please critique hypothesis re mutual bond fund
Rich Franzen
invested in a bond fund. Also assume that the bond fund is part of a Roth
IRA, with maybe $1000 per year going to that fund from after-tax income.
What annualized rate of return should be applied to this investment,
assuming there are no withdrawals during the monitored period?
My hypothesis is this:
Long term annualized rate of return approaches
the annual income rate of the bond mutual fund.
I had been assuming that the proper value was "total return". However, this
led to a problem. Sometimes the annual total return rate can be negative,
even though there was significant bond income earned. The next or previous
year total return will then tend to be artifically high. Graphing such an
investment led to a permanently shifted decrease in value when in fact no
money had been lost. (Negative returns have a stronger weight than positive
returns.)
I am using the Vanguard ® VBIIX fund within a spreadsheet model. The first
pass at this model used an arbitrary value, and it was too low. People
justly criticized that part of the model. Thus I chose to use the actual
rates from VBIIX for past years. For future years I use a total return of
7.5% and an income return rate of 6.75%. Before I republish my spreadsheet
model, I would appreciate a sanity check from you-all concerning my
hypothesis and these numbers.
Raw data from Vanguard for VBIIX may be seen here:
http://flagship3.vanguard.com/VGApp/hnw/FundsPerformance?FundId=0314&FundIntExt=INT
My in-context remarks concerning this hypothesis, along with a derived rate
chart, may be seen here:
http://dbatitan.home.att.net/vp/vl10.html#bondFund
I have two related questions relating to taxes on this sort of investment:
1) Remember the modeled fund is in a Roth IRA.
At what age does the new income being earned by
the bond fund become taxable?
2) Assume the investor is middle class and was able
to intelligently build up a nest-egg over time.
Further assume there was no long term family
illness or other major loss which depleted this.
Also assume no state income tax, and no significant
changes to federal tax law.
What would be an educated guess as to the tax
bracket this individual would be in at
retirement?
I currently use 67 as the "tax" age, but I do not remember where that number
came from. I also use 20% as the tax bracket, chosen quite arbitrarily.
Thank you for all comments and answers.
-- Rich
--- http://rocq.home.att.net
__________________________________________________
Do You Yahoo!?
Yahoo! Autos - Get free new car price quotes
http://autos.yahoo.com
Beliavsky
>
> Long term annualized rate of return approaches
> the annual income rate of the bond mutual fund.
The more credit risk the bond fund takes, the worse this assumption is. High
yield bond funds have higher yields than investment grade bond funds, but also
have much higher default risk.
To estimate the income you will actually receive from the fund, you need to
forecast the default rate of its bonds, which is not easy. Professor Altman of
New York University has studied default rates.
Your assumption will also overestimate the return of mortgage backed securities
MBS (what the Vanguard GNMA fund invests in), because it ignores prepayment
risk. If interest rates fall, your high-yielding MBS will be called away as
homeowners prepay their mortages.
A conservative approach to estimating the 20-year future return of bonds is to
look up the yield of a 20-year zero-coupon Treasury. Barron's publishes
zero-coupon yields in the Market Lab section. You may be able to do better than
this, but you have to take credit or prepayment risk to do so.
>For future years I use a total return of
>7.5% and an income return rate of 6.75%.
Since the VBIIX fund has a current yield of
5.75%, I think that assuming an income return of a bit less than 5.75% (there
are corporates in the fund) and a capital gain of zero is more realistic. If
the yield of VBIIX rises a full 100 bp to 6.75%, you will have a substantial
capital LOSS.
beli...@aol.com
about the VBIIX fund you are asking about, noting that the fund has
recently underperformed the Lehman Brothers 5-10 Year
Government/Credit index because it has held on to bonds with credit
downgrades longer than the index has. This underlines the fact that an
even an investment grade bond fund has credit risk, which will eat
into the income return.
======================================= MODERATOR'S COMMENT:
In the future please consider including a BRIEF portion of the message to which you are responding so that other readers are aware of the discussion. -HWW
Rock
Thank you for the informative response. Hopefully somebody else will
answer my two related questions associated with taxes.
beli...@aol.com (Beliavsky) wrote:
> >For future years I use a total return of
> >7.5% and an income return rate of 6.75%.
>
> Since the VBIIX fund has a current yield of
> 5.75%, I think that assuming an income return of a bit less than 5.75% (there
> are corporates in the fund) and a capital gain of zero is more realistic. If
> the yield of VBIIX rises a full 100 bp to 6.75%, you will have a substantial
> capital LOSS.
I didn't specifically state what my goal was. As part of my Visible
Policy site, I compare my participating whole life policy with a "buy
term and invest the difference" (BTID) strategy. In my first pass, I
made up a return rate for the investment portion, 6%. People
criticized this choice as being too low, and I think they were right.
