Forecasting and Risk Modelling Report: Wells Fargo Stock Analysis

This report presents an analysis of Wells Fargo stock using the Autoregressive Integrated Moving Average (ARMA) model for time series prediction. The study, conducted using Eviews software, examines historical data from the Bloomberg database to forecast stock prices and assess investment opportunities. The report provides an overview of Wells Fargo, including its business operations, earnings, and stock performance, along with a literature review of relevant forecasting techniques. It explores the use of ARMA models for short-term stock price prediction and discusses the process of testing for stationarity, identifying model parameters, and forecasting. The report also investigates the application of an EGARCH model and provides an out-of-sample forecasting analysis. Ultimately, the research aims to evaluate the stock's potential for value investing and guide future investment decisions based on the model's predictive capabilities. The report concludes with insights on the stock's performance and its suitability for value investors.

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Running head: FORECASTING AND RISK MODELLING
Forecasting and risk modelling
Name of the student
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Executive summary
In the finance and economics study, stock prediction is an essential factor for the interest
of the researchers and to make various predictive models. In this research paper the
Autoregrassive integrated moving average, ARMA model has been incorporated for the time
series prediction. This paper also represents the predictive model for the stock price expectation
by using the ARMA method. For this Eviews software is used to analyse the data. The stock has
been selected that is Wells fargo listed in NYSE, Newyork Stock Exchange. Data is extracted
from the Bloomberg database. The consequence that are so obtained from ARMA model, which
has a robust and potential prediction in a short term basis is so favaorable with the existing
mechanism.

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Table of Contents
Introduction......................................................................................................................................3
Overview of the stock......................................................................................................................4
Business keep stagecoach rolling....................................................................................................4
Wells fargo earnings........................................................................................................................4
Stock analysis of Wells Fargo.........................................................................................................5
A boosts in WFC stock....................................................................................................................6
Rating of Wells Fargo stock............................................................................................................7
Reason of decreasing:......................................................................................................................7
Recovery from the current crisis scenario.......................................................................................7
Welss Fargo- Value invest stock?....................................................................................................8
PE ratio............................................................................................................................................8
Bottom line....................................................................................................................................10
Literature review............................................................................................................................11
Testing and ensuring stationary.....................................................................................................12
Identification of p and q.................................................................................................................13
Estimation and Forecasting............................................................................................................13
Optimal ARMA with a stationary error term................................................................................15
Optimal ARMA with EGARCH model.........................................................................................16

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Out of sample forecasting..............................................................................................................18
Fitted values...................................................................................................................................20
Conclusion:....................................................................................................................................21
Reference.......................................................................................................................................22

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Introduction
This paper study about a stock listed on New York Stock Exchange (NYSE), Wells
Fargo. The primary goals of this paper is to investigate the possible investment oppertunitiers,
logically worth of the takis risk and benefits and make an educated investment position. A
critical analysation of understanding the risk and opportunities for high return which is offered in
the investment opportunity through the effortless research and analysis. The derive knowledge
from this paper is to guide the future selection and implimentation of intelligent investment.
A 10 years daily data has been used for the investment purpose this investments tested
several researched and also help in understanding of the stock market in general. Through this
study experience identify and anticipates the market trends and influenced the future investment
decision.
This paper also analyse the statistical analysis of time series, auto regressive moving
average, ARMA model (Isufi et al 2016), it provides a report of a weekly stochastic process in
terms of two polynomials, one for the autoregression (Efendi, Arbaiy and Deris 2018) and
another for the moving average. Generally it is reported in this paper that can be done from two
perspectives: statistical and artificial intelligence techniques (Raedt et al 2016). It is also known
to a robust and efficient “financial time series” allows to forecast short term prediction than the
most popular ANN techniques. In this paper a short term stock price prediction process
(Rounaghi and Zadeh 2016) has been presented by ARMA model. By refering this reserach
paper an investor must evaluate a short term prediction that leads an investment decision making.

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Overview of the stock
Wells fargo and Company is an american and multinational financial services
organizations, which having the headquarter in San Fransisco, in the context of full market
capitalization, Wells fargo is the fourth largest bank. It is listed on the New York Stock
exchange.
There are several reasons to choose this stock-
Business keep stagecoach rolling
In case of community banking (Lux and Greene 2015), it serves the consumers and the
small enterprises, savings account and as well as credit and debit cards.
Wells fargo earnings
In the fourth quarter, Well Fargo received 60 cents per share or 93 cents when leagal
costs are excluded. It has dropped 23% year on year as per the next revealing data. Therefor the
stock has managed to post revenue of 19.9 dollar, which was better than the expected $19.81
billion.
A revenue fell around 8% of the community banking, that is all about to &10.52 biolion
which is driven by the lower interest income. Wholesale banking revenue droped 5% to 6.56
billion dollar. Wealth and investment management (Hastings and Mitchell 2020) revenue grew
3% to 4.07 billion dollar.

