## Historical Seasonality Analysis: What company in DOW 30 is likely to do well in January?

THIS IS NOT INVESTMENT ADVICE. The information is provided for informational purposes only.

Stock Market Seasonality is easy to understand, but hard to justify if you subscribe to Efficient-market hypothesis. For a good summary of seasonality, have a look at Capitalizing On Seasonal Effects article at Investopedia. Another interesting discussion was started by Douglas R Terry in his post Efficient Market Hypothesis and Seasonality that goes into detail analysis how these two ideas can co-exist.

To study Seasonality, I want to introduce the new tool I developed. The Seasonality Tool is a user-friendly, point and click, application to create seasonality statistics and reports.

To demonstrate the Seasonality Tool, I want to show how it can be used to evaluate an investment idea. I want find which company in DOW 30 is likely to do well in January and evaluate it using Seasonality Tool.

Following code loads historical prices from Yahoo Fiance for all companies in the DOW 30 index and computes their average performance in January. I will use the Systematic Investor Toolbox to load and analyze the data:

############################################################################### # Load Systematic Investor Toolbox (SIT) ############################################################################### con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb')) source(con) close(con) #***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') tickers = dow.jones.components() data <- new.env() getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T) for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T) bt.prep(data, align='keep.all', dates='1970::2011') #***************************************************************** # Compute monthly returns #****************************************************************** prices = data$prices n = ncol(prices) # find month ends month.ends = endpoints(prices, 'months') prices = prices[month.ends,] ret = prices / mlag(prices) - 1 # keep only January ret = ret[date.month(index(ret)) == 1, ] # keep last 20 years ret = last(ret,20) #***************************************************************** # Compute stats #****************************************************************** stats = matrix(rep(NA,2*n), nc=n) colnames(stats) = colnames(prices) rownames(stats) = spl('N,Positive') for(i in 1:n) { stats['N',i] = sum(!is.na(ret[,i])) stats['Positive',i] = sum(ret[,i]>0, na.rm=T) } sort(stats['Positive',])

The Walt Disney Co. (DIS) was positive 17 times in January in the last 20 years.

Let’s investigate the Walt Disney Co. (DIS) record using the Seasonality Tool.

The Seasonality Analysis Report confirms Walt Disney Co. (DIS) outstanding track record in January. Next let’s see the details for January.

The Detail Seasonality Analysis Report shows that the Walt Disney Co. (DIS) had an amazing returns in January till 2008. Following by a 3 consecutive negative Januaries which most likely indicates a change in trend (regime) for this company.

So do I expect the Walt Disney Co. (DIS) be positive in the upcoming January? I’m not so sure anymore.

To view the complete source code for this example, please have a look at the bt.seasonality.test() function in bt.test.r at github.

## Happy Holidays and Best Wishes for 2012

This is just a quick note to wish you and your family a very healthy and happy holidays and wonderful New Year! I hope you enjoyed reading my blog and thank you for your comments and emails.

Here is a short R code that implements an interesting idea from the Charting the Santa Claus Rally post by Woodshedder. I will plot and compare the SPY performance this December versus average performance in previous Decembers.

# Load Systematic Investor Toolbox (SIT) setInternet2(TRUE) con = gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb')) source(con) close(con) #***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') tickers = spl('SPY') data <- new.env() getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T) for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T) bt.prep(data, align='remove.na', dates='1970::2011') #***************************************************************** # Prepare Data for the plot #****************************************************************** prices = data$prices n = len(tickers) ret = prices / mlag(prices) - 1 # find prices in December dates = index(prices) years = date.year(dates) index = which(date.month(dates) == 12) # rearrange data in trading days trading.days = sapply(tapply(ret[index,], years[index], function(x) coredata(x)), function(x) x[1:22]) # average return each trading days, excluding current year avg.trading.days = apply(trading.days[, -ncol(trading.days)], 1, mean, na.rm=T) current.year = trading.days[, ncol(trading.days)] # cumulative avg.trading.days = 100 * ( cumprod(1 + avg.trading.days) - 1 ) current.year = 100 * ( cumprod(1 + current.year) - 1 ) #***************************************************************** # Create Plot #****************************************************************** par(mar=c(4,4,1,1)) plot(avg.trading.days, type='b', col=1, ylim=range(avg.trading.days,current.year,na.rm=T), xlab = 'Number of Trading Days in December', ylab = 'Avg % Profit/Loss' ) lines(current.year, type='b', col=2) grid() plota.legend('Avg SPY,SPY Dec 2011', 1:2)

Hope this year will not disappoint and we will see the rally towards the year end.

If you want to find average performance in the other months, I recommend reading Trading Calendar article by CXO Advisory.

To view the complete source code for this example, please have a look at the bt.december.trading.test() function in bt.test.r at github.

## Periodic Table of Investment Returns

To get a better sense of historical data, I like to examine a Periodic Table of Investment Returns. For an example of a Periodic Table, have a look at the Single Country Index Returns Periodic Table for 2001-2010 published by iShares.

I can easily create a similar table with the following R code, using the historical data from the Black-Litterman Model post.

# load Systematic Investor Toolbox setInternet2(TRUE) source(gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))) #-------------------------------------------------------------------------- # Get Historical Data #-------------------------------------------------------------------------- # Country's IA are based on monthly data ia = aa.test.create.ia.country() hist.returns = ia$hist.returns # convert returns to prices hist.prices = cumprod(1 + hist.returns) # extract annual prices period.ends = endpoints(hist.prices, 'years') hist.prices = hist.prices[period.ends, ] # compute simple returns hist.returns = na.omit( ROC(hist.prices, type = 'discrete') ) hist.returns = hist.returns['2000::2010'] #-------------------------------------------------------------------------- # Create Periodic table #-------------------------------------------------------------------------- # create temp matrix with data you want to plot temp = t(coredata(hist.returns)) colnames(temp) = format(index(hist.returns), '%Y') rownames(temp) = 1:ia$n rownames(temp)[1] = ' Best ' rownames(temp)[ia$n] = ' Worst ' # highlight each column col = plota.colors(ia$n) highlight = apply(temp,2, function(x) col[order(x, decreasing = T)] ) # sort each column temp[] = apply(temp,2, sort, decreasing = T) # format data as percentages temp[] = plota.format(100 * temp, 0, '', '%') # plot temp and legend plot.table(temp, highlight = highlight) plota.legend(ia$symbols,col,cex=1.5)

The Canadian and Australian markets outperformed US and Japanese markets in most years.

Here is a slightly different version of Periodic table:

#-------------------------------------------------------------------------- # Create Periodic table, another version #-------------------------------------------------------------------------- # create temp matrix with data you want to plot temp = t(coredata(hist.returns)) colnames(temp) = format(index(hist.returns), '%Y') # format data as percentages temp[] = plota.format(100 * temp, 0, '', '%') # highlight each column separately highlight = apply(temp,2, function(x) plot.table.helper.color(t(x)) ) # plot temp with colorbar plot.table(temp, highlight = highlight, colorbar = TRUE)

To view the complete source code for this example, please have a look at the aa.periodic.table.test() function in aa.test.r at github.

## Adding Equations, Formulas, and Math to your WordPress posts

To incorporate Math Formulas to my WordPress posts, I found following solution that works really well for me. I hope you will find it useful.

Let’s start from the beginning. I wanted to add Math Formulas to my WordPress posts and after searching WordPress support, I found LaTeX tag. It sounds simple: embed your equation’s LaTeX syntax like this **$****latex your-latex-code-here$**.

The only problem is I don’t know LaTeX syntax. I looked around for a stand alone application that can render LaTeX with preview pane. LEd looked promising until I realized that I would need to install an additional LaTeX typesetting, like MiKTeX – a whooping 160 MB.

Instead I decided to look for online solution and CodeCogs LaTeX Equation Editor works perfectly. It has buttons at the top for different operators and formulas and more importantly it renders, very fast, the formula as you type it.

I also found following articles with LaTeX examples very useful:

## Hello world!

This is my first post. In this blog, I plan to discuss systematic investing strategies including Asset Allocation, Black Litterman,Long/Short Optimization, Technical and Fundamental Analysis and Options. I will accompany most of my posts with sample code written in R/Matlab/C++/Python or VBA.