CD vs. Bond Fund: what if no early withdrawal?

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Kevin M
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CD vs. Bond Fund: what if no early withdrawal?

Post by Kevin M »

I like Ally Bank 5-year CDs better than what I consider a comparable bond fund. At 1.74% APY they have almost twice the yield, no credit risk assuming one stays within FDIC insurance limits, no term risk no risk of change in nominal price at maturity due to change in interest rates, and a cheap put option--i.e., an early withdrawal penalty (EWP) of 60 days of interest (all yields and attributes as of today). However, a common concern is: what if Ally Bank changes the EWP or won’t let me do an early withdrawal? Fair question.

To evaluate this risk, I compare the total return of the CD to that of the bond fund under a variety of interest rate scenarios over the next 5 years; i.e., assuming I am unable to do an early withdrawal from the CD. A fairer comparison, assuming no early withdrawal, would be the PenFed 5-year CD currently yielding 2.25% (with a 1 year of interest EWP), but let’s assume I value the cheaper put option on the Ally CD enough to sacrifice the 50 basis points in yield (assuming no problem with early withdrawal, the Ally CD provides a higher return if you break it up until about 4 years).

I believe it’s reasonable to use the Vanguard Intermediate-Term Treasury Fund for a fair comparison. Like the FDIC-insured CD, it has no credit risk. The SEC yield is 0.89% (EDIT: for Admiral Shares), average maturity is 5.2 years, and average duration is 5.2 years. You might prefer to compare the CD to something like Total Bond Market Index fund, but that fund has credit risk, so it’s not a fair comparison; but even so, the CD reward/risk still is asymmetrical compared to the bond fund, and I’d be happy to share those numbers once any flaws in my analysis are uncovered and corrected.

I understand that there are other considerations that might cause one to favor the bond fund (e.g., convenience, simplicity, liquidity, etc.), but here I just want to consider the financial returns of CD vs. bond fund, in isolation (i.e., not how it contributes to overall portfolio return; consider a portfolio of 100% fixed income if it helps). Thus, the primary consideration is the term risk of the bond fund.

Scenario 1: Interest rates are flat for 5 years. CD beats bond fund by 4.3% ($10K grows to $10,901 vs. $10,453).

Scenario 2: Interest rates increase 1% per year for 5 years. CD beats bond fund by 19.5% ($10K grows to $10,901 vs. $9,122)

Scenario 3: Interest rates are flat for 2 years, then increase 1% per year for 3 years: CD beats bond fund by 16.7% ($10K grows to $10,901 vs. $9,344).

Scenario 4: Interest rates drop to 0% in year 1, then remain at 0% for 4 years: CD beats bond fund by 3.8% ($10K grows to $10,901 vs. $10,507). Note that this is the best-case scenario for the bond fund that I can find, and the CD still wins.

I’m using a simple model, with these simplifying assumptions.
  1. Bond fund interest rates change linearly, so annual interest portion of return is the average of the rate at beginning of year and end of year.
  2. Annual change percentage change in bond fund NAV = -1 x Duration x total annual interest rate change (EDIT: in percentage points). EDIT: Convexity not accounted for; i.e., current duration used for all calculations.
  3. Total annual return for bond fund is sum of 1 and 2.
  4. Total return is compounded annually
My intuition is that refining the model (making it more complex) won’t make a huge difference in outcome, but my intuition has been wrong before, so I welcome corrections and inputs about this. EDIT: This currently is my main interest; i.e., how big are the errors in using this simple model. Certainly the non-linear nature of the bond price/yield relationship (convexity) introduces some error, but how much? Enough to worry about? Even if we include convexity in the model somehow, are there other aspects of a bond mutual fund that introduce additional significant errors relative to a standard bond price/yield curve?

So it looks to me like the CD can win by a lot or win by a little, but it always wins. If you add some credit risk to the bond fund for a higher yield, then the bond fund can win by a little, but can lose by a lot (in relative terms).

So what flaws do you see in this analysis?

Kevin

EDITs 2/23/2012:
  • Changed a few things above based on what I've learned so far, and to make the statements more accurate or precise.
  • I still think the CD provides superior risk/return compared to the bond fund, but probably not as much as indicated by the model. Still looking for ways to improve the model.
  • Technical note: The duration used here is Modified Duration, not Macaulay Duration. I assume it's the former and not the latter that is published for bond funds, since it's the former that is used to estimate sensitivity of bond or bond fund price to yield change.
Last edited by Kevin M on Thu Feb 23, 2012 3:43 pm, edited 4 times in total.
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Re: CD vs. Bond Fund: considering term risk only

Post by RenoJay »

Kevin, I'm not as quantitative as you but for those of us in the "bond bubble" camp, your results are not surprising. I keep 75% of my fixed income in CD's right now (Ally, DiscoverBank and a local credit union) and the rest in more risky non-bond investments.
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

Some folks who post over at Ken's blog have been having issues with Ally of late. Un-posted interest, CSR problems, sort of runs the gamut. You might want to review the threads in both the blog and the forum (http://www.depositaccounts.com). Another issue is the rumor that Ally is being shopped. I have no accounts with Ally, personally.
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Re: CD vs. Bond Fund: considering term risk only

Post by Muchtolearn »

OP, this is all fine for amounts that are not that large. Many bogleheads have portfolios in the millions and don't want to deal with having 8 or 10 CDs with constant reinvestments, etc.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

I think this is good way to explore, reasonable assumptions, etc. I hope I can find time to look at it some more. I'm not clear on how you did the calculations, particularly scenario #2. Specifically, what did you assume was the interest rate in years 1, 2, 3, 4, 5, and what did you assume about the composition of the bond fund at the start of the five-year period? What coupon, etc. I'm not challenging you to refine the model down to any crazy level of authenticity, I'm just not sure I understand the model or how I'd reproduce the calculations myself.

My intuition, like yours, is unreliable, and my intuition, like yours, says a roughed in model like this should be quite good enough to show the nature of things. The question is: how sure are you that the fund really does shrink $10,000 to $9,122? I don't mean $9,122 as opposed to $9,235 or $9,060, I mean $9,122 as opposed to $9,800 or $10,100.

The other thing that's nagging at the back of my mind is that at the end of five years, if interest rates now stop rising, the bonds within the fund should have some stored-up spring in them due to the fact that they will rise toward their face value at maturity. But it seems as if the CD holder could just as well buy the fund at the end, at the depressed price, without having to buy it at the beginning for $10,000, so that doesn't change anything.
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Re: CD vs. Bond Fund: considering term risk only

Post by patrick »

What if ... interest rates surge in year 1, stay flat in the middle years, then plummet in the last year!
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Re: CD vs. Bond Fund: considering term risk only

Post by FrugalInvestor »

This is an intriguing question. I hope the analytically inclined will continue to refine the analysis.
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Re: CD vs. Bond Fund: considering term risk only

Post by tfb »

Not sure about the exact numbers but they are directionally correct.

As many times as nisiprius warned about not relying on the early withdrawal, I said the case for CDs doesn't depend on the early withdrawal. If you get it, great; if not, they still come out ahead.

When you compare to an intermediate term Treasury bond fund, the best case for the bond fund would be for rates to stay level to the end of 5 years and then immediately drop to 0%, giving the bond fund a boost. Even then, because of the yield gap during the 5 years, the bond fund at best breaks even with a 5-year CD. In any other scenarios, especially those with rates rising, for each blow, the fund is going to take 5 years to recover. Unless the blow happens immediately -- tomorrow -- there's no way for the fund to recover by the end of 5 years. Even when it recovers, it's recovering to the original state, as if rates didn't go up. That value is lower than the value of a 5-year CD.