Thus, since it is my real whole life policy being documented, I
decided to compare it against some other real investment. This time I
would rather err on the high side than the low. The actual average
income for the last 6 years for VBIIX was 6.69%. I rounded this up to
6.75 as an estimate for future years.
If it is too high, good. The dividend scale assumed for future years
on my policy is calculated from NYLIC's policy illustration, given to
me over 6 years ago. This year NYLIC lowered the scale slightly. So
if my projected policy return will be too high for some years, it is
better that future BTID return be too high as well.
Originally I was planning on modeling with the PIMCO PTRAX fund. I
was familiar with it because it is part of my 401k portfolio. My
charts showed how awfully a negative total-return year affected long
term BTID results. The one bad year results in a permanent shift
downward in that curve, when in fact no loss occurred. People would
still assume I was pimping for NYLIC, intentionally making the BTID
strategy look bad. Researching, I saw that Vanguard, unlike PIMCO,
documents the underlying income element of their funds. The two PTRAX
equivalents offered by Vanguard seemed to be VBIIX and VFICX. Since
VBIIX has done slightly better on past years, I chose it.
-- Rich
--- The Visible Policy
---- http://dbatitan.home.att.net/vp
(PS: Sometimes paper losses are NOT real losses. ;)
Tad Borek
> I didn't specifically state what my goal was. As part of my Visible
> Policy site, I compare my participating whole life policy with a "buy
> term and invest the difference" (BTID) strategy.
>
> Originally I was planning on modeling with the PIMCO PTRAX fund. I
> was familiar with it because it is part of my 401k portfolio. My
> charts showed how awfully a negative total-return year affected long
> term BTID results. The one bad year results in a permanent shift
> downward in that curve, when in fact no loss occurred.
That shouldn't be unless the loss persists because of defaults,
trading by the fund, a long period when the fund's category faces
an unfavorably-changing yield curve, etc. The subsequent rebound
in NAV would make up for it, and if it doesn't, then there is an
actual loss, and that permanent shift downward is "correct."
For an extreme example look at FAHYX, which is essentially a
junk-bond fund - in that type of fund you expect big changes in
NAV and it's a significant part of your return (in both
directions). It may be realized - buy a bond for 70 cents on the
dollar, sell it for 30 cents - that money's gone.
If the NAV drops are introducing inaccuracies, it might be an
issue of your data source, not a problem with total return
figures generally. You could simplify this and just pick an
average annual total return over the period, or even use those
historical total return figures.
-Tad
Rock
> Rock wrote:
>
> > The one bad year results in a permanent shift
> > downward in that curve, when in fact no loss occurred.
>
>
> That shouldn't be unless the loss persists because of defaults,
> trading by the fund, a long period when the fund's category faces
> an unfavorably-changing yield curve, etc. The subsequent rebound
> in NAV would make up for it, and if it doesn't, then there is an
> actual loss, and that permanent shift downward is "correct."
> issue of your data source, not a problem with total return
> figures generally. You could simplify this and just pick an
> average annual total return over the period, or even use those
> historical total return figures.
Tad,
I thought it was an accepted fact that negative years weigh more
heavily than positive years. All my curves have demonstrated this.
Since I cannot put curves here, let me give, by example, four series
of investments:
10,000 * 1.07 = 10,700
10,700 * 1.07 = 11,449
11,449 * 1.07 = 12,250
12,250 * 1.07 = 13,108
13,108 * 1.07 = 14,026, average annual rate = 7%
1.4026^(1/5) = 1.0700, true annualized rate = 7%
10,000 * 1.07 = 10,700
10,700 * 1.15 = 12,305
12,305 * 0.95 = 11,690 (-5%)
11,690 * 1.10 = 12,858
12,508 * 1.08 = 13,887, average annual rate = 7%
1.3887^(1/5) = 1.0679, true annualized rate = 6.79%
10,000 * 1.07 = 10,700
10,700 * 1.11 = 11,877
11,877 * 1.02 = 12,115
12,115 * 1.08 = 13,084
13,084 * 1.07 = 14,000, average annual rate = 7%
1.4000^(1/5) = 1.0696, true annualized rate = 6.96%
10,000 * 1.07 = 10,700
10,700 * 0.94 = 10,058 (-6%)
10,058 * 1.10 = 11,064
11,064 * 1.09 = 12,060
12,060 * 1.08 = 13,024, average annual rate = 7%
1.3024^(1/5) = 1.0543, true annualized rate = 5.43%
To me it is obvious that negative years apply a permanent hit to
overall return. There may be cases which do not act this way, but my
spreadsheet has not shown any yet. I think this is a common error
made by arithmetically challenged MLMs of a certain life insurance
product. They confuse average annual total return with true
annualized return, and end up with faulty conclusions. (Of course,
being taught faulty premises doesn't help them, either...)
