FORECASTING VALUE AT RISK OF UNIT TRUST PORTFOLIO BY ADAPTING GEOMETRIC BROWNIAN MOTION

Transcription

1 Jurnal Karya Asli Lorekan Ahli Matematik Vol. 9 No.2 (Dec 2016) Page Jurnal Karya Asli Lorekan Ahli Matematik FORECASTING VALUE AT RISK OF UNIT TRUST PORTFOLIO BY ADAPTING GEOMETRIC BROWNIAN MOTION Abdul Hafiz Zakaria, Maheran Mohd Jaffar Department of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi Mara, Shah Alam, Selangor, Malaysia. maheran@tmsk.uitm.edu.my Abstract: There are several investment vehicles in Malaysia such as gold investment, fixed deposit, stocks, property investment and unit trust investment. This research focuses on investment in unit trust funds that comply to shariah law. It is important for individual or organization to know the future risk before making an investment in any unit trust fund. This research adapts geometric Brownian motion (GBM) model in the Value at Risk (VaR) model in order to compute the future VaR. The objectives of this research are to forecast the price of unit trust funds and listed stocks in their portfolio by using geometric Brownian motion model, to compute future VaR for stocks and unit trust funds and to calculate the group forecast VaR of unit trust funds using forecast price of listed stocks in fund portfolio. The forecast price of unit trust funds and all stocks in fund portfolio are highly accurate. This research is also able to compute group forecast VaR based on computed forecast VaR of listed stocks in the unit trust fund portfolio. According to ranked forecast VaR, the best unit trust fund to gain profit among the selected six unit trust funds in this research is CIMB Islamic Small Cap fund. Keywords: Unit trust; Stock prices; Value at risk; Geometric Brownian motion; Forecasting. 1. Introduction Investing is the process of purchasing assets with the goal of increasing wealth. There are several investment vehicles in Malaysia such as gold investment, fixed deposit, stocks, property investment and unit trust investment. This research focuses on unit trust investment. According to Theunissen [1], unit trusts or mutual funds as they are known in the United States of America, are investment products that invest pooled of money from investors that have bought into a specific fund in a range of assets that usually include varying proportions of equities, bonds and money market instruments. Investors can purchase unit trust fund by either making a single lump sum investment or by purchasing smaller units on a monthly basis. In Malaysia, Employee Provident Fund (EPF) members can invest in unit trust by withdrawing their money from EPF, since EPF introduced the investment withdrawal scheme in 1996 to enhance retirement savings (Jidwin, Tuyon, & Rosalan, [2]). Their study found that EPF member s experience the highest return was 10% and the lowest return was negative 5%. This contradicted that 2.5% guaranteed minimum return for EPF. However, there are possibilities for EPF members to gain 10% return on their investment in unit trust. In this case the financial consultant plays the main role to assist EPF members in order to make decision while making a decision on investment. Theunissen [1] states that the advantage of investing in unit trust is investors can sleep easier. Meaning that the investors do not need to undertake the burdensome task of having to research each of the individual stocks they choose to invest in. Instead, they outsource this to the asset manager, allowing them to focus on whatever it is they do best. The other advantages of unit trust are diversified, professional selection, tax-free income, return of principle, portfolio monitoring, resale, locked-in yield and reinvestment of income (Dunnan, [3]) Jurnal Karya Asli Lorekan Ahli Matematik Published by Pustaka Aman Press Sdn. Bhd.

