RISK AND RETURN MANAGEMENT OF SHARIA STOCKS IN JAKARTA ISLAMIC INDEX FOR THE PERIOD OF 2009 – 2019 USING MARKOWITZ PORTOFOLIO MANAGEMENT

To reduce risk in investment and at the same time optimize the returns, it is necessary to establish a series of stocks that have high returns, as well as to select a series of stock with negative variance to reduce the risk. In this research, an efficient frontier approach by Harry Markowitz will be applied to JII shares during the period 2009 2019 so that a portfolio with a low risk and optimal return can be formed to reduce risk and optimize return.


The formulation of the problems
The problem that will be discussed in this final project is 1.
How to calculate returns, standard deviations and risks of individual sharia stock investments included in the Jakarta Islamic Index(JII) 2.
How to choose stocks that have a better investment return than the JCI index to be eligible for inclusion in the portfolio. 3.
How to implement the Markowitz Modern Portfolio theory on leading stocks by utilizing the covariance of a combination of shares to reduce risk

Purpose
The objectives to be achieved in the implementation of this research are 1.
To implement the Markowitz Modern Portfolio theory in Sharia Stock which is included in Jakarta Islamic Index 2.
To make investment alternatives with various investment return and risk options

Limitation of Problems
Limitation problems in this research are: 1.
The stock price data used is the stock price data listed on the Jakarta Islamic Index(JII).

2.
The duration of observation in this final project is 10 years, starting in January 2009 to December 2019 3.
Shares that will be combined to form a portfolio are only stocks -stocks that have a higher return than the JCI return

Review Of Literature Stocks
Stocks are one of the most widely recognized financial market instruments by the general public. To get some funding, issuing shares is one of the ways that can be taken by a company. Meanwhile, for investors, stocks are a very attractive investment instrument because they can provide a very satisfactory level of profit.
In addition, shares can also be defined as a sign of capital participation by individual investors or business entity investors in a company or limited liability company. By including this capital, the investor has a claim on company income and company assets, and is also entitled to attend the RUPS (General Meeting of Shareholders). after all company obligations have been paid, the shareholders will not get the results of the liquidation of the company. Thus, this condition is the biggest risk form of stock investment. Therefore, a stock investor must keep abreast of developments in the company's business in which he invests funds.
However, if there is no remaining of the company's wealth, shareholders will not get any results of the liquidation. This condition is the heaviest risk of shareholders. For this reason, a shareholder is required to continuously follow the company's news from time to time. Gambling and games that is classified as gambling; 2) Sharia-restricted trading includes: a) trade that is not accompanied by the delivery of goods / services; and b) trade with fake offers / requests; 3)

Sharia Stock
Usurious financial services, including: a) interest-based banks; b) and interest-based finance companies; 4) Buying and selling risks that contain elements of uncertainty (gharar) and / or gambling (maisir), including conventional insurance; 5) Producing, distributing, trading and / or providing, among others: a) illicit goods or services (illicit li-dzatihi); b) illicit goods or services not because of their substance (haram li-ghairihi) stipulated by and / or 6) Conduct transactions containing elements of bribery (risywah) B. Comply the financial ratios as follows 1) Total interest-based debt compared to total equity of not more than 82% (eighty-two percent); 2) Total interest income and other non-halal income compared to total business income (revenue) and other income not more than 10% (ten percent)

Sharia Stock in Jakarta Islamic Index(JII)
The Jakarta Islamic Index (JII) is a sharia-based stock index which was first launched on the Indonesian stock exchange on July 3, 2000. There are 30 of the most liquid sharia shares included in JII shares. Just like ISSI, a review of Shariah shares that are JII constituents is conducted twice a year, in May and November, following the OJK's DES review schedule.
IDX determines and selects sharia shares which are the constituents of JII. The liquidity criteria used in selecting 30 Sharia shares that constitute the JII constituents are as follows: 1.
Sharia shares included in the constituents of the Indonesian Sharia Stock Index (ISSI) have been recorded for the past 6 months 2.
60 stocks are chosen based on the highest average market capitalization in the last 1 year 3.
Of the 60 shares, 30 shares were then chosen based on the average daily transaction value on the highest regular market 4.
The remaining 30 shares are selected shares.