When you compare to a different fund, say the total bond fund, the yield gap is smaller or negative (1.75% on Ally CD, 2.03% on VBMFX). In the best-case scenario -- rates level, sharp drop at the end -- the bond fund will be worth more than the 5-year CD.
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Re: CD vs. Bond Fund: considering term risk only

Post by linuxizer »

patrick wrote:What if ... interest rates surge in year 1, stay flat in the middle years, then plummet in the last year!
Easy enough to calculate:
http://www.bogleheads.org/forum/viewtop ... 10&t=79874
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

What do we think about a rise of 1% per year for five years? I'm thinking that might be extreme--or then again maybe not? It only happened during the period when it was being driven by double-digit inflation.

Here's the yield for ten-year Treasuries.
Image
Here's a chart of the difference in interest rates between the start and end of a five year period, plotted for the end of the period.
Image
A 5% difference means an average rise or fall of 1% per year. It certainly did exceed 5%, but only during the period of double-digit inflation.
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

nisiprius wrote:I think this is good way to explore, reasonable assumptions, etc. I hope I can find time to look at it some more. I'm not clear on how you did the calculations, particularly scenario #2. Specifically, what did you assume was the interest rate in years 1, 2, 3, 4, 5, and what did you assume about the composition of the bond fund at the start of the five-year period? What coupon, etc. I'm not challenging you to refine the model down to any crazy level of authenticity, I'm just not sure I understand the model or how I'd reproduce the calculations myself.
Initial rate for all scenarios is rate today: 0.89%. For each scenario, interest rate changes by 0% or +/- 1% each year (but minimum 0%), so for scenario 2, 0.89%, 1.89%, 2.89% ... The average rate for each year is the average of the start rate and end rate for that year, so for year 1 in this case it would be 1.39%.

No assumptions other than using current duration to estimate change in NAV; understand that duration vs. rate bond price vs. bond yield is not linear (convexity), but that's one of the simplifying assumptions. So change in NAV in each year in scenario 2 is -5.2%. So first year total return is 1.39% - 5.2% = -2.81%. Apply this to $10K in year 1, then compound that for year 2; repeat.

More later, gotta go make dinner :beer

Kevin
Last edited by Kevin M on Wed Feb 22, 2012 1:28 am, edited 1 time in total.
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

This thread has more than academic interest for me, so thanks to Kevin and all the posters. I'm facing re-balance this month (well, maybe I can procrastinate until March), and I should move roughly $70K - $75K in my IRA from stocks to bonds/CDs to get back to my desired AA. The path of least resistance is to just plop it into PenFed's 7-year IRA CD at 2.76% APY. I have two other IRA CDs there.

I probably wouldn't need the money for quite some time (EWP is not an issue in any event, since partial withdrawals are permitted in IRA CDs without penalty for old codgers like me), but I just haven't found a nice bond fund alternative. The thought of seeing a bond fund bleed as interest rates go up does not appeal to me, even though I understand "duration", "point of indifference", SEC yield, and all those nice concepts which should enable me to bite my tongue and wait for the fund to get back to black.

I just know that, every month, I would do the mental gymnastics and calculate what those bucks would be worth if just plopped in a CD.

Ideas?
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Re: CD vs. Bond Fund: considering term risk only

Post by FrugalInvestor »

john94549 wrote:This thread has more than academic interest for me, so thanks to Kevin and all the posters. I'm facing re-balance this month (well, maybe I can procrastinate until March), and I should move roughly $70K - $75K in my IRA from stocks to bonds/CDs to get back to my desired AA. The path of least resistance is to just plop it into PenFed's 7-year IRA CD at 2.76% APY. I have two other IRA CDs there.

I probably wouldn't need the money for quite some time (EWP is not an issue in any event, since partial withdrawals are permitted in IRA CDs without penalty for old codgers like me), but I just haven't found a nice bond fund alternative. The thought of seeing a bond fund bleed as interest rates go up does not appeal to me, even though I understand "duration", "point of indifference", SEC yield, and all those nice concepts which should enable me to bite my tongue and wait for the fund to get back to black.

I just know that, every month, I would do the mental gymnastics and calculate what those bucks would be worth if just plopped in a CD.

Ideas?
John94549,

I just checked their site and it looks like the no EWP provision expired for certificates purchased after September 1, 2007. I'm still unclear on partial redemptions, that may still be allowed with penalty.

From PenFed's site....
*Note that any IRA Certificates opened prior to September 1, 2007, can be redeemed before maturity without a penalty, if the Member is at least 59 1/2 years old. A penalty will be imposed for early redemption of an IRA Certificate that was opened or renewed after September 1, 2007, regardless of the member's age. This fee could reduce your earnings.
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Re: CD vs. Bond Fund: considering term risk only

Post by bdpb »

Kevin M wrote: Scenario 2: Interest rates increase 1% per year for 5 years. CD beats bond fund by 19.5% ($10K grows to $10,901 vs. $9,122)
Are you sure you're making a fair comparison? The duration of the CD will go down as time passes.
Did you reduce the duration of the bond fund or assume it will always be 5 years?
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

Frugal, PenFed allows partial withdrawals from IRA CDs without penalty for early withdrawal for those over 59 1/2. It's sort of buried in the fine print in the IRA Disclosures (available online) in XIII(4)(g)(3)(iv). It's not widely known, and is offered by very few financial institutions (StateFarmBank is another). A "partial withdrawal" is defined as any withdrawal which does not take the CD below the minimum balance required to open the CD in the first place, i.e., $1000. In plain English, if you have a $100K IRA CD, you can make a "partial withdrawal" in any amount (or amounts) such that your balance does not fall below $1000, and the remaining balance just clicks along at the same rate and term. In effect, it works just like a savings account paying whatever rate you got when you opened it.* Total liquidity, no penalty.

Cool, no?

*My two modest PenFed IRA CDs are at 3.5%. I could, if I wished, harvest some of the amount with no penalty (I'd pay income tax, of course). The point is, with the liquidity and no penalty, the IRA CDs operate just like an IRA savings account, but with a tad more interest. Well, more than a tad.
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Re: CD vs. Bond Fund: considering term risk only

Post by FrugalInvestor »

john94549 wrote:

Cool, no?
Yes, very cool john, and something I will be considering. Thank you for mentioning it.
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

bdpb wrote: Are you sure you're making a fair comparison? The duration of the CD will go down as time passes.
Did you reduce the duration of the bond fund or assume it will always be 5 years?
A CD bought directly from a bank has no duration, since the value does not change with a change in interest rates. A brokered CD would have duration similar to a bond as far as I can figure, but that's not what I'm comparing here.

No, I did not reduce the duration of the bond fund as interest rates rise, which would indeed occur due to convexity. As I mentioned in original post reply to nisiprius above (in garbled language which I will correct have corrected), I did not account for the non-linear relationship between bond price and yield, i.e., convexity, which is one of the simplifying assumptions of my simple model. It certainly would reduce the difference between CD and bond fund returns for an increasing interest rate scenario, but I do not know how significant the convexity impact would be. Would welcome inputs on a simple way to approximate this.

