I haven’t been writing a lot during August, nor have I done many podcast episodes. I feel like I make this apology almost every year, but it seems every year August just gets slower, and slower, and slower – and any content I push out gets less engagement during August than during any other full month (although the end of December, naturally, gets very thin as well. It’s really remarkable how August has changed during my career. In the 1990s, there were maybe a couple of weeks that were a little thin in the markets, but that has metastasized so that now it’s all of August and a week or two into July. I am speaking of the US markets – Europe has always been slow for the second half of the summer, at least in my experience, and I don’t know if there has been much change in that over the last few decades.
In any event, I’m more than happy as a writer to take a little time off and recharge. As an entrepreneur? Not so much.
This is, though, a good time for a ‘utility’ post. As readers know, a few months ago we launched USDi, the first CPI-linked cryptocurrency that’s fully backed by traditional finance assets. Because those assets for the most part reside in a private fund (which, because it’s a private fund issued under Reg D, I can’t talk much about on a public post so forgive my vagueness here about what the fund does and how), there is regularly confusion when potential buyers of USDi think that they are buying a share of the fund. They are not, for two reasons. The first is that a coin that represents a tokenized share of a traditional-finance fund would clearly be a security under US law, which creates lots of other complexities that we don’t want: for example just as I can’t tell you much about the fund, if the token was a security then I couldn’t tell you much about that, either! Which would make distribution difficult, to say the least.
The second reason that we didn’t want the coin to represent a tokenized share of the fund is that then the coin would not exactly track CPI. It is important that the coin be a zero-risk instrument, and I illustrate why that’s important in the post “USELESS Coin vs Very Useful Coin”. Accordingly, USDi’s value is entirely formulaic, and known in advance by at least a few weeks. It’s my purpose today to explain how the value of USDi is derived from CPI prints.
USDi, like TIPS and US CPI swaps, is linked to the Non-seasonally Adjusted Consumer Price Index for All Urban Consumers…the NSA CPI for short. The CPI that is released every month is related to this number – specifically, the ‘headline CPI’ is the month-on-month percentage change in the Seasonally-adjusted number. Here is where you find that number (rounded, of course) in the monthly BLS release found at https://www.bls.gov/news.release/cpi.nr0.htm:
The problem with using a seasonally-adjusted number is, you guessed it, that the seasonal adjustment factors can change. Consequently, all inflation derivatives rely on NSA numbers, which are almost never revised. In the same report linked above, the BLS notes the NSA number:
The highlighted number, 323.048 in this case, is the number that TIPS traders and inflation swaps traders care about. And, if you buy USDi, you will care about this number as well. This is the price index value defined relative to the base of 100.000 representing the average of the 1982-1984 price level. The index value of 323.048 tells you that the (quality-adjusted) price level has risen 223.048% since the early 1980s, slightly more than a tripling!
(As an aside, the BLS has an enormous number of NSA series for different subcomponents available. You can see and chart a lot of them here: )
Now, the BLS reports this number just once a month, and in arrears. It was mid-August when they reported the July CPI referenced above. So we have two things we need to account for when we turn this into an index that USDi (or TIPS or inflation swaps) can track: 1. We have a monthly number, and we need a daily number – or in USDi’s case, one number every block, and 2. We have numbers for every month ending in July, but today isn’t July, so we need something for today. Let’s call the index value that we are going to construct, to use for TIPS/swaps/USDi, the “Reference CPI.”[1]
The second problem is handled in the simplest way possible: we just lag the data.[2]
So when we got the July data this month, we have the Ref CPI for October 1 (the 323.048 number I mentioned above). We already have the Ref CPI for September 1 (that was the June CPI, reported in July, 322.561). So now, we can straight-line interpolate the Ref CPI for any day in between those two dates, based on the number of calendar days in that month. So, the Ref CPI for September 2nd is:
1/30 * 323.048 + 29/30 * 322.561 = 322.57723
Voila, that’s just what the Treasury calculates for September 2nd, which isn’t surprising because that’s how math works.
Now, the only subtlety to USDi is that while TIPS and CPI swaps have one settlement per day USDi in principle is tradeable 24/7. That means that if we changed the Ref CPI for USDi just once per day, at 1 second before midnight every day you could buy USDi and then sell it at 1 second after midnight and get the entire day’s interest. That doesn’t seem fair. The blockchain is much closer to continuous settlement, so we have to interpolate not by day, but by block. On Ethereum (where USDi exists, initially), a block is roughly 10-15 seconds long, so USDi accrues interest basically every 10 seconds. The actual code for USDi looks at the block number and does the exact same calculation that we do above except that it is interpolating between the first block in September and the first block in October. You can get very close to the right answer by simply using spreadsheet NOW() functions, which in Google Sheets has 1-second precision. I do the approximate calculation for USDi on a Google Sheet here:
Let’s see, why did I want to calculate the Reference CPI? Oh, I remember: I want to find the price of USDi for a given time, in the past or present or any time up until (for now) the end of September. We have done all of the work except for the last step, which is to divide the current price level index – the Reference CPI – by the base price level index. For USDi, we defined the denominator as the December 2024 CPI. This is why we say that USDi is a dollar that preserves the purchasing power of a December 2024 dollar.
The December 2024 CPI was 315.605. Since the December 2024 CPI was also the Reference CPI for March 1st (see the handy drawing above), that means the value of USDi on March 1st was (drum roll) 315.605/315.605 = 1.000000. The value of USDi on October 1st will be 323.048/315.605 = $1.023583.
So the USDi coin is not a fund, nor a share of a fund. It is a time machine.
[1] The Reference CPI for TIPS and swaps is identical. The Treasury calculates them too, and reports them at (look for the PDF and XML files for the “Reference CPI Numbers and Daily Index Ratios Table.”)
[2] In principle, we could take the recent data trend and project to the current date, which would make it contemporaneous but lose accuracy…since when the inflation data is actually released, we will find out that method isn’t perfect. It would also be confusing, since on any given day in the past there would now be the actual CPI data and the previously-used projected-trend data. Since the importance of the exact timing of the price level diminishes with distance, while the two-index confusion would persist, the simple-lag method makes sense to me.