Relevant Statistical Theory Average / arithmetic mean or average
If there are n values, where each value is denoted as ai, where i = 1, 2, ...., n, then the arithmatic mean is the sum of all values from a 1 to a n and then divided by n.
where n is the number of data and a is the value of the data.

Average or expected value
If two coins are tossed 16 times and X denotes the number of head appearing on each toss, then the possible value of X is 0.1 and 2. Suppose that the experiment produced no head 4 times, one head 7 times and two head 5 times. Then the average number of heads that appear each toss of two coins is 06 , 1 16 This is an average value and it is not necessary to state a result that might have appeared for the experiment [WAL95].
Let X be a random variable with a probability distribution f (x). The expected value or average of X

Variance
The average or expected value of a random variable X only describes the location of the distribution center, but does not provide sufficient information about the form of distribution. Diversity of distribution needs to be characterized. The measure of diversity of a random variable X is obtained from The positive root variance,  , is called the standard deviation X. But for the discrete, there is a quick way to calculate it, i.e.

Standard Deviation
Standard Deviation (σ), the root of variance, is a benchmark of variation in probability theory. Standard deviation shows how much variation from the average value. Standard deviation is the root of variance.
Covariance measures how much the two variables change together, while variance is covariance which has two identical values.
, where X and Y are real numbers and E [X] is the Expected Value of X. If X, Y, W and W are real and a, b, c and d are constants then Cov (X, a) = 0, meaning X and a are mutually independent Cov (X, X) = Var (X) because X and X are identical Cov (aX, bY) = ab Cov (X, Y) Cov (X + a, Y + b) = Cov (X, Y) Cov (aX + bY, cW + dV) = ac Cov (X, W) + adCov (X, V) + bc Cov (X, V) + bd Cov (Y, V)

Normal Distribution
The most important continuous opportunity distribution in all fields of statistics is the normal distribution. The graph is called a bell-shaped normal curve. A continuous random variable X whose bell-shaped distribution is called a normal random variable [WAL95]. The solid function of the random variable is normal X, where the mean and variance are

Figure Normal Distribution
It can be seen on the normal curve ) 10 , 5 ; (x n shown in Figure II.1, which 5   is the center point and 10   is the standard deviation. There are five normal curve characteristics, namely: 1.
Mode, the point on the flat axis that gives the maximum the curve is on 10   2.
Curve as close to the upright axis as the average  3.
The curve has a turning point on x and concave upward for the other value of x. 4.
Both ends of the normal curve approach the flat axis asymptote if the value of x moves away from  in both left or right direction. 5.
The entire area under the curve and above the flat axis is equal to 1 [WAL95].

Relevant Financial Theories Rate of Return (ROR)
Rate of Return is the ratio of the profit or loss of an investment to the total amount of money invested. r = (Vf-Vi) / Vi Where R = return Vf = Value of the final investment outcome Vi = initial investment value In this final project, the return obtained from an increase or decrease in stock prices compared to the initial stock price. Compound Annual Growth Rate (CAGR) is a term in business and investment to uniform or equalize the annual profit of an investment over a certain period of time. CAGR is often used to compare the growth rates of two investments because CAGR offsets the effects of periodic return volatility which can make arithmetic meaning irrelevant. CAGR is often used to describe growth over a period of time from several business elements, for income or investment value. The CAGR calculation formula is like the formula below Where V (t0) : initial value V (tn) : final value tn is the year at the end of the period t0 is the year at the beginning of the period tn -t0 : number of periods in a year,