If I am wrong, please let me know now!!
Concerning my model -- it begins in 1996, and for past years I am
using historical results. This is when the problem showed up. 1999
was a negative total return year for PTRAX and all of the other
high-quality bond funds I looked at. I am trying to get BTID to look
better than it did when I assumed a flat 6% rate for all years. The
hypothesis in this thread is in hopes of finding a way to use a real
fund fairly, yet not show a loss of principal when no money is
actually lost.
Annual total return rates do not give me this option. I have
convinced myself that "total return" is even the wrong concept for
this model. Total return involves a purchase price, a sell price, and
income in between. Since I am modeling no sells, "total return" is
already not applicable. There are 18 years of an annual out-of-pocket
investment and 58 overlapping years of quarterly reinvested bond
income. There are potentially 250 different purchase prices. This is
what led to my hypothesis. In the long term income counts much, much
more heavily than purchase and sell prices.
The comparison is with my whole life policy. It is now contractually
impossible for it to have a negative year, at least until 2032. Until
then, the annual increase in Guaranteed Cash Value (dGCV) will be
higher than the premium. Between the ages of 77 and 94, the internal
cost of insurance is so high that dGCV drops as much as $600 below
premium. Presuming I still have the policy then, I fully expect to
earn dividends and have other cash value increases. Contractually,
though, it is possible to have negative returns during those years.
Extremely untlikely, but possible.
Maybe I am trying to make BTID look too good. No problem. My whole
life policy model still "wins" in the long term, assuming a flat 6.75%
income rate for the BTID model. The win is only if the policy is
front-loaded with extra money ("OPP"). For the strategy illustrated
by NYLIC, with no OPP purchases and sell-backs of PUA to help pay for
premiums, BTID does win.
Geez, way past bed time. G'nite.
Tad Borek
> I thought it was an accepted fact that negative years weigh more
> heavily than positive years. All my curves have demonstrated this.
> Since I cannot put curves here, let me give, by example, four series
> of investments:
>
Oh, I see what you mean now. What you're calling the "average
annual rate" is definitely a distorted figure - in fact it's a
figure that isn't even worth calculating for the reasons you've
pointed out. The old example is a fund that drops 50% in year 1
then goes up 50% in year two - average return by this method is
zero, but you have only 75 cents on the dollar. So that figure
never figures into any "honest" calculations.
But notice that all your examples end with different FVs. If you
start with a given beginning & end value (say, $10,000 and
$14,026) then any stream of return figures in between will result
in the same average, annualized rate of return, by which I mean
IRR, or geometric mean. As long as you keep to that type of
calculation you won't see the permanently-eroded-NAV problem.
That's my point about the ebb & flow of NAV - as long as it's
recovered in a subsequent year, there's no distortion of your
returns. Taking your example:
> 10,000 * 1.07 = 10,700
> 10,700 * 1.07 = 11,449
> 11,449 * 1.07 = 12,250
> 12,250 * 1.07 = 13,108
> 13,108 * 1.07 = 14,026, average annual rate = 7%
> 1.4026^(1/5) = 1.0700, true annualized rate = 7%
And fixing your future value, with a loss-recovery in between:
10,000 * 1.07 = 10,700
10,700 * 0.87 = 9,309
9,309 * 1.09 = 10,147
10,147 * 1.29 = 13,108
13,108 * 1.07 = 14,026, average annual rate = (who cares?)
1.4026^(1/5) = 1.0700, true annualized rate = 7%
So you lost NAV in Y2, and that 29% year was when NAV recovered
(guess this is a looooong-term bond fund). The annual total
return figures you'd see reported are:
Y1 7%
Y2 (13%)
Y3 9%
Y4 29%
Y5 7%
And you'd read "the annual rate of return for this fund from Y1
to Y5 was 7.0%". This is accurate, you started with 10k and now
have 14,026, which means your return was 7%/year, though we don't
know how you got there.
The distortions would come if you computed the arithmetic mean
[Sum(return) y=1 to 5]/5. As long as you're not doing that it's
OK to work with the annual total-return figures, of course
reading the fine print to make sure that's what is being reported.
You can either keep a running sum, doing the annual calculations
to see how much money you have at the end of each year, or go
from one date to another using the geometric mean return (your
^1/5 figure). From your descriptions it sounds like you're doing
a running sum, which should work fine, and probably makes for a
more interesting data presentation.
Note also that you MUST use the annual total return figures, not
the income figures. In my example above, we don't know (or care)
where the returns came from - interest, appreciation, or both. In
a sense, the component figures are meaningless for a fund, and
your hypothesis is correct only for a Treasury held till maturity
(because of its zero default risk). Unless your modeled bond fund
is doing that (they're not) then the hypothesis you started with
would only sometimes be correct.
-Tad
Rock
> ... From your descriptions it sounds like you're doing
> more interesting data presentation.
I am, and it does. :)
> Note also that you MUST use the annual total return figures, not
> the income figures. In my example above, we don't know (or care)
> where the returns came from - interest, appreciation, or both. In
> a sense, the component figures are meaningless for a fund, and
> your hypothesis is correct only for a Treasury held till maturity
> (because of its zero default risk). Unless your modeled bond fund
> is doing that (they're not) then the hypothesis you started with
> would only sometimes be correct.
Hmmm, you outright disagree with the hypothesis. Beliavsky was not
really positive about it either. I gathered from his post that the
hypothesis might kinda-sorta hold for a high quality bond fund with
low credit risk. He also implied that the 6.75% rate I chose for
future years might be too high.
Both of you seem to be concerned about defaults and credit risk. I
certainly agree that it is an issue, but less so for high quality
funds than "high yield" funds. Net Asset Value (NAV) for a bond fund
is calculated daily, and it tends to change daily. On the high
quality funds, isn't the price variance almost always due to other
factors than defaults or even credit risk?
I'll make what is probably my last attempt to buttress the hypothesis:
Long term annualized rate of return approaches
the annual income rate of the bond mutual fund.
As I understand it, the ongoing price variance is primarily a result
of "relative value". There is probably a more formal term for this.
I'll explain what I mean by a simplified example. FUNDX currently
holds 500 bonds. It bought one of them 2 months ago from ABC Co. It
cost $10,000, matures in 7 years, and earns $200/qtr. Yesterday,
companies XYZ and LMNOP issued 7-year, $10,000 bonds of their own.
Those bonds are paying $225/qtr.
The existence of the new bonds has a relative effect on the asset
value of the ABC bond already within the portfolio. If FUNDX wanted
to sell the bond, it could not get $10,000 any more. It would have to
sell the bond at a reduced price, otherwise people would buy the new
bonds from XYX and LMNOP.
If the new bonds had been issued with an income of $150/qtr, the
relative value of the ABC bond within the portfolio would go up.
FUNDX could sell the bond for more than the $10,000 they paid for it.
Applying this logic and math to each fund within the portfolio, a new
NAV is calculated at the end of each trading day. Yet, shy of an
actual default, every bond in the fund is still earning the income it
is contracted to provide. If they do not sell the bond from ABC Co,
it does not matter in the long run that it may now have a value
somewhat less or more than the price paid for it. If they do sell it,
it is either a gain or a loss which will affect the eventual
earnings/share paid to the shareholders of the fund. Similarly, if
ABC Co did happen to go belly-up, this would also effect the
earnings/share.
Now, consider a long term shareholder, reinvesting his bond fund
earnings into the fund. What is his purchase price? He has paid many
prices. What is his sell price? He has not sold anything.
Over 50 years, many bonds within the FUNDX portfolio have been bought.
Many have been sold. Some may have actually matured or been called
early by the issuing company. And some may have become worthless.
In the end, what is left? My hypothesis says it is the income, not
total return, which matters in the long run. By extension, it implies
that the total return values reported by FUNDX become virtually
meaningless over this 50 year period.
If the shareholder did sell everything at the end of 50 years, total
gain could be calculated:
proceedsFromSell - outOfPocketInvestment
totalGain = ----------------------------------------
outOfPocketInvestment
I don't see how this quantity could map back to the annual total
returns reported by FUNDX. Each of their numbers depended on the
NAV's on the first and last trading days of the year. These are
really irrelevant to Mr. FiftyYearsNextMay, aren't they? What remains
relevant is the sum of all the incomes/share paid him (and reinvested)
over time.
Yes, his individual total return could finally be calculated. If the
hypothesis is true, this number will have a much closer relationship
to the underlying income earned than to numbers affected by transient
variances in relative value.
I admit I may be wrong about all this. If so, please explain how. I
am not on a quest to Be Right. Being wrong will mean I spend 10
minutes modifying a spreadsheet. I can handle that. :)
Beliavsky
>annual rate" is definitely a distorted figure - in fact it's a
>figure that isn't even worth calculating for the reasons you've
>pointed out. The old example is a fund that drops 50% in year 1
>then goes up 50% in year two - average return by this method is
>zero, but you have only 75 cents on the dollar. So that figure
>never figures into any "honest" calculations.
>What you're calling the "average
>annual rate" is definitely a distorted figure - in fact it's a
>figure that isn't even worth calculating for the reasons you've
>pointed out. The old example is a fund that drops 50% in year 1
>then goes up 50% in year two - average return by this method is
>zero, but you have only 75 cents on the dollar. So that figure
>never figures into any "honest" calculations.
I respect Tad Borek's knowledge of investing, but I often seem to disagree with
him :).