2 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page Unit trust has been known in Malaysia relatively earlier than its Asian neighbours. Malayan Unit Trust Ltd was the first company that established the unit trust in However, the unit trust markets in 1959 to 1979 were characterized by slow growth in the sales of units and a lack of public interest in the new investment product during that time. There were only five established unit trust management companies, with 18 funds introduced over that period. Starting from 1980s more unit trust management companies were established, which were subsidiaries of financial institutions. The period of 1991 to 1999 witnessed the fastest growth of the unit trust industry in terms of the number of new management companies established and funds under management. The period from year 2000 to current years shows a very promising future for the unit trust industry. A unit trust is a professionally managed investment fund, which pools together the money of investors having the similar objectives. Investors will invest their funds through purchase of units and the fund manager channels these funds into investment on behalf of unit holders who share in the proceeds of their investment according to the number of units held by them. Fund managers will invest the collected money in portfolio security as share, money market bond and properties to achieve fund objectives. The aggregate sum is then used by the fund to build a diversified investment portfolio that comprises stocks, bonds and other assets in accordance with the investment objective of the fund. The price of a unit reflects its total net asset value, commonly referred to as the NAV. The industry recorded double digit growth every year, growing from RM43 billion in NAV from Year 2000 to RM169 billion at 31 December 2007 (MIDA, [4]). There are two types of unit trust investment, namely Islamic and conventional unit trust. The Islamic unit trust industry is growing due to the increases in demand of investors in Islamic products. In 1993, the number of Islamic funds in Malaysia s private unit trust industry has increased to 146 in As of June 30, 2010, the Islamic fund sector has a NAV of RM26.37 billion, which is about 31 percent of the private unit trust industry in Malaysia (Lipper [5]). The major different between Islamic unit trust and conventional unit trust is its compliance with shariah law. In addition, the portfolio of Islamic unit trust cannot invest in companies that are involved in non-halal transactions such as gambling. Malaysia s unit trust industry has continued to grow steadily with the NAV growing 5.7% to RM354.7 billion until the end of July Since unit trust is a sunrise industry in Malaysia, it is important for individual or organization to know the risk before making an investment in any unit trust fund. There is a study on mutual funds performance evaluation that uses VaR as their tool (Tehrani, Mohammadi, & Nejadolhosseini [6]). The study uses GARCH parametric methods and Monte Carlo Simulation non- parametric method. Their study just focus on VaR of unit trust fund by using unit trust price data, but this information is not good enough to measure the VaR of unit trust fund. Table 1 shows the unit trust fund and the stocks used in the research. 25

3 Abdul Hafiz Zakaria and Maheran Mohd Jaafar Table 1. The major stocks in each unit trust funds Unit trust funds Islamic DALI Equity Growth (DALI1) Islamic DALI Equity (DALI2) Islamic DALI Equity Theme (DALI3) Islamic DALI Asia Pacific Equity Equity Growth (DALI4) Islamic Small Cap (ISC) Islamic Balanced (IB) 26 Stocks Sime Darby Bhd Bhd Axiata Group Bhd Tenaga Nasional Bhd Petronas Gas Bhd Westports Holdings Bhd Telekom Malaysia Bhd Gamuda Bhd Maxis Bhd MISC Bhd - Local Taiwan Semiconductor Manufacturing Cahya Mata Sarawak Berhad Tenaga Nasional Bhd Petronas Gas Bhd Westports Holdings Bhd Telekom Malaysia Bhd Kossan Rubber Industries IJM Co. Bhd MISC Bhd - Local IJM Co. Bhd Axiata Group Bhd Tenaga Nasional Bhd Petronas Gas Bhd Westports Holdings Bhd Telekom Malaysia Bhd Petronas Chemicals Group Bhd Maxis Bhd MISC Bhd - Local Taiwan Semiconductor Manufacturing SK Telecom Co. Ltd Tenaga Nasional Bhd ComfortDelGro Co. Ltd Telekomunikasi TBK PT Link REIT Techtronic Industries Co Chunghwa Telecom Co. Ltd. Singapore Telecommunications UEM Edgenta Bhd Time Dotcom Bhd SKP Resources Bhd Cahya Mata Sarawak Berhad Protasco Bhd Taiwan Semiconductor Manufacturing

4 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page Gamuda Bhd Tenaga Nasional Bhd Gulf Investment Co. Petronas Gas Bhd Link REIT Axiata Group Bhd Chunghwa Telecom Co. Ltd. Cahya Mata Sarawak Berhad 2. MODEL In order to calculate volatility and drift rate for each stock and unit trust funds, the rate of return for each stock and unit trust funds must be calculated first. To compute the rate of return, this study uses equation (2.1) as follows: S t i R i ln. (2.1) Sti 1 where S t i is the price of a stock or unit trust fund at time t i and St i 1 is the price of stock and unit trust funds at time t i 1. Then, the drift rate μ is computed using the formula as equation (2.2) below, M 1 R i (2.2) M t i 1 where M is the number of days of stock prices or unit trust fund and the timestep t 1/ 252. After that, this research applied simple volatility formula as follows: M R i R 1 2 (2.3) M 1 t i 1 where R is the average return of stock prices or unit trust funds. In order to forecast price of unit trust funds and stocks, this research adapts GBM model, which is the equation as below [7]: 1/ 2 Si 1 Si (1 t t ). (2.4) According to the above GBM model the S i 1 is referred to forecast price at time i 1. Then S i is the previous price at time i, represents the drift rate, the time step is represented by t, and the volatility is. The above model involves the random numbers, simulated from a Normal distribution represented by. This research applies the GBM model in a VaR formula to compute the forecast VaR. The equation (2.5) shows the model of VaR, / V S t t 1 1 c 2. (2.5) The equation of the forecast VaR at time i 1 obtained as equation below by substituting equation (2.4) into equation (2.5), 2 2 V S (1 t t ) 1/ t t 1/ 1. (2.6) i 1 i c With the future value of stock prices, the research is able to find the future value of the VaR. 3. RESULTS AND DISCUSSION 27

