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Hi all,
Hoping someone can help me learn here. This may be a dumb question, but thanks for any guidance...I don't have experience buying individual bonds.

Please correct any and all incorrect statements here, even before I pose the question.


So a bond is initially issued at a par value with an interest rate coupon. If one buys that bond when issued, they pay par, and get that interest rate until the bond comes due (or is called early). As the interest rate markets move, the bonds value can go up and down, and the corresponding interest rate would move inversely. Regardless, if the buyer just holds until it's due, they get their full investment back when it's called, and have collected the initial coupon rate along the way.
But if one were to buy the bond later on, after some of this movement, they buy it on the secondary market and pay current face value. Let's say par value was $100, and the price has gone up so one has to pay $110. If the initial coupon was at 5%, the new 'yield to maturity' for the person paying $110 would be 4.5%, correct? When the bond comes due, does that investor get back their initial investment (at the $110 price) or do they get paid back at par value, and thus also lose 10% of their initial capital investment?
I assume the latter (because why would a bond issuer be responsible for paying back the higher value), and if that's the case, the investor has to go into that investment knowing their yield is lower and also calculating in the capital loss at the end, correct? Or does the 'yield to maturity' figure include that capital loss in the calculation?

Thanks for any help!

Howard
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So a bond is initially issued at a par value with an interest rate coupon. If one buys that bond when issued, they pay par

Often, but not always. Even at issue, there can be premiums (pay over par) or discounts (pay under par)

get that interest rate until the bond comes due (or is called early)

Unless the company quits paying for some reason (like going BK). Note: If there is an early call allowed, the company often will have to pay a premium to exercise that option. That premium is supposed to help make up for the future interest payments that won't be made.

As the interest rate markets move, the bonds value can go up and down, and the corresponding interest rate would move inversely.

The coupon rate remains the same, but the effective interest rate will move inversely with the price. For instance, if the coupon rate is 5%, for a single $1000 par value bond, you will receive $50/year. If you buy the bond for $1100 in the secondary market, you will still receive $50/year, so the effective yield is now $50/$1100 = 4.545% Conversely, if you were to buy the same bond at $900, you would still get the $50/year, but the effective yield would be increased to $50/$900 = 5.556%

Regardless, if the buyer just holds until it's due, they get their full investment back when it's called, and have collected the initial coupon rate along the way.

Unless the company doesn't pay it back because they've, for instance, gone BK, or made a deal agreed to by debtholders to pay the bond back at a lower value, so they won't have to declare BK.

But if one were to buy the bond later on, after some of this movement, they buy it on the secondary market and pay current face value. Let's say par value was $100, and the price has gone up so one has to pay $110. If the initial coupon was at 5%, the new 'yield to maturity' for the person paying $110 would be 4.5%, correct?

No, the 'effective yield' would be 4.5% You haven't supplied enough information to know what the 'yield to maturity' is, because you need to know how much time there is left before maturity, and how many interest payments per year there are to calculate the yield to maturity. If there is one year left and the bond pays annually, then the 'yield to maturity' would be -4.55% If there are 10 years left and the bond pays annually, then then yield to maturity will be 3.78% Here's a calculator that will help you figure the YTM https://investinganswers.com/calculators/yield/yield-maturit... Note that for a bond that you pay a premium for, the YTM will be less than the effective yield.

When the bond comes due, does that investor get back their initial investment (at the $110 price) or do they get paid back at par value, and thus also lose 10% of their initial capital investment?

They only get the par value. They don't actually lose 10%, though. They lose $10, which is 9.091% of their initial $110 investment. That's why the YTM can be negative, because the YTM calculation accounts for the loss of the initial capital.

I assume the latter (because why would a bond issuer be responsible for paying back the higher value)

Correct.

if that's the case, the investor has to go into that investment knowing their yield is lower and also calculating in the capital loss at the end, correct?