BOTH the arithmetic and geometric returns of an investment are important
attributes and worth calculating. In Markowitz (mean-variance) portfolio
optimization, you need to specify the mean return of each asset and the
covariances of the assets' returns. I think the mean return used should be the
average arithmetic return,
not the geometric return, because the return of a portfolio is a LINEAR
function of the returns of the underlying asset returns.
Let me illustrate this with an extreme example. Suppose there are two assets, a
risk-free 1-year bond paying 3% interest (say) and a
super-risky stock that will return either +200% or -98%, each with probability
50%. The geometric expected return of the fund is
(sqrt(3.00 * 0.02) - 1) = -75.5%, but the arithmetic expected return is 51%.
Even if you are a risk-averse investor, it makes sense to
allocate some money to this fund, say 10%. If you start with $1000, in a year
you are equally likely to end up with $929 or with $1227.
An asset with a terrible geometric return can be a good investment for part of
your portfolio, if the arithmetic return is high enough.
The more volatile an asset is, the more its arithmetic return will exceed its
geometric return. Using geometric returns as inputs
to asset allocation will overly bias you against volatile assets.
I think that in evaluating your overall portfolio, you should focus on the
geometric return, but for the components of your portfolio, arithmetic returns
are more important.
Rich Carreiro
> I'll make what is probably my last attempt to buttress the hypothesis:
>
> Long term annualized rate of return approaches
> the annual income rate of the bond mutual fund.
The truth of that statement depends on the behaviour of
interest rates and on the average duration of the bond
fund. If said rates generally oscillate around a fixed
point, your statement will be generally true. However,
if rates follow a trend, your statement will be false.
> Applying this logic and math to each fund within the portfolio, a new
> NAV is calculated at the end of each trading day. Yet, shy of an
> actual default, every bond in the fund is still earning the income it
> is contracted to provide. If they do not sell the bond from ABC Co,
> it does not matter in the long run that it may now have a value
> somewhat less or more than the price paid for it.
True, but they DO sell it. Take a look at the turnover figures
for bond funds.
> If they do sell it, it is either a gain or a loss
> which will affect the eventual earnings/share paid to
> the shareholders of the fund. Similarly, if ABC Co
> did happen to go belly-up, this would also effect the
> earnings/share.
Exactly. And that's why total return matters.
> In the end, what is left? My hypothesis says it is the income, not
> total return, which matters in the long run. By extension, it implies
> that the total return values reported by FUNDX become virtually
> meaningless over this 50 year period.
I would be more willing to agree with you if you stated
your hypothesis thusly:
"I hypothesize that over the long run the total return
of FUNDX will become insignificantly different from
the income-only return of FUNDX."
I prefer this form because it acknowledges that total
return is what actually matters, but then asserts that
over time total return will converge to the income-only
return.
By the definition of total return, total return is all
that matters (especially since your scenario assumes
the investor was reinvesting all distributions, not
living off the income thrown off). Given that all
distributions are reinvested, it doesn't matter (except
with regards to risk) what's in the portfolio. All the
considerations are exactly the same whether or not
FUNDX is a money-market fund, a bond fund, a
dividend-paying-stocks fund, or a futures fund. For
someone reinvesting all distributions and who doesn't
care about risk, total return completely encapsulates
the behavior of the fund since it tells you "if I have
$P worth of the fund today, how much of the fund will I
have in N years", which is all an investor like the one
you describe will care about.
The question is then "what is the total return of the
fund?", and so back to your hypothesis for bond funds.
I would agree with your hypothesis IF interest rates
were overall trendless (or at least trendless over the
50 year period in question). If that is the case, all
the capital gains and losses will roughly wash out and
you'll be left with just the income-only return, and so
your hypothesis will be roughly true.
However, if interest rates have a definite trend over
the period in question, the total return (which, by
definition, is what controls how much the fund will be
worth at the end of the period) could be drastically
different than the income-only return, and your
hypothesis will be false.
The duration of the bond fund matters as well. A fund
will a duration of 2 years will be far more likely to
have your hypothesis be true for it (regardless of what
happens to interest rates) than a fund with a duration
of 20 years.
> If the shareholder did sell everything at the end of 50 years, total
> gain could be calculated:
>
> proceedsFromSell - outOfPocketInvestment
> totalGain = ----------------------------------------
> outOfPocketInvestment
>
> I don't see how this quantity could map back to the annual total
> returns reported by FUNDX.
Not only does that quantity in fact "map" to the annual
total returns, it is EXACTLY what you'll get by
chaining the annual total returns together.
When a fund reports an annual total return of X for a
year, it is equivalently stating that someone who
started the year with P worth of the fund will end the
year with P(1 + X) worth of the fund. If the funds has
an annual return of Y the following year, you'll end
that year with P(1 + X)(1 + Y) worth of the fund, and
so on. So at the end of N years, you'll have:
N
Final Value = FV = P * Prod (1 + R[i])
i=1
The cumulative absolute gain is FV - P, or:
N
P * { [Prod (1 + R[i])] - 1 }
i=1
And the cumulative relative gain is then (FV-P)/P, or:
N
[Prod (1 + R[i])] - 1
i=1
which will be EXACTLY the same number as your
"totalGain" value above. That's how your totalGain
"maps" to the reported annual returns. This all
follows from the definition of "total return".
> Each of their numbers depended on the
> NAV's on the first and last trading days of the year. These are
> really irrelevant to Mr. FiftyYearsNextMay, aren't they?
Yes and no :) Yes, they are irrelevant in a trading
sense, but no, they are definitely not irrelevant
because they go into the computation of total return,
which is quite relevant (though I suppose that if you
took total return as a given, then you could consider
the NAVs irrelevant).
> What remains relevant is the sum of all the incomes/share
> paid him (and reinvested) over time.
But that depends on total return, To take a silly
extreme, let's say the fund held a single 5%, 100-yr
bond. You put $10,000 into the fund. Each year you
get paid your $500. In the 50th year, right before you
cash out, the company goes bankrupt and the bond (and
thus your fund holding) becomes worthless. Contrast
that to the scenario where the company doesn't go
bankrupt (at least until after you cash out :). In
both cases the income-only return was the same, but the
total return was significantly different. Are you
really going to say both outcomes are the same?
--
Rich Carreiro rlc...@animato.arlington.ma.us
Tad Borek
> Hmmm, you outright disagree with the hypothesis. Beliavsky was not
> really positive about it either. I gathered from his post that the
> hypothesis might kinda-sorta hold for a high quality bond fund with
> low credit risk. He also implied that the 6.75% rate I chose for
> future years might be too high.
For your next birthday buy yourself a copy of Ibbotson's "Stocks,
bonds, bills and inflation yearbook" - lots of interesting data
that will help you form an opinion about realistic long-term
rates. Some take the view that the best prediction of interest
rates is the current yield curve. Others say, the historical
average yield curve. Either way, it's fundamentally a guess...you
could certainly make a credible case for 4%, or 7.5%, or anything
in between.
> Both of you seem to be concerned about defaults and credit risk. I
> certainly agree that it is an issue, but less so for high quality
> funds than "high yield" funds.
>
> I'll make what is probably my last attempt to buttress the hypothesis:
>
> Long term annualized rate of return approaches
> the annual income rate of the bond mutual fund.
"...if the bond does holds all its bonds to maturity and none of
the bonds default or change credit rating over their entire life
and the yield curve is static for the entire holding period and
there are no redemptions from the fund and..."
It might be helpful to consider the differences between buying
bonds outright (and holding them to maturity) and buying bond funds.
As I said, your hypothesis is indeed correct for an investor
buying, say, a ten-year Treasury held till maturity. There will
be price fluctuations along the way but these will all net out in
the end. There's no default risk so you know you'll get your $10k
back at the end of the pipe.
Bond funds don't do that though - they don't simply buy bonds and
hold them till maturity. Sure, they hold some bonds to maturity,
but they do a decent amount of trading. If you look at a sample
of bond funds you'll see that turnover is quite high.
Why do they trade? Many reasons:
* attain a desired/mandated duration for the fund
* spitting out bonds that don't meet investment criteria for some
reason, such as a decline in credit rating
* raise money for redemptions, or invest new money
* make predictions about interest rate trends (not all do this)
* make predictions about creditworthiness of companies
* participate in an "desirable" issue
* align more closely with a benchmark
The net result of this trading manifests itself not only in your
distributions, but also in NAV changes. You hope it works in your
favor, but it might not.
In a managed fund or junk bond fund there are some clear examples
where NAV will drop irreparably, and so it's easy to see why
total return is the important figure. Lots of defaults, or bad
guesses about interest rate trends, can result in NAV drops that
never come back. You seem OK w/that.
You'll even see it in the investment-grade funds, even the index
funds. There was an article (WSJ?) recently about how many
(including Vanguard's Total-bond) had larger tracking errors over
the past couple of quarters. The problem is that there are
thousands of bonds in the Lehman Aggregate index (6,000+) and
they need to sample from these, they simply can't hold them all.
So if your fund was heavy telecom or energy (investment grade not
long ago) you took a hit. A hit to NAV, that is.
