FINC621 Winter 2018-19 Lab Worksheet 05

Technical Analysis & Fundamentals (finc621-lab05)

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!

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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")

there is no package called <U+393C><U+3E31>fArma<U+393C><U+3E32>Installing package into <U+393C><U+3E31>C:/Users/Yue Huang/Documents/R/win-library/3.5<U+393C><U+3E32>
(as <U+393C><U+3E31>lib<U+393C><U+3E32> is unspecified)

Warning in install.packages :
  package ‘fArma’ is not available (for R version 3.5.1)

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("MCD")

[1] "MCD"

chartSeries(MCD,theme=chartTheme('white',up.col='black',dn.col='red'),subset='2018-01::2018-12',TA=c(addSMA(n=50,col="blue"), addSMA(n=20,col="red")),type="line")

As shown in the picture, the red line represents simple moving average over the periods n=20 and the blue line represents simple moving average over the periods n=50.

##### 1B) Select a particular crossover point to explain how you would implement a trading strategy (ref p184)

From the picture above we can see that on April 10th, 2018, the red line crosses the blue line from bottom to top. It means that before April 10th, 2018, the value of moving average of 20 periods is lower than that of 50 periods; after that day, the value of moving average of 20 periods is higher than that of 50 periods. Therefore, we should go to long the MCD stock on April 11th, 2018 at open price.

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)

chartSeries(MCD,subset='2018-01::2018-12', theme=chartTheme('white',up.col='green',dn.col='red'),TA=c(addBBands(n=20,sd=2)))

From the picture above we can see that on June 10th, 2018, the MCD stock price breaks upper band. And we know that its movement will continue a while. Therefore, we should go to long the MCD stock on June 11th, 2018.

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)

chartSeries(MCD,subset='2018-01::2018-12', theme=chartTheme('white',up.col='green',dn.col='red'),TA=c(addRSI(n=14)))

In practice, the parameter ET of RIS is taken at 30. If RSI(t) is close to ET (respectively, 100 ??? ET) then the stock is oversold (resp. overbought) and so a turning point in the trend of prices is imminent. From the picture above we can see that on March 2nd, 2018, the RIS of MCD stock is lower than 30, which means the stock is oversold. Therefore, we should go to long the MCD stock on March 3rd, 2018.

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("GBP/USD")

[1] "GBPUSD"

a=as.numeric(GBPUSD) 
n=length(a)-4
ar1 = arima(GBPUSD[1:n], order = c(1,0,0),method = "CSS")
print(ar1)

Call:
arima(x = GBPUSD[1:n], order = c(1, 0, 0), method = "CSS")

Coefficients:
         ar1  intercept
      0.9634     1.2867
s.e.  0.0189     0.0087

sigma^2 estimated as 1.756e-05:  part log likelihood = 709.8

summary(ar1)

          Length Class  Mode     
coef        2    -none- numeric  
sigma2      1    -none- numeric  
var.coef    4    -none- numeric  
mask        2    -none- logical  
loglik      1    -none- numeric  
aic         1    -none- logical  
arma        7    -none- numeric  
residuals 175    ts     numeric  
call        4    -none- call     
series      1    -none- character
code        1    -none- numeric  
n.cond      1    -none- numeric  
nobs        1    -none- numeric  
model      10    -none- list     

The result above shows the intercept of AR(1) is 1.2867, and the slope of AR(1) is 0.9634. Therefore, the corresponding mathematical representation of the model is:

\(GBPUSD_{t}\)-1.2867=0.9634(\(GBPUSD_{t-1}\)-1.2867)+\(W_{t}\), \(W_{t}\)~N(0, 0.00001756)

\(GBPUSD_{t}\)=0.0471+0.9634\(GBPUSD_{t-1}\)+\(W_{t}\), \(W_{t}\)~N(0, 0.00001756)

Next we apply the derived model to predict the rates, within confidence levels, for the out-of-sample points.

##### 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.

predict(ar1,4)

$`pred`
Time Series:
Start = 176 
End = 179 
Frequency = 1 
[1] 1.292864 1.292638 1.292421 1.292212

$se
Time Series:
Start = 176 
End = 179 
Frequency = 1 
[1] 0.004190522 0.005818950 0.006999260 0.007939324

predict(ar1,n.ahead = 4,n.back=10)

$`pred`
Time Series:
Start = 176 
End = 179 
Frequency = 1 
[1] 1.292864 1.292638 1.292421 1.292212

$se
Time Series:
Start = 176 
End = 179 
Frequency = 1 
[1] 0.004190522 0.005818950 0.006999260 0.007939324

We can know the actual value of GBPUSD on Jan.18th, 2019 is 1.293098. By using the AR(1), we can calculate the predicted value of GBPUSD on Jan.19th,2019: \(GBPUSD_{t}\)=0.0471+0.9634\(GBPUSD_{t-1}\)+\(W_{t}\)=0.0471+0.9634*1.293098+\(W_{t}\), =1.29287+\(W_{t}\), which is close to the predicted value 1.292864 shown above.

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.

We now know that the actual values of GBPUSD from Jan.19th to Jan.22nd are 1.287740, 1.287687, 1.287328 and 1.291670 and the predicted value of them are 1.292864, 1.292638, 1.292421 and 1.292212. To test the goodness of fit of the model, we calculate the Mean Squared Error of these two data sets. The formula is:

MSE=\(1/4*\)\(\sum_{n=1}^{4} (GBPUSD_{t}-\hat{GRPUSD_{t}})^2\),

and we get the result is 0.00001925, which is quite small. Therefore, we can conclude that the fitness of this model is good.

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.

For IBM stock, the P/B ratio is 6.10, the P/E ratio is 9.4, and the Debt/Assets ratio is 37.1%. The Fiscal Calendar Year is 12/2018.

For CSCO stock, the P/B ratio is 4.68, the P/E ratio is 18.6, and the Debt/Assets ratio is 23.5%. The Fiscal Calendar Year is 07/2018.

##### 3B) Based on solely the three reported ratios which company has a stronger financial condition. Explain your logic.

As we can see, IBM has higher P/B ratio, higher Debt/Assets ratio and lower P/E ratio and CSCO has a lower P/B ratio, lower Debt/Assets ratio and higher P/E ratio. Since both companies have P/E ratio that higher than 1, which means that both their stock prices are overvalued. Besides, higher Debt/Assets means higher leveraged company, which means that IBM is more leveraged than IBM. Also, lower P/E ratio is better, which mean the performance of CSCO is better than IBM. From these three ratios above, I conclude that the financial condition of CSCO is better than that of IBM.

*http://computationalfinance.lsi.upc.edu