Bond fund versus individual bonds, definitive answer

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Bond fund versus individual bonds, definitive answer

Postby linuxizer » Fri Oct 16, 2009 6:29 pm

There have been a dozen or more threads in which advocates of individual bonds spread fear that, were rates to drop at exactly the wrong time, you would not get your money back out of the bond fund when you needed it, and therefore buying individual bonds must be safer. In response, others (at least some of whom I would consider experts in the bond market) have responded that as long as your duration is greater than your need for the funds, you will not lose money, and that comparing a non-rolling bond ladder to a fund--equivalent to a rolling bond ladder--is not a valid comparison.

More recently, the final twist on this endless circle has been a claim by anti-bond-fund posters that since at some point you will need the money, even if you are investing for the long-term, at some point you will need the money and your principal will not be safe.

In response to this, I will excerpt and summarize one of the major academic books elucidating how bonds respond to price changes, Fabozzi's Fixed Income Mathematics (1993), pp175-190 or so, the chapter called "Price Volatility Measures: Duration," sub-chapter "Role of Duration in Immunization Strategies." Note that Fabozzi uses the term "immunize" to mean ensuring that the amount that you get out of a "bond portfolio" (the term here can mean either a ladder of individual bonds, a bond fund, or a grouping of bond funds, as long as the duration is the same across types).

"Because the interest rate risk and reinvestment risk offset each other, however, is it possible to select a bond or bond portfolio that will lock in the yield at the time of purchase, regardless of interest rate changes in the future? That is, is it possible to immunize the bond or bond portfolio against interest rate changes? Fortunately, under certain circumstances, it is. This can be accomplished by constructing a portfolio so that its Macaulay duration is equal to the length of the investment horizon."

You'll note that Fabozzi uses bond and bond portfolio interchangeably because there is no difference in how they respond to market conditions. Indeed, the examples he goes on to provide make it clear that the optimal way to meet a future obligation is NOT to purchase a bond or group of bonds which matures when the obligation is due, but rather a bond or group of bonds whose duration is the length of time remaining until the obligation comes due. Since for any bond which pays a coupon, the duration is shorter than the maturity, this means you will wind up selling the supposedly safe bond on the open market, and be subject to the same market pricing that people worry about with bond funds. The reason to invest even an individual bond towards a fixed future obligation based on duration rather than maturity is that you face reinvestment risk on the coupon payments. If interest rates drop, you will not be able to meet your obligation, because you will be making less on the reinvested coupon payments than you expected to. Therefore to ensure meeting your obligation, you will need to invest more than you would otherwise.

"To immunize a portfolio's target accumulated value (target yield) against a change in the market yield, a portfolio manager must invest in a bond (or a bond portfolio) such that (1) the Macaulay duration is equal to the investment horizon*, and (2) the present value of the cash flow from the bond (or bond portfolio) equals the present value of the liability."
The footnote: "* This is equivalent to equating the modified duration of the portfolio to the modified duration of the investment horizon."

Point (1) is what has been advocated here. Point (2) simply means that you should invest enough money to reach your goal!

In his examples, he assumes the market yield changes immediately after the bond is purchased, as a one-time event. This point has been raised in discussions here as well, that if yields constantly increase, you could fail to make up the lost NAV by the time you need the fund's principal. The response in other posts was to suggest that the duration should be lowered smoothly as the fixed need for the money approaches, so that the duration always equals the remaining time. This can be accomplished by moving money from e.g. an intermediate-term fund to a short-term fund over time, in the same way that one rebalances from stocks to bonds over time. The duration of the bond portfolio is simply the dollar-weighted average of the durations of the funds or bonds within the portfolio.

Fabozzi has the following to say on this topic:
"In the face of changing market yields, a manager can still immunize a portfolio by rebalancing it so that the Macaulay duration of the portfolio is equal to the remainder of the investment horizon."

Finally, there is a caveat, which is that if the shape of the yield curve changes (that is, if bonds of different duration do not all change by the same amount), the immunization will be imperfect. This will result in a loss (practically speaking, a pretty small one) if short-term yields fall (reducing interest on reinvested coupon payments) but long-term yields rise (causing NAV loss which is not compensated completely for by the higher interest rates due to low short-term rates). He suggests a strategy elucidated by Fong and Vasicek in the Journal of Finance, December 1984, to minimize this risk. I would guess that this strategy is likely too complicated for individual investors, and the need is quite small, since this risk is minimal.

Indeed it should be possible to "insure" against this risk by overestimating your actual need by a small amount. This is almost certainly an amount smaller than that needed to "insure" a coupon-paying individual bond in case the interest rate changes on the reinvestment of the coupons. Indeed, in practice what most advocates of the individual-bonds-are-safe philosophy seem to do--quite reasonably so--is use the maturity value of the bond to meet their obligation, and the coupon payments become income or get reinvested into the general portfolio. This is in effect over-"insuring" by the value of the coupon payments plus their reinvested interest.

If even this miniscule amount of risk is too much to bear, and building in a small cushion as insurance against the small loss if the yield curve shifts the wrong way (applicable to either individual bonds or funds, as was discussed) is not possible, then a zero-coupon bond is appropriate.

Finally, I want to thank everyone for the discussions of the past several months about bond funds. As frustrating as the discussions have been, in the end they have forced me to read further and further (and even run the numbers myself) to understand why the experts were in fact correct. As a result I have gone from only the most basic understanding of bond funds to feeling considerably more comfortable with how they will respond to a variety of market conditions. I strongly recommend looking up Fabozzi's book, either at the library or the latest revision.

Thanks everyone, and I look forward to more discussion which will inevitably follow :-).
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Postby Jack » Fri Oct 16, 2009 8:00 pm

The important point that you bring up is that the bond or bond fund duration, not the maturity, should match the date of obligation.

A bond whose maturity matches the obligation will be of shorter term than a bond whose duration matches the obligation. Since under normal conditions shorter bonds have lower yields than longer bonds, you need to invest more money to pay your obligation if you match maturity instead of duration. Or as you said, you are over-insuring. The reason bond-holders who hold to maturity are so sure of their outcome is that they over-paid to achieve that outcome. One could achieve the same desired result for less investment money by buying a longer term bond that matches the duration and selling it before maturity.
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Postby AzRunner » Fri Oct 16, 2009 10:20 pm

linuxizer,

Thanks for the post. I don't think you will end the debate, but you provide excellent references, quotes and examples to help explain the use of matching a bond funds duration to future cash flow needs.

Everyone seems to have an opinion. It is always good when you can back up that opinion with real math.

Norm
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Postby linuxizer » Fri Oct 16, 2009 10:55 pm

AzRunner wrote:linuxizer,

Thanks for the post. I don't think you will end the debate, but you provide excellent references, quotes and examples to help explain the use of matching a bond funds duration to future cash flow needs.

Everyone seems to have an opinion. It is always good when you can back up that opinion with real math.

Norm


I don't think this will end the debate either, and frankly I hope the debate doesn't end. My hope is that the debate will move on to discussing and learning about and illuminating more intricate aspects of how bonds and portfolios of bonds behave, so that we can stop endlessly debating the basics--basics which are well established and really not at all controversial. As I said, I've learned a lot in the course of all of these threads. Just ready to move on a bit and hope this post moves the discussion forward.
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Re: Bond fund versus individual bonds, definitive answer

Postby RobG » Fri Oct 16, 2009 11:33 pm

I think the length of your post is indicative of the barriers that you need to overcome so that you can get equal performance from a bond fund vs individual bonds, assuming you will need the money at a time similar to the duration of the fund you chose.

rg
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Postby Dinero » Sat Oct 17, 2009 6:23 am

Thanks very much, this is very helpful.

