Bond Funds - worth it?
Bond Funds - worth it?
With the ongoing decrease in interest rates, all my bond fund holdings are having a great year. The yield though on many of them is approaching what I would earn basically risk-free in my money market option in my 401k. (It's a 401k with Fidelity and the money market option is called Managed Income Portfolio and currently yields 1.72%). Why would I keep money in my total bond market fund with a SEC yield of 1.87% (distribution yield is a bit higher) and a duration of 5.7 years?
thanks
thanks
Re: Bond Funds - worth it?
You wouldn't. You've got it, and right on. I'm in a very similar situation as a TSP/Fed. I can get the G fund with no duration for 1.5% yield, or (using your numbers) 1.87% for the F fund with almost 6 years duration. I'm not going to take 6 yr duration risk to earn an extra 0.37%.ge1 wrote:With the ongoing decrease in interest rates, all my bond fund holdings are having a great year. The yield though on many of them is approaching what I would earn basically risk-free in my money market option in my 401k. (It's a 401k with Fidelity and the money market option is called Managed Income Portfolio and currently yields 1.72%). Why would I keep money in my total bond market fund with a SEC yield of 1.87% (distribution yield is a bit higher) and a duration of 5.7 years?
thanks
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Re: Bond Funds - worth it?
I wrestle with this as well. But if rates actually drop (despite perennial predictions of them rising), your bond funds would appreciate in value. Something to consider at least.
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Re: Bond Funds - worth it?
Now I'm wondering how my total bond market index fund works...Does buy low / sell high not apply with bond funds? Also, how does duration impact my returns? I can sell the fund whenever I wish.
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Re: Bond Funds - worth it?
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Re: Bond Funds - worth it?
That's right, but all other things being equal, duration risk is undesirable. To my knowledge, one wouldn't intentionally add duration risk without additional and adequate compensation for having done so, unless for some reason, they actually knew which way interest rates would go or were more likely to go.50ismygoal wrote:I wrestle with this as well. But if rates actually drop (despite perennial predictions of them rising), your bond funds would appreciate in value. Something to consider at least.
Re: Bond Funds - worth it?
When "we" casually refer to "stocks & bonds" we should probably be more accurately be referring to "stocks and fixed income". Fixed income includes a wide variety of things like bonds, CDs, cash, etc.ge1 wrote:With the ongoing decrease in interest rates, all my bond fund holdings are having a great year. The yield though on many of them is approaching what I would earn basically risk-free in my money market option in my 401k. (It's a 401k with Fidelity and the money market option is called Managed Income Portfolio and currently yields 1.72%). Why would I keep money in my total bond market fund with a SEC yield of 1.87% (distribution yield is a bit higher) and a duration of 5.7 years?
The important thing is to have some part of your portfolio that is a mitigator of stock volatility and it sounds like you are thinking properly about that, however you choose to do it.
"Never underestimate one's capacity to overestimate one's abilities" - The Dunning-Kruger Effect
Re: Bond Funds - worth it?
For the long term, buy-and-hold investor, the bulk of the return from a bond fund will be the distributions from the fund, not from appreciation of the price of the fund. Bond funds tend to have a very stable NAV over the long term. Over the short term there is movement in the NAV, and price, so short-term traders actively trade to take advantage ("buy low, sell high") of that.seanmerron wrote:Now I'm wondering how my total bond market index fund works...Does buy low / sell high not apply with bond funds? Also, how does duration impact my returns? I can sell the fund whenever I wish.
Personally, I pay little attention to things like YTD and 1-year return in a bond fund. What I mostly care about are distributions rather than short-term price fluctuations which tend to mean revert anyway.
Kolea (pron. ko-lay-uh). Golden plover.
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Re: Bond Funds - worth it?
Thanks yeah I can see how the NAV wouldn't matter then for bonds. What about duration though? How does duration matter with a bond fund? You're not locked in but OP seems to care about it.kolea wrote:For the long term, buy-and-hold investor, the bulk of the return from a bond fund will be the distributions from the fund, not from appreciation of the price of the fund. Bond funds tend to have a very stable NAV over the long term. Over the short term there is movement in the NAV, and price, so short-term traders actively trade to take advantage ("buy low, sell high") of that.
Personally, I pay little attention to things like YTD and 1-year return in a bond fund. What I mostly care about are distributions rather than short-term price fluctuations which tend to mean revert anyway.
