Mixed- Asset Portfolio Optimization

Document Type : پژوهشی

Authors

• soudeh sabahi ¹
• Farimah Mokhatab Rafiei ²
• MohammadAli Rastegar ³

¹ Master of Financial Engineering of Tarbiat Modares University

² Associate Professor of Faculty of Industrial and Systems Engineering of Tarbiat Modares University

³ Assistant Professor of Faculty of Industrial and Systems Engineering of Tarbiat Modares Universi

https://doi.org/10.22067/pm.v27i19.84579

Abstract

 
Introduction
At the core of any investment lies the return on investment. To gain a favorable return, an investor should take investment-related risks. The interaction between risk and return can lead to decisions on asset allocation. A key strategy in investment discussions is diversification in investment portfolio.
Investment strategy is undetermined in different assets such as security, gold, currency and cryptocurrency. Despite the temporary recession and success of certain assets, it is hard to prioritize investment among assets (in terms of risk and return) to ensure that the investor makes the highest profit at the lowest risk. Thus, the present research used the Mean-CVaR model along with the Extreme value theory (EVT) based on Copula’s theory to estimate the correlations among time series. It used the dynamic conditional correlation (DCC) estimation method to measure the joint distribution of assets regardless of the normality assumption of data, collinearity, priorities and weights of investment in assets as optimal values.
Theoretical Framework
Diversification of conventional investment portfolio which only involves cash and security with alternative assets such as goods, currency and estate helps to decrease the correlation of assets and increase its resistance to severe changes in stock market. It, thus, helps to improve the performance of investment portfolio (Fischer & Lind-Braucher, 2010). Moreover, due to the low correlation between conventional assets and cryptocurrency and its high-efficiency, cryptocurrency is a good instrument to be combined with diverse investment portfolios and can increase the Sharpe ratio (Chuen et al., 2017).
One assumption of the distribution of financial return time series is the normality of data. However, in actuality, many financial return time series are not normal. When the normality assumption is violated, Value at Risk (VaR) is a proper measure.
Risk exposure value is not an integrated risk measurement and due to the lack of sub-aggregation property, may be inefficient in optimizing investment portfolio. Thus, researches introduced Conditional Value at Risk (CVaR) as an integrated measure and an alternative for VaR.
Methodology
As the return on financial assets is marked by a fat tail and is not marked by a normal distribution of data, to better predict the distribution of series, EVT was used. Moreover, Copula’s theory was adopted and the structure of correlations among series as time-varying was modelled via the dynamic conditional correlation estimation and the joint distribution of assets was analyzed regardless of data normality and collinearity. Then, the Mean-CVaR model was used to estimate the risk exposure value and set the investment priorities and weights among assets in Tehran Stock Exchange, Gold Coin, USD and Bitcoin as optimized values.
In this research, for an optimal allocation of investment among four above assets in daily return, Tehran Stock Exchange index (TEPIX) was used. The daily return on investment in Gold Coin (the old version) was estimated in Rials. That of USD was estimated in Rials in Tehran free market. Finally, the daily return on investment in Bitcoin was estimated in Rials between October 2014 and April 2018.
Results & Discussion
A negative correlation was estimated via DCC-Copula between certain assets, which shows that when a particular asset gains higher return on investment (than the mean value), the other asset does not follow the same trend. Thus, investors are capable of diversifying their portfolio accordingly.
Prediction of return on assets showed that the highest expected daily return on investment belonged, respectively, to Bitcoin, Gold Coin, Dollar and Tehran Stock Exchange. Moreover, as the optimized weights showed for zero CVaR, due to the low variance, the greatest investment weight was investment in Tehran Stock Exchange. The higher the investor’s risk-taking, the greater the investment weight of Gold Coin and Bitcoin.
Conclusions & Suggestions
Considering the investor’s risk-taking level, if s/he tolerates the least risks, s/he is suggested to make the most investment in securities. An increase in the minimum expected return on investment is followed by an increase in the investment share of Gold Coin and Bitcoin. Thus highly risk-taking investors are suggested to invest in Bitcoin and low risk-taking counterparts are suggested to invest in Gold Con. 
Considering the conditional Sharp (C-Sharp) ratio optimal portfolio indicated a better performance of various portfolios than any other asset, and the best performance of the portfolio includes Gold Coin with more than 70% and Dollars and Bitcoins with an equal weight. Furthermore, according to the C-Sharp ratio in the optimal portfolio, the minimum weight of Gold Coin is 60% and the maximum share of Dollar and Bitcoin is 20%.

Keywords

• DCC
• EVT
• Copula
• CVaR
• Optimization
• Mixed-Asset Portfolio

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