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This research aims to select the best-fitting model(s) of equal risk contribution portfolios (ERC). ERC is a robust estimation in the absence of reasonable expectations about future returns.

The portfolio consists of five environmental-friendly exchange-traded funds (ETFs). It applies equal risk optimization, beneficial when the assets are firmly linked, such as the ETFs. This paper operationalizes 20 covariance models in portfolio construction, and a portfolio with classic covariance is the benchmark to beat. To select the best-fitting model(s), the paper applies statistical inferences of the model confidence set. This research also constructs the newly-developed minimum connectedness optimization method and utilizes maximum drawdown as the primary evaluation tool.

The outbreak of COVID-19 hugely impacts the portfolio drawdown. The results also show that the classic covariance is hard to beat, partly explained by estimation error and model misspecification. This paper suggests that equal risk contribution can benefit from copula-based covariance. It consistently and significantly outperforms the other models in various robustness tests.

In the absence of substantial predictions about future returns and the existence of strongly linked assets, selecting appropriate portfolio components by risk contribution is a sound choice.

This is the first paper to select the best-fitting model(s) of ERC portfolio during the COVID-19.

The recent development of the European debt sovereign crisis showed that sovereign debt is not “risk free.” The traditional index bond management used during the last two decades such as the market-capitalization weighting scheme has been severely called into question. In order to overcome these drawbacks, alternative weighting schemes have recently prompted attention, both from academic researchers and from market practitioners. One of the key developments was the introduction of passive funds using economic fundamental indicators.

In this chapter, the authors introduced models with economic drivers with an aim of investigating whether the fundamental approaches outperformed the other models on risk-adjusted returns and on other terms.

The authors did this by constructing five portfolios composed of the Eurozone sovereigns bonds. The models are the Market-Capitalization RP, GDP model RP, Ratings RP model, Fundamental-Ranking RP, and Fundamental-Weighted RP models. These models were created exclusively for this chapter. Both Fundamental models are using a range of 10 country fundamentals. A variation from other studies is that this dissertation applied the risk parity concept which is an allocation technique that aims to equalize risk across different assets. This concept has been applied by assuming the credit default swap as proxy for sovereign credit risk. The models were run using the Generalized Reduced Gradient (GRG) method as the optimization model, together with the Lagrange Multipliers as techniques and the Karush–Kuhn–Tucker conditions. This led to the comparison of all the models mentioned above in terms of performance, risk-adjusted returns, concentration, and weighted average ratings.

By analyzing the whole period between 2006 and 2014, it was found that both the fundamental models gave very appealing results in terms of risk-adjusted returns. The best results were returned by the Fundamental-Ranking RP model followed by the Fundamental-Weighting RP model. However, better results for the mixed performance and risk-adjusted returns were achieved on a yearly basis and when sub-dividing the whole period in three equal periods. Moreover, the authors concluded that over the long term, the fundamental bond indexing triumphed over the other approaches by offering superior return and risk characteristics. Thus, one can use the fundamental indexation as an alternative to other traditional models.

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. The authors enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. The authors also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

It is crucial to find a better portfolio optimization strategy, considering the cryptocurrencies' asymmetric volatilities. Hence, this research aimed to present dynamic optimization on minimum variance (MVP), equal risk contribution (ERC) and most diversified portfolio (MDP).

This study applied dynamic covariances from multivariate GARCH(1,1) with Student’s-t-distribution. This research also constructed static optimization from the conventional MVP, ERC and MDP as comparison. Moreover, the optimization involved transaction cost and out-of-sample analysis from the rolling windows method. The sample consisted of ten significant cryptocurrencies.

Dynamic optimization enhanced risk-adjusted return. Moreover, dynamic MDP and ERC could win the naïve strategy (1/N) under various estimation windows, and forecast lengths when the transaction cost ranging from 10 bps to 50 bps. The researcher also used another researcher's sample as a robustness test. Findings showed that dynamic optimization (MDP and ERC) outperformed the benchmark.

Sophisticated investors may use the dynamic ERC and MDP to optimize cryptocurrencies portfolio.

To the best of the author’s knowledge, this is the first paper that studies the dynamic optimization on MVP, ERC and MDP using DCC and ADCC-GARCH with multivariate-t-distribution and rolling windows method.

The purpose of this study is to provide a new way to optimize a portfolio and to show that combining the Hurst exponent and wavelet analysis may help to increase portfolio returns.

The authors use the Hurst exponent and wavelet analysis to study the long-term dependencies between sovereign bonds and sectoral indices of India. The authors further construct and evaluate the performance of three portfolios constructed on the basis of Hurst standard deviation (SD) – global minimum variance (GMV), most diversified portfolio (MDP) and equal risk contribution (ERC).