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Stock analysis of Wells Fargo
It has been projected more than 47% of its value for the Wells fargo stock in 2020. As per
the analysis of Market Smith, it shows a stock gapped down in the following weak Q4 results, it
has again shown a plunging during this month after a hard trading and it has been sinking like a
stone.
For the recent times the big bank stocks are facing a massive trouble, outperforming the
S&P 500 index over the long run, in case of Wells Fargo stocks it has tendency of slow motion
or laggard, but in a long run it will be a leading stock (Drakopoulou 2016).
Recently WFC stock has IBD Composite Rating of 16. The measuring tool has shown
that Wells fargo earnings are better than the performance of its stock market. A Can Slim
investing system is required for 25% quarterly growth.

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In the recent reaserch, the several analyst has expected that the Wells fargo stock has
been sink 12% in 2020, but it will show growth around 12% in 2021. It will be moving up from
its lower base.
A boosts in WFC stock
In the mid 2019, Timothy Solan was stepped down after struggleing to make a clean
image of bank. Solan was replaced on an interim basis by the general counsel, C. Allen Parker. It
can be seen that A new CEO can revive a struggeling company. As per Martinez who ranks the
Wells Fargo as neutral, it is more needs to be done to assure there is a more than a short term
price boost. Moreover such improvement will not happen overnight it takes a long time.
Rating of Wells Fargo stock
As per the CFRA research, recommend the WFC stocks as hold, the target price is 42 but
it will move slight down because of its plunging.

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Due the speared of corona virus in all over the world as decleared by The World Health
Organization in the end of January besides of all other stocks WFC stock has lost 36 percent of
its value (Yan et al 2020).
Reason of decreasing:
It has fallen because the situation on the ground has changed. It has a sizable loan
portfolio of around $399 billion in the community loans and the commercial loan is 456 billion
dollar. In the year 2019, the commercial bank and the community bank both are generated 72%
of the banks revenue, which implies that the banks is heavily dependent on the segments. On the
other view, it can expect that the business could suffer a loss due to accumulated effect of less
consumer demand, disruption of supply chain and the global economic slowdown (Hall 2016).
Recovery from the current crisis scenario
Knocking the mind that, although the WFC stock has fallen 36% this time but it is lower
as compared to 2008 recession, it was around 65%. The research assures and expect, once the
economic scenario is getting improved the WFC stock will show better by 25%. This will be
marked at empirical recovery of 46 dollar. This stock was gained a global momentum before the
coronavirus outbreak.
Welss Fargo- Value invest stock?
This study can use some methods to evaluate whether the WFC stocks can be value
investing or not.

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PE ratio
Often the value investors looks at the price earning ratio (PE ratio) (Arkan 2016). It
simply can describes that how much an investors are wish to pay for each dollar of earnings in a
given stock. In this line Wells Fargo has twelve months PE ratio of 9.84 as you can see in the
chart below.
This level is actually compares with the market, as the PE ratio of the S&P 500 is 17.8. if
we concentrate the PE of Wells Fargo, we can see the current PE stands on the mid point over
the past five years.

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Apperently the selection of WFC might be a good option for the value investors (Otuteye
and Siddiquee 2015). There are also other factors to be considered before investing in this stock.
It had an impact of its current consensus as the current quarter consensus estimates has decreased
3.3% in the past two months, on the other hand the full year estimation was 4.4% approximately.
The below mentioned chart shows the consensus estimation trend and recent price action for the
stock:

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Though the bearish trend is shown but we can except an in line performance in the near term
future.
Bottom line
Wells fargo stocks is an impacable selection for the value investors. Though on the
ranking basis it is hard to get too excited about this company, however over the two years, the
industry has performed not very well, therefore the value stockholder can wait. A favourable
industry factor can boost up this stock and once it will happen the stock will fly straightway.