Thanks,

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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

Muchtolearn wrote:OP, this is all fine for amounts that are not that large. Many bogleheads have portfolios in the millions and don't want to deal with having 8 or 10 CDs with constant reinvestments, etc.
Acknowledged. As mentioned in OP, I understand that there are reasons not to go with CDs, but in this thread, really want to focus on the trade off of the term risk of the bond fund vs. none for the CD.

<begin thread detour>

But since I can't resist responding ... I do find the $250K FDIC insurance limit constraining for IRA accounts, but not for taxable accounts, for which there are a number of ways to go way above it (for me, living trust or POD with 4 beneficiaries gets me to $1M on top of the $250K for the IRA). Between PenFed and Ally I could hold $2M in taxable and $500K in IRAs. I could do this with 4 CDs if I wanted, but choose to use many more at Ally because they do not allow partial withdrawals. It's no big deal at all for me.

The FDIC limit on the IRA accounts is one reason I continue to hold about 50% of my fixed income in bond funds and money market funds.

For folks who want to hold multiple millions in fixed income, we're getting beyond the realm of the "retail" investor for whom FDIC insurance provides a free lunch. Although I do understand there are programs to manage this for the big players.

Constant reinvestments? You mean rolling over or rolling out the CDs in 5 years? This is a big deal?

<end thread detour>

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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

nisiprius wrote:I'm just not sure I understand the model or how I'd reproduce the calculations myself.
Maybe this will help. This is a snapshot of the formulas for the flat interest rate scenario:

Image

(Cell G5 should say "CD Rate")

For a scenario with rate increasing in year 2, the formula in cell B7 would be =B6+$B$4
The question is: how sure are you that the fund really does shrink $10,000 to $9,122? I don't mean $9,122 as opposed to $9,235 or $9,060, I mean $9,122 as opposed to $9,800 or $10,100.
You tell me. That's why I'm throwing this out there. It's a very simple model with simplifying assumptions. How much impact will convexity have (decreasing duration with increasing interest rates)? Are any of the other simplifying assumptions used to build this simple model throwing the projections off much? Is a simple model like this good enough to at least give us ballpark estimates of the differences in terminal values?

It seems reasonable to me, but I'd like to know if I'm way off.
The other thing that's nagging at the back of my mind is that at the end of five years, if interest rates now stop rising, the bonds within the fund should have some stored-up spring in them due to the fact that they will rise toward their face value at maturity.
Shouldn't duration and convexity capture this? Is there something about the way the bond fund is managed that will cause a big discrepancy relative to this simple model, even if we somehow build convexity into it? I don't know.
But it seems as if the CD holder could just as well buy the fund at the end, at the depressed price, without having to buy it at the beginning for $10,000, so that doesn't change anything.
Who's on first? Absolutely. What's the guy's name on first base? No, no--What is on second base. :lol: Sorry, that just popped into my mind when I read this.

http://www.youtube.com/watch?v=sShMA85pv8M

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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

john94549 wrote:Frugal, PenFed allows partial withdrawals from IRA CDs without penalty for early withdrawal for those over 59 1/2.
OK,this is another detour from the objective of the thread, but I guess that's just gonna happen, so I might as well join in the fun.

I actually verified this by phone with a PenFed rep before opening my first CD with them in October a year ago (7-year at 3.75%--seemed like a low rate at the time).

I was actually thinking I could use this feature to do a rollover with no penalty if rates were to rise much. Have only done trustee to trustee IRA transfers before (and have done many of those), and would be a bit nervous about doing a rollover, but would consider it. PenFed rep told me I could not use this feature to cash out the CD and have funds deposited into my PenFed IRA savings account, then roll it back into another CD; that would be way cool, but apparently you actually need to withdraw the funds from PenFed.

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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

nisiprius wrote:What do we think about a rise of 1% per year for five years? I'm thinking that might be extreme--or then again maybe not? It only happened during the period when it was being driven by double-digit inflation.
In mid-2007 the SEC yield on int-term treasury fund was about 5%, so it has dropped more than 4% in less than 5 years. Seems reasonable that it could rise by that much in 5 years. That's an increase of about 0.83 percentage points per year. Using that I come up with the CD being ahead by 16.7% (granted, the precision is overdone, so call it 15%-17%).

Obviously the smaller the increase in interest rates, the less the bond fund loses to the CD. That's why I want to look at various scenarios.

Forgot to mention in OP that I'm using numbers for Admiral Shares of the bond fund. SEC yield for investor shares is only 0.80%.

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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

I'm going to post a some inchoate and half-baked thoughts. I think I'm doing this in a spirit of inquiry. My mindset is that I am a VBMFX investor, I don't want to be bothered to do anything complicated and anxiety-provoking, and it troubles me not to stay the course, so of course I'm raising points consistent with that mindset. As evidence of partially open-mindedness I find that I'm brooding about how it might be done--most of my VBMFX is in a rollover IRA and I don't even know if banks offer traditional IRAs and whether transfers between rollover and "regular traditional" IRAs are possible. I expect I can convince/delude myself into doing nothing.

Overview:

I think Kevin M's analysis is overly slanted toward favoring CDs, and I think the soft spots from my personal point of view as a Vanguard Total Bond Fund (VBMFX) investor:
  • the question of what is actually in the bond fund's portfolio at the beginning of the five-year period, because at the start of the period it is going to contain some good old bonds issued before 2008;
  • what are appropriate assumptions for how fast interest rates might rise;
  • I don't think the "credit risk" differences between bank CDs, an intermediate-term Treasury bond fund, and a BarCap Aggregate bond index fund matter, it's different degrees of "negligible." So when it comes right down to it, I don't care about VFITX, I care about VBMFX. Your mileage may vary.
Point #1: Sensitivity to rate of interest rate rise.

I have a sloppy computer program of my own that I'm tinkering with and it might be buggy. It models a mutual fund as a laddered portfolio, composed of individual bonds issued at 1-year intervals, bought at issue, held to maturity, with each bond being rolled over into a freshly issued bond. I assume that reinvestment is done into the fund itself, that is that interest is used to purchase more of the current portfolio mix.

Assume that the fund starts with the prevailing interest rate at 0.89%, that all the bonds within the portfolio initially have yields of 0.89%. Assume ten-year bonds in the portfolio, which gives it an average maturity of 5 years and (I did this experimentally--I cranked in a 1% step-rise 1 month in and saw what happened to the value) an average duration of something like 4.65 years.

Assuming interest rates rise 1% per year, I'm seeing the value of a $10,000 investment drop to a minimum of $9,368.60 at 42 months, and then rise to $9,473.36 at 60 months, i.e. the end of the period. To me, this confirms Kevin M's calculation. I'm not in a situation to analyze the differences or stress over them, and as I say my calculation might be buggy, but it's the right ballpark. Under the stated conditions, the value of the bond fund falls by something like 5-10% at the end of the five-year period.

OK, but here's one thing. If I change that to an assumption that the interest rate rises only 1/2% per year, then the minimum value is $9826.10, reached at 36 months, and then it climbs to $9939.60 at the end of five years.

I don't want to debate what interest rate rise assumptions should be used--other than my suggestion, above, that 1% per year is pretty high. My point here is this. The strongest thing in Kevin's presentation is the robustness of the conclusions--CDs beat the bond fund under a nice basket of different, relevant scenarios.