The consideration of duration of a bond, bond portfolio, or bond fund and the need for the funds always made sense to me.

However, the one aspect of a bond fund that has always bothered me is that the internal composition of the fund constantly changes as bonds mature (or are sold) and are replaced. Even if the fund manager keeps the duration constant, buying and selling bonds in variable interest rate environments could subtract (or add) value to the portfolio in ways that are not obvious to me.

With a bond (or bond portfolio, ladder, etc.) that one self-assembles you don't have this uncertainty.
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Postby mfen » Sat Oct 17, 2009 7:17 am

From the Vanguard blog yesterday concerning this topic:
http://www.vanguardblog.com/2009.10.16/bond-gene.html
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Postby spam » Sat Oct 17, 2009 7:34 am

Hi Linuxer,

Thank you for the concise report. The ongoing discussion has had the same effect on me also. I even read two more books specifically about bonds this summer. I suspect that you have the ability to think more deeply about this topic technically than I.

If I invest 10k in a 4% bond that has a maturity of 10 years, then I will recieve about $400 each year in coupon payments or roughly 4.5k total over the 10 year period. Therefore, the guarenteed return of my principal after 10 years is about twice as important to me than the accrued interest payments. With an individual CD (or bond) I can truely set it and forget it. I buy individual issues for specific events, or as insurance (emergency fund ladder).

I think it is worthwhile noting that the duration of a fund or bond is also the "point of indifference" meaning that it is the point at which the return of your principal is theoretically guarenteed. The time period beyond the duration would represent the accumulation of interest payment above principal. I think you would be looking for a guarenteed return of 0% after 10 years (principal only)

See Bernstein http://www.efficientfrontier.com/ef/999/duration.htm

There is one concern specific to bond funds that I have never seen addressed on this board. The SEC mandates that 80% of a funds holdings match the description in the funds name. For example, 80% of the bonds in a Long Term Treasury fund would need a maturity greater than 10 years. When more than 20% are outside this metric, then an adjustment is required. I believe the turnover rate for Vanguards LT Treasury fund is around 80%. This adds cost. Turnover changes duration.

As you pointed out, interest rate risk is offset by reinvestment risk, so I really dont know what type of long term effect the SEC ruling would have. However, the individual is not bound by this, and can hold to maturity.

Now, on this matter of turnover and cost. I can open a hold-to-maturity account at Treasury direct, and my total expenses will be 0.00. Vanguard is very low, but not that low.

I own both funds and individual issues, and I like them both for different reasons. I like mutual funds for ease, diversification, book keeping, and liquidity. I would buy a junk bond fund but never an individual issue that was below investment grade.

I like both, and I use both. I like my CD ladder better than my MM fund because it is for a specific purpose. I have to change the purpose before using it spuriously. My MM fund is not completely safe from that shiny new boat.
Last edited by spam on Sat Oct 17, 2009 7:51 am, edited 2 times in total.
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The thing I have a hard time understanding is the duration.

Postby Hexdump » Sat Oct 17, 2009 7:42 am

Dinero wrote:Thanks very much, this is very helpful.

The consideration of duration of a bond, bond portfolio, or bond fund and the need for the funds always made sense to me.

However, the one aspect of a bond fund that has always bothered me is that the internal composition of the fund constantly changes as bonds mature (or are sold) and are replaced. Even if the fund manager keeps the duration constant, buying and selling bonds in variable interest rate environments could subtract (or add) value to the portfolio in ways that are not obvious to me.

With a bond (or bond portfolio, ladder, etc.) that one self-assembles you don't have this uncertainty.


and I believe Dinero alluded to it.

(1) the Macaulay duration is equal to the investment horizon*

With an individual bond, the investment horizon is fixed and steadily approaching whereas with the fund the duration is a moving target.
As an example, the ETF= CSJ has a duration of 1.9 years however it has been 1.9 years ever since I have been watching it and will probably stay there for some time. But, had I wanted to invest in a 1.9 year maturing individual bond, so I could have the $$$ at the end of the 1.9 years, I would been assured(mostly) of the return of principal.
The same $$$ invested in the ETF would not be as assured.

I did not read the article, but I am assuming that he is not referring to TIPS and that the dividends/interest is to be reinvested in the Fund.

The bit about matching the duration to your time horizon is the sticking point for me.
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Postby spam » Sat Oct 17, 2009 7:50 am

Hexdump wrote:

The bit about matching the duration to your time horizon is the sticking point for me.


I think this just refers to the "point of indifference". The point that you are guarenteed the return of principal. Beyond this point, coupon payments accumulate.

See Bernstein http://www.efficientfrontier.com/ef/999/duration.htm
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Postby linuxizer » Sat Oct 17, 2009 7:53 am

RobG -
There is a big difference between the difficulty of implementing a strategy and the difficulty of fully understanding a strategy. Implementing the strategy is simple: as I pointed out, rebalancing between two funds of different durations is no more difficult than rebalancing between stocks and bonds at a regular interval. In theory, one should be doing this with individual bonds as well (unless you are over-"insuring" by immunizing only the principal), since duration is a function of the current market interest rate as well as the bond maturities. In practice, the difference in duration due to market rate fluctuations is too small to care about. Here's a bond purchased with a 10% coupon rate, only to have rates rise to 15%:
> b <bond> summary(b,market.rate=.15)
5-year bond with interest of 10% under a current market yield of 0.15%.
Current maturity of 5.
Par value is $100, paying $5 every 0.5 year.
Present value (price) of the bond under current market conditions is $82.84
Duration is 3.67 years.
> summary(b,market.rate=.1)
5-year bond with interest of 10% under a current market yield of 0.1%.
Current maturity of 5.
Par value is $100, paying $5 every 0.5 year.
Present value (price) of the bond under current market conditions is $100
Duration is 3.86 years.

That leaves the major factor being the average duration of the portfolio. Personally, I find it easier to manage two funds. I can see how others would find it easier to manage a portfolio of individual bonds (although hitting a precise duration target would seem to be quite difficult unless you have an extremely large portfolio). The point is, claims about there being no way to ensure the return of capital with a bond fund are moot--you can always get your money out (assuming the only risk is interest rate risk).
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Postby linuxizer » Sat Oct 17, 2009 8:02 am

Dinero and Hexdump-
I should clarify terminology (sorry!). "Investment horizon" means the time remaining until you need the money. Therefore, "With an individual bond, the investment horizon is fixed and steadily approaching whereas with the fund the duration is a moving target," isn't quite what I meant given the terminology. With both an individual bond and a fund, the investment horizon approaches linearly with time, because that is the investor's goal. With an individual bond, the maturity decreases linearly with time. However, the duration decreases non-linearly with time. That is because the duration is determined by the proportion of the discounted total revenue fund of the bond which comes from coupon payments vs. principal. Since the par value is much greater than the coupon, it will not increase linearly. I will try to play around with some numbers and better explain this in a bit. With a fund, the duration obviously stays approximately the same. As noted in my last post, for both an individual bond and a bond fund, the duration will also vary slightly according to current market interest rates, but it is a minor effect.
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Postby Call_Me_Op » Sat Oct 17, 2009 8:19 am

There are a couple of potential risks associated with bond funds that I did not see addressed in the OP's post:

1.) Manager Risk - The risk that the fund manager will do something stupid, such as invest in questionable securities looking for higher yield. There are countless examples where this has happened. In some cases, results have been disastrous.