They should know that the effective yield is lower. They may or may not be planning on taking the capital loss at the end. If they don't plan to hold until maturity, especially if they think interest rates will be dropping, or that the company is going to get an upgrade in their credit rating. If either of those happens, the investor may be able to sell it for an even higher price than they paid (and will have collected interest in the interim).

Or does the 'yield to maturity' figure include that capital loss in the calculation?

YTM does assume that one holds it to maturity and realizes the loss of capital. Effective yield is calculates the interest rate one receives based on the coupon rate and the price paid.

And then for the yield calculation that you didn't ask about: Yield to Worst. For bonds with early call provisions, YTW is calculated based on the price that you would receive if the bond is called at one of the early call dates allowed. If there are different payouts based on the date called, you would need to look at the amount received for each of those different payouts to determine which one was the YTW.

AJ
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But if one were to buy the bond later on, after some of this movement, they buy it on the secondary market and pay current face value. Let's say par value was $100, and the price has gone up so one has to pay $110. If the initial coupon was at 5%, the new 'yield to maturity' for the person paying $110 would be 4.5%, correct? When the bond comes due, does that investor get back their initial investment (at the $110 price) or do they get paid back at par value, and thus also lose 10% of their initial capital investment?

Actually the *Current yield* will be about 4.55%. The *Yield to Maturity* will be much different, depending on how much time remains until maturity. That 10% premium you pay would be spread over the remaining time to maturity, which affects the calculation. Say you have 5 years remaining to maturity. That 10% premium reduces your YTM by about 2% per year, to about 3%. That's not exact, because it's usually figured on a compound basis, conventionally semiannually or quarterly, as the bond interest payments go. Actually, as you can see, a 10% premium is a pretty big deal.

I assume the latter (because why would a bond issuer be responsible for paying back the higher value), and if that's the case, the investor has to go into that investment knowing their yield is lower and also calculating in the capital loss at the end, correct? Or does the 'yield to maturity' figure include that capital loss in the calculation?

Here, your assumption is correct. The premium you pay produces the capital loss component, and is factored into the YTM calculation.

Bill
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Thanks Bill and AJ. Appreciate all the great info!

Howard
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The premium you pay produces the capital loss component, and is factored into the YTM calculation.

Conversely if you are able to buy the bond at a discount from par (as when interest rates rise or news causes investors to doubt the safety of their investment) then when the bond matures you will have a capital gain.
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Paul,

As an recent example of the cap-gains that are possible with bonds, on 11/15/18 I bought an issuer's bonds at 91.830 that closed Friday at 97.222, or a gain of 5.87% for a 23-day holding-period. Whether I hold to maturity or flip will depend on what else happens. But for right now, the position is doing better than what is available in the equity markets, unless one is a short.

Arindam
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Just a heads up on paying interest when you buy a bond on the secondary market:

If a bond pays interest twice a year, in january and july for example, and you buy that bond in june, you're gonna pay the seller the selling price for the bond...and commission...AND the interest that the bond has earned between January and June.

Of course, then in July, you'll collect the full bi-annual interest payment due in July...just as if you've held the bond since January.

Hope I did not repeat anyone else's response above, I just sort of skimmed through them. My aplogies if I did. (dealing with a nasty cold right now, reffed some games in the rain and cold last few days, paying cosequences. But gives a good excuse to stay inside and watch premier league games for the week end. :)
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When the bond comes due, does that investor get back their initial investment (at the $110 price) or do they get paid back at par value, and thus also lose 10% of their initial capital investment?

For a "standard" bond, the issuer will usually pay back at the par value. But for all bonds, it depends on exactly what the "contract" of that bond states. For example, bonds that are inflation adjusted will usually pay back at higher than par value. I own some TIPS that I purchased for $10,000 a while back and they've paid me interest every 6 months, and when they mature, they will remit more than $10,000 (currently about $11,693.10, and when they mature soon, might be a bit higher than that).
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