And I'm saying that I think the model is quite sensitive to assumptions about how fast the interest rate rises. That's unfortunate, because it puts us back in the land of "maybe," since I don't think we want to make quantitative predictions about that.

By the way, yes, I do understand that a CD that matures and pays back deposit plus five years' interest is much better than a bond fund that starts at $10,000 and ends at $9939.60.
Last edited by nisiprius on Wed Feb 22, 2012 8:59 am, edited 3 times in total.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

Point #2--not a point, really, just looking at the structure of the problem.

If we ignore the possibility of breaking the CD, which are the rules we're playing under, then we are planning to buy a 5-year CD and hold it to maturity. Apart from the interest rate paid, this is no different from buying a 5-year bond and holding it to maturity. The fact that it is CD doesn't come into play directly. It comes into play only in the sense that CDs come from a world only open to small retail investors where they have an edge and get better rates than the big boys.

Suppose I proposed the following strategy to deal with current conditions. Pretend I own VFITX. I propose to sell $1000 of VFITX, with a current distribution yield of 1.46% and a current SEC yield of 0.80%, buy a five-year Treasury at current yield of 0.92%, hold it five years and buy back into VFITX when it matures.

Exit from the bond fund into a single five-year bond, then re-enter five years later.

What do you think of that? I know what I would think if someone proposed it. I'd think it was, hmm, maybe yes, maybe no, depends so much on assumptions. Even if someone could show that it prevailed under the sort of range of scenarios Kevin proposed, which I think is a decent set to look at, I'd still think it was pretty iffy and amounted at best to a "plausible market timing move." Too many questions. How do you know five years is the right number? Would anyone reading this thread seriously argue that "Bond fund to single bond for five years, then back" is a sure thing?

If we ignore the possibility of breaking the CD, the presumed superiority of CDs stands on two legs. Split the CD value into interest and return of principal at maturity. The CD is presumed to have

1) Higher interest rates, thus at the end of five years, you've collected more interest from the CD than you have the bond fund.

2) No interest rate risk; at the end of five years, besides the CD, you get back precisely $10,000 in principal whereas the bond fund has probably lost NAV.

Well, I think the second leg must be shaky, because if I reframe it using a single five-year bond instead of a CD, it suddenly sounds shaky. The key to the robustness of the argument is higher interest rates from the CD, not immunity to interest rate sensitivity.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

Point #3: what do we know from history? This isn't a very good point because I'm not at all clear what was really in the bond funds I look at, and because the time period I'm showing was devastating in real terms because it is the period that ends in double-digit inflation. (No matter how carefully I acknowledge that upfront, the "bonds are the suxx0rs" crowd always points out that "I didn't consider inflation...") but it speaks to the question of "how much could a bond fund lose, in nominal dollars, over a period of five years?"

I fully expect different people to interpret this data differently.

Here are two bond funds that existed during the period of rising rates, and the BarCap index which, alas, only started circa 1975. I do want people to play with the sliders themselves on the live chart, it's awfully hard to find a "fair" set of endpoints.
Image
Here's what I'm seeing. I think we can agree that the period shown, and particularly 1973-1981, represent an extremely severe interest-rate stress test. Within that period, there are some panic-inducing shocks, as in 1974 where the growth chart for Putnam Income A (PINCX) drops 14% and Fidelity Investment-grade Bond (FBNDX) drops 10%, and similarly in 1979-80, but they are short-lived--over in less than a year. I don't see any five-year periods in which you put invest X dollars into a bond fund and see a smaller number five years later.

I don't have a good proxy for CDs during that time frame.

The point here is that in the past, real-world combinations of conditions didn't seem to produce nominal dollar total-return losses in intermediate-term bond funds over five-year holding periods. For that to happen, it appears you need conditions that are more extreme then occurred during the "rising interest rate environment" leading up to 1981.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

[Added] See #cruncher's post below, I'm out to lunch on thinking distribution yield is relevant.

Point #4. What's the composition of the bonds in a bond fund and what interest rates are they and will they be paying?

I think it is a soft spot in Kevin M's analysis. I've argued that the "no interest rate risk" leg is shaky, because it sounds shaky if you reframe it as "exit from a bond fund into one five-year bond, then re-enter the bond fund five years later." The other leg is "CDs pay higher interest." Do CDs pay, are CDs going to pay better than bond funds? I think what's being missed is the presence of "good old bonds" within the bond funds.

This is one where I can really use some help though.

Write me down as someone who does not understand SEC yield. I do not want to use "SEC yield," I want to use "distribution yield," but of course I'm worried that I only want to do that because it's the bigger number. I just read the explanation in Annette Thau's "The Bond Book," and I still don't get it. I get the impression that SEC yield is not a meaningful number to me. It is designed to be a figure of merit for making a fair comparison between bond funds in the short term, and, specifically, a way to prevent bond fund managers from gaming the system and producing artificially high yield numbers by selecting bonds that have something or other about their NAV. Or something.

What I want is the interest payments from the bonds themselves.

If I look at the actual distribution numbers for Total Bond, and throw out the ones labelled as "capital gains," then I think I am left with the interest payments from the bonds themselves. But I'm not sure. What I do see is stable monthly dividend distributions of about $0.028 a month on a share price of about $11, or about 3% per year. That's about the same as the listed "distribution yield."

So, here are the distribution yield values for Vanguard Total Bond Index Fund (VBMFX) and Vanguard Intermediate-Term Treasury Fund (VFITX), for those distributions that are listed as "dividend" distributions:

Image

I think this shows something about the composition of the bonds in the fund--I probably need to figure out how to get something meaningful out of the "schedule of investments." I think these are the numbers that CD interest rates need to be compared to, and that the relevant number for VBMFX "about 3%, for now." I think what I'm seeing here is that the bonds VFITX have a shorter average maturity, and those bought in Ye Good Olde Days before about 2008 are maturing and being purged out of the fund, while VBMFX still has a fair amount of older, higher-interest bonds in it. If interest rates stay low, then VBMFX will continue to coast for a while at the higher rates and then start to decline.

If my interpretation is correct, then part of the picture is that if I were to swap VBMFX, specifically VBMFX, not VFITX, for a CD at this point in time, I'd be foregoing some number of in which VBMFX will continue to pay out 2-3% for a CD which pays somewhat less. Over a five-year period, VBMFX will likely start out paying more, end up paying less, and it's another shrug, who knows? comparison.

For me, it's clear that the appropriate comparison is VBMFX. Whatever its degree of credit and other kinds of risk, I've always been willing to accept in the past. If I'd decided to pull back from VBMFX to VFITX already, for whatever reason, then VFITX might be more appropriate, and VFITX might indeed be more comparable to a CD, but in that portion of my portfolio, the difference in "risk" elements between VBMFX and VFITX is not one I personally am willing to pay for.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

By the way, this is not intended as a rebuttal, but as an exploration. So, summarizing: I think Kevin's spreadsheet calculations are probably about right given the stated assumptions.

I think the hypothetical scenario of 1%/year interest rises is a pessimistic one, but what is more serious, I think the model is sensitive to how fast interest rates rise. The most appealing feature of Kevin's presentation is the robustness--CD's just win no matter what. But the more sensitive it is to assumptions, the less robust it is. I'm saying the rate of interest rate rise is highly uncertain, so the if the model is sensitive to that, the results of the model will also be uncertain.

I don't think the historical data for Putnam Income Fund and Fidelity Investment-grade Bond Fund, crude and such as they are, bears out the idea that $10,000 in an intermediate-term bond fund is likely to shrink to a lower number in five years.

