to be parametric functions of a set of state variables describing the evolution of the economy. The empirical application of this methodology to a portfolio of cash, bonds and stocks reveals that a) financial leverage limits the reaction of investors to changes in the investment opportunity set; b) individuals increase leverage during recessions and deleverage in expansionary periods; c) optimal portfolio weights and financial leverage are negatively related to the degree of investor's risk aversion and positively related to the investment horizon.

Portfolio Optimization of the Mean-Absolute Deviation Model of Some Stocks using the Singular Covariance Matrix

Investing in the stock sector, investors often face risk problems. Usually, forming an investment portfolio is done to minimize risk. In this research, investment portfolio optimization is discussed. The data analyzed are 8 shares traded on the capital market in Indonesia through the Indonesia Stock Exchange (IDX). Optimization is performed using the Mean-Absolute Deviation model with the singular covariance matrix to determine the optimal weights. The results of portfolio optimization Mean-Absolute Deviation model with singular covariance matrix method, was obtained optimal portfolio weights that is of 17.22% for BBCA shares; 26.64% for TKIM shares; 9.96% for BBRI shares; 9.96% for BBNI shares; 8.70% for BMRI shares; 3.75% for ADRO shares; 6.52% for GGRM shares; and 17.25% for UNTR shares. Where the optimal portfolio composition is obtained the expected rate of return (expected return) of 0.18% with a portfolio risk level (standard deviation) of 0.07%.

Bayesian inference of the multi-period optimal portfolio for an exponential utility

We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing the Jeffreys non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their point estimates together with uncertainties and their asymptotic distributions. Furthermore, we present the posterior predictive distribution for the investor’s wealth at each time point of the investment period in terms of a stochastic representation for the future wealth realization. This in turn makes it possible to use quantile-based risk measures or to calculate the probability of default, i.e the probability of the investor wealth to become negative. We apply the suggested Bayesian approach to assess the uncertainty in the multi-period optimal portfolio by considering assets from the FTSE 100 in the weeks after the British referendum to leave the European Union. The behaviour of the novel portfolio estimation method in a precarious market situation is illustrated by calculating the predictive wealth, the risk associated with the holding portfolio, and the probability of default in each period.

Volatility spillover impact of world oil prices on leading Asian energy exporting and importing economies’ stock returns

Today Asia accounts for about 40% of the world oil trade and most of the trade is transpired within the region. This study presents an investigation of the volatility spillovers among leading Asian oil exporting countries and oil importing countries’ stock exchanges and crude oil returns. The model selection from multivariant GARCH models include BEKK-GARCH, DCC-GARCH, ABEKK-GARCH and ADCC-GARCH estimation techniques which are applied using daily data from 1st September 2009 to August 31st, 2018 for the three oil exporting countries (Saudi Arabia, United Arab Emirates, Iraq) and four oil importing countries (China, Japan, India, South Korea) stock exchanges with spot crude oil. Further, these estimation results are used to analyze the optimal portfolio weights for oil-stock portfolios. The bidirectional spillover is accepted for the correlation of two oil exporting countries (Saudi Arabia, Iraq) and South Korean stock return with oil returns. the Overall the results of all the oil exporting and oil importing countries show a different level of significant correlation with oil but the influence of oil shock are more pronounced on oil exporting countries. We also present a graphical picture of the stock correlation with oil by employing DCC-GARCH model that shows great shock and volatility correlation in the period of the oil crisis of 2014–2016. According to optimal portfolio weights and hedge ratios, the oil assets are a useful instrument to minimize the portfolio risk in studied markets. The investors, however, should choose more stocks than oil assets to form an optimal portfolio in case of oil importing countries and equal ratio for the oil exporting countries.

Conditional dependence structure between oil prices and international stock markets

PurposeThe purpose of this paper is to analyze the optimal hedging strategy of the oil-stock dependence structure.Design/methodology/approachThe methodology consists to model the data over the daily period spanning from January 02, 2002 to May 19, 2016 by a various copula functions to better modeling the dependence between crude oil market and stock markets, and to use dependence coefficients and conditional variance to calculate optimal portfolio weights and optimal hedge ratios, and to suggest the best hedging strategy for oil-stock portfolio.FindingsThe findings show that the Gumbel copula is the best model for modeling the conditional dependence structure of the oil and stock markets in most cases. They also indicate that the best hedging strategy for oil price by stock market varies considerably over time, but this variation depends on both the index introduced and the model used. However, the conditional copula method with skewed student more effective than the other models to minimize the risk of oil-stock portfolio.Originality/valueThis research implication can be valuable for portfolio managers and individual investors who seek to make earnings by diversifying their portfolios. The findings of this study provide evidence of the importance of stock assets for making an optimal portfolio consisting of oil in the case of investments in oil and stock markets. This paper attempts to fill the voids in the literature on volatility among oil prices and stock markets in two important areas. First, it uses copulas to investigate the conditional dependence structure of the oil crude and stock markets in the oil exporting and importing countries. Second, it uses the dependence coefficients and conditional variance to calculate dynamic hedge ratios and risk-minimizing optimal portfolio weights for oil–stock.

