Category Archives: Finance

Posts about finance

Using ggplot to make candlestick charts alpha

Posted by mark

In my investments class, we have to produce charts and perform technical analysis. Though quantmod has the mucho excellente chartSeries() function, I can't leave well enough alone and decided to try to write some functions that will draw a chart using ggplot and add technical indicators.

I got basic functionality down, but want to continue to add things to the function. call ggChartSeries() and provide an OHLC object from quantmod, along with start and end dates in as.Date() form. It calculates moving averages and after that trims the data series, as opposed to chartSeries(), which has issues with this since it takes the pre-trimmed data as an input.

^?Download ggChartSeries.r

require(quantmod)
require(ggplot2)
 
getSymbols('AAPL')
x<-AAPL
start <- Sys.Date()-200
end <- Sys.Date()
 
#Pass an OHLC object into this function
#also pass two dates formatted as.Date()
ggChartSeries <- function(x, start, end){
 
# the below is done redundantly for ease of maintenance later on
#First, strip OHLC data (need to vectorize)
  date <- as.Date(time(x))
  open <- as.vector(Op(x))
  high <- as.vector(Hi(x))
  low <- as.vector(Lo(x))
  close <- as.vector(Cl(x))
 
#Then build the data frame
  xSubset <-data.frame('date'=date,'open'=open,'high'= high,'low'=low,'close'=close)
 
#We want to construct our candlesticks  
  xSubset$candleLower <- pmin(xSubset$open, xSubset$close)
  xSubset$candleMiddle <- NA
  xSubset$candleUpper <- pmax(xSubset$open, xSubset$close)
  xSubset$fill <- ''
  xSubset$fill[xSubset$open < xSubset$close] = 'white'
  xSubset$fill[xSubset$fill ==''] = 'red'
 
#Add Moving Averages
  xSubset$ma200 <- SMA(xSubset$close, 200)
  xSubset$ma50 <- SMA(xSubset$close, 50)
 
#Trim Data
  xSubset <-subset(xSubset, xSubset$date > start & xSubset$date < end)
 
#Graphing Step
  g <- ggplot(xSubset, aes(x=date, lower=candleLower, middle=candleMiddle, upper=candleUpper, ymin=low, ymax=high)) 
  g <- g + geom_boxplot(stat='identity', aes(group=date, fill=fill))
  g <- g + geom_line(aes(x=date, y=ma50))+ geom_line(aes(x=date, y=ma200))
  g 
}
 
#call our graphing function
ggChartSeries(AAPL, start, end)

Todo list:

Add titles and labeling
Add more TA indicators
Tweak colors
Add/refine options to the function
Add volume bars at the bottom

Posted in Finance, R

Calculate Aumann-Serrano riskiness with R

Feb 9

Posted by mark

I completed a preliminary function to calculate Aumann-Serrano riskiness in R

^?Download asRisk.r

asRisk <- function(x){
  if (mean(x)<0|min(x)>=0){
    return(0) #If expected value is  < 0 or there are no negatives, return 0
  } else {
      asNumber <- 0.00001
      total <- 2
      while (total > 1){
        total <- sum((1/length(x))*exp(-x/asNumber))
        asNumber <- asNumber + .00001
      }
      return(sprintf("%.5f",asNumber))
  }
}

To use this function, input a vector of returns. If AS risk cannot be calculated, the function will return "0". If the gambles can be used, it will calculate AS riskiness to 5 decimal points. If more or less are desired, you can change

Generally, to use this, I would recommend using one of the functions in quantmod such as weeklyReturn() or dailyReturn(). An example of this would be

^?View Code RSPLUS

1	asRisk(dailyReturn(AAPL['2010']))

This example will return the AS risk of AAPL stock in 2010. Quantmod uses the TTR package which allows a lot of quick and powerful date selection.

In the future I will add errors/warnings, and maybe make precision adjustable or switch to a solver package. I also need to revise the function to meet a few more of my design parameters. This seems to be a good start and perfect for my research project next semester though!

Posted in Finance, R

Using R and quantmod to find cost of equity

Feb 8

Posted by mark

Recently, in my financial statements analysis class, I had to perform a valuation of Apple Inc. with a number of different valuation methods. One of the things that made valuation simpler is the lack of long-term debt on Apple's balance sheet. This simple fact means that Apple's WACC is equal to the cost of equity.

