# SOFR - calculation of the volume-weighted median and percentile

Federal Reserve Bank of New York web page provides some information on the computation of the SOFR rate.

### Part 1

According to this webpage, the SOFR is calculated as the volume-weighted median:

"The SOFR, the BGCR, and the TGCR are each calculated as a volume-weighted median, which is the rate associated with transactions at the 50th percentile of transaction volume. Specifically, the volume-weighted median rate is calculated by ordering the transactions from lowest to highest rate, taking the cumulative sum of volumes of these transactions, and identifying the rate associated with the trades at the 50th percentile of dollar volume. At publication, the volume-weighted median is rounded to the nearest basis point."

Question 1: What does exactly "a volume-weighted median" mean?

### Part 2

According to the webpage presented at the begining of my post:

"DVP repo transactions with rates below the 25th volume-weighted percentile rate are removed from the distribution of DVP repo data each day."

Question 2: What does exactly "25th volume-weighted percentile" mean?

• Please see details here: newyorkfed.org/medialibrary/media/markets/…. Especially the footnote: ‘5 For example, assume that on a given day, 10 million of federal funds transactions occurred at each of 5, 10, 15 and 20 basis points, and 60 million occurred at 25 basis points. This represents 100 million of total volume. The median would be the rate at the ‘middle dollar’, or 50 million, which is 25 basis points in this example. The mean of this data is 20 basis points.’ – Magic is in the chain Dec 31 '20 at 21:34
• Thanks! In the case of the second question shall one compute the cumulative dollar volume, calculate 25% of this amount and then find the interest rate associated with this dollar volume? – B_B Dec 31 '20 at 22:19
• I thought the bottom 25% transactions are just removed- meant to capture the specials, whose interest rate is mainly driven by the desirability of the collateral as opposed to lending/borrowing. – Magic is in the chain Jan 1 at 15:47
• This would not take into account the dollar volume weights. – B_B Jan 1 at 16:11
• It is indeed 25% in terms of volume- If total volume is 100m,you exclude the bottom 25m. – Magic is in the chain Jan 1 at 16:24