بهینه‌سازی سبد سرمایه‌گذاری با دارایی‌های متنوع

یکی از مهم‌ترین دغدغه‌های همیشگی سرمایه‌گذاران انتخاب بهترین فرصت‌های سرمایه‌گذاری با بیشترین ارزش سرمایه‌گذاری است و با توجه به گزینه‌های مختلف برای سرمایه‌گذاری، تنوع بخشی در سبد سرمایه‌گذاری یک استراتژی مفید و مطرح در مباحث سرمایه‌گذاری می‌باشد. اما استراتژی سرمایه‌گذاری در بین دارایی‌های مختلف نظیر بورس اوراق بهادار، طلا، ارز و رمز ارز نامشخص بوده و معلوم نیست که علیرغم رکود و رونق موقت برخی از دارایی‌ها (همانند بورس و طلا) و همچنین تاثیرات آن‌ها بر یکدیگر، اولویت‌بندی سرمایه‌گذاری (به لحاظ ریسک و بازده) بین دارایی‌های فوق چگونه تخصیص یابد. هدف از انجام این تحقیق، پیشنهاد اوزان بهینه سرمایه‌گذاری بین دارایی‌های بورس اوراق بهادار تهران، سکه بهار آزادی، دلار آمریکا و بیت‌کوین از طریق حداقل‌سازی ارزش در معرض ریسک شرطی با روش میانگین– ارزش در معرض خطر شرطی می‌باشد. بدین منظور با توجه به دم‌پهن بودن توزیع بازدهی دارایی‌های مالی جهت پیش‌بینی توزیع دنباله‌ها از نظریه ارزش فرین، رویکرد فراتر از آستانه استفاده شده است. همچنین برای محاسبه ارتباط بین این دارایی‌ها از ترکیب روش همبستگی شرطی پویا و کاپولا استفاده شده است که همبستگی علاوه بر غیرخطی بودن، پویا و متغیر با زمان نیز باشد. با استفاده از اطلاعات روزانه شاخص دارایی‌های فوق در فاصله زمانی مهر 1393 تا فروردین 1397، مرز کارای سرمایه‌گذاری رسم شده است. نتایج نشان می‌دهد در سطح ریسک (ارزش در معرض ریسک شرطی) صفر به دلیل تغییرات کم واریانس، بیش‌ترین وزن سرمایه‌گذاری در بورس اوراق بهادار و در بالاترین سطح ریسک، بیش‌ترین وزن سرمایه‌گذاری در رمز ارز (بیت‌کوین) به دلیل بازده بالاتر، تخصیص یافته است. همچنبن مقایسه پرتفوهای بهینه با استفاده از نسبت شارپ شرطی حاکی از عملکرد بهتر پرتفوهای متنوع نسبت به هر دارایی است و بهترین عملکرد را پرتفو شامل سکه با اختصاص بیش از 70 درصد و دلار و بیت‌کوین با وزن برابر داشته است. همچنین با توجه به نسبت شارپ شرطی در پرتفو بهینه حداقل وزن سکه 60 درصد وحداکثر سهم دلار و بیت‌کوین 20 درصد می‌باشد.

Mixed- Asset Portfolio Optimization

Introduction At the core of any investment lies the return on investment. To gain a favorable return, an investor should take investmentrelated 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 MeanCVaR 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 LindBraucher, 2010). Moreover, due to the low correlation between conventional assets and cryptocurrency and its highefficiency, 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 subaggregation 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 timevarying was modelled via the dynamic conditional correlation estimation and the joint distribution of assets was analyzed regardless of data normality and collinearity. Then, the MeanCVaR 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 DCCCopula 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 risktaking, the greater the investment weight of Gold Coin and Bitcoin. Conclusions Suggestions Considering the investor’s risktaking 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 risktaking investors are suggested to invest in Bitcoin and low risktaking counterparts are suggested to invest in Gold Con.  Considering the conditional Sharp (CSharp) 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 CSharp ratio in the optimal portfolio, the minimum weight of Gold Coin is 60% and the maximum share of Dollar and Bitcoin is 20%.