About
This worksheet looks at some common trading rules, modeling and forecasting, and some fundamental analysis.
Setup
Remember to always set your working directory to the source file location. Go to ‘Session’, scroll down to ‘Set Working Directory’, and click ‘To Source File Location’. Read carefully the below and follow the instructions to complete the tasks and answer any questions. Submit your work to RPubs as detailed in previous notes.
Note
Always read carefully the instructions on Sakai. For clarity, tasks/questions to be completed/answered are highlighted in red color (visible in preview) and numbered according to their particular placement in the task section. Quite often you will need to add your own code chunk.
Execute all code chunks, preview, publish, and submit link on Sakai follwoing the naming convention. Make sure to add comments to your code where appropriate. Use own language!
Task 1: Technical Trading Rules
This task follows the example in the book R Example 6.1/p 185 A new package will be required for this worksheet. All packages are included, for your convenience, in the code chunks below.
#Install package quantmod
if(!require("quantmod",quietly = TRUE))
install.packages("quantmod",dependencies = TRUE, repos = "https://cloud.r-project.org")
#Install package fArma for modelling ARMA time series processes
if(!require("fArma",quietly = TRUE))
install.packages("fArma",dependencies = TRUE, repos = "https://cloud.r-project.org")
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The following questions are for a stock of your choice from S&P500 (other than AAPL and your colleague!) and for the time-period from Jan 1, 2015 to present.
Observing the crossings or intersections between two simple moving averages can provide signals for buying or selling.
##### 1A) Create a chart of close prices and add the two simple moving averages over the periods n=20 and n=50. Clearly label the plots or provide a legend
getSymbols("TWTR")
[1] "TWTR"
Warning message:
In strsplit(code, "\n", fixed = TRUE) :
input string 1 is invalid in this locale
chartSeries(TWTR,subset='2015-01::2019-01’,
+ theme=chartTheme(’white’,up.col=’green’,dn.col=’red’),
+ TA=c(addBBands(n=20,sd=2,),addSMA(n=50,col="blue"),
+ addSMA(n=10,col="black"),addRSI(n=14))
Error: Incomplete expression: chartSeries(TWTR,subset='2015-01::2019-01鈥?
+ theme=chartTheme(鈥檞hite鈥?up.col=鈥檊reen鈥?dn.col=鈥檙ed鈥?,
+ TA=c(addBBands(n=20,sd=2,),addSMA(n=50,col="blue"),
+ addSMA(n=10,col="black"),addRSI(n=14))
sorry professor, I failed to create the moving average graph, I do not know the particular reason , but it may have sth to do with the unavailability of the package 2. I will try to interpret questions with some theoretical words since I fail to get a specific graph.
##### 1B) Select a particular crossover point to explain how you would implement a trading strategy (ref p184)
Bollinger bands are a kind of a trading bands or moving average envelopes. The high and low limits of a Bollinger band are calculated based on a x-number of standard deviation (usually 2) away from the moving average. A standard deviation is also a measure of volatility, as such the band will widen when volatility increases and contract when volatility decreases. As with bands and envelopes the idea of Bollinger band is that prices tend to stay within the band. When prices reach the top band it is assumed that resistance will be encountered and the price will fall. Opposite true when the lower band is reached. When the price moves outside the bands, a continuation of the current trend is expected.
##### 1C) Chart the Bollinger Bands based on the 20-days moving average and two standard deviations. Select a particular point to explain how the BB can be used in a trading strategy (ref p185)
RSI measures the velocity of price changes. Rapid price increases is an indication of stock overbought conditions, and rapid price decreases result in oversold conditions. When used properly RSI can assist in optimizing proper entry and exit decisions.
##### 1D) Chart the Relative Strength Index (RSI) based on 14-days moving average. Select a particular point to explain how RSI can be used in a trading strategy (ref p206) 
Task 2: Modeling & Forecasting
Similar to lab03 pick a currency exchange rates of your choice. Follow R Example 4.2/p 119. Pay special attention to Remark 4.1/p 112 and class notes for the correct interpretation and representation of results. Depending on the R version, the package fArma may not be available (true for 3.5 and up). One can use instead the function arima() to fit an AR(1) and the print to obtain the model coefficients. Check the illustrated example below and read the Help in R, as needed, for more insights on how to use commands.
#ar1 = arima(dataset, order = c(1,0,0)) to obtain the equivalent of an AR(1) model fit. dataset is in reference to your particular currency exchange pair like RUBUSD for example.
#print(ar1) to print the coffecients of the model. Pay attention to the interpretation of intercept
First we derive an autoregressive model of order 1, excluding the out-of-sample points. To exclude ppints check the example below
#ar1 = arimadataset[1:n], order - c(1,0,0)). This will build an AR(1) model based on the time series dataset [1:n] where n is the length of the tie series minus the last four points. For example EURUSD[1:175] is for the case where the total time series for the EURUSD is 179 observation points.
##### 2A) Derive an AR(1) model excluding the last four points from your time series (the out-of-sample). Note the values of the model coefficients, and write down the correspondng mathematical representation of the model.
getFX("EUR/USD") #download EUR/USD rates from oanda.com
[1] "EURUSD"
plot(EURUSD)

