Portfolio Rebalancing with GARCH Model at Jarvis Balanced Fund

: With high inflation economy, investors must find another way to minimize their risk, but also maximize their return of the portfolio. Various instruments used for finding the most suitable amount of portfolio allocation. Single instruments, such as stocks, bonds, and time deposits is chosen by investors to secure their assets from inflation. The other investors chose mutual funds to grow their investments. One of the solutions to find the portfolio allocation is to rebalance the portfolio. In other perspectives, time-series model will help investors to predict the volatility that will happen in the future. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model is used for finding volatility and generalized it from the ARCH Model. With GARCH Model, the total amount of residual and GARCH has to be less than 1. Either way, it will be categorized as a volatile asset. From the top 5 balanced fund in 2021, Jarvis Balanced Fund is one of the best-balanced funds with return of 55.85%/year. Using Jarvis Balanced Fund (JBF) portfolio from 2021 prospectus as the sample of this research, it is concluded that JBF has to reduce the number of stocks and increase the risk-free assets to prevent volatility that happen in the portfolio. Following with the macro economy of high-inflation economy era.


INTRODUCTION
After CoVID-19 pandemic that had been running since 2020, The indicator of Indonesia's economy is getting better represented with inflation, consumer confidence, consumer price index (CPI), and GDP growth that had been increasing since 2021.The Jakarta Composite Index (JCI) is also recovered, from the lowest point from 24 th March 2020 at 3911.71 to the all time high level from 15 th September 2022 at 7377.49.Contrary from Indonesia, the global economy is weakened [1] because of Russia-Ukraine war, supply chain disruption, and high-inflation era.Besides the commodity supercycle that happened with commodity price in 2021, the decision from Jerome Powell to increase rates to fight the inflation made the economy volatile [2].According to the data from November 2022 [3], market capitalization of JCI has already hit Rp 9,559.87 trillion, excluding mutual funds and other products from capital market.According to OJK [4] total assets under management are at Rp 508.18 trillion with declination from 2021 that hit Rp 579.95 trillion or 12.37% declined.While the risk-asset is discussed, it's also being a threat because of macro economy issue that triggered capital outflow, with the bonds outflow at Rp 227 trillion and inflow at stock market for Rp 78.86 trillion (Elena, 2022).The stock market is still interesting to be invested in, rather than the bond market.According to the OJK [4] there are several types of mutual funds such as money market mutual funds, fixed income mutual funds, stock mutual funds, balanced funds, and syariah mutual funds.Each type of mutual fund has its own proportions and advantage to get profit in the market.The data [5] shows that top 5 balanced funds in 2021 are Jarvis Balanced Fund (55.85%/year), Syailendra Balanced Opportunity Fund (24.42%/year), Sucorinvest Flexi Fund (22.94%/year), Sucorinvest Citra Dana Berimbang (19.11%/year), and STAR Balanced II (18.41%/year).From mutual funds, the balanced funds are chosen because it can prevent risk with flexible proportion of maximum 79% on each asset (time deposit, bonds, stocks).To count the flexible proportions of balanced fund, GARCH Model is used to forecast volatility with more flexible lag on it.To develop the GARCH Model, the previous ARCH Model is used and using the ARMA Model to find the fit model to be used.Using eviews as the tool to solve the heteroskedasticity data and finding the volatility from the Jarvis Balanced Fund data in 2021 prospectus.

BUSINESS ISSUE
As we can see from the net asset value of Jarvis Balanced Fund, from April until July 2022, Jarvis' net asset value per unit had been declined up to 19.18%.The slightly decreasing of net asset value is caused by many factors, such as investors, financial markets, and technical factors.The NAV declining should be a warning for Jarvis Balanced Fund to improve their methods in their portfolio.On previous holding in 2021, this is the composition and graphs of Jarvis Balanced Fund.To get the purpose of the same and/or the higher return in 2023, Jarvis wanted to secure their return to this level or increasing it with this current economy condition.Choosing the sector that supported interest rate hike will be their advantage to get the better return in 2023, also securing it with the bonds and time deposits that offers higher rate contract.Choosing the assets with valuations from fundamental analysis and GARCH model can help choosing the right asset to be invested other than low-risk asset for the balanced fund.