5 Abdul Hafiz Zakaria and Maheran Mohd Jaafar The study used the proposed equations above in order to forecast the price of unit trust and also some chosen stocks 3.1 Forecast prices Table 2 shows the drift, volatility values and the forecast prices for all the unit trust funds and the stocks in Table 1 by using equations (2.2), (2.3) and (2.4) respectively. Table 2 shows the drift and volatility values of each stock and fund. These values are used in equation (2.4) to forecast the prices of two months. MAPE was calculated for each stock to compare the forecast values at end of June and July with their actual prices. The MAPE are very small that shows the model is very accurate in forecasting the prices. Table 2. Unit trust funds and stocks used in the study with drift, volatility and MAPE values. No Unit trust/stocks Drift Volatility MAPE (%) (μ) (σ) June July Averag e 1 Sime Darby Bhd Axiata Group Bhd Tenaga Nasional Bhd Petronas Gas Bhd Westports Holdings Bhd Telekom Malaysia Bhd Gamuda Bhd Maxis Bhd MISC Bhd Local Taiwan Semiconductor Manufacturing 11 Cahya Mata Sarawak Berhad Chunghwa Telecom Co. Ltd ComfortDelGro Co. Ltd Telekomunikasi TBK PT Gulf Investment Co Link REIT Petronas Chemicals Group Bhd 18 Singapore Telecommunications 19 SK Telecom Co. Ltd IJM Co. Bhd Protasco Bhd Techtronic Industries Co Kossan Rubber Industries Time Dotcom Bhd UEM Edgenta Bhd SKP Resources Bhd Islamic DALI Equity Growth (DALI1) 28 Islamic DALI Equity

6 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page (DALI2) 29 Islamic DALI Equity Theme (DALI3) 30 Islamic DALI Asia Pacific Equity Equity Growth (DALI4) 31 Islamic Small Cap (ISC) Islamic Balanced (IB) Below are the graphs of forecast and actual prices for each chosen stock. 29

7 30 Abdul Hafiz Zakaria and Maheran Mohd Jaafar

8 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page

9 Abdul Hafiz Zakaria and Maheran Mohd Jaafar Figure 1. Graph of Forecast Price for 26 Stocks. 32

10 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page Value at risk of unit trust fund and stocks By using equations (2.5) and (2.6), VaR is calculated for the confidence level of 90%, 95%, 97.75%, 99% and 99.9%. The VaR are shown in Table 3 below: Table 3. Value of Single and Group Forecast VaR in Percentage. Confidence Level No. Unit Trust Fund Group Forecast VaR Single Forecast VaR 90% 95% 97.50% 99% 99.90% 90% 95% 97.50% 99% 99.90% 1 IB DALI DALI DALI DALI ISC *forecast Price from June 2015 until July 2015 Table 0 Ranked Selected Unit Trust Fund Based on Single and Group Forecast VaR in Percentage from Lowest to Highest with Respect to Each Confidence Level. Confidence Level No. Group Forecast VaR Single Forecast VaR 90% 95% 97.50% 99% 99.90% 90% 95% 97.50% 99% 99.90% 1 DALI1 DALI1 DALI4 DALI1 DALI1 IB IB IB IB IB 2 DALI3 DALI3 DALI3 DALI3 DALI3 DALI2 DALI2 DALI2 DALI2 DALI2 3 IB IB IB IB IB DALI4 DALI4 DALI4 DALI4 DALI4 4 DALI4 DALI4 DALI4 DALI4 DALI4 DALI1 DALI1 DALI1 DALI1 DALI1 5 DALI2 DALI2 DALI2 DALI2 DALI2 DALI3 DALI3 DALI3 DALI3 DALI3 6 ISC ISC ISC ISC ISC ISC ISC ISC ISC ISC *forecast Price from June 2015 until July

