Bad math at Bloomberg for T-bills

Demand for T-bills is so great that the 3-month T-bill was trading at a negative discount today. That means that you would receive less at maturity than you paid a trader for the T-bill. Bloomberg covers the story in an article by Daniel Kruger and Cordell Eddings entitled "Treasury Bills Trade at Negative Rates as Haven Demand Surges", but they screwed up their math in one example. They say:

If you invested $1,000 in three-month bills today at a negative discount rate of 0.01 percent, for a price of 100.002556. At maturity you would receive the par value for a loss of $25.56.

Not quite. $1,000 in 3-month T-bills would have cost $1,000.02556. The value at maturity would be $1,000, for a net loss of $0.02556. They were off by a factor of 1,000.

I suspect that they meant to refer to a purchase of 10,000 T-bills or a face value of $1,000,000. At a price of $100.002556 per T-bill, $100 face or par value, the total cost would be $1,000,025.56. Paying $1,000,000 at maturity, the net loss would be their $25.56.

That is if you bought the T-bills on the open market, but if you bought them directly from the U.S. Treasury via TreasuryDirect in the weekly auction today, the price was $99.998736 per $100 T-bill (a rate of 0.005%) or a total cost of $999,987.36, so you would have a net gain of $12.64. So much for $1 million being "wealth", earning you a mere 50 bucks a year.

Note that a single T-bill has a face value of $100, but you can only buy them in units of $1,000 face value, or multiples of 10.

The 4-week T-bill actually auctioned at a price of $100 per $100 face value or a rate of 0.000%, which is unheard of. What kind of person gives their money to the government for free?!?! Well, some funds have a requirement to be liquid and to be in Treasuries, so they have little choice.

-- Jack Krupansky