You'll see it in all funds for another reason: the net trend in
the yield curve over the holding period, relative to the fund's
duration (as set by its type - eg intermediate, long). This isn't
much of an issue with shorter-term funds, but definitely is there
for longer-term ones. Consider a bond fund purchased in the
mid-90s that had a relatively long duration, and sold today. You
should have seen quite a bit in appreciation along the way (which
may have been spat out as distributions, depends on how the fund
traded its holdings). So the net trend was in your favor, and you
benefitted through a higher NAV. Look:
http://quote.yahoo.com/q?d=c&c=%5Etyx&k=c1&t=my&s=vbltx&a=v&p=s&l=on&z=m&q=l
(VBLTX vs. ^TYX, which is the 30-year bond yield)
Conceptually, the same thing can happen over long holding periods
(2/82 long bonds yield 14.5% from auction price). Maybe there
will be a steady decline in long-term interest rates over the
next 25 years, or a huge increase - we don't know, both have
happened in the past. That will end up having a net effect on
returns (again: TOTAL returns) for fund holders, and the longer
term you fund's holdings, the more it will affect you. If you
only look to income, you won't see the net effect of rate changes.
-Tad
Tad Borek
> I respect Tad Borek's knowledge of investing, but I often seem to disagree with
> him :).
That's OK, this board, and life in general, would be boring if
everyone agreed all the time.
> BOTH the arithmetic and geometric returns of an investment are important
> attributes and worth calculating. In Markowitz (mean-variance) portfolio
> optimization, you need to specify the mean return of each asset and the
> covariances of the assets' returns.
<SNIP>
I think we agree more often than you think we do!
This thread has nothing to do with portfolio optimization...Rock
is trying to calculate the long-term returns of an investment in
a bond fund, based on the annual return data reported by
Vanguard. In that context the arithmetic mean of the Vanguard
data is meaningless, and would introduce errors into his
calculations.
We can come up with scenarios where we might look at the
arithmetic mean - this just isn't one of them. As I recall it may
even be improper for a mutual fund to advertise its returns based
on the arithmetic mean, because of the potential for distorting
your results.
-Tad
Rock
> ...
> I would be more willing to agree with you if you stated
> your hypothesis thusly:
> "I hypothesize that over the long run the total return
> of FUNDX will become insignificantly different from
> the income-only return of FUNDX."
>
> I prefer this form because it acknowledges that total
> return is what actually matters, but then asserts that
> over time total return will converge to the income-only
> return.
I could live with that as well. But I won't. I'll pretty-much
concede instead, and just use total return. Thanks (all) for the
interesting discussion!
For a sanity check on the hypothesis, I ran a comparison using rates
Vanguard provides for VBIIX:
1994 1995 1996 1997 1998 1999 2000 2001 2002.5
Income 5.32 7.81 6.47 7.00 6.63 5.95 7.41 6.69 2.67
TotRtn -2.88 21.07 2.55 9.41 10.09 -3.00 12.78 9.28 3.34
1994-2002.5 (all available data)
55.95 62.64 arithmetic sum
6.58% 7.37% average ( / 8.5 )
1.719 1.794 product
6.58% 7.12% geometric mean ( ^ 1/8.5)
1996-2001 (life insurance policy years)
40.15 41.11 arithmetic sum
6.69% 6.85% average ( / 6)
1.475 1.477 product
6.69% 6.71% geometric mean ( ^ 1/6)
I'll still use 6.75% rate on future years. It seems fair whether I
model with total return or income. (Wouldn't you know it! This
particular data set has a larger difference on the longer time. My
(amended) hypothesis would expect just the opposite.)
> > If the shareholder did sell everything at the end of 50 years, total
> > gain could be calculated:
> >
> > proceedsFromSell - outOfPocketInvestment
> > totalGain = ----------------------------------------
> > outOfPocketInvestment
> >
> > I don't see how this quantity could map back to the annual total
> > returns reported by FUNDX.
>
> Not only does that quantity in fact "map" to the annual
> total returns, it is EXACTLY what you'll get by
> chaining the annual total returns together.
Here I disagree slightly. The quoted total return periods are
calendar-annual (quarterlies sometimes available). Any given
individual investor has unique money-in and money-out dates, hence
unique prices, hence unique individual total return.
Extreme example:
An individual may have purchased $10,000 worth of a fund on May 2.
During that week there could have been a market distortion due to a
war scare or some other temporary event, and he paid 85 cents/share
higher than the weeks before or weeks after. The PUBLISHED total
return won't reflect his results. Yes, he can track his own results
from the point he started, as best he can. But all the published
numbers he sees will reflect a higher return than he personally
experiences, because he bought at an expensive point.
If he makes regular out-of-pocket purchase, this cost distortion will
tend to average out. Or, in the case of Mr. FiftyYearsNextMay, the
ongoing reinvestments will help average out his original high cost.
This is one of the reasons I wanted to factor out the price variance.
Buy and sell prices on the quoted returns seemed too arbitrary. The
other was to not have negative spikes -- they won't show up on the
life insurance curves (it just starts out extremely negative), and I
was trying to avoid charges of an unfair comparison.
> ...
