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Special purpose companies issue stocks to raise money to finance development of real estate and infrastructure. The advantage of a stock issue is that it does not entail financial cost such as interest on a loan. However, financing obtained in this way has been insufficient due to low interest by investors because of the large variability of the stocks’ earnings rates. The purpose of this paper is to propose methods to improve investment earnings rate for financing.

The proposed methods are Markowitz’s model and a combination of Markowitz’s model and Monte Carlo simulation. The proposed methods were verified by comparison with actual earnings rate.

The earnings rate was increased by as much as 23 percent over the actual value. Then, earnings rate compared with risk was analyzed using the Sharpe ratio which is a method to measure investment performance. The performance was also increased by as much as 23 percent over the actual value. The proposed method can help activate investment by increasing investors’ interest in the stock issue.

This study verified that Markowitz’s portfolio model, which is used for econometrics, could be applied for financing of construction project. It is valuable because the previous studies did not propose the method for financing.

The notion that asset diversification reduces risk is ancient and can be traced as far back as the Talmud which states, “A man should always keep his wealth in three forms: one-third in real estate, another in merchandise, and the remainder in liquid assets” (Baba Metzia, verse 42a). Somewhat more recently, in 1738, Daniel Bernoulli observed, “it is advisable to divide goods which are exposed to some small danger into several small portions rather than to risk them all together” (1738/1954, p. 30). Arguably, however, it was not until 1935 that the future Nobel laureate J. R. Hicks offered some early direction for modern portfolio theory. Although his research was more concerned with explaining the demand for money, he points out two important considerations for modeling risk. Hicks writes, “The risk factor comes into our problem in two ways: First, as affecting the expected period of investment, and second, as affecting the expected net yield of investment” (Hicks, 1935, p. 7). Regarding Hicks' first point, both Markowitz (1952) and Roy (1952) emplace their analyses in a one-period investment horizon. Second, and even more relevant to modern portfolio theory, is Hicks' suggestion of using an expected value calculated with subjective probabilities. Hicks continues, “It is convenient to represent these probabilities to oneself, in statistical fashion, by a mean value, and some measure of dispersion” (1935, p. 8). Clearly, Hicks comes very close to articulating a mean–variance solution. Crucially, and unlike Roy or Markowitz, Hicks does not develop this line of reasoning nor does he suggest the particular use of variance or standard deviation as that measure of risk. Nonetheless, Hicks' suggestion anticipates the work of Markowitz and Roy.¹

Portfolio selection has been extensively studied in field of business and economics. Many methods have been developed to construct a well-diversified portfolio that is expected to result in higher investment return with minimum risk. One of the most foundational works contributing to modern portfolio selection is the Markowitz mean variance optimization approach. The Markowitz approach heavily relies on past stock price performance, both in term of correlation structure and the return, to predict the future outcome. We constructed both Markowitz portfolio and the Fundamental Indexing portfolio independently, then using Buffet ratio to weight, combined both portfolio into a newly blended portfolio, test out-of-sample the new portfolio in term of return and then compare it to the Indonesian LQ45 benchmark index. The result shows that the new combined portfolio returns annually on average 43.89% higher than the benchmark index.

This issue of Managerial Finance is devoted to modern portfolio theory which has evolved since the pioneering work of Markowitz in 1952. Before the development of modern portfolio theory investors and their advisers used the “traditional approach” to investment management and portfolio selection.

Factor investment is booming in global asset management, especially environmental, social, and governance (ESG), dividend yield, and volatility factors. In this chapter, we use data from the US securities market from 2003 to 2019 to predict dividends and volatility factors through machine learning and historical data–based methods. After that, we utilize particle swarm optimization to construct the Markowitz portfolio with limits on the number of assets and weight restrictions. The empirical results show that that the prediction ability using XGBoost is superior to the historical factor investment method. Moreover, the investment performance of our portfolio with ESG, high-yield, and low-volatility factors outperforms baseline methods, especially the S&P 500 ETF.

This study aims to make investment decisions in stock markets using forecasting-Markowitz based decision-making approaches.