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Re: Bond Funds - worth it?
So since NAV is not a factor with our Fixed Income allocation is it just a matter of always shuffling your fixed income allocation to the currently highest yielding security? Whether it be Bonds, CD, Cash, etc...?BolderBoy wrote:When "we" casually refer to "stocks & bonds" we should probably be more accurately be referring to "stocks and fixed income". Fixed income includes a wide variety of things like bonds, CDs, cash, etc.
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Re: Bond Funds - worth it?
How is there duration risk with a fund? They can be sold at anytime? Or does this fund require x years?azanon wrote:You wouldn't. You've got it, and right on. I'm in a very similar situation as a TSP/Fed. I can get the G fund with no duration for 1.5% yield, or (using your numbers) 1.87% for the F fund with almost 6 years duration. I'm not going to take 6 yr duration risk to earn an extra 0.37%.
Re: Bond Funds - worth it?
The risk is not duration, the risk is with changing interest rates. Picking a short duration is the cure for interest rate risk. But short duration also comes with lower interest rates so the key is to balance interest rate risk against low returns. Many people go for durations of 4-6 years as a good balance between the two. Some professionals (like Bill Bernstein) recommend very short duration bonds.seanmerron wrote: How is there duration risk with a fund? They can be sold at anytime? Or does this fund require x years?
Many/most bond funds are constructed around a target duration and maturity so you can pick the duration you want to have and find the fund that will deliver on that. But be aware that some funds will meet the target with barbell (very long + very short) distribution of durations while other funds will try to get all bonds close to the target.
Kolea (pron. ko-lay-uh). Golden plover.
Re: Bond Funds - worth it?
Duration is a technical term that is the measure of interest rate risk as mentioned in a reply just above. The longer the duration the bigger the response to changes in interest rates. As a rough approximation you can multiply the duration number by the amount of change of interest rate to get the change in NAV that will be produced in your fund. The nuances are more complicated than that, however.seanmerron wrote:How is there duration risk with a fund? They can be sold at anytime? Or does this fund require x years?azanon wrote:You wouldn't. You've got it, and right on. I'm in a very similar situation as a TSP/Fed. I can get the G fund with no duration for 1.5% yield, or (using your numbers) 1.87% for the F fund with almost 6 years duration. I'm not going to take 6 yr duration risk to earn an extra 0.37%.
Larry Swedroe wrote somewhere that in his opinion duration risk is justified if you can get 20bps increased yield for a year increase in duration. It is probably a 50/50 chance when that opportunity is or isn't available in the bond market. You need to look at the yield curve for the kind of bonds you are buying to see.
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Re: Bond Funds - worth it?
What does this mean for the oft recommended Total Bond Market fund usually suggested on here? Like the poster above I'm not sure I entirely understand bonds or bond funds. I am doing a tax-deferred to tax-deferred rollover which later this year I will do a portion of to rollover to a Roth. I was thinking of putting a little more than that portion in the total bond market fund as a temporary holding spot so I wasn't buying/selling equities in such a short period of time. Does that not make sense?
Where the tides of fortune take us, no man can know.
Re: Bond Funds - worth it?
Not everyone has as good of alternatives as the OP, or in my case (G Fund). If you look at Vanguard's offerings, there's a more compelling reason to use an intermediate-term fund. Comparing VBRIX at 1.09% yield and almost 3 yr duration, vs. total bond fund at 1.96% yield and 5.7 yr duration, the total bond looks far more compelling in that case.Engineer250 wrote:What does this mean for the oft recommended Total Bond Market fund usually suggested on here? Like the poster above I'm not sure I entirely understand bonds or bond funds. I am doing a tax-deferred to tax-deferred rollover which later this year I will do a portion of to rollover to a Roth. I was thinking of putting a little more than that portion in the total bond market fund as a temporary holding spot so I wasn't buying/selling equities in such a short period of time. Does that not make sense?
Also, just speaking real generally and over a very long term, the intermediate term bond tends to be a sweet spot on a yield curve (maximum risk adjusted return). So if one is taking more of a long-term view instead of a timing, year-to-year viewpoint, buying an intermediate term bond for the long-term is a great choice, and is typically a default recommendation.