To find the cost of equity, I use CAPM, which states

$E(R_i) = R_f + \beta_{i}(E(R_m) - R_f)\,$

where $E(R_i)$ is the expected return on capital, after accounting for the market risk premium. To find the component pieces $R_f$ , $R_m$ , and $\beta_{i}$ , I will use R with the quantmod package, and I will also use the PerformanceAnalytics Package, although I will show you how to avoid using it if you choose.

The sourcecode for the project:

^?Download betacalc.r

#Packages required
require(PerformanceAnalytics)
require(quantmod)
require(car)
 
#Here we get the symbols for the SP500 (GSPC), AAPL, and 5yr Treasuries (GS5)
getSymbols("^GSPC", src = "yahoo", from = as.Date("2008-01-01"), to = as.Date("2011-12-31"))
getSymbols("AAPL", src = "yahoo", from = as.Date("2009-01-01"), to = as.Date("2011-12-31"))
getSymbols("GS5", src = "FRED", from = as.Date("2008-12-01"), to = as.Date("2011-12-31"))
 
#Market risk R_m is the arithmetic mean of SP500 from 2009 through 2011
#Riskfree rate is arithmetic mean of 5yr treasuries
marketRisk<- mean(yearlyReturn(GSPC['2009::2011']))
riskFree <- mean(GS5['2009::2011'])
 
#My professor advised us to use weekly returns taken on wednesday
#so I take a subset of wednesdays and use the quantmod function
#weeklyReturn()
AAPL.weekly <- subset(AAPL,weekdays(time(AAPL))=='Wednesday')
AAPL.weekly <- weeklyReturn(AAPL['2009::2011'])
GSPC.weekly <- subset(GSPC,weekdays(time(GSPC))=='Wednesday')
GSPC.weekly <- weeklyReturn(GSPC['2009::2011'])
 
#Here I use PerformanceAnalytics functions for alpha+beta
#Then we calculate Cost of equity using our calculated figures
AAPL.beta <- CAPM.beta(AAPL.weekly,GSPC.weekly)
AAPL.alpha <- CAPM.alpha(AAPL.weekly,GSPC.weekly)
AAPL.expectedReturn <- riskFree + AAPL.beta * (marketRisk-riskFree)
 
#For my graph, I want to show R^2, so we get it from the
#lm object AAPL.reg
AAPL.reg<-lm(AAPL.weekly~GSPC.weekly)
AAPL.rsquared<-summary(AAPL.reg)$r.squared
 
#Lastly, we graph the returns and fit line, along with info
scatterplot(100*as.vector(GSPC.weekly),100*as.vector(AAPL.weekly), smooth=FALSE, main='Apple Inc. vs. S&P 500 2009-2011',xlab='S&P500 Returns', ylab='Apple Returns',boxplots=FALSE)
text(5,-10,paste('y = ',signif(AAPL.alpha,digits=4),' + ',signif(AAPL.beta,digits=5),'x \n R^2 = ',signif(AAPL.rsquared,digits=6),'\nn=',length(as.vector(AAPL.weekly)),sep=''),font=2)

The code is commented, but I will make some additional comments on specific sections to explain the process for those unsure. I apologize for my unstandardized variable names as well!

First of all, I use the getQuotes() function, which has a few sources. In this example, I use Yahoo data for equity data and FRED for information on 5yr Treasuries. For reference, the ticker for retrieving the SP500 on Yahoo is "^GSPC", and the FRED code for 5yr treasuries is "GS5". Other symbols should be self explanatory.

Next is the issue of regression parameters. To find alpha and beta, I use the capm functions of PerformanceAnalytics, but to find $R^2$ I read it out of the the regression object using

^?View Code RSPLUS

1 2	AAPL.reg <- lm(AAPL.weekly~GSPC.weekly) AAPL.rsquared <- summary(AAPL.reg)$r.squared

It is possible to do this with beta and alpha, however, I did not do this because I did not originally did not start out to find $R^2$ , and turned to PerformanceAnalytics out of convenience.

Finally, I graphed the results and regression line for the benefit of my teacher, the results of which can be seen here: