Stephen J. Barr

A very simple first question to ask is, along what dimension am I looking at leverage?

There are actually quite a few possibilities:

1. Take the average, pooled over all firms and time periods. However, it seems that there is more to say about the entire data set of corporate leverage ratios than can be expressed by one number.
2. At every distinct point in time, pool all firms. This would create a 1-dimensional time series. This is doing a little better.
3. For every period, compute means by industry. This creates a panel. However, doing this naievely creates a few problems (see the next section for help). At any given time, some firms enter the sample and some firms are leaving the sample. One way to mitigate this is take a slice of the data set known as a balanced panel, where the firms are chosen such that they exist for the entire window of time of interest. But, this introduces survivorship bias, because the sample is biased towards firms which endure all the economic woes of throughout the timeframe and do not leave the sample.
4. Look at leverage by leverage decile, year by year. This is an interesting way to see what the bottom, top, and middle leverage levels are doing. It is important to realize that this does not necessarily capture what the firms at each level are doing. This is because firms are free to change their leverage and thus their relative usage of leverage may change over time.
5. As a response to #4, At time period 1, sort leverage by decile and see which firms are in each decile. Then track these firms over time. This can be very interesting, taking caution that picking different starting time periods will most definitely change the groupings of firms.

There are plenty more.

I wrote some code to detect the largest balanced panels in the Compustat database. That code is coming tomorrow. I picked a balanced panel that started in the mid 1980′s for this analysis. I used the data.table package to hold the data, as it allows for keyed data tables that allow extremely fast, in-place subsetting.

For the first plot, the code was as follows.

Subset the data to get just the first time period. Using cut2 from Hmisc library, divide into deciles and label them A..J.

min.date = min(dt.t$date);
dt.tmin = subset(dt.t, date == min.date);
dt.tmin$initialDEC = with(dt.tmin, cut2(book_lev, g=10), labels=1:10);
dt.tmin$initialDEC = factor(dt.tmin$initialDEC, labels = LETTERS[1:10]);

initialDEC is a factor representing the initial decile. The merge does exactly what you think it should, meaning add a column called initialDEC to the the original data set, dt.t, merging on the column cusip.

## prepare to merge
setkey(dt.tmin, cusip);
setkey(dt.t, cusip);

## do the merge
dt.t = dt.t[dt.tmin]

Create a factor called timedec, which is the interaction of the initial decile (initialDEC) and each time period. There should be 10 * (max(dt.t$year) - min(dt.t$year) + 1) distinct values of this factor. Then, set this as they key, and take the means according to this group.

dt.t$timedec = paste(dt.t$date, "--", dt.t$initialDEC, sep="")
setkey(dt.t, timedec)
td.means = dt.t[,list(tdmean=mean(book_lev)), by=timedec]

This unwraps the data. td.means becomes a nice little data.table with 10 * (max(dt.t$year) - min(dt.t$year) + 1) rows.

timedate =  strsplit(as.vector(td.means$timedec), "--")
tddf = as.data.frame(matrix(unlist(timedate), ncol=2, byrow=TRUE))
colnames(tddf) = c("DATE", "iDEC");
td.means$date = tddf$DATE;
td.means$iDEC = tddf$iDEC;
td.means$year = extractyear(td.means$date)

Then, use ggplot2 to do the plotting:

p = ggplot(td.means, aes(x=year, y=tdmean, group=iDEC))
p = p + geom_line(aes(colour=iDEC))
p = p + opts(title = expression("Firm leverage at t=0 decile sort"))
p = p + scale_y_continuous('Book leverage')
print(p)

How to use R (and lots of cores) to find all possible balanced panels in a ragged data set.