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Literature review
According to Kristjanpoller and Minutolo 2016, this paper focus and to determine
wheather the improvements can be achieved to forecast the oil price volatility using a hybrid
model and incorporating financial variables. The main reflection is that the hybrid model
developes the volatility forecasting precision by 30% over the previous model depends a
measurement by a heteroscedasticity adjusted mean square error.
According to Chen, Jeong and Härdle 2015, refers a support vector regression to forecast
a nonlinier ARMA model based on the simulated data and real data of financial returns. As a
result it can be said that the recurrent SVR model is consistently better than benchmark models
for forecasting both the magnitude and turning points and satistically improves the forecasting
performance.
According to Dana 2016, financial factors has an impact on both taking and assessing
various financial decisions in firms. Hence volatility modelling in the capital markets is one of
the aspects that have a direct role and effect on pricing, risk and portfolio management.
Therefore this study reflects to examine the volatility characterstics on the capital market.
According to Quaicoe et al 2015, this research paper is aimed for modelling the
variations in the exchange rate. It evaluates the applicability of a range of ARCH/ GARCH,
which specifies the modelling volatility of the series. The specific variants includes ARMA,
GARCH, EGARCH specifications. The null hypothesis of no ARCH effect lies a rejection level
at 5% significance which indicates the presence of an ARCH effect. All the significant of ARMA
and GARCH indicates the most suitable model and conditional mean and conditional variance.

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According to Angelidis and Degiannakis 2018, A model of Value at Risk (VaR) suggests
an unique risk management technique that generates an accurate VaR estimations for the long
and short trading positions. Therefore the developed testing frameworks have not been widely
accepted.
This reasech paper has taken the WFS stocks on daily data for the last 10 years. Close
price has taken to forcast the expected return. It also evaluates the holding period return. The
calculated ARR is 3.20% with taking a risk of 24.86%, here Standard deviation (SD) indicates
the concerned risk. Variance is 0.0618 which indicates the volatility of the stocks.
This paper presents an optimal ARMA model to test the prediction of performance of the stock.
The ARMA model also known as BOXjenkins approach, which makes a non stationary
data to stationary by the different series of Yt .
This model called as Autoregressavie Integrated Moving Average or ARMA, follows
some basic steps:
Testing and ensuring stationary
Here, we evaluate stationary by approaching the Augmented Dickey-Fuller unit root test.
The resulting P-value from the ADF or regression (Kokotović and Kurečić 2016) test should be
0.05 or 5% for a time series to be stationary (Cheng et al 2015). If the concerned P value is more
than 0.05 then we accomplish that the time series is non-stationary.

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Identification of p and q
In this segment, identify an appropriate order of Autoregressive and Moving average
process by using the Autocorrelation function, ACF (Dürre, Fried and Liboschik 2015) and the
Partial autocorrelation function, PACF (Bakar and Rosbi 2017). Here PACF is used to identify
the p order of AR model. If we get spike at lag on the PACF then it is AR model of the order
that is AR(1) and if we have significant spikes at lag 1,2 and 3 on the PACF, then we will have
an AR model of the order 3, that is AR(3).
In case of Moving Average, (MA) model (Yuan, Liu and Fang 2016), the PACF will
reduce exponentially and the ACF plot will be used find the order of MA process. Significant
spike at lag 1 on the ACF, then we have MA model that is MA(1) and if we have significant
spikes at lag 1,2 and 3 on the ACF then we have MA model of the order 3 that is MA(3).
Estimation and Forecasting
If we have evaluated the limitations p,q then we estimate the accuracy of the ARMA
model. It is used a fitted model to forcast the values of the test data set and forecasting the
function. Therefore we forcasted the values are in line with the actual values.
After running the Eviews, we can see that the expected average return 0.000210 with the
standard devision of 0.0171778, that means the whole return is .017 volatile. It describes the
below mentioned table:

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ARMA (4,5)
Testing Auto Regressive (AR) (Qu and Lee 2015)Moving Average (MA), deleivers result
with 4,5 is -5.34, it defines the linear difference equations with a constatnt coefficient (Willert
and Popov 2016).

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Optimal ARMA with a stationary error term
An optimal ARMA, after running with the Eviews, checks a stationary error term which
shows below:

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Optimal ARMA with EGARCH model
Testing the EGARCH model to justify the error, we need to mark on the below table:

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Forecasting the returns on the basis of ARMA model with keeping the daily data are as
follows:

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Forecasting on the basis of EGARCH model:
Out of sample forecasting
This section suggests future 3 years forecasting, that is 2017 to 2020, out of sample
forecasting on the basis of ARMA model are as follows

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Below graph has shown forecasted 3 years model of EGARCH

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Fitted values
ARMA
In the ARMA model, below mentioned graph has been forecasted the fitted values:
EGARCH

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Therefore the relevant statistics validate the optimality of the forcast by the implementation of
EGARCH model, the EGARCH statistics shows how it effects with the volatility.
Conclusion:
From the above discussion, it can be concluded that, this paper presents an effective
process of establishing ARMA model for the stock price prediction. The experiment reveals the
potential ARMA model forcast the stock price satisfactory on a short term basis. Using of
EGARCH model specifically to test the optimality variation on the stock returns and signified
the forcsting. This study make a guidance to the investors in the stock market to make profitable
investment decisions. Depending on the results obtained by ARMA model can evaluate
significantly well and developing forecasting methods in ashort term prediction.