Relationship between the United States housing and stock markets: Some evidence from wavelet analysis

We revisit the relationship between the United States housing and stock markets in time-frequency domain. Earlier research does not have satisfactory results on the interactions between the two markets because traditional methods average different relationships in time domain only. Our novel and informative wavelet-based multi-resolution analyzes indicate that the US housing and stock markets are at best moderately integrated and with scale-dependent co-movement, connectivity and causality. The interplay between the US housing and stock markets is stronger in the long run, with the two asset markets being bilaterally causally linked and have stronger return and volatility transmission effects. Finally, we demonstrate that the decomposition of the relationship between the real estate and stock markets over the different scales has important implications in studying the optimal portfolio weight and the hedge ratio in risk management.

Realized correlations, betas and volatility spillover in the agricultural commodity market: What has changed?

This article provides new insights on the changes in the dynamics of price correlations and spillover effects in the commodity market. Using US-traded futures price data at a 1-min frequency over the 2002–2017 period, we consider the interaction within soft and grain commodities and between these commodities and oil. We rely on a recently introduced volatility model – the realized Beta GARCH model of Hansen et al. (2014). Our results reveal that soft commodities were segmented prior to 2008 and became correlated thereafter. The nature of the increase in correlation is only temporary. The correlations within grains – already significant and positive – increased only marginally, indicating that this group has been less affected by recent events. The correlation between oil and agricultural commodities, which reached its peak in 2008, has also reverted to pre-crisis level. Spillover effects between oil and commodities have become more prominent prior to the commodity price crash. However, this increase in volatility transmission tends to precede the increase in correlations. Finally, the impact of these findings on the performance of hedging strategies and optimal portfolio weights is discussed. Our results are important for investors exposed to the commodity market as they show that while the diversification benefits of investing in this market have decreased, volatility transmission risk and hedging costs have increased.

Model Pengoptimuman Portofolio Mean-Variance dan Perkembangan Praktisnya

Many research about portfolio optimization in Indonesia still uses the ‘original’ mean-variance model as proposed by Markowitz more than 60 years ago. This article reviews the development and modification of the Markowitz’s mean-variance model, especially that dealing with real stock-market features, which could help the investor to create their own portfolio. There were several real-stock market features that implemented in the modification of mean-variance portfolios optimization models, such as the minimum transaction lots, the transaction cost, the cardinality constraint, the weight constraint, and the sectoral constraint. To implement these features, several heuristic methods were used to obtain the optimal portfolio weight, such as genetic algorithm, Tabu search, bee colony algorithm, particle swarm algorithm, and simulated annealing. These methods become alternative to the mathematical programming method.

Correlations and volatility spillovers between oil, natural gas, and stock prices in India

This study investigates the extent of time-varying volatility and correlations between crude oil, natural gas, and stock prices in India using various multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) models with and without asymmetry. Our empirical results reveal that there is no long-run cointegration between crude oil, natural gas, and stock prices in India. We find that the VARMA-DCC-GARCH model is more efficient compared to the CCC model with asymmetry in estimating time-varying correlations. We also analyze optimal portfolio weights and hedging ratios through pair trading between stocks and energy commodity futures. Our results have several implications for portfolio investors dealing with the Indian stock market and energy commodity futures for forecasting potential market risk exposure and determining the existence of portfolio diversification benefits.

Markowitz with regret

Providing a framework to integrate regret as an additional decision criterion in Markowitz’s model of portfolio selection, we propose two different views on regret: An investor might feel regret with respect to the ex-post best alternative either in terms of return or in terms of preference value. Under both views, regret can be captured by adjusting the vector of expected returns or alternatively by adjusting the return covariance matrix, retaining the tractability of the Markowitz model. The regret model, however, has very different implications for how asset characteristics affect optimal portfolios. While the impact of the skewness of an asset is strengthened, the impact of the variance shrinks. Moreover, we show for a variety of real portfolios that the effects of regret on optimal portfolio weights and the ex-ante return distribution are large.

