Archives for category: Finance

For our investments class, we had to conceive and test a trading strategy using technical analysis. As a lover of R, I decided to reference some code I had seen earlier on Modern Toolmaking via R-Bloggers:Backtesting a Simple Stock Trading Strategy. The example provided R code that was very helpful in getting me to understand the math behind the testing part (as opposed to the conceptually easy trading rules).

Only one problem stood out: our professor wanted us to use SAS!

SAS is still an industry leader and will be surely be seen in our future jobs, so I took the opportunity to try to use the concept behind the R code and translate it to SAS' language. Though I didn't have time to implement the extra features found in the excellent PerformanceAnalytics package for R, I did manage to replicate the basic rule selection and calculation of cumulative return and win/loss. So with that said, I will start with the R script I started from:

?View Code RSPLUS
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  #inspired by code here: http://moderntoolmaking.blogspot.com/2011/09/backtesting-simple-stock-trading.html #Set important variables ticker <- '^GSPC' start <- as.Date('2005-01-01') end <- as.Date('2012-04-01') period <- 10 tradingCost <- .001 riskFree <- .035 #End set important variables   library(quantmod) library(PerformanceAnalytics)   bias <- function(x,period){ biasResult <- ((x-SMA(x,n=period))/SMA(x,n=period))*100 }   tradingRule <- function(stock,numDays) { close <- Cl(stock) volume <- Vo(stock) position <- ifelse(((bias(close,numDays) + bias(volume,numDays)) > 0),1,-1) }     stock <- getSymbols(ticker, from=start, to=end, auto.assign=FALSE) position <- tradingRule(stock,period)     underlyingReturn <- dailyReturn(Cl(stock),type='arithmetic')   ruleReturn <- ifelse(Lag(position,k=1)==Lag(position,k=2),underlyingReturn * Lag(position,1),underlyingReturn * Lag(position,1) - tradingCost)     ruleReturn[1:(period+1)] <- 0;     names(underlyingReturn) <- 'SP500' names(ruleReturn) <- 'Trading'   charts.PerformanceSummary(cbind(ruleReturn,underlyingReturn), colorset=redfocus)

The code is minimized since it is not too important. Keep in mind that R allows us to download data from Yahoo, so I use quantmod to do that, rather than including it in a data step as I did in SAS. Here is the code minus the data step containing OHLC data to conserve screen space:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57  /*Set length of moving average and costs of trading*/ %let n=10; %let cost=.001;   /*Find closing moving average*/ data work.GSPC (drop = s); retain s; set work.GSPC; s = sum(s,Close,-lag&n(Close)); closeMA = s / &n; run;   /*find volume moving average*/ data work.GSPC (drop=s); retain s; set work.GSPC; s = sum(s,Volume,-lag&n(Volume)); volumeMA = s / &n; run;   /*find cumulative returns*/ data work.GSPC; set work.GSPC; dailyReturn = (close - lag(close))/lag(close); retain cumulativeReturn 1; if _N_ >1 then cumulativeReturn = cumulativeReturn*(1+dailyReturn); if dailyReturn > 0 then assetWinLoss = 1; else assetWinLoss = 0; run;   /*run trading strategy*/ data work.GSPC (drop=temp); set work.GSPC; retain flag 0; retain tradingReturn 1; retain tradingwinloss 0; temp = (lag(close)-lag(closeMA))*(lag(volume)-lag(volumeMA));   /*Find Portfolio Return*/ if _N_ > &n then if temp > 0 then flag = 1; else flag = -1; if _N_ >1 then tradingReturn = tradingReturn * (1 + (dailyReturn * flag)); if lag(flag) ~= flag and _N_ >1 then tradingReturn = tradingReturn * (1-&cost);   /*Make a portfolio to test alpha/beta*/ portfolioValue = 1000 * tradingReturn;   /*Find win/loss of our strategy*/ if (dailyReturn* flag) < 0 then tradingWinLoss = 0; else tradingWinLoss = 1; run;     proc means; var tradingWinLoss assetWinLoss; run;

First of all, our data is entirely self-contained within the SAS Code. We use a data step and input cards directly, rather than using code. In the R version, quotes are downloaded directly from Yahoo Finance using an addon called quantmod. Example:

 1 2 3 4 5 6  data GSPC; input Date Open High Low Close Volume; datalines; 1/3/05 1211.92 1217.8 1200.32 1202.08 1510800000 1/4/05 1202.08 1205.84 1185.39 1188.05 1721000000 1/5/05 1188.05 1192.73 1183.72 1183.74 1738900000

To get a moving average, we use an algorithm with a macro variable and retain a rolling selection of length &n observations. We then divide this total by &n to get the simple moving average and drop the temporary variable used to hold the rolling total:

 1 2 3 4 5 6 7 8 9 10 11  /*Set length of moving average and costs of trading*/ %let n=10; %let cost=.001;   /*Find closing moving average*/ data work.GSPC (drop = s); retain s; set work.GSPC; s = sum(s,Close,-lag&n(Close)); closeMA = s / &n; run;

After that, we also use the same technique to find the simple moving average of volume. After those data steps, we find the daily+cumulative returns of the underlying assets and its win/loss percentage. We do these steps all in separate data steps for ease of debugging.

 1 2 3 4 5 6 7 8 9  /*find cumulative returns*/ data work.GSPC; set work.GSPC; dailyReturn = (close - lag(close))/lag(close); retain cumulativeReturn 1; if _N_ >1 then cumulativeReturn = cumulativeReturn*(1+dailyReturn); if dailyReturn > 0 then assetWinLoss = 1; else assetWinLoss = 0; run;

Our next data step runs the trading strategy. We make the assumption that we will buy at close instantaneously if our rule is triggered at the end of the trading day. We then set a flag that equals our position for that next day. 1 for long, -1 for short, and 0 for no position. We multiply the underlying asset return times the “flag” variable to get our return, then do the same calculation of cumulative return and win/loss percentage:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  /*run trading strategy*/ data work.GSPC (drop=temp); set work.GSPC; retain flag 0; retain tradingReturn 1; retain tradingwinloss 0; temp = (lag(close)-lag(closeMA))*(lag(volume)-lag(volumeMA));   /*Find Portfolio Return*/ if _N_ > &n then if temp > 0 then flag = 1; else flag = -1; if _N_ >1 then tradingReturn = tradingReturn * (1 + (dailyReturn * flag)); if lag(flag) ~= flag and _N_ >1 then tradingReturn = tradingReturn * (1-&cost);   /*Make a portfolio to test alpha/beta*/ portfolioValue = 1000 * tradingReturn;   /*Find win/loss of our strategy*/ if (dailyReturn* flag) < 0 then tradingWinLoss = 0; else tradingWinLoss = 1; run;

Finally, we run a proc means to give our win/loss percentage for our trading rules and underlying asset

 1 2 3  proc means; var tradingWinLoss assetWinLoss; run;

Returns Distribution:

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.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  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 I completed a preliminary function to calculate Aumann-Serrano riskiness in R ?Download asRisk.r  1 2 3 4 5 6 7 8 9 10 11 12 13  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! 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  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37  #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:

S&P500 vs. Apple, 2009-2011