METHODOLOGY
The data that used is prospectus of Jarvis Balanced Fund in 2021 consists of Time Deposits, Bonds, and Stocks.Also, the details of this data will be on 5 years (from 2017 to September 2022) for each assets.In this research, the author will use eviews as the econometrics tools to run the GARCH process.The steps of eviews are ADF Test, finding the correlogram, selecting the ARMA Model (whether it will be AR, MA, or ARMA based on the smallest amount of Akaike Info Criterion), finding the ARCH, and the last step is finding the GARCH Model with the heteroskedasticity.The GARCH Model that will be used is GARCH Model (1,1) because it's easier to be applied for every data [6] The analysis steps to reach the GARCH model are as follows: GARCH model is used for predicting volatility on the stock market that is chosen by Jarvis Balanced Fund.Bollerslev [7] said that there are some models for this research.GARCH (p,q) process For GARCH (p,q) model, the process reduced from p = 0 into the ARCH(q) process, and for the p = q = 0 is white noise.

GARCH (1,1) Process
where From this theorem of GARCH (1,1) process, it has been used by many researchers because GARCH (1,1) process is more simple than other GARCH process.
where ( 6) For the 2mth moment expressed as below: For the lag process of GARCH (1,1) expressed as below: Median lag for GARCH (1,1) is found below: From previous research, Bollerslev [7] said that GARCH (1,1) process is more simple than GARCH (p,q) process.GARCH (p,q) process allows lagged conditional variances to enter as well.In general, GARCH (p,q) model can be shown as an ARCH (∞) model.Using GARCH (p,q) model and (1,1) model depends on the lag from the data.ARIMA model and ARCH model will help to determine the GARCH model that will be chosen.

BUSINESS ANALYSIS AND SOLUTIONS 1) Business Analysis
From this data, the Augmented Dickey-Fuller (ADF Test) or the unit root test from time deposits, bonds, and stocks are as below:  With this correlogram, there will be know about the lag of data.In this research, the author used daily data for 5 years.From this data, the correlogram of BUKA is at 33, followed by Bank Ina Perdana with 5 days lag, HRUM, ASSA at 4 days lag, TNCA with 3 days lag, and ADRO, AKRA, FREN with 2 days lag.The correlogram anomaly is from BUKA, and the others are less than 10.Therefore, the rest of data is stationary.In this data, we can see that the GARCH Model is applied to 19 stocks and FR0086.From the p-value of GARCH (1,1) model, the EXCL and TNCA is showing amount of numbers (0.0393 and 0.0374).From the constanta, it should be less than 5%.BUKA showed 0.6298, TNCA is at 0.1503, and NFCX is at 0.3248.The next step is finding the heteroskedasticity test GARCH (1,1) model.The heteroskedasticity test shows value more than 5% or 0.05.From the data, we will see below: As we can see from the table, the f-value of ARTO, TBIG, and NFCX has value for less than 5% or <0.05, but the rest is more than 5%.From this data, we will eliminate the heteroskedasticity data, that is ARTO, TBIG, and NFCX.After the step of heteroskedasticity test GARCH (1,1) model, we can predict the volatility through the total of residual value (-1)^2 and GARCH (-1)^2.The data as below: The data shows the total of residual added by GARCH results.If it shows more than 1, it will be more volatile assets.In this analysis, the total for more than 1 are ASSA, BBYB, ERAA, HRUM, BOLA, MDKA, TNCA, FREN, DMMX, TFAS.This is the list of stocks that will have a chance to be more volatile, based on GARCH (1,1) model calculation (Resid (1)^2 + GARCH (-1)^2).The least total is from LINK (0,888069) and DSNG (0,890106), and FR0086 (0,915008).For EXCL, ADRO, AKRA, BUKA, it's near to the number of 1.
2) Business Solutions From this previous holding on Jarvis Balanced Fund 2021 and from the calculation of total volatility, ASSA, BBYB, ERAA, HRUM, BOLA, MDKA, TNCA, FREN, DMMX, TFAS should be reduced from portfolio.From the macro economy perspectives, with the high inflation that happens in Indonesia since 2022, the risk-on assets should be reduced and looking for the risk-free assets, such as time deposits.The composition of majority in time deposit gives Jarvis Balanced Fund an option of risk-free assets.While Jarvis Balanced Fund put their fund into risk-free assets, they can find the undervalue company with strong balance sheets and a major story in the year of 2023.In this portfolio rebalancing model, the lesser volatility, the better for Jarvis Balanced Fund.With less number of stocks, and added more proportions on time deposits, it will secure JBF money in a few quarter of 2023 to purchase stocks from the bottom price.
Otherwise, the stock that kept will fall from the current price and the demand of Jarvis Balanced Fund will be decreased in the next few quarters.Choosing the right asset for JBF is important to maintain customer and attract new customers with survival conditions of Jarvis Balanced Fund.
3) Implementation Plan The plan is to reduce the portion of stock portfolio and add time deposits in the portfolio.The plan should be implemented before 2023 or in the year of 2023, because asset management has time to do the plan before another investor anticipated the action of big funds to exit the stock market.Looking at these current economic conditions, it will be better to do it early.While the asset management exit the market, they will have time to do the valuations entry the stock market at a discounted price.Looking at the risk-on assets will take time, because not only the statistics from econometrics (GARCH Model), but also the stock valuations and business sectoral cycle will help asset management to purchase new assets again.One of the solutions is to put the money on time deposits.As for the econometric tools (GARCH Model), it will help their decision to find the volatility movements, alongside their valuations model.The combination of valuations and econometrics will give a new insight into stock market return and volatility.

