Forecasting Stock Data For Apple Inc.

Moving Average Technique

The data has been collected from apple inc. Stock price from date 1/3/2022 to 1/19/2022. Different methods have been used for forecasting the stock data: moving average, weighted moving average, exponential smoothing, and linear forecasting.

The moving average means the average change in the data series over time. This process is very useful in finance as this keeps a track done by technical analysts to track the price trends for a specific period. Moving average is calculated by adding the stock prices over a certain period and dividing the sum by the total period number.

The formula is given by with MA given for moving average. 

The weighted moving average is a type of moving average where the recent prices are provided greater weight in the calculation, which is more relevant for making analysis, but for moving average equal weight is given to all the data.

The weighted average formula is given by WMA given for the weighted moving average. 

The exponential moving averages assigns decreasing weights, and the highest weight is given to the latest price. The weights exponentially decrease as the previous weight may be 1.0 smaller than the weight in front of it.

The formula of exponential moving average given as EMA is given as:  

The prediction of price has been done for 1/19/2022 and compared with the actual price of the stock price and found the deviation of different ways used for forecasting with the actual price using root mean square deviation. It is observed from the above analysis that the least value is found for exponential smoothing with the standard deviation of 0.002 followed by weighted moving average with the value of 0.529 then is liner forecast with the value of 0.636 and highest for moving average value of 1.046. Thus, exponential smoothing should be used for this future prediction as there is the least value of root mean square deviation for the forecasting as lesser is the value more is the precision to the future forecasting.

Apple inc.	Actual	Moving	Weighted	Exponential	Linear
Date	Stock Price	Average	Moving Average	Smoothing	Forecast
1/3/2022	182.01
1/4/2022	179.70
1/5/2022	174.92
1/6/2022	172.00
1/7/2022	172.17
1/10/2022	172.19
1/11/2022	175.08
1/12/2022	175.53
1/13/2022	172.19
1/14/2022	173.07
1/18/2022	169.80
1/19/2022	166.23	169.70	167.98	166.24	168.34
Root-Mean-Square Deviation	1.046	0.529	0.002	0.636

As provided in the question, there are three sources of locations, L1, L2 and L3, to its distribution outlets R1, R2 and R3. The calculations show that the total demand is highest for L2 with 500, followed by L1 with 300 and lowest for L3, 200. The total demand is found by adding the values for supply for all R1, R2 and R3 for each L1, L2 and L3. The total capacity is highest for R3 with 400, followed by R2 with 350 and the lowest for R1, which is 250. The total capacity for each R1, R2 and R3 is found by adding the supply for all L1, L2 and L3 locations. The shipping cost for each location and distribution outlet is found by multiplying the unit shipping cost with supply for each outlet and location. The least shipping cost is found for L1 and L3 locations, which is 400 euros, and higher for L2 locations, 1200 euros. The total shipping cost is found to be 2000 euros. The total cost for each L1, L2 and L3 is found by adding the cost for all R1, R2 and R3 outlets.

Let’s assume
z = Minimum Shipping Cost
Optimum quantity for Minimum Shipping Cost
	R1
L1	a1
L2	b1
L3	c1
Linear Equation for minimum shipping cost:
z=[(1*a1) +(3*b1) +(2*c1)] +[(3*a2) +(4*b2) +(2*c2)] +[(2*a3) +(2*b3) +(5*c3)]
Constraints:
a1+a2+a3=300
b1+b2+b3=500
c1+c2+c3=200
a1+b1+c1<=250
a2+b2+c2<=350
a3+b3+c3<=400
a1, b1, c1, a2, b2, c2, a3, b3, c3>=0

Weighted Moving Average Technique

The linear equation for minimum shopping cost is estimated from the above chart, indicated by z.

The main purpose of optimization is to allocate the resources, which reduces the time for taking management decisions, and those algorithms are used to solve the problem of resource allocation. Thus, it reduces the execution time for the job to be solved. Resource allocation is managing the assets and assigning them aligned to the organization’s goals and strategies. The main goal is to make a balance of the demand of the resources with the resources that are available. Various steps are involved in allocating resources: knowing the scope, identifying the resources, knowing the dependent resource, keeping track of the time, using various tools to make the analysis, and not making over allocation. It can also be termed resource management or resource scheduling, which means scheduling the tasks and associated resources needed to be completed. The resource allocation is knowing the resources and then scheduling them with the project timeline. Project allocation can be for various reasons, which are administration, operations, support, etc. If the project requirement is changed, the allocation is also changed. With the project being assigned, it is also important to manage the project’s lifecycle and keep up with the changes. This will help keep the cost down and create customer satisfaction by best overcoming and delivering the project successfully.

