اندازه‌گیری حداکثر ضرر سبد بهینه سهام با مقایسه ساختار وابستگی مفصل گوسی و تی
فصلنامه بورس اوراق بهادار

فصلنامه بورس اوراق بهادار

اندازه‌گیری حداکثر ضرر سبد بهینه سهام با مقایسه ساختار وابستگی مفصل گوسی و تی

نوع مقاله : مقاله پژوهشی

نویسندگان
1 گروه ریاضی مالی، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی(ره)، بروجرد، ایران.
2 گروه ریاضی و آمار، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی (ره)، بروجرد، ایران.
چکیده
با توجه به اهمیت موضوع ریسک در بازارهای مالی، برآورد صحیح و دقیق آن همواره دغدغه اصلی حاضران در این بازارها است. بحران‌های پیاپی و پیوسته مالی ناشی از ریسک مالی که در دو دهه اخیر در مقاطع مختلف در سطح جهان روی‌ داده است لزوم برآورد دقیق ریسک مالی با تمرکز بر ریسک بازار را بیش از پیش مطرح ساخته‌ است. در این پژوهش ابتدا بهینه‌سازی سبد سهام با معیار میانگین انحراف مطلق (MAD) انجام می‌شود سپس به اندازه‌گیری ضرر سبد با به کار بردن تابع مفصل، به منظور در نظر گرفتن وابستگی مولفه‌های مورد بررسی، پرداخته می‌شود که در آن برای تخمین ضرر سبد بهینه از ارزش در معرض خطر شرطی (CVaR) استفاده می‌گردد. در این راستا اندازه ریسک سبد بهینه برای داده‌های تاریخی محاسبه می‌شود، سپس با شبیه‌سازی مونت‌کارلو ریسک سبد در یک دوره بعد پیش‌بینی می‌گردد. در انتها برای رسیدن به دقیق‌ترین برآورد از ضرر سبدبهینه، مقدار ضرر شبیه‌سازی شده با توزیع‌های مختلف، با مقدار ضرر به‌دست آمده از داده‌های تاریخی مقایسه می‌شود. داده‌های مورد مطالعه مربوط به شش سهام از بورس اوراق بهادار تهران هستند که در بازه زمانی فروردین 1396 تا خرداد 1400جمع‌آوری شده است. نتیجه‌های به‌دست آمده نشان می‌دهد که مفصل نرمال برای بازده دارایی‌ها، تخمین کمتری از ضرر سبدبهینه را نشان می‌دهد و استفاده از مفصل تی- استیودنت با درجه آزادی کم‌تر منجر به تخمین دقیق‌تری از ریسک سبد بهینه می‌شود.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Measuring the maximum optimal portfolio loss by comparing the dependency structure of Gaussian and t copulas

نویسندگان English

Mohammad Reza Haddadi 1
Manizheh Goudarzi 2
1 Financial Mathematics Department, Faculty of Basic Sciences, Ayatollah Borujerdi University, Borujerd, Iran.
2 Department, of Mathematics. Faculty of Basic Sciences, Ayatollah Borujerdi University, Borujerd, Iran.
چکیده English

Given the importance of risk in financial markets, the accurate estimation of it has always been a primary concern for participants in these markets. The recurrent financial crises resulting from financial risk over the past two decades globally have underscored the necessity of precise financial risk estimation, with a focus on market risk. In this study, portfolio optimization is initially performed using the Mean Absolute Deviation (MAD) criterion, followed by portfolio loss measurement using the copula functions to account for the dependencies between the examined components. The CVaR is employed to estimate the loss of the optimal portfolio. The size of the optimal portfolio risk is calculated based on historical data, and then Monte Carlo simulation is used to forecast portfolio risk for the next period. Finally, to achieve the most accurate estimate of the optimal portfolio loss, the simulated loss using various distributions is compared with the loss derived from historical data. The data examined pertain to six stocks from the Tehran Stock Exchange, collected from April 2017 to June 2021. The results indicate that the normal copula for asset returns shows a lower estimate of the optimal portfolio loss, while using the Student's t-copula with lower degrees of freedom provides a more accurate risk estimation for the optimal portfolio.

کلیدواژه‌ها English

Conditional value at risk
Copula function
Market risk
Monte Carlo Simulation
Dependence tail
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