The authors find that an ERC portfolio generates positive superior return as compared other two. Since our sample includes periods of two crisis – post-2007 financial crisis and the ongoing pandemic, this study reveals that combining government bond with equities and gold provides a higher returns when the portfolios are constructed using the risk exposures of each asset in the overall portfolio risk.

The findings provide guidance to portfolio managers by helping them to select assets using the Hurst approach and wavelet analysis thereby increasing the portfolio returns.

In this study, the authors use a combination of Hurst exponent and wavelet analysis to understand the long-term dependencies among various assets and provide a new methodology to optimize a portfolio. As far as the authors’ knowledge, no study in the past has attempted to provide a joint framework for portfolio optimization and therefore this study is the first to apply this methodology.

The aim of the study was to analyze the performance of Black-Litterman (BL) portfolios using a views estimation procedure that simulates investor forecasts based on technical analysis.

Ibovespa, S&P500, Bitcoin and interbank deposit rate (IDR) indexes were respectively considered proxies for the national, international, cryptocurrency and fixed income stock markets. Forecasts were made out of the sample aiming at incorporating them in the BL model, using several portfolio weighting methods from June 13, 2013 to August 30, 2022.

The Sharpe, Treynor and Omega ratios point out that the proposed model, considering only variable return assets, generates portfolios with performances superior to their traditionally calculated counterparts, with emphasis on the risk parity portfolio. Nonetheless, the inclusion of the IDR leads to performance losses, especially in scenarios with lower risk tolerance. And finally, given the impact of turnover, the naive portfolio was also detected as a viable alternative.

The results obtained can contribute to improve investors practices, specifically by validating both the performance improvement – when including foreign assets and cryptocurrencies –, and the application of the BL model for asset pricing.

The main contributions of the study are: performance analysis incorporating cryptocurrencies and international assets in an uncertain recent period; the use of a methodology to compute the views simulating the behavior of managers using technical analysis; and comparing the performance of portfolio management strategies based on the BL model, taking into account different levels of risk and uncertainty.

In asset management, what if clients want to purchase protection from risk factors, under the form of variance risk premia. This paper aims to address this topic by developing a portfolio optimization framework based on the criterion of the minimum variance risk premium (VRP) for any investor selecting stocks with an expected target return while minimizing the risk aversion associated to the portfolio according to “good” and “bad” times.

To accomplish this portfolio selection problem, the authors compute variance risk-premium as the difference from high-frequencies' realized volatility and options' implied volatility stemming from 19 stock markets, estimate a 2-state Markov-switching model on the variance risk-premia and optimize variance risk-premia portfolios across non-overlapping regions. The period goes from March 16, 2011, to March 28, 2018.

The authors find that optimized portfolios based on variance-covariance matrices stemming from VRP do not consistently outperform the benchmark based on daily returns. Several robustness checks are investigated by minimizing historical, realized or implicit variances, with/without regime switching. In a boundary case, accounting for the realized variance risk factor in portfolio decisions can be seen as a promising alternative from a portfolio performance perspective.

As a new management “style”, the realized volatility approach can, therefore, bring incremental value to construct the conditional covariance matrix estimates.

The authors assess the portfolio performance determined by the variance-covariance matrices that are derived by four models: “naive” (Markowitz returns benchmark), non-switching VRP, maximum likelihood regime-switching VRP and Bayesian regime switching VRP. The authors examine the best return-risk combination through the calculation of the Sharpe ratio. They also assess another different portfolio strategy: the risk parity approach.

Sees the objective of teaching financial management to be to help managers and potential managers to make sensible investment and financing decisions. Acknowledges that financial theory teaches that investment and financing decisions should be based on cash flow and risk. Provides information on payback period; return on capital employed, earnings per share effect, working capital, profit planning, standard costing, financial statement planning and ratio analysis. Seeks to combine the practical rules of thumb of the traditionalists with the ideas of the financial theorists to form a balanced approach to practical financial management for MBA students, financial managers and undergraduates.

In order to succeed in an action under the Equal Pay Act 1970, should the woman and the man be employed by the same employer on like work at the same time or would the woman still be covered by the Act if she were employed on like work in succession to the man? This is the question which had to be solved in Macarthys Ltd v. Smith. Unfortunately it was not. Their Lordships interpreted the relevant section in different ways and since Article 119 of the Treaty of Rome was also subject to different interpretations, the case has been referred to the European Court of Justice.