The authors’ approach offers the use of time series prediction methods including autoregressive, autoregressive moving average and artificial neural network, rather than calculating the expected rate of return based on distribution.

The results show that using time series prediction methods has a significant effect on improving investment decisions and the performance of the investments.

In this study, in contrast to previous studies, the alteration in the Markowitz model started with the investment expected rate of return. For this purpose, instead of considering the distribution of returns and determining the expected returns, time series prediction methods were used to calculate the future return of each asset. Then, the results of different time series methods replaced the expected returns in the Markowitz model. Finally, the overall performance of the method, as well as the performance of each of the prediction methods used, was examined in relation to nine stock market indices.

In recent times, behavioural models for asset allocation have been getting more attention due to their probabilistic modelling for scenario consideration. Many investors are thinking about the trade-offs and benefits of using behavioural models over conventional mean-variance models. In this study, the authors compare asset allocations generated by the behavioural portfolio theory (BPT) developed by Shefrin and Statman (2000) against the Markowitz (1952) mean-variance theory (MVT).

The data used have been culled from BRICS countries' major index constituents from 2009 to 2019. The authors consider a single period economy and generate future probable outcomes based on historical data in order to determine BPT optimal portfolios.

This study shows that a fair number of portfolios satisfy the first entry constraint of the BPT model. BPT optimal portfolio exhibits high risk and higher returns as compared to typical Markowitz optimal portfolio.

The BRICS countries' data were used because the dynamics of the emerging markets are significantly different from the developed markets, and many investors have been considering emerging markets as their new investment avenues.

Should we include cryptocurrency in risky portfolio investing? Bitcoin, given its status as the leader of cryptocurrencies and a speculative asset due to its non-dividend-paying trait and high volatility as well as high returns, poses an interesting question whether it can also be beneficial in a portfolio of risky assets. In order to find an answer, we revisit the conventional dual objective of minimizing risk and maximizing expected return for risky assets. Various models are tested to analyze the risk-return trade-off of risky portfolios including Bitcoin. Given an initial budget for a finite portfolio, the cumulative filtration yields the expected return and the covariance matrix. With the addition of Bitcoin, we compare the performance of the portfolio generated from the optimization models and technical analysis. The main implications are follows: (1) risk tolerance and diversification constraints are the key factors in portfolio optimization; (2) including cryptocurrency enhances portfolio returns; and (3) the Markowitz model (Kataoka’s and conditional value-at-risk models) recommends to fully weigh (unload) Bitcoin in (from) the portfolio.

One important study in the portfolio investment is the study of the optimal asset allocations. Markowitz is the pioneer of modern portfolio theory that analyses the performance of portfolio based on the mean (reward) and variance (risk). Motivated by the Markowitz's mean variance model, the purpose of this paper is to propose a new portfolio optimization model that takes into consideration both processes of purification and screening, which are key to constructing a Shariah-compliant portfolio. In practice, this paper introduces a stochastic purification variable and a probabilistic screening constraint into a portfolio model.

First, the authors study the stochastic nature of purification variable and apply it to both investment and dividend purification. Second, recognizing that the importance of on-going screening could adversely affect the portfolio strategy, the authors impose probabilistic constraints to control the risk of compliance change. They evaluate the proposed model by formulating the screening constraints at both asset and portfolio levels, together with three different financial screening divisors that are broadly used by the international Shariah boards. The authors also conduct an extensive empirical study using a sample of Shariah-compliant public companies listed on the Indonesia Stock Exchange.

Based on the empirical example presented in this paper, the authors found that the purification variable in the proposed model is closer to the practice in the Sharia capital market in terms of the nature of the non-constant data, and this variable reduces the total income of portfolio which has not been captured in the previous literature. The authors also have successfully derived the portfolio screening constraint to mitigate the risk of the asset change to be non-compliant in the future.

Based on the authors’ knowledge, this is the first paper that proposed the stochastic purification and the dynamic of screening processes into the Shariah portfolio model. This paper also examines the impact of non-short-selling, purification and screening policies to the performance of Shariah portfolio.

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.