I think the "CDs don't lose value to an interest rate rise" is shaky if you do not assume you might take advantage of breaking them, because if you reframe that strategy as "exit your bond fund in favor of a single five-year-bond, then re-enter five-years later," that amounts to the same thing--and it doesn't sound very convincing.

If you assume holding to maturity, the value of the strategy depends mostly on the assumption that CDs are going to pay higher interest than bond funds. I think that's likely to be true but not a slam dunk and not a huge difference, because a) in my case I'd be moving to CDs out of Total Bond, not Intermediate-Term Treasury, b) the bond funds contain older bonds that pay higher interest in them and will go on paying higher interest for a little while, c) the distribution yield for VBMFX is higher than CDs right now and I think that's going to last long enough to complicate the comparison.
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Re: CD vs. Bond Fund: considering term risk only

Post by moproblems »

Another important difference between CDs and treasury bonds is that with CDs the coupon is reinvested at the rate offered upon issuance whereas treasury coupons are reinvested at current rates. This has the effect of increasing duration for a given maturity (I dispute the notion that CDs don't have duration...illiquidity does not change the duration which is the same as a liquid bond offered with equivalent terms).

So a CD is really a zero coupon bond and, thus, the comparison should be between a CD ladder and a short term STRIPS ladder (ie treasuries which don't have coupons but are instead sold at a discount to face value)...except I don't think STRIPS are available with less than 10 year maturities (nor are CDs typically available with greater than 10 year maturities).
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

Nisi, the problem I have with plopping a goodly chunk of maturing IRA CD money (June is really creeping up fast; funny how the time flies) into a bond fund as opposed to a five- or seven-year CD is that I can't get a real good handle on my "point of indifference". I know I "should" be looking at intermediate-term bond funds with a duration of 5 and an SEC yield of 2% (or thereabouts) as a reasonable alternative to a five-year CD at 2%, but I can't wrap my arms around the idea that "duration" is a bit of a moving target. Not "duration" itself, mind you, but the idea that (in a rising-rate environment) you have to keep adjusting your expectations. Stated another way, that $100K you plop into VBMFX might be worth the same in five years as a 5-year 2% CD, unless, of course, rates go up more than once, then you take the (downwardly-adjusted) fund amount, start the duration clock all over again (with a new SEC yield), and so on.

So, I guess I'm a bit hesitant to roll the dice. I know I'd feel kind of stupid five years from now if a couple hundred thou had shrunk to, well, less, when it could have been a couple hundred thou plus compounded interest. Even if inflation rears its ugly head, that's more than beer money.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

john94549 wrote:Nisi, the problem I have with plopping a goodly chunk of maturing IRA CD money (June is really creeping up fast; funny how the time flies) into a bond fund as opposed to a five- or seven-year CD... So, I guess I'm a bit hesitant to roll the dice.
Oh, I certainly wouldn't suggest that anyone happy with CDs should exchange them for a bond fund. I don't mean for anything I say to sound like advocacy. I'm not saying "bond funds are better than CDs." I want to stick to Total Bond because I'm in it now and I'm hesitant to roll the dice. Approximately 5% of our portfolio is in CDs, mostly my wife's, and we have and will continue to roll those over--because we're hesitant to roll the dice. I have a strong presumption that the best thing is to do not to make changes, and the question I am asking myself is whether there's actually a case for switching from a bond fund to CDs that is strong enough to justify breaking that rule.
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Re: CD vs. Bond Fund: considering term risk only

Post by #Cruncher »

nisiprius wrote:Point #1: Sensitivity to rate of interest rate rise. I have a sloppy computer program of my own that I'm tinkering with and it might be buggy. It models a mutual fund as a laddered portfolio, composed of individual bonds issued at 1-year intervals, bought at issue, held to maturity, with each bond being rolled over into a freshly issued bond. I assume that reinvestment is done into the fund itself, that is that interest is used to purchase more of the current portfolio mix.

Assume that the fund starts with the prevailing interest rate at 0.89%, that all the bonds within the portfolio initially have yields of 0.89%. Assume ten-year bonds in the portfolio, which gives it an average maturity of 5 years ... Assuming interest rates rise 1% per year, I'm seeing the value of a $10,000 investment drop to a minimum of $9,368.60 at 42 months, and then rise to $9,473.36 at 60 months, i.e. the end of the period. ... OK, but here's one thing. If I change that to an assumption that the interest rate rises only 1/2% per year, then the minimum value is $9826.10, reached at 36 months, and then it climbs to $9,939.60 at the end of five years.
Nisi, I did a similar calculation and got results close to yours. Specifically I modeled the fund as equal weights of ten bonds: one maturing in 1 year, another in 2 years, up to the last one which matures in 10 years. As each one matures the proceeds are reinvested in a new 10-year bond, keeping the average maturity at 4.5 - 5.5 years. I get a value after 10 years of $9,425 assuming an initial 0.89% yield which rises 1% point per year. Both your figure and mine are somewhat higher than Kevin's $9,122. I also get a similar value to yours when assuming only a 0.5% point increase each year: $9,894.

Here are the figures along with similar ones using an initial yield of 2.20% which corresponds to the Total Bond Fund instead of the Intermediate Term Treasury fund:

Code: Select all

     0.89% (1)        2.20% (2)     Initial Interest Rate (SEC Yield)
  -------------   ---------------
   1.0%    0.5%     1.0%     0.5%   Annual % Point Increase
  -----   -----   ------   ------
  9,425   9,894   10,158   10,610   Value of $10,000 (Ten $1,000 bonds) after 5 Years
   -1.2%   -0.2%     0.3%     1.2%  Annual Return
Another thing my calculation shows is that the rolling ladder of 10 bonds is riskier over a 5-year period than simply holding one bond that matures at the end of the 5 years. This is because holding to maturity eliminates the interim interest rate risk.

Code: Select all

     0.89% (1)        2.20% (2)     Initial Interest Rate (SEC Yield)
  -------------   ---------------
   1.0%    0.5%     1.0%     0.5%   Annual % Point Increase
  -----   -----    -----    -----
  1,047   1,046    1,120    1,117   Value of One $1,000 bond after 5 Years
    0.9%    0.9%     2.3%     2.2%  Annual Return
By the way, Nisi, distribution yield is not a good measure of future performance of a bond fund. It overstates return if the fund holds bonds with coupons higher than prevailing interest rates. Extra cash is indeed rolling in, but the NAV of the fund falls as bonds selling at a premium approach maturity.

(1) Vanguard Intermediate-Term Treasury Fund Admiral Shares (VFIUX)
(2) Vanguard Total Bond Market Index Fund Admiral Shares (VBTLX)
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

#Cruncher wrote:By the way, Nisi, distribution yield is not a good measure of future performance of a bond fund. It overstates return if the fund holds bonds with coupons higher than prevailing interest rates. Extra cash is indeed rolling in, but the NAV of the fund falls as bonds selling at a premium approach maturity.
Ah. That's important. I think.
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Re: CD vs. Bond Fund: considering term risk only

Post by Doc »

Look at it the easy way.

It seems to me that the easiest way to make the comparison is between the 5 yr Cd with a YTM (?) of 1.74 and a 5 year Treasury Zero with a YTM of ~0.93. Both have a duration of five years if you define duration as the point of indifference. If all you care about is the return and not the correlation with the rest of the portfolio which is the premise of the discussion, you are done. Excel not required. (The individual bond vs. bond fund has been discussed many times and it's a simple trade off between e/r and convenience.)