Markowitz Portfolio Theory Basic concepts
The basic concept of the Markowitz portfolio theory states that assets or stocks in an investment portfolio should not be chosen singly or alone, but should be combined with other stocks that have small or negative covariance, Thus the standard deviation of returns is smaller. In the early 1960s, investors always discussed risk, but at a time when there were no specific measurement methods. The basis of the portfolio model was developed by Harry Markowitz which reduced the expected rate of return and for portfolio assets. Markowitz shows that the variance rate of return is an important measure for designing a portfolio. This formula of portfolio variance shows the importance of diversifying investments. The Markowitz model has several assumptions about investor behavior, namely: 1.
Investors consider each investment alternative as a probability of distribution of expected returns within a certain period 2.
Investors maximize one expected utility period, and their utility curve points 3.
It will reduce the marginal utility of wealth. 4.
Investors make portfolio risk estimates based on expected return variability 5.
Investors base their decisions solely on expected results and risks, so that their utility curve is a function of expected results and expected variance (or standard deviation) returns only. 6.
For certain levels of risk, investors prefer a higher return than a lower return. Likewise, for the expected rate of return, investors prefer smaller risks Based on this assumption, a single asset or asset portfolio is considered efficient if there are no other assets or portfolios that offer a higher expected return with lower or equal risk, or with a lower risk but the same expected return.

Mathematical Model
In the mathematical model, the following are definitions of return and volatility that will be used: Returns from a portfolio are returns of a combination of assets based on the proportion of their weights. Portfolio validity is a function of the correlation of the component assets. Generally, Expected Return ( ) = ∑ ( ), , where Rp is the return from the portfolio, Ri is the return of asset i and wi is the weighting of asset i.

Variety of Return Portolio
Where Pij is the correlation coefficient of the two assets Portfolio volatility Return For a portfolio with two assets Portfolio return

Efficient Frontier on Markowitz Portfolio Management Theory
Efficient Frontier describes the relationship between the return that can be expected from a portfolio and the magnitude of the risk (volatility) of the portfolio. This can be described as a curve in the risk graph against the expected return of the portfolio. Efficient Frontier provides the best return that can be expected for a certain level of risk or the lowest level of risk needed to achieve the expected level of return.
Efficient Frontier is a key concept in modern portfolio theory. What is quite interesting in post-modern portfolio theory is that there are a variety of Efficient Frontiers that can be adjusted according to the risk profile of investors.
The Efficient Frontier concept can be used to illustrate the benefits of investment diversification. An undiversified portfolio can be moved closer to Efficient Frontier by diversifying by combining it with other forms of investment that have little or even negative covariance. By diversifying, returns can be increased without the need to increase risk, or conversely reduce risk without reducing returns.
By using the solver from Microsoft Excel, we can find a portfolio arrangement with minimal risk from the combination of the fourteen stocks above. If the result we want to get is a very low-risk portfolio.
In the Microsoft Excel solver, we select cell D33 (slope of return) as the target cell, then in the equal to section, we select Max so that the results obtained are maximal. We also put E5 -E26 as the changing variable cells, so that Microsoft excel's solver will find the maximum value of cell D33 by changing the aforementioned variable cells.
The result of Microsoft Excel's solver calculation is the maximum value of the slope is 0.59 that has a combined average return 2.7% per month and combined standard deviation of return 5.1%.
Besides maximizing the slope in the cell D33, we also put D32 (standard deviation of return) as the objective and select Min in the equal to section, so that the value of the standard deviation of return will be minimized. The result of Microsoft Excel's solver calculation is the minimum value of the standard deviation is 4.09% with the combined average return 1.59% per month.
Based on these two calculations, we then know that the average return will range from 1.59% per month to 7.57% per month if we put all of the money in the SCMA stock. Thus, we use Microsoft Excel's solver to calculate all the rounded average returns from 2% to 7%. The calculation results are shown in the above table, with 9 scenarios of portfolio arrangements.
As we can see, two scenarios have a competitive edge. The first one is the safest portfolio shown in scenario 1 since the combined standard deviation of return can be reduced to 4.09%. The second one is the optimized portfolio selection shown in scenario 9 which has maximum slope of the return at 0.529 with the average return at 2.7% per month and the standard deviation of return at 5.1%.

Business Solution Implementation
These two scenarios can not be implemented directly in the real stock market easily since we have a constraint in the size of lot in Indonesian stock market. In the Indonesian stock market,