The uses of linear programming make optimum decisions with certain constraints, which is linear inequalities. In easy words, it takes the problems as the solution of maximization and minimization problems which is a subject to linear inequalities which are stated in terms of certain variables. The term linear means the functions maximized of degree one, and programming means the activities planned in the manner that led to some optimum results with limited resources. The program can be said as optimal if it can maximize or minimize the firm’s output, cost, or profit. Thus, the LP model can thus be explained as the method to make decisions of the combination of factors optimally to find the given output or the products with the combination.  

The limitation of the LP model is that it is not an easy tool to define the objective function specifically. If the specific objective is not laid, it might not be easy to understand various technological, financial, or other constraints. With the set objective and constraints, this might be possible that constraints may not be expressible as linearly having inequalities. Estimating various values might also be an issue to enter into the LP model. For inputs and outputs, various linear relations are taken as assumptions. But in real life, most of the relations taken into consideration are not linear though they can be added, multiplied, or divided. Many terms are taken as constant. But in reality, these terms can increase or decrease return as the firm experiences’ changes in production. This technique is highly complex and mathematical. The solution consists of linear programming that needs maximization or minimization specified as variables. Thus, many variables are not considered, and the method becomes more complex if considered. Conclusion: Many solutions have trial and error solutions, and this might be difficult to make optimal solutions to the various economic problems.

Exponential Smoothing Technique

Here in the given problem, the company director wants to look after the expanding capacity into a new market. For that purpose, three service streams are considered S1, S2 and S3. These expansion plans depend on whether a recent defense bid is accepted or not. A payoff table is given, which reflects the realized profits based on different situations faced by the firm.

Maxi max criterion: This is the criterion which the decision makers select the choice which will give the result of the maximum of maximums, an optimistic criterion. For each service streams max profits are chosen and then the max value among all the max profits will be considered as the Maxi max. So, in the given table if we consider S1 max value is 10. Also, for S2 the max value is 30 and for S3 max value is 40. Then the max value among all the max is 40 which is under S3.

Maxi min criterion: In this criterion the decision makers select the option that will tell the maximum of the minimums which a pessimistic criterion. For each service streams max profits are chosen and then the min value among all the max profits will be considered as the Maxi min. So, in the given table if we consider S1 max value is 10. Also, for S2 the max value is 30 and for S3 max value is 40. Then the min value among all the max is 10 which is under S1.

The Laplace criterion: In this criterion each of the service streams will be multiplied by equal weight, assuming that all the streams have equal chance to occur. Here in this case all the values of service streams will be multiplied by 0.5 and the difference will be calculated within every service streams. Now after doing the calculation, it is found that the max value is under S3.

Minimax Regret Criterion: For this thing first Minimax criterion needs to be found. In this criterion min values are chosen from all streams and the max among all the min values will be considered the minimax. For the given table Min value for S1 is 5. For S2 min value is 4 and for S3 min value is 2. So, among all the min values S1 has the max value 5. Now Regret is the nothing but the difference between the best decision and all other decision. Here maximum regret for S1 is 30. For S2 it is 10 and for S3 it is 3. So, we will minimize the max regret and choose S1.

Linear Forecasting Technique

After all the above calculations, we have seen that for most cases, we have chosen S3. So that means S3 is an ideal condition. So, if there is a 65% chance of bid acceptance and a 35% chance of the bid being rejected, the expected value under perfect information will be 25.3.

In Maximax Max of all max values are taken into consideration. So, it is the optimistic approach towards the situation. In Minmax max among all the min values are taken into consideration which is the pessimistic value towards the situation. In Maximin the max value of all mins will be considered which is optimistic view towards the situation. In Laplace criterion we are considering equal weightage to all the situations and S3 is chosen at that criterion.

