Negative yield on T-bill

CFA Level I Fixed Income
#1

Hello All,

I found thisarticle while researching something on T-bill. I have three questions,

#1- Portfolio theory taught me that T-bill is risk-free. Hence, I would think that as an investor and as a buyer of T-bill, the US government won’t pay me coupons. Is it really possible?

#2 - What does it mean by negative yield? I used my calculator to calculate the FV based on what’s in the article.

I/Y= -0.01

n= 3

PV = (-1000002.556)

PMT = 100

FV = ?

I got FV 999,402.6152. How could the face value be less than $1MM? If so, I believe that US government will default on its T-bills?

#3- I also read that foreign banks increased buying of such bills, as compared to what happened the year before. If my argument about the loss of money is true (in #1 and #2 above), then why would other banks buy additional funds, when they know that they won’t get their money back?

This sounds like a paradox to me. My knowledge is limited to a few chapters I have read in CFA1 (I have just started reading Fixed Income), and I don’t have any exposure to Finance. Hence, I believe I am missing something something fundamental, so I thought of posting this.

I would appreciate any thoughts. Thanks in advance.

#2

Yes. T-Bills are zero-coupon bonds.

It means exactly what you think it means: you lose money on the investment.

The face value isn’t less than $1MM; it’s $1MM exactly. If you read paragraph 6 of the article you cited, it says you will receive par.

There are a few problems with what you did on your calculator. First, you put in the annual yield of -0.01%, instead of the yield per period (where the period is 90 days). Second, you put in three periods. I don’t know whence that number came. Third, you put PV = -1,000,002.556; it should have been PV = -1,000,025.56. Fourth, you put in a payment of 100. There is no coupon payment on a T-Bill. Fifth, T-Bills are quoted at a bank discount yield, not an effective annual yield; the TVM buttons on your calculator assume effective yields.

Perhaps because they believe that it’s better to lose 0.01% on your money (guaranteed) than losing more than 0.01% in their next best investment.

#3

Hello S2000magician,

Thank you for your detailed response. I now realize my folly. I shouldn’t have used TVM for calculating T-Bill yields.

I have recalculated this.

Bank discount rate Rbd = (D/F) * (360/t)

Therefore, -0.01% = (D/1,000,000) * 360/90; t=90 because they have told three months. Rbd= -0.01%

Therefore, D = -25.

Therefore, price will be 1,000,025. Can you please let me know why I am not getting the initial price of 1,000,025.56? I would appreciate your help.

Secondly, I thought of experimenting to see what happens if I use TVM for T-bills.

I took the question from your blog : A 90-day T-Bill has a BEY of 1.46%. What is its BDY?

Here’s what I did to get D and PV. Let’s assume that FV = $1000.

Therefore, Semi-annual equivalent yield = 1.46%/2 = .73%.

Therefore, EAY = (1+.73%)^2 = 1.4653%

Now, I would have to HPY to calculate D.

HPY = {(1+EAY)^(90/365) - 1} = .35933%

Therefore, Pinitial = 1000/(HPY+1) = $996.419, very close to what you got.

Now,

N= 1; PV= -996.419; PMT = 0; FV = 1000; I/Y = Calculate. I got I/Y = HPY. This makes sense. However, how do I get EAY using TVM function on the calculator? I am curious.

Thanks in advance.