11 Abdul Hafiz Zakaria and Maheran Mohd Jaafar Table 3 shows all value of single forecast and group forecast VaR in percentage and Table 4 shows the ranked of selected unit trust fund based on single forecast and group forecast VaR in percentage from lowest to highest with respect to each confidence level. The objective of the table is to select the best unit trust fund based on VaR. Based on Table 4, the safest unit trust fund for June until July for group forecast VaR is DALI1. It has the lowest VaR for all confidence levels, but based on single forecast VaR, the safest unit trust fund is IB fund having the lowest VaR compared to other funds. In investment, the higher the return is then the bigger is risk. Therefore, this research concludes that IB fund and DALI1 fund is not the best fund to grow money in the short term. By referring to the Table 4 the best fund to gain profit in the short term is ISC fund. This is because ISC fund shows the highest forecasts VaR for single and group forecast VaR. Table 5 shows the average MAPE value (%) of VaR from June until July based on daily and weekly data. In order to select the best unit trust fund this data was ranked from lowest to highest value of VaR (%). Table 5 shows ranked selected unit trust fund based on daily and weekly data of forecast VaR in percentage from lowest to highest with respect to each confidence level. Based on Table 6, both weekly and daily data show IB fund as the safest fund and ISC fund as the best fund for gaining profit. Next, daily data shows DALI1 as the third and weekly data show DALI4 as the third based on the safest fund. The different can be seen in column 90% confidence level. 34

12 Jurnal KALAM Vol. 9 No. 2 (Dec 2016), Page No. Fund Table 5 Average MAPE Value (%) Of VaR from June Until July 2015 Based on Daily and Weekly Data. Daily Data Confidence Level Weekly Data 90% 95% 97.50% 99% 99.90% 90% 95% 97.50% 99% 99.90% 1 IB DALI ISC DALI DALI DALI Table 6 Ranked Selected Unit Trust Fund Based on Daily and Weekly Data of Forecast VaR in Percentage from Lowest to Highest with Respect to Each Confidence Level. No. Daily Data Confidence Level Weekly Data 90% 95% 97.50% 99% 99.90% 90% 95% 97.50% 99% 99.90% 1 IB IB IB IB IB IB IB IB IB IB 2 DALI2 DALI2 DALI2 DALI2 DALI2 DALI2 DALI2 DALI2 DALI2 DALI2 3 DALI1 DALI1 DALI1 DALI1 DALI1 DALI4 DALI4 DALI4 DALI4 DALI4 4 DALI4 DALI4 DALI4 DALI4 DALI4 DALI1 DALI1 DALI1 DALI1 DALI1 5 DALI3 DALI3 DALI3 DALI3 DALI3 DALI3 DALI3 DALI3 DALI3 DALI3 6 ISC ISC ISC ISC ISC ISC ISC ISC ISC ISC 35

13 Abdul Hafiz Zakaria and Maheran Mohd Jaafar 4.0 CONCLUSION This research adapts geometric Brownian motion in order to compute forecast VaR. The proposed model is highly accurate and able to forecast price of unit trust funds and the listed stocks of the funds based on July 2015 fund factsheets. Based on the result, average MAPE value of forecast price from June until July for all stocks and unit trust funds are less than 10%. This research used the forecast price of the stocks and unit trust funds to compute the future VaR for each of them. Therefore, the compute future VaR is also highly accurate. This research finds that, the MAPE value of forecast price and the MAPE value of forecast VaR are the same. This research finds that the confidence level and VaR has a linear relationship. When the confidence level increases, the VaR also increases. As a conclusion, this research is very useful for financial consultants in order to help their client to gain profit by diversifying their investment in different class of risk by the measure value of the risk of unit trust fund. Other than that, this research can increase the confidence among financial consultants when guiding their client in unit trust investment. Besides that, this research can help fund managers to make decision before setting up a unit trust fund s portfolio. Acknowledgement The authors would like to thank the Faculty of Computer and Mathematical Sciences, Universiti Teknologi Mara, Shah Alam,Selangor, Malaysia for giving us the opportunity to present the findings of the study at The 7 th International Conference on Numerical Optimization and Operation Research (ICNOOR VII), Hanoi, Vietnam. References [1] Theunissen, G. (2014). What Are Unit Trusts. Finweek, 13 March 2014, [2] Jidwin, A. P., Tuyon, J., & Rosalan, B. A. (2011). The malaysian employees provident fund's members' investment scheme survey of fund selection, performance and perceptions. Asia-Pacific Management Accounting Journal, 6(1). [3] Dunnan, N. (1989). Annuities. ABAJ, 75, 98. [4] MIDA, M. I. D. A. (2013). Perfomance of The Manufacturing and Related Services Sectors Retrieved from [5]Lipper. (2010). Understanding Islamic Unit Trusts Retrieved from [6] Tehrani, R., Mohammadi, S. M., & Nejadolhosseini, N. S. (2014). Value at Risk as a tool for mutual funds performance evaluation. International Business Research, 7(10), p16. [7] Wilmott, P. (2007). Paul Wilmott introduces quantitative finance.united Kingdom: John Wiley & Sons. [8] Mohd Alias, L. (2007). Introductory business forecasting: A practical approach: Pusat Penerbitan Universiti, Universiti Teknologi MARA. 36