	Bid	Bid			Equal	Regret	Hurwicz
	Accepted	Rejected	Maximum	Minimum	Likelihood	Accepted	Rejected	Criteria
S1	10	5	10	5	7.5	30	0	4.75
S2	30	4	30	4	17	10	1	18.1
S3	40	2	40	2	21	0	3	25.3
Maximax	40	S3
Maximin	5	S1
Laplace	21	S3
Minimax	3	S3
Expected Value	25.3	S3

Ethics is nothing but a principle which is based on the context of nature and mind frame of a given socio-economic condition. Ethical standards are not uniform in nature. A leadership needs dedication, perception and eagerness to make a good balance between morals and ethical principles. Every time companies around the globe take strong decisions on the basis of circumstances and situations. Very often they make a comparison of normal responses to ethical issues, so that the operating approach can produce a least harm. To sustain for a long term every business leader and their business farms need a decision-making framework. Business structure, Customer dealing, Marketing, and financial investments these different aspects of business are affected by the actions that company choose. Ethical infrastructures are made and applied to see that an organization’s or company’s actions and decisions reflect and respect its ethics. Frameworks, rather than giving step-by-step approaches, define the fundamental features of moral solutions to common problems. The frameworks that are told below help to approach some challenges that are necessary for novel solutions. Rather than a structured collection of moral principles, virtue ethics delts with lots of development for human morality. Business executives, employ ethical principles in their judgement, need to be concerned about how the decisions reflect organization’s thinking and characteristics. In a corporate way, virtue ethics may aid in the development of connections with workers, customers, consumers, and the community by utilizing personal qualities like honesty, sincerity, empathy, and discipline. These personal qualities frequently connect with business abilities and financial goals. Unfortunately, while virtue ethics may appear straightforward in theory, it may also be difficult to put into practice. Because defining what is “good” or “right” in morality is not uniform, the framework may skip the amount of thought and logic that are needed to consider the problem. The consequentialist theory is a moral framework for determining an acceptable course of action depending on the outcomes. The outcomes are analyzed pragmatically before making a choice. Once the intended outcome has been determined, the moral decision-making model identifies various ways to achieve that goal. The objective is to select a plan of action that will result in the greatest amount of good. The consequentialist hypothesis is ethically advantageous as a result of this process. As stages are matched with the morally reflective purpose, it delivers definitive transparency Because it optimizes good effects for some while minimizing negative consequences for others, this ethical approach works effectively with thoughts and decisions that influence large number of people. There are certain drawbacks to this idea. Because of unknown factors, calculating the repercussions of activities can be challenging. This uncertainty may end up causing more damage than benefit. The inference is nothing, but the aim justifies the purpose, which may end in sacrificing the pleasure of minority for the sake of majority as a whole. In business, these actions do not always have a negative impact on huge groups, but they can have an impact on a company’s monetary condition and longevity. When a firm markets its service or product, it is not doing moral work, and the impact on consumers’ purchasing patterns might have long-term consequences. Ethical decision-making framework could be used by the leaders to look into the effectiveness of any aspects of business. Advantages of these frameworks can be used to connect various aspects of an organization through ethical vision. To produce more planned, expandable and equal decision making this type of ethical vision is required. Ig a business owner wants to become successful and more conscious it is important to learn out the ethical framework. It is a complex and challenging situation for a leader to stick with the principal and moral values while obligations are coming from other parts. It may be found that there will be a risk or a reward while examining the different factors of the decision-making framework. This type of situation will boast the confidence level to clarify any required context or to make an effective communication for business. This type of dilemma will transform to further opportunity to redefine the decision-making skills and will help to grow the ability to make right choices that are helpful for the growth of an organization and its performance. A leader will face different types of ethical issues and that will not be solved in a single approach. There are so many approaches which are applicable for different situations.  By choosing and executing the available approaches will make a company high gainer. By these situations a leader can improve the clarification and to build the mid set to balance ethics, responsibilities and morality of an organization.

A framework has been formed for the managers to tackle the situations with different variables that an organization will face day by day.

Identify: The initial step is to understand each scenario for the standpoint that is ethical.

Consider – Business leaders need to access the decision making before they act.

Act – Actions are carried that has been decided and if authority is required take issue to appropriate management level.

Reflect – This is the thing that is called on to see the overall result of its actions  

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