# User:Devon McCormick/Research/HoldingWinnersSellingLosers2CumulativeReturns

Originally presented on 5/27/2007 to the NYC Financial Engineering Meetup. It illustrates the use of J to manipulate data quickly and easily in order to explore topics in quantitative financial research. The previous work is here and the continuation of this is here.

# Working with Cumulative Returns

We start with price data, then difference this to get daily (price) return data. Accumulating these daily returns gives us accumulated return data which is a handy form with which to work because we can calculate the return between any two arbitrary points simply by subtracting one accumulated return from the other. This simplifies the calculation because we don’t have to consider all the points between the two points as we would if we were working with simple daily returns.

Interestingly enough, since we’re creating cumulative sums out of differences, we, in a sense, end up with the same numbers with which we started. This is handy too since it may help us devise buy and sell rules based on our simple price series. The following page illustrates this.

However, before we look at that, let’s take a brief look at the distribution of slopes for different windows of cumulative returns.

(These observations are winsorized at plus and minus 4% to better focus on the bulk of the observatons.)We use information like this to help us narrow down a good period over which we should consider winners and losers. Notice how the shorter windows give more dramatic slopes than do the longer periods.

## Prices versus Cumulative Returns

To see how the starting price series closely resembles the final cumulative return series, consider the following graphs.

First, look at the price series for two stocks – our most and least volatile ones. Now, look at the cumulative returns for the same two stocks.

Note how the two sets of series are very similar to each other. However, the lower graph lets us see that, for some periods, indeed for the entire period, the less-volatile WOR out-performed the highly-volatile GLW.

Working with cumulative returns better lets us compare different price series on a common basis.

The previous work is here and the continuation of this is here.