2.) Sell-Off Risk - I am still not clear on this one, but is is mentioned in several books, including (I believe) Annette Thau's "The Bond Book." It is the risk that a massive sell-off of the fund will leave long-term investors saddled with capital losses. Again, I am not thoroughly convinced that this is a real risk.

-Op
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Postby linuxizer » Sat Oct 17, 2009 8:36 am

spam and mfen- Thank you for both the articles. I think one thing that is missed when the duration as point of indifference gets talked about (which is not often enough, frankly, given comments by Suze Orman and the like) is that when you actually need the money, there is a way to reduce the duration such that your duration is never shorter than your investment horizon.

[quote=Dinero]However, the one aspect of a bond fund that has always bothered me is that the internal composition of the fund constantly changes as bonds mature (or are sold) and are replaced. Even if the fund manager keeps the duration constant, buying and selling bonds in variable interest rate environments could subtract (or add) value to the portfolio in ways that are not obvious to me.

With a bond (or bond portfolio, ladder, etc.) that one self-assembles you don't have this uncertainty.[/quote]

If the yield curve doesn't change shape, and if the only risk factor which changes is the interest rate, then the duration--of an individual bond, or of a group of individual bonds, or of a bond fund--is what matters. The reason you don't have to worry about buying and selling bonds in a shifting interest rate environment is that you're buying and selling at the current market yield/price. It really shouldn't matter at all, any more than selling your individual bond at the reduced price and buying a new bond at the market price won't make a difference. Jack explains this nicely in a thread last week on funds vs. individual bonds.

spam wrote:If I invest 10k in a 4% bond that has a maturity of 10 years, then I will recieve about $400 each year in coupon payments or roughly 4.5k total over the 10 year period. Therefore, the guarenteed return of my principal after 10 years is about twice as important to me than the accrued interest payments. With an individual CD (or bond) I can truely set it and forget it. I buy individual issues for specific events, or as insurance (emergency fund ladder).

I think it is worthwhile noting that the duration of a fund or bond is also the "point of indifference" meaning that it is the point at which the return of your principal is theoretically guarenteed. The time period beyond the duration would represent the accumulation of interest payment above principal. I think you would be looking for a guarenteed return of 0% after 10 years (principal only)


One of the things that became more clear to me in the process of looking into this is that the oft-quoted "point of indifference" is not the point where you get your principal back, it is the point at which the principal, coupon payments, and reinvested coupon payments are constant no matter what the interest rate does. Since this is a much greater sum than just the principal (if it weren't, why would you invest in a bond at all, current market conditions notwithstanding), relying on an individual bond to return the principal guaranteed in order to meet a fixed future obligation requires a much larger bond to be bought in the first place--the over-"insuring" phenomenon I referred to.

If you are looking to what happens beyond the duration, that is entirely a function of whether market rates rise or fall, and there's no way to know that (you could, however, just increase your duration). For that kind of ultra-long-term investing, though, the standard advice here of picking an intermediate-term bond fund and just letting it muddle along works just fine.

spam wrote:There is one concern specific to bond funds that I have never seen addressed on this board. The SEC mandates that 80% of a funds holdings match the description in the funds name. For example, 80% of the bonds in a Long Term Treasury fund would need a maturity greater than 10 years. When more than 20% are outside this metric, then an adjustment is required. I believe the turnover rate for Vanguards LT Treasury fund is around 80%. This adds cost.

Now, on this matter of turnover and cost. I can open a hold-to-maturity account at Treasury direct, and my total expenses will be 0.00. Vanguard is very low, but not that low.


You are totally right that there are other differences between bond funds and a portfolio of individually-held bonds. Some of them are in funds' favor (lower trading costs and better diversification with corporates), some of them are in favor of rolling your own mini-fund (lower costs with Treasuries, where there's no need to diversify credit risk). The Wiki acknowledges these differences pretty well, I think.

I wouldn't worry about 20% of a fund's holdings being of a different maturity than the fund's name, as that will be taken into account in the duration. The risk there is I guess manager risk, where the LT manager could decide that rates are going up, use the 20% to shorten the duration, and be wrong. Not an issue with a bond index fund, however. Now if the LT Treasury manager is using the 20% flexibility to buy ST junk bonds.... ;-)
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Postby linuxizer » Sat Oct 17, 2009 8:43 am

Call_Me_Op wrote:There are a couple of potential risks associated with bond funds that I did not see addressed in the OP's post:

1.) Manager Risk - The risk that the fund manager will do something stupid, such as invest in questionable securities looking for higher yield. There are countless examples where this has happened. In some cases, results have been disastrous.

2.) Sell-Off Risk - I am still not clear on this one, but is is mentioned in several books, including (I believe) Annette Thau's "The Bond Book." It is the risk that a massive sell-off of the fund will leave long-term investors saddled with capital losses. Again, I am not thoroughly convinced that this is a real risk.


Hi Op,
I was addressing one specific claim that has drawn a lot of controversy around these parts over the last few months. I agree completely that there are other risks and costs of bond funds.
Manager risk is eliminated by only investing in bond index funds where available. Of course you could also argue that when you manage your own bond portfolio, you are being tricked by the illusion of control (similar to why people feel more safe in cars than trains) and that there is considerable risk you will not be able to manage your portfolio optimally. Certainly Dr. Bernstein has made claims recently that individuals for the most part aren't able to manage their own assets (I believe his claim was mostly on the basis of emotions but partly on knowledge as well, and for the whole portfolio not just bonds). I don't necessarily agree, but when I see people here making claims of watching the market for days and then snapping individual corporates that they think are mispriced, that sure sounds a lot like manager risk to me.
Sell-off risk is not something that I understand. Perhaps someone can explain further or link to some articles?
Thanks!
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Postby Call_Me_Op » Sat Oct 17, 2009 9:02 am

Hi Linuxizer,

Thanks for your reply. Larry Swedroe discusses "sell-off risk" (but doesn't use that term) on page 194 (third paragraph) in his book "The Only Guide for a Winning Bond Strategy". Here is a link on Google Books.

-Op

http://books.google.com/books?id=F61Eoa ... q=&f=false
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Postby linuxizer » Sat Oct 17, 2009 9:21 am

I ran some numbers for the decline in duration of an individual bond as time passes. As you can see, even under constant market interest rate conditions it is not linear for reasons explained in my last post, and therefore, since duration (of a bond or of a fund of bonds) is the point of indifference, using an individual-bond strategy is not any less complicated than a fund-based strategy if you do not want to over-"insure" by only relying on the principal return at maturity. The implication of duration decline being non-linear is that to keep the duration equal to the remaining investment horizon, you will need to constantly adjust the portfolio duration as time passes. This is difficult to do in a small portfolio of individual bonds.

For instance, in the first year of life of a 20-year 10% bond with constant market interest rates, the duration declines from 8.6 to 8.4. Were the claim of perfect adjustment for investment horizon by individual bonds true, it should decline by exactly 1 year. In contrast, from the 15th to the 16th year of the same bond's life, the duration declines from 3.9 to 3.2, substantially closer to the claim. I will try to post a graph of these numbers as soon as I figure out an image hosting service, as the graph makes a lot more sense than the table of values.

Code: Select all
> b <bond> t.e <seq> n <length> ds <rep> for(x in seq(n)) {
+ ds[x] <summary> plot(ds~t.e,xlab="Time elapsed (y)",ylab="Duration of bond",main="20-year 10% bond under constant interest rates")
> data.frame(t.e,round(ds,1))
     Time        Duration
1   0.0          8.6
2   0.5          8.5
3   1.0          8.4
4   1.5          8.4
5   2.0          8.3
6   2.5          8.2
7   3.0          8.1
8   3.5          8.0
9   4.0          7.9
10  4.5          7.8
11  5.0          7.7
12  5.5          7.6
13  6.0          7.4
14  6.5          7.3
15  7.0          7.2
16  7.5          7.0
17  8.0          6.9
18  8.5          6.7
19  9.0          6.6
20  9.5          6.4
21 10.0          6.2
22 10.5          6.0
23 11.0          5.8
24 11.5          5.6
25 12.0          5.4
26 12.5          5.2
27 13.0          4.9
28 13.5          4.7
29 14.0          4.4
30 14.5          4.2
31 15.0          3.9
32 15.5          3.6
33 16.0          3.2
34 16.5          2.9
35 17.0          2.5
36 17.5          2.2
37 18.0          1.8
38 18.5          1.4
39 19.0          0.9
40 19.5          0.5


Edit: I can't seem to link directly to the image, but the graph is here: http://grafodexia.blogspot.com/2009/10/not-usual-topic-here-but-i-have-been.html
Last edited by linuxizer on Sat Oct 17, 2009 9:28 am, edited 1 time in total.
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Postby Qtman » Sat Oct 17, 2009 9:27 am

I own both funds and indv bonds, don't really see the need for constant debate. Each has their good and bad aspects. Your purpose and needs should drive these decisions.
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Postby linuxizer » Sat Oct 17, 2009 9:32 am

Call_Me_Op wrote:Thanks for your reply. Larry Swedroe discusses "sell-off risk" (but doesn't use that term) on page 194 (third paragraph) in his book "The Only Guide for a Winning Bond Strategy". Here is a link on Google Books.


Thanks for the reference. Larry obviously has a great sense of how these things actually work in the market when risks show up. I didn't get a sense of how big a deal sell-off risk was likely to be in the paragraph you reference in his book (not a criticism at all, by the way, it's an amazing book and covers a vast amount of territory, not all of which can be inspected with a magnifying glass). If the risk is rare but potentially large in magnitude it might worry me. Vanguard tends to have less hot money flowing in/out in general, but I imagine for an ETF it could potentially be a huge problem.
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Postby spam » Sat Oct 17, 2009 10:54 am

linuxer wrote

Edit: I can't seem to link directly to the image


Image

Hi Linuxer,

windows method.

Right click on your graph.
Choose properties.
Copy the http:// address that is listed and paste it into your message (ctrl+c for copy, ctrl+v for paste)
Next, add [img] to the front of the address
Last, add [/img] to the end of the address
Last edited by spam on Sat Oct 17, 2009 11:10 am, edited 2 times in total.
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Postby linuxizer » Sat Oct 17, 2009 11:08 am

spam wrote:Image

Hi Linuxer,

windows method.

Right click on your graph.
Choose properties.
Copy the http:// address that is listed and paste it into your message (ctrl+c for copy, ctrl+v for paste)
Next, add [img] to the front of the address
Last, add [/img] to the end of the address


Thanks for inserting it directly. I actually tried using [img] tags initially, but the image failed to appear in the post when I submitted it, so I went back and edited it as a link. I assumed that Blogger had some sort of controls in place to prevent linking from outside sources using the HTML meta tags, but perhaps it was just momentary weirdness.

At any rate, much obliged.
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Postby dbr » Sat Oct 17, 2009 11:12 am

This is indeed very interesting, but I think is still unclear as to how to extend to balanced portfolios held indefinitely to support withdrawals very small compared to portfolio size, aka retirement investing.

I am a long way from believing the use of bond funds in such a situation is a bad idea that needs to be fixed by structuring individual bond portfolios, and that is the question here.
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Postby linuxizer » Sat Oct 17, 2009 11:20 am

dbr wrote:This is indeed very interesting, but I think is still unclear as to how to extend to balanced portfolios held indefinitely to support withdrawals very small compared to portfolio size, aka retirement investing.

I am a long way from believing the use of bond funds in such a situation is a bad idea that needs to be fixed by structuring individual bond portfolios, and that is the question here.


Hi dbr,
My goal was in some sense to show that when the indefinite horizon becomes definite (e.g. when you reach the spend-down phase in retirement) that you do not need to transition to individual bonds and that you will not lose anything if rates rise. The question of what to do when investing for horizons longer than the duration of the longest-term fund available (as is my situation, since I am 40 years out from the conventional retirement age) seems less controversial. Either invest in a rolling bond ladder or a bond fund (since the two are equivalent as long as you keep rolling the ladder over). The recommendation I have seen here and in many places is to use an intermediate-term fund, as the incremental yield with long-term funds is claimed to be insufficient to justify their greater volatility. I have no reason to question this claim, although you are correct that it is an interesting question in its own right and would benefit from some exploration.
Last edited by linuxizer on Sat Oct 17, 2009 6:43 pm, edited 1 time in total.
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Postby RobG » Sat Oct 17, 2009 11:26 am

linuxizer wrote:RobG -
There is a big difference between the difficulty of implementing a strategy and the difficulty of fully understanding a strategy. Implementing the strategy is simple: as I pointed out, rebalancing between two funds of different durations is no more difficult than rebalancing between stocks and bonds at a regular interval. In theory, one should be doing this with individual bonds as well (unless you are over-"insuring" by immunizing only the principal), since duration is a function of the current market interest rate as well as the bond maturities. In practice, the difference in duration due to market rate fluctuations is too small to care about. Here's a bond purchased with a 10% coupon rate, only to have rates rise to 15%:
> b <bond> summary(b,market.rate=.15)
5-year bond with interest of 10% under a current market yield of 0.15%.
Current maturity of 5.
Par value is $100, paying $5 every 0.5 year.
Present value (price) of the bond under current market conditions is $82.84
Duration is 3.67 years.
> summary(b,market.rate=.1)
5-year bond with interest of 10% under a current market yield of 0.1%.
Current maturity of 5.
Par value is $100, paying $5 every 0.5 year.
Present value (price) of the bond under current market conditions is $100
Duration is 3.86 years.

That leaves the major factor being the average duration of the portfolio. Personally, I find it easier to manage two funds. I can see how others would find it easier to manage a portfolio of individual bonds (although hitting a precise duration target would seem to be quite difficult unless you have an extremely large portfolio). The point is, claims about there being no way to ensure the return of capital with a bond fund are moot--you can always get your money out (assuming the only risk is interest rate risk).


Linuxer, even the BH wiki says that if you need the money at a certain date then a non-rolling ladder is the way to go. (For me it would make sense just to buy a single bond, or a zero if you must). Actually, on the last thread I was chastised for suggesting anyone here had a different opinion, yet you persist. That is not to say that indi-bonds is the only way to go.

Why don't you give Orman's show a call and describe your procedure? I'm sure she will have a field day with it.
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Postby dbr » Sat Oct 17, 2009 11:29 am

Hi and thanks for the above comment.

I would quibble that part of my point is that reaching retirement is NOT a conversion from an indefinite to a definite time line, a confusion that is causing a lot of trouble in these discussions. Since people do not, at least should not, plan on a definite date of demise, retirement is an indefinite time line. The time line is also indefinite due to the mathematical condition that withdrawals are small compared to balance and because the portfolio is not all bonds.

Also, a new question, how is the holding of bonds vs funds affected by the practice of rebalancing stocks to bonds and vice-versa over an extended time during retirement?
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Postby Oicuryy » Sat Oct 17, 2009 11:40 am

linuxizer wrote:The response in other posts was to suggest that the duration should be lowered smoothly as the fixed need for the money approaches, so that the duration always equals the remaining time. This can be accomplished by moving money from e.g. an intermediate-term fund to a short-term fund over time, in the same way that one rebalances from stocks to bonds over time. The duration of the bond portfolio is simply the dollar-weighted average of the durations of the funds or bonds within the portfolio.

Fabozzi has the following to say on this topic:
"In the face of changing market yields, a manager can still immunize a portfolio by rebalancing it so that the Macaulay duration of the portfolio is equal to the remainder of the investment horizon."

That sounds very different from the often-heard advice to just buy and hold a bond fund with duration X if your time horizon is X+ years.

Why aren't there any target duration bond funds?

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Postby RobG » Sat Oct 17, 2009 11:56 am

Oicuryy wrote:
linuxizer wrote:The response in other posts was to suggest that the duration should be lowered smoothly as the fixed need for the money approaches, so that the duration always equals the remaining time. This can be accomplished by moving money from e.g. an intermediate-term fund to a short-term fund over time, in the same way that one rebalances from stocks to bonds over time. The duration of the bond portfolio is simply the dollar-weighted average of the durations of the funds or bonds within the portfolio.

Fabozzi has the following to say on this topic:
"In the face of changing market yields, a manager can still immunize a portfolio by rebalancing it so that the Macaulay duration of the portfolio is equal to the remainder of the investment horizon."

That sounds very different from the often-heard advice to just buy and hold a bond fund with duration X if your time horizon is X+ years.



Yes, thank you!
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Postby spam » Sat Oct 17, 2009 12:07 pm

Oicuryy wrote:

That sounds very different from the often-heard advice to just buy and hold a bond fund with duration X if your time horizon is X+ years.

Why aren't there any target duration bond funds?


I think the attempt has been made by establishing funds of different maturities. For example, the Long-Term Treasury fund. While the relationship between maturity and duration is not linear, duration does tend to increase with maturity.

Enter my question from an earlier post in this thread:

The SEC mandates that 80% of a Long-Term Treasury fund has treasury bonds with a maturity of over 10 years. The 20 and 30 year bonds must be sold when a sufficient number of them have a maturity less than 10 years. How does this extra turnover factor in? Even the Vanguard Long Term Treasury fund has an 80% turnover rate. What long-term impact will this turnover actually have as the economic climate changes?

Interest rate increases tend to hurt short term, but help long term. Hopefully, the anomoly will not occur at the most destructive moment. I can see how it could help on one hand, but hurt on the other.

With a bond of a specific maturity, you know exactly what the outcome should be in 20 or 30 years. It is more difficult to predict the outcome when selling 100% of a bond fund at the same specified future date.
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Postby Jack » Sat Oct 17, 2009 12:56 pm

spam wrote:Enter my question from an earlier post in this thread:

The SEC mandates that 80% of a Long-Term Treasury fund has treasury bonds with a maturity of over 10 years. The 20 and 30 year bonds must be sold when a sufficient number of them have a maturity less than 10 years. How does this extra turnover factor in? Even the Vanguard Long Term Treasury fund has an 80% turnover rate. What long-term impact will this turnover actually have as the economic climate changes?

Interest rate increases tend to hurt short term, but help long term. Hopefully, the anomoly will not occur at the most destructive moment. I can see how it could help on one hand, but hurt on the other.

When you sell one bond and buy another, there is no loss of value. Bond markets are efficient. The replacement bond has exactly the same value as the bond sold. The only thing you have lost are transactions costs which appear to be very small. If you compare the performance of a Vanguard bond fund to its benchmark index, the difference is the sum of the expense ratio and the transaction costs. This is about 15 basis points for Admiral shares.

Interest rate "anomalies" do not harm a bond fund any more than they harm a bond ladder.

The SEC rules aren't forcing the bond fund to do something they don't want to do. They are simply there to prevent false advertising. A long bond fund should hold long bonds. A short bond fund should hold short bonds.
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Postby Dinero » Sat Oct 17, 2009 1:01 pm

With a bond of a specific maturity, you know exactly what the outcome should be in 20 or 30 years. It is more difficult to predict the outcome when selling 100% of a bond fund at the same specified future date.


I've been pondering the fund versus non-fund issue for a while, and I'm starting to think that a reasonable goal as one accumulates investment assets is to replace all or part of certain funds with the underlying assets where it can be done reasonably (reasonable, in the eye of the beholder). TIPS instead of TIPS funds, Treasury Notes/Bonds instead of Treasury funds, gold (i.e. Krugerrands) instead of GLD (if you are into that), etc.

The math on bond funds indicates that funds and bonds are semi-equivalent, but there remain risks and costs with funds that are not present in bonds. And there are clearly situations where funds are superior (diversification, ease of purchase, as a rebalancing vehicle).

So, as is often the case, it probably makes sense to do both!
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Postby alec » Sat Oct 17, 2009 2:04 pm

Oicuryy wrote:
linuxizer wrote:The response in other posts was to suggest that the duration should be lowered smoothly as the fixed need for the money approaches, so that the duration always equals the remaining time. This can be accomplished by moving money from e.g. an intermediate-term fund to a short-term fund over time, in the same way that one rebalances from stocks to bonds over time. The duration of the bond portfolio is simply the dollar-weighted average of the durations of the funds or bonds within the portfolio.

Fabozzi has the following to say on this topic:
"In the face of changing market yields, a manager can still immunize a portfolio by rebalancing it so that the Macaulay duration of the portfolio is equal to the remainder of the investment horizon."

That sounds very different from the often-heard advice to just buy and hold a bond fund with duration X if your time horizon is X+ years.

Why aren't there any target duration bond funds?

Ron


American Century has zero coupon US gov't bond funds that mature at certain dates. Their called "Target" funds.

Also, I'm pretty sure there are closed end bond funds that mature on certain dates, but these may only be munis.
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Postby conundrum » Sat Oct 17, 2009 3:05 pm

Great discussion so far.

As mentioned by previous posters above, we utilize both individual bonds and bond funds. We utilize individual bonds for our TIPS and funds for municipal bonds.


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Postby linuxizer » Sat Oct 17, 2009 3:20 pm

RobG wrote:Linuxer, even the BH wiki says that if you need the money at a certain date then a non-rolling ladder is the way to go. (For me it would make sense just to buy a single bond, or a zero if you must). Actually, on the last thread I was chastised for suggesting anyone here had a different opinion, yet you persist. That is not to say that indi-bonds is the only way to go.

Why don't you give Orman's show a call and describe your procedure? I'm sure she will have a field day with it.


Hi Rob,
The bar keeps moving. Before, you claimed:
"My point is that a bond fund has potential to lose more money than holding individual bonds. This occurs because you have to sell longer term funds to shorten your duration."
"Actually there is a good portion of people who point out that you can lose principal as you shorten the duration (e.g. going from long to intermediate) during a rising rate environment. This won't happen if you buy the individual bonds since they shorten the duration automatically."
"You lose when you make the jump from the long to short fund. For example, say you are in the long term index with a duration of 12.1 years and you want to switch to intermediate (duration 6.3 years). If the interest rates jump 1% the LT fund will drop 12.1% and you will be buying into a fund that only dropped 6.3%. You just had 6% of your money vaporize as you were trying to shorten the duration - something that wouldn't have happened if you just owned a single bond matched to your need. You can gradually shift over but in a rising rate environment you will lose."

I believe I have addressed these assertions. Do you still believe them to be true?

Now in this thread, you have not yet re-asserted your previous declarations. Instead, your current criticism is that the strategy is too complicated. Unlike your prior claims, which are inaccurate, I have no problem with you claiming that changing your average duration by slowly shifting from an IT fund to an ST fund is complicated, because it is your opinion. I do think it is disingenuous to suggest that an individual bond does not suffer from the same problem, as I have tried to illustrate above. The only reason it does not appear complicated is that you are investing substantially more than necessary to get your guaranteed return of principal if you invest so that the bond matures when you need the money rather than has a duration of when you need the money. When you throw extra money at the problem, the problem disappears, but that does not mean it is an optimal solution.

And my opinion is that, in the unlikely event you need to satisfy a fixed obligation at a known future date, keeping the average duration of your portfolio equal to that date by shifting funds when you do your other portfolio rebalancing is not difficult at all. I say it is an unlikely event because, as dbr points out and Dan Kohn before him, most people simply do not spend money in this way for most events. One big example for which it might make sense to explicitly partition out money would be for a child's college education. But for expenses in retirement, say you wanted to have your next five years of expenses guaranteed. You could purchase a 1-, 2-, 3-, 4-, and 5-year bond, dump the coupon payments back into your investment accounts, and transfer the principal into your cash accounts to be spent over the year as each bond matures. But since you will hopefully keep living beyond 5 years into the future, you now must purchase a new 5-year bond as the 1-year bond matures. What you now have is a rolling bond ladder--a bond fund of your own construction.
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Postby linuxizer » Sat Oct 17, 2009 3:27 pm

Oicuryy wrote:That sounds very different from the often-heard advice to just buy and hold a bond fund with duration X if your time horizon is X+ years.

Why aren't there any target duration bond funds?


It turns out I proposed just such a thing but got no replies. Apparently one has to post on bond funds vs. individual bonds to get responses! :wink:

If your time horizon is X+ years, then you are fine investing in a fund of duration X. It is when your duration becomes X-, so to speak, that you must lower the average duration of your portfolio. So the conventional advice is correct, but complete only if you continue to follow the advice as your need for the money approaches.
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Postby danbek » Sat Oct 17, 2009 3:42 pm

RobG wrote:Linuxer, even the BH wiki says that if you need the money at a certain date then a non-rolling ladder is the way to go. (For me it would make sense just to buy a single bond, or a zero if you must). Actually, on the last thread I was chastised for suggesting anyone here had a different opinion, yet you persist. That is not to say that indi-bonds is the only way to go.


I was the one who chastised you, and it seems that I owe you an apology!

But just to make sure we are all on the same page, let me ask Linuxizer a question.

Linuxizer,

Say I have a chunk of money saved for my child's first year college tuition, that will be due in 4.4 years, and I want to make sure that money is "safe" when I need it, but also get a little return (to cover books and a cheap laptop, say).

Are you claiming that the return and risks are the same for both of the following plans:

1. Use the money to buy a zero-coupon bond with maturity of 4.4 years, sell it in 4.4 year.
2. Put all the money in Vanguard Total Bond Market Index fund (edited to add that this fund currently has duration 4.4 years).
Last edited by danbek on Sat Oct 17, 2009 3:47 pm, edited 1 time in total.
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Postby danbek » Sat Oct 17, 2009 3:46 pm

RobG,

I'd also love to see a detailed answer to the question of what individual bond strategy you think is appropriate for a person saving for retirement.
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Postby spam » Sat Oct 17, 2009 4:08 pm

linuxer wrote:

If your time horizon is X+ years, then you are fine investing in a fund of duration X. It is when your duration becomes X-, so to speak, that you must lower the average duration of your portfolio. So the conventional advice is correct, but complete only if you continue to follow the advice as your need for the money approaches


I recently did this in an account that is allocated 20 - 80. I have a balanced global fund at 40%, and I used to have 5 fixed income positions at 12%. The last time I rebalanced, I kept 40% for the global balanced fund, rebalanced to 10% instead of 12% which created 6 fixed income positions instead of 5. The new slice will be hold-to-maturity fixed income.

I did this for two reasons. First to reduce my average duration while maintaining the same allocation and positions, and second because all of my bond funds in this account are trading at or above historic highs. For some of them, this difference is meaningful.

So, for the near term, my cash position is roughly double in this fixed income account.
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Postby linuxizer » Sat Oct 17, 2009 4:09 pm

danbek wrote:Say I have a chunk of money saved for my child's first year college tuition, that will be due in 4.4 years, and I want to make sure that money is "safe" when I need it, but also get a little return (to cover books and a cheap laptop, say).

Are you claiming that the return and risks are the same for both of the following plans:

1. Use the money to buy a zero-coupon bond with maturity of 4.4 years, sell it in 4.4 year.
2. Put all the money in Vanguard Total Bond Market Index fund (edited to add that this fund currently has duration 4.4 years).


Risks for those plans are very different. The following strategies should be equivalent, though:
1. Buy a zero-coupon bond with a maturity of 4.4 years and hold it to maturity.
2. Put money in a short-term and an intermediate-term bond fund with the same risk factors as the bond (e.g. if the bond is a Treasury, the fund should be a treasury), weighted to produce an average duration of 4.4 years, and rebalancing at an interval that seems appropriate to you. If you assume an IT duration of 5 years and ST duration of 2 years, you would want to start out with 20% ST and 80% IT.

I think it is wise that you chose a zero-coupon bond as the comparison, which doesn't seem to be what most people do. For a bond which pays a coupon, the situation is equivalent to a bond fund (otherwise you have to invest considerably money than is necessary to meet your obligation). If you have a fixed obligation at some point in the future (again, not the most common situation, but it does happen), a zero-coupon bond is the perfect way to go, because you don't have to worry about rebalancing.
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Postby danbek » Sat Oct 17, 2009 4:30 pm

linuxizer wrote:Risks for those plans are very different.


Thanks for the clarification. So I think you are saying the following:

* If you need the money in 10 years, using a bond fund with duration 5 years is totally fine.
* But 6 years from now, when your need is only 4 years away, the bond fund will still have a duration of 5 years. So you have a mismatch, and should manage this by selling some of the 5 year bond fund and replacing with, say, a 1 yr bond fund.
* Repeat as needed, etc. etc.

This totally makes sense to me. But I think you made some other statements on the other tread that could be interpreted as:

* If you need the money in 10 years, using a bond fund with duration 5 years is totally fine, and will be totally fine until the day you need the money.

I think that *this* reading of your beliefs what RobG is reacting against.

RobG,

I think we've now clarified that linuxizer doesn't believe what you thought he believed. No how about that individual bond strategy for people accumulating savings for retirement?
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Postby tfb » Sat Oct 17, 2009 4:32 pm

linuxizer wrote:There is a big difference between the difficulty of implementing a strategy and the difficulty of fully understanding a strategy. Implementing the strategy is simple: as I pointed out, rebalancing between two funds of different durations is no more difficult than rebalancing between stocks and bonds at a regular interval. In theory, one should be doing this with individual bonds as well (unless you are over-"insuring" by immunizing only the principal), since duration is a function of the current market interest rate as well as the bond maturities.

For retail investors, practicality is very important. Duration matching requires constant shifting, whereas buying a single bond does not, over-immunizing notwithstanding.

1) If I have an investment horizon of five years, do I just buy a bond fund with a duration of five years and hold it for five years?

No, you have to shift some money from your bond fund to a shorter-term fund or money market as you move along.

2) If I have an investment horizon of five years, do I just buy an individual bond with a duration of five years and hold that bond for five years?

No, you have to sell some small pieces from your bond every year and balance it with a shorter-term bond or money market as you move along.

3) If I have an investment horizon of five years, do I just buy an individual bond with a maturity of five years and hold that bond for five years?

Yes, that will work. Put the interest elsewhere.

You use different tools for different purposes.
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Postby linuxizer » Sat Oct 17, 2009 4:39 pm

danbek wrote:But I think you made some other statements on the other tread that could be interpreted as:

* If you need the money in 10 years, using a bond fund with duration 5 years is totally fine, and will be totally fine until the day you need the money.

I think that *this* reading of your beliefs what RobG is reacting against.

RobG,

I think we've now clarified that linuxizer doesn't believe what you thought he believed. No how about that individual bond strategy for people accumulating savings for retirement?


If I said things in the other thread that could be interpreted that way, then that was not my intent. Sorry about that. Logically, if duration>=investment horizon is what you need to immunize, then that should always be the case, even as your investment horizon narrows. I am not sure that the differing views held by RobG (and others) and I (and others) are the result of a miscommunication, however, given his statements about bond funds losing money as you shorten the duration: "You can gradually shift over but in a rising rate environment you will lose." That is a direct contradiction of what I have tried to show here. I am happy to be proven wrong and learn from it, but as of yet no such proof has been forthcoming.

I can answer the question which you post to RobG, although obviously I cannot speak for him and his perspective on this may be different. Just take a rolling bond ladder of intermediate duration and keep rolling it over as bonds expire. You now have what is essentially an IT bond fund.
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Postby Jack » Sat Oct 17, 2009 5:01 pm

tfb wrote:3) If I have an investment horizon of five years, do I just buy an individual bond with a maturity of five years and hold that bond for five years?

Yes, that will work. Put the interest elsewhere.


But this is also true.

linuxizer wrote:I have no problem with you claiming that changing your average duration by slowly shifting from an IT fund to an ST fund is complicated, because it is your opinion. I do think it is disingenuous to suggest that an individual bond does not suffer from the same problem, as I have tried to illustrate above. The only reason it does not appear complicated is that you are investing substantially more than necessary to get your guaranteed return of principal if you invest so that the bond matures when you need the money rather than has a duration of when you need the money. When you throw extra money at the problem, the problem disappears, but that does not mean it is an optimal solution.

To be honest you must be willing to admit that the simple strategy is not optimal and you are paying for that simplicity. There's nothing wrong with preferring simplicity as long as one recognizes the cost of that simplicity. The fallacy occurs when people claim that they prefer the simple method because it has lower risk. That is mathematically incorrect. In fact, simplicity is one of the reasons some people prefer bond funds but I don't think anyone has claimed that a bond fund has no costs.

Simplicity and costs are not really at dispute. What is at dispute is the fact that both strategies have similar risk. One is not necessarily better than the other because of lower risk.
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Postby linuxizer » Sat Oct 17, 2009 5:08 pm

tfb wrote:For retail investors, practicality is very important. Duration matching requires constant shifting, whereas buying a single bond does not, over-immunizing notwithstanding.

1) If I have an investment horizon of five years, do I just buy a bond fund with a duration of five years and hold it for five years?

No, you have to shift some money from your bond fund to a shorter-term fund or money market as you move along.

2) If I have an investment horizon of five years, do I just buy an individual bond with a duration of five years and hold that bond for five years?

No, you have to sell some small pieces from your bond every year and balance it with a shorter-term bond or money market as you move along.

3) If I have an investment horizon of five years, do I just buy an individual bond with a maturity of five years and hold that bond for five years?

Yes, that will work. Put the interest elsewhere.

You use different tools for different purposes.


That's a nice summary. Continuing on,

4) What if I have exactly $X saved for college and with interest I will just make my target--I can't afford to put the coupons somewhere else. Is my only option investing in two bond funds and keeping the average duration equal to the time remaining by rebalancing?

No, you can buy a zero-coupon bond instead. Since the maturity of a couponless bond equals its duration, you will have exactly enough when the time comes.

5) I don't know when I will need this money (or I won't need it for a long time, or I don't know exactly how much I need but I'm well over how much I need). Do I need to worry about losing principal in a bond fund if the market moves the wrong way?

No, as long as you keep the duration equal to or shorter than your need for the money if you ever see a point at which you want to be withdrawing a lump sum. Buying an individual bond, holding a portfolio of bonds that you roll over yourself as old ones mature, or buying a bond fund are all perfectly acceptable alternatives in this situation. Each has advantages and disadvantages which matter but which are fairly small in magnitude.
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Postby Oicuryy » Sat Oct 17, 2009 5:29 pm

Let me see if I understand how immunizing would work with bond funds. Say I want $100,000 in 2020. So I want a bond fund portfolio with a duration of 11 years.

Long-Term Investment-Grade (VWESX) has a duration of 12.3 years and an SEC yield of 5.64. Intermediate-Term Investment-Grade (VFICX) has a duration of 4.9 years and an SEC yield of 4.31. If I split my investment 82% in VWESX and 18% in VFICX then the duration of my portfolio is 11 years.
.82*12.3+.18*4.9=11

Do I use the same formula to calculate the yield of my portfolio?
.82*5.64+.18*4.31=5.4
Then discount my $100,000 goal by 5.4% for 11 years.
100000/(1.054^11)=56069
I invest a total of $56,069 today; split $45,977 in VWESX and $10,092 in VFICX.

Every so often (quarterly? yearly?) I recalculate what my split between funds needs to be to keep my duration equal to the years remaining to 2010, and rebalance to that split. At some point I will need to add a short-term fund to the mix and maybe eventually a money market fund.

If none of the other risks show up, I can be confident that my portfolio will be worth $100,000 in 2010 no matter how interest rates (and my portfolio value) bounce around between now and then.

Does that sound right?

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Postby linuxizer » Sat Oct 17, 2009 5:55 pm

Oicuryy wrote:Let me see if I understand how immunizing would work with bond funds. Say I want $100,000 in 2020. So I want a bond fund portfolio with a duration of 11 years.

Long-Term Investment-Grade (VWESX) has a duration of 12.3 years and an SEC yield of 5.64. Intermediate-Term Investment-Grade (VFICX) has a duration of 4.9 years and an SEC yield of 4.31. If I split my investment 82% in VWESX and 18% in VFICX then the duration of my portfolio is 11 years.
.82*12.3+.18*4.9=11

Do I use the same formula to calculate the yield of my portfolio?
.82*5.64+.18*4.31=5.4
Then discount my $100,000 goal by 5.4% for 11 years.
100000/(1.054^11)=56069
I invest a total of $56,069 today; split $45,977 in VWESX and $10,092 in VFICX.

Every so often (quarterly? yearly?) I recalculate what my split between funds needs to be to keep my duration equal to the years remaining to 2010, and rebalance to that split. At some point I will need to add a short-term fund to the mix and maybe eventually a money market fund.

If none of the other risks show up, I can be confident that my portfolio will be worth $100,000 in 2010 no matter how interest rates (and my portfolio value) bounce around between now and then.

Does that sound right?

Ron


That sounds right, but I'm not sure about how one would go about calculating the exact interest rate you will get out of the portfolio over time. It's an excellent question--how do you work backwards to get the interest rate you are guaranteed (barring yield curve shifts) to achieve, and therefore the amount you need to invest to exactly achieve your goal?

My sense is it will be the money-time-weighted, weighted average of the two funds, if that makes any sense at all :-). As a simple example, assume you spend half your time 75% IT and 25% MM, then half your time 100% MM, and the IT rate is 10% with a MM rate of 5%. Then you will have spent half the time at (.75*10+.25*5=8.75%) and half your time at 5%. But the second half has more money sitting at that interest rate, because all the prior coupon payments have built up and are now earning interest. So you need to weight by the amount of money you are spending in each time period.

My guess is that the method you used winds up in the right range (possibly a little on the high side, since your LT allocation has nowhere to go but down), but I will see if I can find the formal answer somewhere, or take my usual approach to such problems, which is to simulate them until a pattern emerges :shock: .

And yes, I freely admit that this is complicated, but you have the same problem with individual bonds if you want to exactly meet your obligation. Hopefully there will be some good ballpark formula here, perhaps even in a newer edition of Fabozzi. Even if not, this is all somewhat academic, as for most purposes with individuals, guessing at your liabilities works just fine. "The beauty of simplicity" indeed.
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Postby RobG » Sat Oct 17, 2009 6:11 pm

linuxizer wrote:
RobG wrote:Linuxer, even the BH wiki says that if you need the money at a certain date then a non-rolling ladder is the way to go. (For me it would make sense just to buy a single bond, or a zero if you must). Actually, on the last thread I was chastised for suggesting anyone here had a different opinion, yet you persist. That is not to say that indi-bonds is the only way to go.

Why don't you give Orman's show a call and describe your procedure? I'm sure she will have a field day with it.


Hi Rob,
The bar keeps moving. Before, you claimed:

"My point is that a bond fund has potential to lose more money than holding individual bonds. This occurs because you have to sell longer term funds to shorten your duration."
"Actually there is a good portion of people who point out that you can lose principal as you shorten the duration (e.g. going from long to intermediate) during a rising rate environment. This won't happen if you buy the individual bonds since they shorten the duration automatically."
"You lose when you make the jump from the long to short fund. For example, say you are in the long term index with a duration of 12.1 years and you want to switch to intermediate (duration 6.3 years). If the interest rates jump 1% the LT fund will drop 12.1% and you will be buying into a fund that only dropped 6.3%. You just had 6% of your money vaporize as you were trying to shorten the duration - something that wouldn't have happened if you just owned a single bond matched to your need. You can gradually shift over but in a rising rate environment you will lose."

I believe I have addressed these assertions. Do you still believe them to be true?

I later acknowledged (in that thread, that part you left out for obvious reasons) that you could probably come up with a scheme that would work, but that it would be complicated. I don't appreaciate you suggesting otherwise. That said, I do not see how your scheme could work. It seems to fall apart with simple tests, such as a long term bond fund and a money market to duplicate the results obtained by a single bond somewhere in between.

FWIW, I jumped into the conversation to counter two points. 1) a bond fund equals a rolling ladder (although you might get similar results). 2) Holding a bond fund with X duration for money you need in X years is a safe as holding indi bonds.
Last edited by RobG on Sat Oct 17, 2009 6:33 pm, edited 1 time in total.
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Postby linuxizer » Sat Oct 17, 2009 6:32 pm

RobG wrote:I later acknowledged (in that thread, that part you left out for obvious reasons) that you could probably come up with a scheme that would work, but that it would be complicated. I don't appreaciate you suggesting otherwise. That said, I do not see how your scheme could work. It seems to fall apart with simple tests, such as a long term bond fund and a money market to duplicate the results obtained by a single bond somewhere in between.

FWIW, I jumped into the conversation to counter two points. 1) a bond fund does not equal a rolling ladder (although you might get similar results). 2) Holding a bond fund with X duration for money you need in X years is a safe as holding indi bonds.


Your acknowledgment that one could construct a similar portfolio using funds or directly-held bonds is here:
"Assuming we throw out the principle of investing in bond funds because it is simpler, I expect that you can come up with a scheme that will mimic a ladder - but that is a long ways from saying a (single) bond fund is a ladder. And it is a long ways from saying a bond fund (or even a group of bond funds) is no different than owning individual bonds.
Mimicking a particular duration with a mix of funds may or may not work - funds on either side of a maturity are not equal to that maturity because interest rates do not rise uniformly across the ranges.
The difference may be relatively small, but that argument is not the one that is being made. "


Your next pertinent post was:
"I don't understand. I did a calculation earlier. Everything is fine until you need to cash in the bond fund.
Here is another thought example: Buy a 10 year Tsy note for $1000 and spend the coupons. You will have $1000 at the end of ten years.
Invest $1000 in a bond fund and spend the coupons. You don't know how much you will have in ten years. Obviously the bond fund is more risky. You can't know the end point by mixing bond funds to synthesize a declining duration bond either.
(Investing the coupons doesn't reverse this - both will invest at the current rate)."


So your acknowledgment was limited to only the reinvestment/rolling phase, and you returned to your claims of bond funds being risky (with an example whose duration exceeded the time horizon for most of its term).

You then somewhat graciously acknowledged:
"The bond fund = indi bonds argument falls apart as soon as you need to start drawing principal. This is not a special case; it is what every portfolio is designed for!
Now if you want to say that a big kludge of bond funds updated daily to shorten the duration as you get older (zero coupons apparently help too) can be made to give the same performance as a individual bonds, I'm with you all the way. Wink"

The first half of which sounds like the same argument, and the second half of which sounds like your conceding that the "scheme" could work but would be complicated.

But wait, the next post is:
"My point is that a bond fund has potential to lose more money than holding individual bonds. This occurs because you have to sell longer term funds to shorten your duration."

And the one after that:
"This is just saying that bond funds have more risk, which was my point. You can't tell in advance if you will gain or lose."

It is a personal point of pride that I do not misquote people, even by selective quotation or taking their words out of context. I do not believe I have done so here.

As for your questioning how it could be true given the gap between ST and IT/LT interest rates, I am very interested in exploring this point. Fabozzi seems to be pretty clear that short-term rates will be lower in his explanations, but he conveniently omits it in his examples, presumably for simplicity's sake. I will try simulating it and seeing if we can learn more when I have time. My guess for now is that it doesn't matter as long as the gap remains constant when the interest rate changes (i.e. the yield curve is still shaped the same way). If that is not what you meant but instead you meant that a LT/MM combination fails to achieve the same average returns starting out as a bond portfolio, then of course it does. That's because it is a sub-optimal combination to begin with. If you want a duration of 10-years when LT is 11 years' duration, IT 5, ST 2, MM 0, why on earth would you construct your portfolio to be 91% LT 9% MM instead of 83% LT, 17% IT?
Last edited by linuxizer on Sat Oct 17, 2009 6:41 pm, edited 1 time in total.
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Postby RobG » Sat Oct 17, 2009 6:34 pm

Your problem is obviously with me. Have a nice day.
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Postby linuxizer » Sat Oct 17, 2009 6:43 pm

RobG wrote:Your problem is obviously with me. Have a nice day.


It's really not, and I'm sorry if it feels like I am attacking you. I have no desire to do so, truly.
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Postby RobG » Sat Oct 17, 2009 9:39 pm

I got to thinking, and this idea can't possibly work like a individual bond because it fails in a simple example: consider the case were the scheme works perfectly until the very last transfer from the LT bond to the ST bond. The final value will fluctuate in accordance with the fluctuation of the LT bond value. I'm sorry, this can't possible be as "safe" as an indi bond.

Don't get me wrong, there is nothing terribly wrong with this method; I would have no problem recommending it to anyone. On the other hand, it does not appear to be equivalent to buying bonds that will mature exactly when you need them.

I should also point out that I feel bond funds of appropriate duration are perfectly fine. I'm certainly not trying to instill fear in people! I'm just trying to challenge the two common assertions that I listed earlier.

rg
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