CONCLUSIONS
From this analysis, the author concluded that the asset is having more volatility, especially for stocks and FR (government bonds).For corporate bonds (INKP01BCN3) it must be stopped in heteroskedasticity ARCH (0.089 > 0.05) and other time deposits, it has to be stopped on ARMA model (Deutsche Bank) and heteroskedasticity ARCH (Bank Ina Perdana: 0,1954 > 0.05).The volatility is on the ASSA, BBYB, ERAA, HRUM, BOLA, MDKA, TNCA, FREN, DMMX, TFAS with total value for more than 1.The other stocks (EXCL, ADRO, AKRA, BUKA) are near 1, with value of more than 0.9.But for LINK, DSNG, and FR0086 is less than 0.9.So, it's less volatile, but it will have a chance for less return.

2581-8341 Volume 06 Issue 02 February 2023 DOI: 10.47191/ijcsrr/V6-i2-56, Impact Factor: 5.995 IJCSRR @ 2023 www.ijcsrr.org 1364 * Corresponding Author: Irvan Liunardi Senjaya Volume 06 Issue 02 February 2023 Available at: www.ijcsrr.org Page No. 1362-1373 From
this data, we can see that the composition dominates with commodity with value of 21.37% (ADRO, HRUM, MDKA, AKRA), financials with total of 15.92% (ARTO, BBYB), Transportation & Logistics (ASSA, TNCA) with 10.23% and technology sectors with 6.36% (BUKA, LINK, DMMX, TFAS, NFCX).From the portfolio component, Jarvis held on to technology aspects with differentiate sectoral.With the high inflation and interest rate hike that already happened in U.S. and European Countries, Jarvis Asset Management should be cautious with the activities that happened.Interest rate hike should be the alert of new business cycle that should be taken by Jarvis Balanced Fund.Alongside of the falling of technology sector in 2022, Jarvis couldn't get the same amount of return in 2021.

Table 4 -3: Akaike
Info Criterion (Source: Author, 2022) After the data is stationary, the next step is to find the ARMA Model.The decisions will be from the smallest amount of Akaike Info Criterion.According to the Akaike Info Criterion table, this has been list from the smallest amount of AIC.With this data, the

2581-8341 Volume 06 Issue 02 February 2023 DOI: 10.47191/ijcsrr/V6-i2-56, Impact Factor: 5.995 IJCSRR @ 2023 www.ijcsrr.org 1367
AIC is from INKP01BCN3 and Bank Ina Perdana.But, the Deutsche Bank data is not applicable for AR, MA, and ARMA model.Therefore, the data of Deutsche Bank can't be continued.After looking at the ARMA model, the next step is analyzing the Heteroskedasticity ARCH Model.From the table, this is the data of Heteroskedasticity Test ARCH Model (F-Value).

Table 4 -9: Portfolio
Rebalancing of Jarvis Balanced FundWith the analysis from GARCH model, the proposed portfolio rebalancing should be as the table above.The composition of stocks is 19.36% with ADRO, EXCL, AKRA, DSNG.Bonds with 1.42% with FR0086 at 1.26% of portfolio and INKP01BCN3 with ISSN: