# Meaning of cross sectional rank

This paper mentions the concept of rank which is defined as cross sectional rank. For e.g. one of the alphas (#3) is

(-1 * correlation(rank(open), rank(volume), 10))

10 is just the number of days to take any correlation over. I think we can rank the securities according to Open and Volume each day. So we will be getting different set of securities each day. I don't understand how can this daily varying set be used to get a correlation value.

I thus need guidance on now to calculate this alpha. Any help will be appreciated. Thanks

Update I understand what rank is. What I don't get is how do you calculate correlation between changing values.

Lets say the universe is 3 stocks. On Day 1, Rank Open is 1,2,3 and Rank Volume is 3,2,1. On Day 2, Rank Open is 1,3,2 and Rank Volume is 2,3,1. On Day 3, Rank Open is 3,2,1 and Rank Volume is 1,2,3. This happens for n days (in this case 10).

My primary question is how do you calculate correlation between such vectors to arrive at a single value. Because normal correlation is between two same type of vectors.

• The open and the volume can vary widely across stocks (by orders of magnitude in the case of volume). To tame these wild numbers somewhat, as is commonly done in nonparm statistics, you replace the value with its rank within the 1000 (say) stocks that you are looking at, so ranked volume is a number between 1 (for MSFT which traded 20,000,000 shares) and ACME at 1000 (volume of 20 shares). – noob2 Sep 29 '16 at 20:05
• That paper, by the way, is a waste of time. He never describes things precisely enough to really pin down how everything works. It is Fool's Gold. – noob2 Sep 29 '16 at 20:14
• I understand what rank is. What I don't get is how do you calculate correlation between changing values. Lets say the universe is 3 stocks. On Day 1, Rank Open is 1,2,3 and Rank Volume is 3,2,1. On Day 2, Rank Open is 1,3,2 and Rank Volume is 2,3,1. On Day 3, Rank Open is 3,2,1 and Rank Volume is 1,2,3. This happens for n days (in this case 10). My primary question is how do you calculate correlation between such vectors to arrive at a single value. Because normal correlation is between two same type of vectors. – user1434997 Sep 30 '16 at 0:56