acf(EURUSD)

pacf(EURUSD)

library(fArma)
Error in library(fArma) : 不存在叫‘fArma’这个名字的程辑包
Next we apply the derived model to predict the rates, within confidence levels, for the out-of-sample points.
sorry professor, I fail to get a graph as the PDF shows,since the package library(fArma) is not available.
##### 2B) Using the fitted model, predict the rates for the excluded points corresponding to the four days ahead. Select one particular forecasted day to illustrate manually how the reported predicted rate can be reproduced using the derived AR(1) model.
getFX("EUR/USD") #download EUR/USD rates from oanda.com
[1] "EURUSD"
plot(EURUSD)

library(fArma)
Error in library(fArma) : 不存在叫‘fArma’这个名字的程辑包
if these codes above can de excuted successfully, one can Use the fitted AR(1) time series to predict plots 4.back points of the process and forecasts and plots 10.ahead values. Finally we want to assess the goodness of the model by conducting a quantitative analysis.
##### 2C) Formulate and execute a way to test the fitness of the model. Share your results.
### Task 3: Fundamental Analysis
Consider two stocks of your choice. Unfortunately the code in the R Example 6.2/p 202 is no more valid as Google stopped providing such data as of March 2018. Instead you are advised to use Bloomberg or other sources to extract the needed information. The information in Bloomberg is available in the security description page of a stock.
##### 3A) For each stock report the P/B, P/E, and Assets/Debts ratios. Note also the fiscal calendar date associated with the reported ratios.
getFinancials('AAPL',src = "google") #returns AAPL.f to "env"
Error: ‘getFinancials.google’ is defunct.
Google Finance stopped providing data in March, 2018.
You could try some of the data sources via Quandl instead.
See help("Defunct") and help("quantmod-defunct")
since we cannot get the data on financial statement from Google, I resort to “Havard Business Publishing” to get the financial statement of two companies, Blue Mountain and Auto Supplier Brog warner. 1.For Blue Mountain,the total assets in 2011 is 3918 million, and total liability is 1581 million, Assets/Debts ratios=2.478 P/E ratio =price per share/EPS=35/6.35=5.512 in year 2011. P/B ratio=current share price/bvps=35/30=1.17 in year 2011. 2.For Auto Supplier Brog warner, total assets in 2011 is 874 million, toal equity is 625 million ,Assets/Debts ratios=874/(874-625)=3.51. P/E ratio =price per share/EPS=66/9.43=6.95 in year 2011. P/B ratio=current share price/bvps=66/35=1.89 in year 2011. ##### 3B) Based on solely the three reported ratios which company has a stronger financial condition. Explain your logic. I consider taht the Blue Mountain company has a stronger financial condition, since it has the smaller P/E ration ,it means the the Blue Mountain has a more rational stock price.Besides,the P/B ratio of Blue Mountain is more close to 1.0, it means the value of the company is fairly valued.
*http://computationalfinance.lsi.upc.edu
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