> And the cumulative relative gain is then (FV-P)/P, or:
> N
> [Prod (1 + R[i])] - 1
> i=1
>
> which will be EXACTLY the same number as your
> "totalGain" value above. That's how your totalGain
> "maps" to the reported annual returns. This all
> follows from the definition of "total return".
Yes, but only with the proviso that one is able to supply a BUY adjust
factor and a SELL adjust factor to the annual total return numbers
provided by the fund. At that point, their numbers become personally
significant. Without these factors, what you have is a report of how
the fund is doing, not what your personal results were.
-- Rich
--- The Visible Policy (available now at a computer near you!)
---- http://dbatitan.home.att.net/vp
Rich Carreiro
> Here I disagree slightly. The quoted total return periods are
> calendar-annual (quarterlies sometimes available). Any given
> individual investor has unique money-in and money-out dates, hence
> unique prices, hence unique individual total return.
Absolutely true. My formula in that post will definitely
not give the proper total return when money is added to
or withdrawn from the portfolio during the computation
period.
But in your post you were talking about someone who made a one-time
investment and then never added anything new, only reinvesting
distributions. Or at least that's sure how it sounded.
And note that my formula is exactly true when all distributions are
reinvested, since distribution reinvestments are NOT "new purchases"
with respect to return calculations because they do not represent any
new money flowing into the portfolio.
Individual total return is completely determined by:
(a) Dollar balance at start of the computation period.
(b) Dollar balance at end of the computation period.
(c) Dollar amounts of deposits/withdrawals from/to the "outside"
to/from the portfolio.
(d) Dates of said deposits/withdrawals.
If you know that information and nothing else, you can faithfully and
truthfully compute the total return that the investor experienced.
See our earlier discussions on Internal Rate of Return... :)
--
Rich Carreiro rlc...@animato.arlington.ma.us
Rock
For a sanity check on the hypothesis, I ran a comparison using rates
Vanguard provides for VBIIX:
1994 1995 1996 1997 1998 1999 2000 2001 2002.5
Income 5.32 7.81 6.47 7.00 6.63 5.95 7.41 6.69 2.67
TotRtn -2.88 21.07 2.55 9.41 10.09 -3.00 12.78 9.28 3.34
Inc. T.R. 1994-2002.5 (all available data)
55.95 62.64 sum
6.58% 7.37% average (x / 8.5 )
1.719 1.794 product
6.58% 7.12% geometric mean (x ^ 1/8.5)
Inc. T.R. 1996-2001 (life insurance policy years)
40.15 41.11 sum
6.69% 6.85% average (x / 6)
1.475 1.477 product
6.69% 6.71% geometric mean (x ^ 1/6)
(In my last post, I didn't realize that the columns were not labeled.
Originally I had all of it laid-out in three columns, but at the
last minute decided to save vertical space on the raw data. When I
reformatted it, the original column labels were gone.)
I might as well add something new... Observe the Income averages
and means are the same for both periods. Whether this is a fluke
of the data or a mathematically determinate behavior, I don't know.
Michael Sullivan
> In a managed fund or junk bond fund there are some clear examples
> where NAV will drop irreparably, and so it's easy to see why
> total return is the important figure.
The one caveat is that looking at total return from bond funds in order
to predict the future is fraught with the same problems as using the
same data to predict stock returns. The last 20 years have seen mostly
declining interest rates. Most long bond funds have really impressive
total return figures about now for this reason. But long bonds are
approproaching historical lows. To get the same kind of returns in the
next 20 years that we had in the last 20, interest rates would have to
go negative, and I don't think any of us want to live in the economy
where that's a realistic prediction.
Similar with junk, which has a tendency to follow the stock market (the
market's guesses about credit risk of dicey issues is based on similar
information to its guesses about equity values). If we've had a really
bad year or three, junk bond fonds will have shitty total returns, but
that's as likely to mean good news for junk bonds in the future as bad,
just as low prices in the stock market are as likely to represent a
low-price buying opportunity as signal merely the tip of a total market
meltdown.
You certainly can't say "The market has lost between 10 and 20% the last
3 years straight, so that means it'll probably continue to do so
indefinitely..." Well, same with junk -- at some point, if the economy
recovers, the companies that are going to default have mostly done so,
and the ones that made it through are getting enough stronger to become
fair to good credit risk -- suddenly junk values go up a great deal.
I realize you know this, I'm just trying to flesh out what I think
you've left unsaid.
There is a way in which looking at yield is worth doing. What I'd like
to see published for bond funds is the historical difference between
yield and total return, because on average that might give you a
coefficient to use with yield to predict future results.
A short term fund that does very little or no trading and uses only high
quality issues should have right around a 1 (modulo expenses). A junk
fund that buys and holds will generally be less than 1, other funds that
trade a fair bit will have results that vary depending on how well they
traded on interest rate and credit risk fluctations.
Michael