Price risk and hedging strategies in Nord Pool electricity market evidence with sector indexes

Electricity markets become more competitive due to their liberalization; therefore, electricity prices are considerably more volatile compared to other commodity prices. As the electricity is an integral part of production and economic growth processes, the electricity price may influence the stock market through affecting the real output and consequently the sum of cash flows. Hence, investors are facing electricity price risks, and need to protect their benefits. This paper investigates the impacts of electricity market variations on the Nordic stock market returns using hourly observations of electricity spot prices pairwise in aggregate market index and some sector indexes. Our sample is divided into three sub-periods according to the electricity volatility structure. A generalized long memory model is adopted to estimate the conditional mean of the studied time series, and the FIGARCH process is used to model the conditional variance. Thereafter, a VaR, c-DCC-FIGARCH, CVaR and ΔCVaR models are applied to assess electricity market exposure. Moreover, in order to evaluate the optimal portfolio, we calculated the optimal portfolio weights, the optimal hedge ratios and the hedge effectiveness index of the electricity market commodity in several sectors stock portfolios. Our results show evidence of long run dependence between electricity market returns and sectoral stock market returns, and they indicate that the tail dependence is significant and varies across sectors and over periods. Finally, the optimal weights and hedge ratios for electricity/stock portfolio holdings are sensitive to the considered sectors. Therefore, electricity market commodities can be adopted to diversify and hedge against stock market risks.

Connectedness and hedging between gold and Islamic securities: A new evidence from time-frequency domain approaches

This paper investigates the dynamic connectedness between gold, sukuk and Islamic equities at multiple investment horizons, it also computes optimal hedge ratios and portfolio weights for these assets. Our findings suggest that gold hedges the risk of sukuk in the short and medium terms, and that gold plays an average but stable role in hedging and diversifying Islamic equities across all investment horizons. Moreover, we document a diversification benefits of portfolios combining gold and Islamic equities in the short term. These empirical findings highlight the important role that gold plays in the diversification and hedging of Islamic assets.

Optimal Vs 1/N Diversification and Portfolio Evaluation: A study on Indian Stock Market

The Modern portfolio theory of Markowitz (1952) proposed maximisation of expected utility and minimisation of the risk of the optimal portfolio for the risk-averse investors. We used the linear programming technique to estimate the optimal portfolio weights for the mean-variance efficient optimal portfolio using rebalanced and non-rebalanced portfolios and compared the performances against the 1/N heuristic portfolio. We found that the minimum-variance optimal portfolio performed better than the 1/N heuristic portfolio.

Analytic approach to variance optimization under an \u21131 constraint

The optimization of the variance of a portfolio of N independent but not identically distributed assets, supplemented by a budget constraint and an asymmetric ℓ1 regularizer, is carried out analytically by the replica method borrowed from the theory of disordered systems. The asymmetric regularizer allows us to penalize short and long positions differently, so the present treatment includes the no-short-constrained portfolio optimization problem as a special case. Results are presented for the out-of-sample and the in-sample estimator of the regularized variance, the relative estimation error, the density of the assets eliminated from the portfolio by the regularizer, and the distribution of the optimal portfolio weights. We have studied the dependence of these quantities on the ratio r of the portfolio’s dimension N to the sample size T, and on the strength of the regularizer. We have checked the analytic results by numerical simulations, and found general agreement. Regularization extends the interval where the optimization can be carried out, and suppresses the large sample fluctuations, but the performance of ℓ1 regularization is rather disappointing: if the sample size is large relative to the dimension, i.e. r is small, the regularizer does not play any role, while for r’s where the regularizer starts to be felt the estimation error is already so large as to make the whole optimization exercise pointless. We find that the ℓ1 regularization can eliminate at most half the assets from the portfolio (by setting their weights to exactly zero), corresponding to this there is a critical ratio r = 2 beyond which the ℓ1 regularized variance cannot be optimized: the regularized variance becomes constant over the simplex. These facts do not seem to have been noticed in the literature.Graphical abstract

Portfolio selection: shrinking the time-varying inverse conditional covariance matrix

In this paper we consider a portfolio selection problem under the global minimum variance model where the optimal portfolio weights only depend on the covariance matrix of asset returns. First, to reflect the rapid changes of financial markets, we incorporate a time-varying factor in the covariance matrix. Second, to improve the estimation of the covariance matrix we use the shrinkage method. Based on these two key aspects, we propose a framework for shrinking the time-varying inverse conditional covariance matrix in order to enhance the performance of the portfolio selection. Furthermore, given the shortcoming that the inverse covariance matrix is inaccurate in a number of cases, we develop a new method that transforms the inverse of the covariance matrix into a product to improve the performance of the inverse covariance matrix, and prove its theoretical availability. The proposed portfolio selection strategy is applied to analyze real-world data and the numerical studies show it performs well.