Treasury yields

Water Cooler Investing
#1

Hi!

I was reading The Wall Street Journal and didn’t find the information on how treasury yields are quoted. In particular, what does 10-year Treasure Yield of 2.88 mean? For example, if the yield was calculated for a zero-coupon bond, then 2.88 can be used in discounting money 10 years from now. However, there is no information on whether the quoted number is for zero-coupon bonds. Could somebody explain?

Thank you.

#2

It means USTs yield 2.88 percent regardless of the coupon.

#3

Specifically it means the on-the-run 10y UST note (currently 912828WE6 2 3/4 11/15/23) had a closing price that results in YTM of 2.88.

#4

Thank you for your and the previous answer. However, I still have a question. I would really appreciate if you find time to answer the question. The internet has dissenting explanations of YTM formula.

Assume, we have the following quote in The Wall Street Journal

Rate (11.125) Maturity (Aug 13, 2003) Bid (108:15) Ask (108:16) Ask Yield (1.66)

The quote is for is Sept. 15, 2002. Face value of the bond is $100,000.

Problem. Find out how 1.66 was calcuated.

Solution.

1. Evaluate the accrued interest on Sept. 15, 2002. The last coupon payment of $5,562.50 was paid on August 13, 2002, or, 33 days ago. The next coupon payment is on March 13, 2003, or, in 149 days. This means that

Accrued Interest = 33/(33+149) x $5,562.50 = $1,008.60.

2. The price for the bond is therefore: $100,000 x (108 + 16/32)/100 + $1,008.60 = $109,508.60. This is the actual price for the bond.

3. The Ask Yield is the number q that solves the equation

$5,562.50/(1+q(149/365)) + $105,562.50/(1+q(332/365)) = $109,508.60.

The solution to the equation is 0.0166. Is this is the right approach?

Thank you.

#5

Uhhhh… sure, I guess.

I use BBG or a custom analytics package we have built into excel. No one has time for that kind of math. :slight_smile:

#6

LOL

#7

But to understand what that number (1.66) actually means, I think one should know how it is obtained. Could someone please tell whether this is the way 10 year Tresuries yields are evaluated in The Wall Street Journal?

#8

It’s the YTM… or the yield earned by the purchaser of that bond at that price if they held it to maturity.

Or, in terms of your equation, the quoted yield (YTM) is the discount rate that makes the sum of all future cashflows equal the current price… just like solving for the IRR of a stream of cashflows: (actually not just LIKE it… this is EXACTLY what you’re doing)

C0 (Price paid for bond)

C1: Coupon

C2: Coupon

…

Cn: Coupon + Principal

Bonds are evaluated like this because YTM is an easily calculated metric and is a universal among many assets. Easy to compare different YTMs.

#9

Thank you very much. It is confusing how different sources quote the yields. For example, the Treasury Department quotes bond-equivalent yields obtained from bonds that are priced at par. But their numbers are different from that of The Wall Street Journal. Again thank you veru much!