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Reference
Arkan, T., 2016. The importance of financial ratios in predicting stock price trends: A case study
in emerging markets. Finanse, Rynki Finansowe, Ubezpieczenia, 79(1), pp.13-26.
Bakar, N.A. and Rosbi, S., 2017. Autoregressive integrated moving average (ARIMA) model for
forecasting cryptocurrency exchange rate in high volatility environment: A new insight of bitcoin
transaction. International Journal of Advanced Engineering Research and Science, 4(11).
Cheng, C., Sa-Ngasoongsong, A., Beyca, O., Le, T., Yang, H., Kong, Z. and Bukkapatnam, S.T.,
2015. Time series forecasting for nonlinear and non-stationary processes: A review and
comparative study. Iie Transactions, 47(10), pp.1053-1071.
Drakopoulou, V., 2016. A review of fundamental and technical stock analysis
techniques. Journal of Stock & Forex Trading, 5.
Dürre, A., Fried, R. and Liboschik, T., 2015. Robust estimation of (partial)
autocorrelation. Wiley Interdisciplinary Reviews: Computational Statistics, 7(3), pp.205-222.
Efendi, R., Arbaiy, N. and Deris, M.M., 2018. A new procedure in stock market forecasting
based on fuzzy random auto-regression time series model. Information Sciences, 441, pp.113-
132.
Hall, S.M., 2016. Everyday family experiences of the financial crisis: getting by in the recent
economic recession. Journal of Economic Geography, 16(2), pp.305-330.
Hastings, J. and Mitchell, O.S., 2020. How financial literacy and impatience shape retirement
wealth and investment behaviors. Journal of Pension Economics & Finance, 19(1), pp.1-20.

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FORECASTING AND RISK MODELLING
Isufi, E., Loukas, A., Simonetto, A. and Leus, G., 2016. Autoregressive moving average graph
filtering. IEEE Transactions on Signal Processing, 65(2), pp.274-288.
Kokotović, F. and Kurečić, P., 2016, January. The MINT countries: A regression analysis of the
selected economic features. In 14th International Scientific Conference on Economic and Social
Development.
Lux, M. and Greene, R., 2015. The state and fate of community banking. M-RCBG associate
working paper, 37(31), pp.2-3.
Otuteye, E. and Siddiquee, M., 2015. Overcoming cognitive biases: A heuristic for making value
investing decisions. Journal of Behavioral Finance, 16(2), pp.140-149.
Qu, X. and Lee, L.F., 2015. Estimating a spatial autoregressive model with an endogenous
spatial weight matrix. Journal of Econometrics, 184(2), pp.209-232.
Raedt, L.D., Kersting, K., Natarajan, S. and Poole, D., 2016. Statistical relational artificial
intelligence: Logic, probability, and computation. Synthesis Lectures on Artificial Intelligence
and Machine Learning, 10(2), pp.1-189.
Rounaghi, M.M. and Zadeh, F.N., 2016. Investigation of market efficiency and financial stability
between S&P 500 and London stock exchange: Monthly and yearly forecasting of time series
stock returns using ARMA model. Physica A: Statistical Mechanics and its Applications, 456,
pp.10-21.
Willert, E. and Popov, V.L., 2016. Impact of an elastic sphere with an elastic half space with a
constant coefficient of friction: Numerical analysis based on the method of dimensionality

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reduction. ZAMM
‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte
Mathematik und Mechanik, 96(9), pp.1089-1095.
Yan, B., Stuart, L., Tu, A. and Zhang, T., 2020. Analysis of the Effect of COVID-19 on the
Stock Market and Potential Investing Strategies. Available at SSRN 3563380.
Yuan, C., Liu, S. and Fang, Z., 2016. Comparison of China's primary energy consumption
forecasting by using ARIMA (the autoregressive integrated moving average) model and GM (1,
1) model. Energy, 100, pp.384-390.