I think this whole issue has less to do with if/when interest rates are going to rise but the fact that Treasury yields are artificially low because of Fed stimulus action. And that has to have a finite end. I think at least past 2014 has been mentioned. Solution to problem buy a two (or three) year CD or Treasury note.
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

I am somewhat convinced that the more I read and study (about bond funds), the more I am driven to "what I understand." I most assuredly understand the concepts of bond funds, but do I really "understand" them? I most assuredly do not. Bond funds seem to be subject to many variables, some of which I understand, most of which I do not.

Do I think it is worth the aggravation to deviate from something I really, truly, understand (read:compound interest)?

As paltry as CD rates might be these days, at least I can quantify the "paltriness".
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Re: CD vs. Bond Fund: considering term risk only

Post by tfb »

This thread shows how strong the status quo bias is. When something would touch the status quo, we are very good at finding reasons for maintaining it. Here we are talking about bonds and CDs, relatively simple, without as much uncertainty as stocks. Think how hard it is to make a change on the equities side. Mutual funds are more diversified than individual stocks? But I'm in Apple (or Berkshire Hathaway, or ...). Index funds outperform 80% of active funds? But I'm in Wellington (or Wellesley, Winsor, Primecap, or ...). People would change only *after* the status quo fails to deliver.

Now, to address some of the questions raised so far ...
nisiprius wrote:What do we think about a rise of 1% per year for five years? I'm thinking that might be extreme
Agreed. Possible but not likely.
nisiprius wrote:I don't even know if banks offer traditional IRAs and whether transfers between rollover and "regular traditional" IRAs are possible.
Yes they do and transfers are possible and routinely performed.
nisiprius wrote:I don't think the "credit risk" differences between bank CDs, an intermediate-term Treasury bond fund, and a BarCap Aggregate bond index fund matter, it's different degrees of "negligible." So when it comes right down to it, I don't care about VFITX, I care about VBMFX.
VBMFX is 43% Treasury/Agency, 27% Government Mortgage-Backed, 30% other investment grade. Even though you don't care about VFITX, at least 40% of your money is already in it. If you think the case for CD is stronger against VFITX, replacing VBMFX with a % in CDs and a % in investment-grade bond fund would still give you the combo currently under the cover of VBMFX.
nisiprius wrote:By the way, yes, I do understand that a CD that matures and pays back deposit plus five years' interest is much better than a bond fund that starts at $10,000 and ends at $9939.60.
Maybe that $9939.60 number, being so close to $10,000, isn't making that click. We are still talking about a 10% differnce here under the new assumption of 0.5% a year for 5 years. 10% difference for filling out some forms? I would do that.
nisiprius wrote:How do you know five years is the right number? ... ... Would anyone reading this thread seriously argue that "Bond fund to single bond for five years, then back" is a sure thing? Well, I think the second leg must be shaky, because if I reframe it using a single five-year bond instead of a CD, it suddenly sounds shaky.
What exactly is shaky? If we are talking about Treasury fund to a single Treasury bond, I think it's a reasonable thing to do. Five years may not be the perfect number but we already said we are not looking for precision here. If we are talking about VBMFX to a single Treasury bond, it becomes shaky because you would lose yield (VBMFX 2%, 5-year Treasury 0.86%).
nisiprius wrote:The point here is that in the past, real-world combinations of conditions didn't seem to produce nominal dollar total-return losses in intermediate-term bond funds over five-year holding periods.
In the past, the starting yield was higher. The high starting yield was able to absorb the price drops and stay above water in nominal dollars. A 8% yield each year would easily overcome a 10% drop in price over five years. It'll be much more difficult to do so with a 2% yield.
nisiprius wrote: VBMFX still has a fair amount of older, higher-interest bonds in it. If interest rates stay low, then VBMFX will continue to coast for a while at the higher rates and then start to decline.
If having older, higher-interest bonds in a bond portfolio makes any difference in performance, all bond traders would buy up older, higher-interest bonds and shun the newer, lower-interest bonds, to a point the difference goes away.
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

john94549 wrote:I am somewhat convinced that the more I read and study (about bond funds), the more I am driven to "what I understand." I most assuredly understand the concepts of bond funds, but do I really "understand" them? I most assuredly do not. Bond funds seem to be subject to many variables, some of which I understand, most of which I do not.

Do I think it is worth the aggravation to deviate from something I really, truly, understand (read:compound interest)?

As paltry as CD rates might be these days, at least I can quantify the "paltriness".
It's a puzzlement. The following chart is not intended to be snarky or a riposte. It is what it is. It embodies the puzzle. I did find some data on CDs at some point but can't put my hand on them right now, but for most of the time they've existed, up until a couple of years ago, money market funds paid considerably more than bank accounts and were roughly comparable to CDs. $52 thousand versus $28 thousand, wow! But, past performance, future results, blah blah. Thirty-year bull market in bonds, blah blah. My own feeling is that stocks, bonds and cash are all part of a balanced breakfast...
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Re: CD vs. Bond Fund: considering term risk only

Post by nisiprius »

tfb wrote:
nisiprius wrote:What do we think about a rise of 1% per year for five years? I'm thinking that might be extreme
Agreed. Possible but not likely.
nisiprius wrote:I don't even know if banks offer traditional IRAs and whether transfers between rollover and "regular traditional" IRAs are possible.
Yes they do and transfers are possible and routinely performed.
Yeah, I called them today and asked. I owe that much to my left brain.
tfb wrote:
nisiprius wrote:How do you know five years is the right number? ... ... Would anyone reading this thread seriously argue that "Bond fund to single bond for five years, then back" is a sure thing? Well, I think the second leg must be shaky, because if I reframe it using a single five-year bond instead of a CD, it suddenly sounds shaky.
What exactly is shaky? If we are talking about Treasury fund to a single Treasury bond, I think it's a reasonable thing to do. Five years may not be the perfect number but we already said we are not looking for precision here.
Well, (shrug) I'm not convinced. Yes, I'm talking about apple-to-apple, sell Treasury fund, but single Treasury bond, at maturity by Treasury fund again. Hard for me to believe that's a sure thing if you don't have a working crystal ball.
tfb wrote:
nisiprius wrote: VBMFX still has a fair amount of older, higher-interest bonds in it. If interest rates stay low, then VBMFX will continue to coast for a while at the higher rates and then start to decline.
If having older, higher-interest bonds in a bond portfolio makes any difference in performance, all bond traders would buy up older, higher-interest bonds and shun the newer, lower-interest bonds, to a point the difference goes away.
RIght, Magician sort of hinted at that. I was wrong, a victim of my own failure to understand inexorable bond math. I was thinking "I bought VBMFX when it had highest-interest bonds in it, why would I want to trade them for new lower-interest bonds?" Answer: because they've appreciated enough in price so that doing such a thing is neither a gain nor a loss.
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

Thanks for all the inputs. It was nice to have tfb respond to many of nisi's comments (many similar to responses I was compiling in my mind as reading through nisi's posts). I still want to go through and see if anything was missed, but a couple of quick comments (EDIT: OK, more than a couple, and not so quick):

If you want to discount the early withdrawal option entirely, then please use the PenFed 5-year at 2.25% or the 7-year at 2.75%. Per Larry's guidelines, a 50 basis point bump for extending maturity 2 years is attractive, so perhaps would favor the 7-year. I mentioned in my OP that the PenFed 5-year was a better comparison if discounting the cheap Ally put option entirely. You still have a put option on the PenFed CD, just more expensive. The PenFed CDs make the argument for CDs more compelling, especially if you want to compare to holding a single 5-year or 7-year treasury bond until maturity.

