The Effect of Meta-Malmquist Index on Portfolio Optimization
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
Z. Taeb
1
(
Department of Mathematics, Yadegar Imam Branch, Islamic Azad University, Tehran, Iran.
)
SH. Banihashemi
2
(
Department of Mathematics, Faculty of Mathematics and Computer Science, Allameh Tabataba'i University, Tehran, Iran.
)
کلید واژه: efficiency score, portfolio optimization, Negative data, Meta Malmquist index, Conditional Value at Risk,
چکیده مقاله :
Since the change of conditional value at risk (CVaR) in different confidence levels is very effective in portfolio optimization, the meta-Malmquist index (MMI) is utilized. For this purpose, mean-CVaR models by MMI in the presence of negative data are introduced. Like Markowitz theory in mean-variance framework, we use Conditional Value-at-risk as a risk measure and propose our models without considering the skewness and kurtosis of assets return. In our study there are some negative data, so our models is based on Range Directional Measure (RDM) model that can be taken positive and negative data. In this paper efficiencies are obtained in all confidence levels by mean-CVaR models and MMI is calculated on confidence levels as periods in the presence of negative data. This method could help the investors to construct their profitable portfolio by using MMI index. We, also carry out an empirical study within Iran stock exchange market .
از آنجائیکه تغییر ارزش در معرض خطر شرطی (CVaR) در سطوح مختلف اطمینان برای بهینه سازی سبد بسیار موثر است، شاخص متا مالمکوئیست (MMI) دراین پژوهش استفاده شده است. برای این هدف، مدلهای میانگین- ارزش در معرض خطر شرطی با شاخص متا مالمکوئیست در حضور داده منفی معرفی گردیده است. مشابه تئوری مارکوویتزدر چارچوب میانگین- واریانس، ارزش در معرض خطر شرطی به عنوان سنجه ریسک بکار رفته و مدلها بدون در نظر گرفتن چولگی و کشیدگی بازده مطرح شده است. در این مطالعه تعدادی داده منفی وجود دارد، بنابراین مدلهای برمبنای مدل اندازه جهت دار مبنایی (RDM) است که مقادیر مثبت و منفی را می پذیرد. در این مقاله، کارائیها در همه سطوح اطمینان در مدل های میانگین- ارزش در معرض خطر شرطی و شاخص متا مالمکوئیست روی سطوح اطمینان به عنوان دوره ها در حضور داده منفی محاسبه شده است. این روش به سرمایه گذاران کمک می کند که سبدهای سودآورشان را با شاخص متا مالمکوئیست بسازند. همچنین یک مطالعه عملی روی بازار بورس ایران انجام گرفته است.
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