Now for my added personal preference, i use VG int-term gov bond fund (outside my TSP) in lieu of Total Bond. To briefly summarize why, I've been compelled by much of Larry S.'s work that credit risk is generally not proportionally rewarded, and also I like my bond fund to be as uncorrelated as possible with my stocks, so gov bonds give me more of that in comparison to bond funds that hold corporates. So where there's a flight to safety (e.g. brexit), I've observed that gov/treasuries seem to do best while stocks are getting hammered.
Re: Bond Funds - worth it?
thanks all as always for the knowledgeable responses
- Phineas J. Whoopee
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Re: Bond Funds - worth it?
What does the tax-deferred account you'll be transferring and then partially converting presently hold? It sounds like equities. If so, in tax-advantaged accounts you're best off buying and selling quickly: on the same day if possible.Engineer250 wrote:... I am doing a tax-deferred to tax-deferred rollover which later this year I will do a portion of to rollover to a Roth. I was thinking of putting a little more than that portion in the total bond market fund as a temporary holding spot so I wasn't buying/selling equities in such a short period of time. Does that not make sense?
If the stocks in tax-deferred are up, so will be the stocks in the Roth account, and if down, the same thing. If you're happy with your asset allocation, there's no reason to change it just because of a change in custodians and tax treatment. You can read more about that from our wiki: Tax-adjusted asset allocation.
I hold 40% of my portfolio in indexed US and international equities. Should I sell it all today, put it into Total Bond, then buy stocks back over time? If not, it makes no sense to do the same thing for the transfer and then conversion, where it sounds like you would be going to cash just for the move's sake.
Does that make engineering sense to you?
PJW
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Re: Bond Funds - worth it?
Sorry I didn't clarify. It's currently part of a defined contribution pension, so it's probably in some mix of cash, treasuries and bonds or however pension programs are likely to be invested. So in a way I'm taking a chunk of money that was all conservatively invested and will likely be putting all/most of it in equities eventually. It probably makes up about 30% of my total retirement money but I never really thought about it in such a way, I only get to mess with it since I left the company that held it and can now roll it over and invest it however I want (like many others here have suggested, I treated it as non-existent and tried to save without thinking about its being there). The rest of my portfolio is 100% equities, and I think in the next 5-10 years I'd like to stay 90-100% equity invested. If I was going to treat it like the rest of my portfolio, I would just get it in 100% equities right away. But since I'm going to try to do some Roth conversions on it in the next couple years I don't know if it makes sense to keep part of it in bonds (or something conservative) for that reason. My Roth will certainly be 100% equities. So I don't know whether it makes sense to stash some in bonds before it moves over, or to just buy index funds now and then sell/buy those index funds again when I move it over to the Roth.Phineas J. Whoopee wrote:What does the tax-deferred account you'll be transferring and then partially converting presently hold? It sounds like equities. If so, in tax-advantaged accounts you're best off buying and selling quickly: on the same day if possible.Engineer250 wrote:... I am doing a tax-deferred to tax-deferred rollover which later this year I will do a portion of to rollover to a Roth. I was thinking of putting a little more than that portion in the total bond market fund as a temporary holding spot so I wasn't buying/selling equities in such a short period of time. Does that not make sense?
If the stocks in tax-deferred are up, so will be the stocks in the Roth account, and if down, the same thing. If you're happy with your asset allocation, there's no reason to change it just because of a change in custodians and tax treatment. You can read more about that from our wiki: Tax-adjusted asset allocation.
I hold 40% of my portfolio in indexed US and international equities. Should I sell it all today, put it into Total Bond, then buy stocks back over time? If not, it makes no sense to do the same thing for the transfer and then conversion, where it sounds like you would be going to cash just for the move's sake.
Does that make engineering sense to you?
PJW
Where the tides of fortune take us, no man can know.
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Re: Bond Funds - worth it?
I do have access to the wonderful G Fund. However, my asset allocation today is 100% equities. I'm only debating temporarily putting some of this tIRA in bonds in prep for a Roth conversion. And I don't know whether that makes any sense or not. In my head I was thinking I would use the G Fund in the future as my substitution for bonds. That I in fact won't even bother with the F Fund or a bond fund in any of my tax-deferred or tax free accounts. I was debating possibly some tax exempt bonds in an after tax account in the long term but as of yet my after tax is pitiful and so all cash.azanon wrote: Not everyone has as good of alternatives as the OP, or in my case (G Fund). If you look at Vanguard's offerings, there's a more compelling reason to use an intermediate-term fund. Comparing VBRIX at 1.09% yield and almost 3 yr duration, vs. total bond fund at 1.96% yield and 5.7 yr duration, the total bond looks far more compelling in that case.
Also, just speaking real generally and over a very long term, the intermediate term bond tends to be a sweet spot on a yield curve (maximum risk adjusted return). So if one is taking more of a long-term view instead of a timing, year-to-year viewpoint, buying an intermediate term bond for the long-term is a great choice, and is typically a default recommendation.
Now for my added personal preference, i use VG int-term gov bond fund (outside my TSP) in lieu of Total Bond. To briefly summarize why, I've been compelled by much of Larry S.'s work that credit risk is generally not proportionally rewarded, and also I like my bond fund to be as uncorrelated as possible with my stocks, so gov bonds give me more of that in comparison to bond funds that hold corporates. So where there's a flight to safety (e.g. brexit), I've observed that gov/treasuries seem to do best while stocks are getting hammered.
Just wondering is that your plan as well? Do you think G Fund is an acceptable substitute for bond investment?
Where the tides of fortune take us, no man can know.
Re: Bond Funds - worth it?
Absolutely. I'm going to use the G fund as much as possible for my bond component. It has the return of approximately a 11-yr treasury for 0 duration risk (can't lose money). (technically they say the return is the sum total of all treasuries with 4+ years of duration, but i did the math once, and its about what the rate of a 11-yr tbond would be)Engineer250 wrote:Just wondering is that your plan as well? Do you think G Fund is an acceptable substitute for bond investment?
So, what can compete with that? I would say, from a risk-adjusted return basis, no bond fund can.
Re: Bond Funds - worth it?
There is some rebalancing benefit to holding bonds like treasuries. When stocks drop a lot then often safe bonds rise. Some flight to safety, The Fed buying back bonds and lowering interest rates. So when your stocks are falling and your bonds are rising your rebalancing bands are met and you sell bonds high to buy stocks low.
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Re: Bond Funds - worth it?
I'm genuinely curious: for those who compare the current yield on different duration bond funds to the G fund or to other fixed income options like CDs, is this simply market timing / performance chasing for bonds? Asking in a serious way. You never hear folks here say "REITs are getting better returns right now than total US, so you might think about doing REITs." I know this isn't an apples-to-apples comparison, but isn't this pretty close to saying "current total bond market yields are only a touch above a CD, so you should go with a CD ladder instead," with the implicit assumption being that you'd transition back out of your CD ladder of bond yields started going back up. Isn't that market timing? Why does it seem so much more palatable to everyone?
And if this is straying off topic, I trust the mods will reign me in or create a new thread...
And if this is straying off topic, I trust the mods will reign me in or create a new thread...
Pardon typos, I'm probably using my fat thumbs on a tiny phone.
Re: Bond Funds - worth it?
I think this is correct, but bond funds may be a good place to be currently, though there is excellent advice to hold them continually. When there are major redemptions in bond funds, the managers must sell in order to pay the redeeming parties. When those sales represent gains, these are passed along to those owning the fund. For long term holders, times when redemptions are large may be a positive occurrence if they are reinvesting interest and gains. Is this a correct statement?
Tim
Tim
Re: Bond Funds - worth it?
Regarding the additional rebalancing potential from holding treasuries. Is there a good scale that shows what that can add versus holding a bond fund that has some corporates or credit risk?
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Re: Bond Funds - worth it?
I keep hearing how great the G fund is and I realized that I am not sure I understand if you are a buy and hold type. It is not easy to access so if you are planning to leave it alone for decades why is it better than a long term bond? I can see how it is good in disbursement phase. I am just having trouble understanding its advantage in accumulation phase unless you are thinking about market timing or rebalancing.
Thank you
Thank you
- arcticpineapplecorp.
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Re: Bond Funds - worth it?
Good points. Below is a link from what I thought was an article by Rick Ferri about intermediate vs. short term bonds and how much was lost by those who preferred to go short rather than intermediate. That's what google found after typing "Rick Ferri Intermediate bonds." The article looks like what I remember him writing and I believe he was with portfolio solutions, but remember hearing maybe he sold the company? I don't see him anywhere on the site or the article having his name on it for what it's worth.kolea wrote:The risk is not duration, the risk is with changing interest rates. Picking a short duration is the cure for interest rate risk. But short duration also comes with lower interest rates so the key is to balance interest rate risk against low returns. Many people go for durations of 4-6 years as a good balance between the two. Some professionals (like Bill Bernstein) recommend very short duration bonds.seanmerron wrote: How is there duration risk with a fund? They can be sold at anytime? Or does this fund require x years?
Many/most bond funds are constructed around a target duration and maturity so you can pick the duration you want to have and find the fund that will deliver on that. But be aware that some funds will meet the target with barbell (very long + very short) distribution of durations while other funds will try to get all bonds close to the target.
Of course, it's often recommended that you only pick a duration that matches the timeframe with your holding period. So if you're not planning on holding the bond fund for at least 5-7 years, then it would be wiser to go shorter term.
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Re: Bond Funds - worth it?
No, because it isn't in the market. For securities traded in the market, it's unlikely that you know more than the market does; higher-yielding bonds have higher risk. But non-marketable fixed-income options may have higher yields with the same risk, or equal yields with less risk. They are good deals created by your retirement provider.Nearly A Moose wrote:I'm genuinely curious: for those who compare the current yield on different duration bond funds to the G fund or to other fixed income options like CDs, is this simply market timing / performance chasing for bonds?
Re: Bond Funds - worth it?
That fund has a .78% E/R ..IMO, that's pretty high for a relatively low return devicege1 wrote:With the ongoing decrease in interest rates, all my bond fund holdings are having a great year. The yield though on many of them is approaching what I would earn basically risk-free in my money market option in my 401k. (It's a 401k with Fidelity and the money market option is called Managed Income Portfolio and currently yields 1.72%). Why would I keep money in my total bond market fund with a SEC yield of 1.87% (distribution yield is a bit higher) and a duration of 5.7 years?
thanks
Just an observation
Edited for clarity
- saltycaper
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Re: Bond Funds - worth it?
It's somewhat easier to compare fixed income products because their future returns and risks are often easier to estimate. If you have a 5-yr Treasury bond yielding 1.5% and a 5-yr FDIC-insured direct bank CD yielding 2.0%, you know the latter is practically guaranteed to outperform if both are held to maturity, barring some type of catastrophe regarding FDIC insurance.Nearly A Moose wrote:I'm genuinely curious: for those who compare the current yield on different duration bond funds to the G fund or to other fixed income options like CDs, is this simply market timing / performance chasing for bonds? Asking in a serious way. You never hear folks here say "REITs are getting better returns right now than total US, so you might think about doing REITs." I know this isn't an apples-to-apples comparison, but isn't this pretty close to saying "current total bond market yields are only a touch above a CD, so you should go with a CD ladder instead," with the implicit assumption being that you'd transition back out of your CD ladder of bond yields started going back up. Isn't that market timing? Why does it seem so much more palatable to everyone?
And if this is straying off topic, I trust the mods will reign me in or create a new thread...
Less perfect comparisons can be made between bond funds, and some investors do fail to consider asymmetric credit risk, call risk, and other risks as well as how different funds interact with the rest of the portfolio. In this way, knowing a little and assuming too much can be costly.
Quod vitae sectabor iter?
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Re: Bond Funds - worth it?
What you and Grabiner say about individual bonds and CDs makes sense. Perhaps I should have focused on the choice to jump in and out of bond funds. If I understand things right, an indexed bond fund is periodically buying and selling bonds to maintain the target duration, right? Or I guess they could buy bonds and hold them to maturity in a ratio that achieves the average duration? Either way, you have new bonds coming into the fund and old bonds going out or maturing. And that should change the fund's yield, right? Is it just that bond fund yields change slowly enough and predictably enough that it's easier to effectively change between a bond fund and something like a CD or individual bond?saltycaper wrote:
Less perfect comparisons can be made between bond funds, and some investors do fail to consider asymmetric credit risk, call risk, and other risks as well as how different funds interact with the rest of the portfolio. In this way, knowing a little and assuming too much can be costly.
Pardon typos, I'm probably using my fat thumbs on a tiny phone.
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Re: Bond Funds - worth it?
In the next stock market downturn, investors will learn very quickly the importance of asset allocation and specifically a bond fund.
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Re: Bond Funds - worth it?
[quote="Nearly A Moose" If I understand things right, an indexed bond fund is periodically buying and selling bonds to maintain the target duration, right? Or I guess they could buy bonds and hold them to maturity in a ratio that achieves the average duration? Either way, you have new bonds coming into the fund and old bonds going out or maturing. And that should change the fund's yield, right? [/quote]
The fund's yield changes even if it doesn't buy or sell any bonds. For the simplest example, consider a zero-coupon bond, which pays nothing until it matures in five years, then pays $1000. If the bond is worth $906 today, its yield is 2%, as a 2% return on $906 becomes $1000 in five years. If the bond's price falls to $863, its yield rises to 3%, as you will now get a 3% return if you wait five years to get the $1000 on the new lower balance.
CDs aren't traded on the market, but they work similarly.
The fund's yield changes even if it doesn't buy or sell any bonds. For the simplest example, consider a zero-coupon bond, which pays nothing until it matures in five years, then pays $1000. If the bond is worth $906 today, its yield is 2%, as a 2% return on $906 becomes $1000 in five years. If the bond's price falls to $863, its yield rises to 3%, as you will now get a 3% return if you wait five years to get the $1000 on the new lower balance.
What happens to either an individual bond (as in the example above) or a bond fund is that yields rise when prices fall. If you buy a bond fund with a 2% yield and a 5-year duration, the yield will rise to 3% if the fund price falls by 5%. Therefore, if you hold the fund for five years, the extra yield will make up for the 5% loss.Is it just that bond fund yields change slowly enough and predictably enough that it's easier to effectively change between a bond fund and something like a CD or individual bond?
CDs aren't traded on the market, but they work similarly.
- saltycaper
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Re: Bond Funds - worth it?
Yes, although most bonds will be sold before maturity, and I believe funds usually target average maturity, not duration. (If two bonds mature on the same day but one has a higher coupon, it will have a lower duration, if all else is equal such as no call provisions.) Also, while many do, not all bond funds have a targeted average maturity.Nearly A Moose wrote:
If I understand things right, an indexed bond fund is periodically buying and selling bonds to maintain the target duration, right? Or I guess they could buy bonds and hold them to maturity in a ratio that achieves the average duration?
As grabiner pointed out, the yield on bond funds can change without any buying or selling, just as the yield on individual bonds can change. Price up, yield down; price down, yield up. Don't confuse yield with a bond's coupon, which is fixed. When people say "yield", they are usually referring to yield to maturity, which varies inversely with bond prices and is the rate earned if you hold the bond to maturity, assuming no default or calls. (Though if you ever see the word "yield" in investment literature, it's always important to identify what type of yield is being referenced.) The closest thing to obtaining a yield to maturity for a bond fund is the SEC yield.Nearly A Moose wrote:
Either way, you have new bonds coming into the fund and old bonds going out or maturing. And that should change the fund's yield, right?
Changes in yield are definitely not predictable, and they are not always slow. I picked two individual fixed income products that most investors view as having comparable credit risk and call risk, pretty much zero. They are also the only two fixed income products I would suggest considering owning individually. Meanwhile, comparing bond funds is more difficult if the funds don't have equal credit risk or call risk.Nearly A Moose wrote:
Is it just that bond fund yields change slowly enough and predictably enough that it's easier to effectively change between a bond fund and something like a CD or individual bond?
I also said if held to maturity it's easy to see which will outperform. But, in the interim, it's not clear what will happen to the Treasury, which may change in price substantially if rates increase or decrease. Since the CD is not a tradeable security, we can't see its value change, although a 5-yr CD at 2% may be seen as being worth more a year later if 4-yr CDs are only available for 1% by that time, even if you can't sell it.
If the two products you're comparing, whether funds or individual bonds, don't have very similar risk profiles (same credit risk, same interest-rate risk, etc.), then merely comparing yield is not sufficient. You have to decide how much more yield you require to take on any extra risk. But the reason comparison is possible at all is the bond math behind yield to maturity and SEC yield. It makes some variables known. It also drives a lot of investors crazy, because we can estimate some things with reasonable accuracy, which makes it tempting to try to predict the future, but we can't, since we don't know everything.
Quod vitae sectabor iter?
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Re: Bond Funds - worth it?
Thanks Grabiner and saltycaper. Good explanations that I imagine I'll have to read a few times to fully internalize. Trying to really understand bonds give me a headache.
Pardon typos, I'm probably using my fat thumbs on a tiny phone.