I'm not stuck on 1% per year increase. That's why I presented an annual increase that would be consistent with the annualized decrease over the last 4.5 years. Use 0.5% per year as your worst case if you prefer. Just pop your assumption into the spreadsheet.

I'm wondering if a big part of the difference between my simple model and the more sophisticated models are due to convexity. #Cruncher, do you know if this might be the case?

As I've already acknowledged, positive convexity will result in decreasing duration as yield increases, so would decrease the difference between bond fund and CD returns with rising interest rates. I believe positive convexity is a characteristic of treasuries, whereas it's negative for GNMAs (a point Larry often emphasizes as I recall). I just don't know how big the impact is.

I'm thinking about pulling out my investment textbook to see if there's a relatively simple way to include convexity in my simple model. I doubt it, since I believe you need to start with an equation for bond price vs. yield, then take the first derivative divided by price to get duration (rate of change of bond price vs. yield divided by price), and I doubt I can do this in a simple spreadsheet.

I just want to reinforce how simple it is to do an IRA trustee to trustee transfer from Fidelity or Vanguard to PenFed or Ally. At PenFed it's a one page form you can actually scan and email to them (to my surprise, didn't even have to mail a hardcopy as I recall). Well actually, there were a few confusing elements in filling out the form, but they were resolved with a 5-minute phone call.

At Ally you can open the CD online with a few clicks (or do it by phone), then fill out the one page form and mail it to them. Again, the form has a confusing element or two, but I actually discovered I could fill it out different ways and it still worked! They apparently were able to discern my intention despite putting certain account numbers in different places on the form (I did it at least 3 different ways for different transfers).

At either, once they get the form, they take care of the rest. No contact with Vanguard or Fidelity required on your part.

To poster who says bank CDs (bought directly from a bank) have duration, I just don't see it if we consider duration as price change vs. yield change. Bank CDs are not marketable, so there is no price change. There is simply the option to exercise the early withdrawal and pay a penalty. The penalty is fixed, so does not vary with changes in interest rate. Again, a brokered CD, which is marketable, is like a bond, and of course also has a duration. For purposes of this comparison, a bank CD has no term risk similar to that of a bond fund. If compared to a bond held to maturity, then it's irrelevant.

That's what comes to mind without reviewing all of the comments in detail. Back with more later I'm sure.

Thanks!

Kevin
Last edited by Kevin M on Thu Feb 23, 2012 3:11 am, edited 1 time in total.
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Re: CD vs. Bond Fund: considering term risk only

Post by tfb »

The biggest hole in the OP is the assumption that rate will rise. When we compare an intermediate-term Treasury bond fund to a single 5-year Treasury bond, under the assumption that rate will not rise but instead *fall*, the fund will come out ahead. I gave the example in the earlier post: rates stay level for 5 years and immediately drop to 0% at the end. The single bond matures at par while the bond fund gets a boost. That's probably why nisi intuitively senses it's shaky. Not a sure thing, but only because rates can fall.

The same applies to VBMFX versus 5-year PenFed CD. If rates stay level for 5 years and immediately drop to 0% at the end, the CD matures at par while the bond fund gets a boost. You don't need it to be that dramatic. Yield on VBMFX can't drop 0.5% a year for 5 years, but it certainly can drop 0.2% a year for 5 years. Model this and see what happens.

So, CD vs intermediate-term Treasury fund? With the large yield gap (2.25% vs 0.9%), at best the fund will break even. At worst we are looking at a 10%+ shortfall in the fund.

CD vs VBMFX? It depends on your assumption whether rates will rise, stay level, or fall in the next five years.

x% CD + (100-x)% intermediate-term investment-grade bond fund vs VBMFX? I would do the combo, basically replacing the Treasury component with a CD.
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

tfb wrote:The biggest hole in the OP is the assumption that rate will rise.
But I didn't make that assumption. I want to look at different scenarios, and posted a few of the ones I looked at.
When we compare an intermediate-term Treasury bond fund to a single 5-year Treasury bond, under the assumption that rate will not rise but instead *fall*, the fund will come out ahead. I gave the example in the earlier post: rates stay level for 5 years and immediately drop to 0% at the end. The single bond matures at par while the bond fund gets a boost. That's probably why nisi intuitively senses it's shaky. Not a sure thing, but only because rates can fall.
OK for comparing single bond to bond fund. In comparing CD to bond fund, I plugged my approximation of this in using 0.89% for 4 years then dropping to 0% during year 5 (not at year end, but evenly throughout year), and used 2.25% for CD (since we're ignoring early withdrawal). My spreadsheet shows CD coming out ahead by about 3%, but I'm happy to assume this advantage gets wiped out due to oversimplification of model, and call it pretty much a wash.

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Re: CD vs. Bond Fund: considering term risk only

Post by tfb »

Kevin M wrote:In comparing CD to bond fund, I plugged my approximation of this in using 0.89% for 4 years then dropping to 0% during year 5 (not at year end, but evenly throughout year), and used 2.25% for CD (since we're ignoring early withdrawal). My spreadsheet shows CD coming out ahead by about 3%, but I'm happy to assume this advantage gets wiped out due to oversimplification of model, and call it pretty much a wash.
I agree. That's why I said the IT Treasury fund at best breaks even with the CD. However, nisi wants to compare with VBMFX, which is reasonable, because most people have money in VBMFX, not IT Treasury. Plugging in 2.20% (Admiral) for 4 years then dropping to 0% in year 5. You will see the fund coming out ahead, by quite a bit. That's the term risk. It cuts both ways.
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Re: CD vs. Bond Fund: considering term risk only

Post by Bongleur »

>At either, once they get the form, they take care of the rest. No contact with Vanguard or Fidelity required on your part.

Surely Vanguard will contact you to confirm before actually transferring the funds ?

***
Since the OP only wants to consider term risk, why not also compare CDs to a High Yield Junk fund? At some point you need to go back and consider the other risks that go into the yield you are reaching for.
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

OK, OK, I'll make it simple fer ya. I'm gonna take that $75K of the re-balance money and plop it into PenFed. Seven year.

Then, when my next "biggee" comes due in June, I'm gonna plop that in some weird thing called a "bank" (maybe, if I get daring, a credit union), probably for five years.

Pow! I'm so, well, reckless.
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Re: CD vs. Bond Fund: considering term risk only

Post by moproblems »

Kevin M wrote: To poster who says bank CDs (bought directly from a bank) have duration, I just don't see it if we consider duration as price change vs. yield change. Bank CDs are not marketable, so there is no price change. There is simply the option to exercise the early withdrawal and pay a penalty. The penalty is fixed, so does not vary with changes in interest rate. Again, a brokered CD, which is marketable, is like a bond, and of course also has a duration. For purposes of this comparison, a bank CD has no term risk similar to that of a bond fund. If compared to a bond held to maturity, then it's irrelevant.
Sure there's a price change. It's the change in the present value of the bond
Modified Duration = Macaulay Duration / (1 + APY)
and, for a zero coupon bond like a CD,
Macaulay Duration = Maturity

So the duration of a CD is simply Maturity/(1+APY):
http://en.wikipedia.org/wiki/Bond_duration
http://faculty.darden.virginia.edu/conr ... f-1238.pdf

So, to a good approximation, all we have to do is compare the interest rate of the CD with another treasury bond of equivalent duration and if the rate is higher, then we get a free lunch (or reward for accepting the illiquidity). Using bond funds doesn't change anything because a bond fund is simply the equivalent of a rolling bond ladder, which we can compare bond-by-bond to a rolling CD ladder. Only thing we lose is the ability to speculate (ie profit from price fluctuations), but if that were advantageous then volatility would be good and risk wouldn't be rewarded.

