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I am trying to understand investing in (non-us) government bonds. Looking at data I can find online regarding the bonds available in my broker is giving me information I can't make sense of. For example, take the Netherlands government bond NL0010071189.

This website is currently saying that its yield is -0.04%. The current price is listed as 134.67, issue price is 96.29 and the coupon rate at 2.5%.

Where is that -0.04% figure coming from? The definition of bond yield I have found is the coupon value, divided by the current price. In this case, as far as I can tell, that would be (0.025 * 96.29) / 134.67, or 1.78%

I've tried a few online yield calculators (1 2 3) and their Yield calculation seems to match mine, but their YTM seems to error or produce 0. calculatestuff.com gave -0.286%. For the years to maturity, I entered 14, as at time of writing, 2033 (maturity date) is 14 years away.

What is going on here? What do these numbers (especially the -0.04%) mean, and how are they calcuated?

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The yield represents the present value of the coupons and the redemption value, relative to the current price. In order to calculate the yield, you need to know the expected future interest rates in order to discount the coupons to their value in today's currency.

When a bond has a negative yield, it means that you are paying more today for the bond than you get back in coupons (indeed in this case, you're paying 134.67 for about 132.50 in future payments (coupons and principal). Financially, it measn that you're paying the bank/government/company to hold your money for you.

  • But where does the -0.04% come from? – EasyGasket Jul 22 at 21:49
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A negative yield just means you paid $101 to receive $100 in the future. Negative yields are occurring for reasons including but not limited to an expectation that yields will be even lower in the future.

Unless you are well over the insured limit for savings accounts in your country negative yields mean nothing to you.

To expand, YTM (Yield to Maturity) is a complicated calculation particularly when you venture in to multi year bonds. As an example you buy a 10 year, $100 bond with a 5% coupon for $99 (Lets just assume that the coupon payments are once per year for simplicity sake.)

In year 1, pay $99 you recieve $5 in coupon payments. So your yield in year 1 is 5.05% (5/99 = 0.050505)

The future years are a little different because in year 2 you receive another $5, but this time it took 2 years to receive. In year 3 it's the same story, another $5 coupon payment and so on until year 10 when you receive $105; the face amount and final coupon payment. YTM calculates a present value of all of this. It's not just one simple formula. IRR (Internal Rate of Return) is another sort of long term cash flow type return calculation that can be reasonable for bond comparisons.

Buying bonds after they've been issued adds the complicating factor of pre-paying accrued coupon payments. If you were to buy this bond exactly six months in to the third year you the seller may want the $2.50 of the $5 coupon payment that has accrued. Now the bond only has 6.5 years remaining and you've included $2.50 in your purchase price that's really only applicable to the first year's coupon payment both of these factors will impact the YTM.

  • Ok, but how is that -0.04% calculated? – EasyGasket Jul 22 at 21:46
  • Roughly (face amount + expected coupon payments - price paid) divided by price paid then annualized. – quid Jul 22 at 21:49
  • So, ((96.29 + (0.025 * 96.29 * 14) - 134.67) / 134.67) / 14 ? That gives approximately -0.25% – EasyGasket Jul 22 at 21:55
  • The issue price is irrelevant; the face value is 100 (probably). It's 100 * .025 * 14. But the time line is not exactly 14 years and you're only prepaying accrued coupon payments in the first year. YTM is generated using guess and check estimating. But back of the envelope gets you close enough to weigh your options. – quid Jul 22 at 22:04
  • Where did you get the 100 from? From what I've read, the calculation should be done with the face value, which I presumed would be the issue price. I don't see anything indiating a face value of 100 (or anything indicating any value of 100, for that matter). Sorry if I seem ignorant about the basics, I'm just trying to understand the numbers people are showing me properly before I go and use them for anything important. – EasyGasket Jul 22 at 22:07

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