Or for an exact valuation that includes convexity and everything we can look at the secondary market for treasury STRIPS:
http://online.wsj.com/mdc/public/page/2 ... trips.html
STRIPS maturing in 5 years are currently trading at 0.96% APY...so Ally is paying you precisely an extra 0.78% APY to forgo liquidity (which includes the hassle of dealing with the FDIC)

But the real question is, if you can get an extra 0.78% APY on your "STRIPS", then what else should you be replacing with Bank CDs? Clearly all treasuries except ones with duration above 8 years, but what about things with credit risk? That's what I'd like to know.
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Re: CD vs. Bond Fund: considering term risk only

Post by #Cruncher »

Kevin M wrote:I'm wondering if a big part of the difference between my simple model and the more sophisticated models are due to convexity. #Cruncher, do you know if this might be the case?
Not that my method is sophisticated, but the difference between it and yours doesn't have anything to do with convexity. It's something more basic: namely that your method doesn't account for the movement back toward par value as each bond in the fund approaches maturity. Here is the method you used to arrive at a value of $9,122 after 5 years:
Kevin M wrote:So change in NAV in each year in scenario 2 is -5.2%. So first year total return is 1.39% - 5.2% = -3.81% [I corrected your -2.81 to -3.81]. Apply this to $10K in year 1, then compound that for year 2; repeat.
The 2nd column of the table below shows the value each year using your formula. The 3rd column shows the value, including interest, of a 5-year bond under the same rising interest rate assumption. Note how its value also falls after one year and after two years, but then climbs back to above par when it matures in 5 years. This effect also occurs with the other nine bonds in my model, but is most striking with the 5-year maturity.

Code: Select all

Interest   Your     5 Yr   
  Rate     Calc     Bond
  -----   ------   -----
  0.89%   10,000   1,000   Initial Value
  1.89%    9,619     971   After 1 Year
  2.89%    9,349     961   After 2 Years
  3.89%    9,179     970   After 3 Years
  4.89%    9,105     998   After 4 Years
  5.89%    9,122   1,047   After 5 Years
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

tfb wrote:However, nisi wants to compare with VBMFX, which is reasonable, because most people have money in VBMFX, not IT Treasury. Plugging in 2.20% (Admiral) for 4 years then dropping to 0% in year 5. You will see the fund coming out ahead, by quite a bit. That's the term risk. It cuts both ways.
Sure, but I can do that one in my head. Similar yields for 4 years (a wash), and then roughly -1 x -2 x 5 = 10% increase for the bond fund.
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Re: CD vs. Bond Fund: considering term risk only

Post by john94549 »

Kevin M wrote:
tfb wrote:However, nisi wants to compare with VBMFX, which is reasonable, because most people have money in VBMFX, not IT Treasury. Plugging in 2.20% (Admiral) for 4 years then dropping to 0% in year 5. You will see the fund coming out ahead, by quite a bit. That's the term risk. It cuts both ways.
Sure, but I can do that one in my head. Similar yields for 4 years (a wash), and then roughly -1 x -2 x 5 = 10% increase for the bond fund.

Puleeze, ain't gonna happen. If we might abstain from the academic convolutions, the real issue is what am I gonna do with my money?

I have yet to find a reasonable alternative to your garden-variety 5-year 2% CD. Much less a 2.76% APY PenFed 7-year.
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

#Cruncher wrote:Not that my method is sophisticated, but the difference between it and yours doesn't have anything to do with convexity. It's something more basic: namely that your method doesn't account for the movement back toward par value as each bond in the fund approaches maturity.
But doesn't this just come down to saying that we can't use duration to accurately estimate the change in value of the bond fund for relatively small changes in interest rates (for larger changes, we need to include convexity)? Doesn't this kind of contradict the definition of duration?

I don't really know how they manage the bonds inside the fund, or even if they do it in a consistent manner. Maybe they don't hold them to maturity. I note that only 0.4% of ITT bonds have maturity of less than 1 year; doesn't that support this? I imagine they're frequently buying and selling bonds to maintain the target characteristics. I know I've seen very high turnover rates for bond funds in the past, and was somewhat surprised, but I think I saw an explanation that it was to be expected in a bond fund (unlike a stock index fund).

I guess we could look at some historical data and look at change in NAV compared to change in SEC yield. I believe in doing this before that what I saw did not match my expectation.

Thanks for the explanation.

Kevin
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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

Bongleur wrote:>At either, once they get the form, they take care of the rest. No contact with Vanguard or Fidelity required on your part.

Surely Vanguard will contact you to confirm before actually transferring the funds ?
Nope, the form authorizes the originating firm to do the transfer. I guess you've provided enough info on the form for them to believe you've authorized it. I've seen warnings that some firms may require a signature guarantee, but neither Fidelity nor Vanguard has done so.
Since the OP only wants to consider term risk, why not also compare CDs to a High Yield Junk fund? At some point you need to go back and consider the other risks that go into the yield you are reaching for.
Hmmm, I think this exactly misses the point. I'm trying to eliminate credit risk from the comparison by choosing a bond fund that has none.

There is no credit risk in a treasury fund, and as far as I'm concerned, there is virtually no credit risk in an FDIC-insured CD.

I would use your comment as an argument not to compare Total Bond Market to a CD, because there is credit risk in TBM. For someone who wanted to ignore credit risk, I might then ask the question you asked, and ask why not move from TBM to Investment Grade or even to high-yield.

Am I misunderstanding your comment?

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Re: CD vs. Bond Fund: considering term risk only

Post by Kevin M »

moproblems wrote: Sure there's a price change. It's the change in the present value of the bond
Sorry, but your explanation is too academic, and does not match the reality of the situation that I'm interested in. A bank CD is not marketable, so a theoretical change in price does not matter to me. A change in price is only of interest to me if I can sell the CD on an open market of some sort, and I cannot. I only have two choices: either hold the CD to maturity, in which case price change is irrelevant, or do an early withdrawal, in which case the price does not depend at all on how much interest rates have changed since I bought it. Hence, from a practical perspective, duration is an irrelevant concept for a bank CD.

Huge contrast with a brokered CD, bond or bond fund, where a change in interest rate definitely has an impact on what I can sell it for.

So you may be right based on some theoretical model, but it does not matter to me in practice.

Kevin
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Re: CD vs. Bond Fund: considering term risk only

Post by Bongleur »

>For someone who wanted to ignore credit risk, I might then ask the question you asked, and ask why not move from TBM to Investment Grade or even to high-yield.
>
Yup. Somebody added TBM to the discussion...

Worst case I can think of is that FDIC might take a long time to give you your money if something happens to "the banking system" which causes a lot of low rated banks to fail.
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