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Comment by ctchocula | Hacker News Reader

This is something I've always wondered: Are treasury bond ladders strictly better than an equivalent treasury bond fund (say VFITX), because the interest rate risk can cause the bond fund to lose value while the treasury bond ladder is guaranteed to not lose value if held to maturation?

Or is there some finance black magic that causes treasury bond ladders and treasury bond funds with the same effective maturity to have the same return (ignoring expense ratio for now) after a long period of time?

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No, bond ladders are not strictly better than a bond fund. In theory, they are equivalent. In a bond fund, you simply see your loss on rising interest rates more directly.

Scenario 1 (holding bonds to maturity, i.e. bond ladder):

Let's imagine you invest in a $100 1yr bond at a 2% rate. You will be paid $102 in a year's time. Immediately after you buy the bond, the rate goes to 3%. You are locked into the bond, so you can't switch to the higher rate (i.e. you've lost out on a potential $1).

Scenario 2 (bond funds, ignoring reinvestment):

Instead imagine that you invest $100 in a fund that currently holds 1yr bonds at a 2% rate. You expect to be able to sell this fund in a year's time for $102. Now the rate changes to 3%. You are not locked into the fund, but the fund is locked into the bonds that they bought. If you can sell your shares in the fund for $100, you could then buy the new 3% rate bonds directly (i.e. you have avoided the loss due to the interest rate change). This would be a risk-free arbitrage between the fund and the new bonds. The price of the fund needs to drop to ~$99 to be "fair" (to be precise, it's 1.02/1.03, not exactly 99). If you sell at ~$99 and buy new 3% bonds directly, you will receive $102 in a year's time, just like scenario 1.

In short, the bond fund loses value because you maintain the optionality to withdraw whenever you want (and invest at higher rates if rates go up). The expected value between bond funds and bond ladders is still the same. In essence, the difference is between holding bonds to maturity and having the possibility of selling them, which doesn't change the expected value.

Addendum: I say you're "locked into" a bond here because most people don't consider the possibility of selling bonds (i.e. they plan to hold to maturity). However, you can sell most bonds (not directly back to the issuer but to other people). This may make the similarity between funds and ladders clearer. In the scenario 1 example, if you were to sell your bond, it would also be worth ~$99 (using the same argument as in scenario 2). In other words, the fact that you don't think of this as a loss if you don't sell the bond doesn't change the fact that the bond lost value (the comment by ThrustVectoring further down this chain says this well). If you assume the market pricing of interest rates is fair and that the market is perfectly efficient (i.e. no transaction fees, management fees, etc.), then the expected value of holding, rolling, or investing in a bond holding fund is all the same.

VFITX is down ~2% since January. If I had bought shares of it in January, I would have less money than I started with. If I had bought individual treasury bonds in January, I would have more money than I started with. That seems like a significant difference between bonds and bond funds.

I looked up VFITX. It looks like they pay distributions (i.e. dividends) that are roughly proportional to the expectation of the interest rate over the average maturity of their holdings, so you need to take this into account when considering "what-if". They have paid approximately 1.4% in dividends during 2018. That makes their total losses around 0.6%.

This doesn't fully explain the underperformance of VFITX compared to a 3 year bond (which should have made 8 mo/12 mo * 2% = 1.3% in interest and lost around 0.7% on rising interest rates), a net gain of 0.6%.

So VFITX underperformed a three year bond by 1.2%. 0.13% of this is their management fee (0.2% * 8 mo/12 mo). I'm not able to explain the last 1% of difference.

However, in theory, a bond fund loses just as much value on an interest rate rise as the bonds it is holding lose. In my example above, the bond is worth ~$99 after the increase to a 3% rate, just like the fund. The only difference between the bond and the fund is the choice of when to liquidate or roll.

It's possible that VFITX got unlucky on the timing of their bond rolling (see cousin comment).

According to the VFITX portfolio page (https://investor.vanguard.com/mutual-funds/profile/portfolio...), the average maturity of its holdings in 6 years, which probably explains why its performance is different than that of a 3 year treasury bond.

Five and ten year US bonds have had lost less value than the three year bond in the past 8 months, so that doesn't seem sufficient to explain it (i.e. it makes the difference worse).

That said, I was very loose in my calculations. Without exact knowledge of their holdings and careful calculations, I'm not surprised that the numbers don't fully add up.

Fair enough, but if someone is interested in holding bonds to maturity it seems like investing in a fund is not actually the same as doing that.

If you attempted to sell those treasury bonds now on the secondary, you would have to accept the same $99 the shares of VFITX are worth. The immediate, liquid value is the same either way. (You need a common unit to comapre in instead of VFITX in now-$ to bonds in principle-$.)

If you hold the bonds and/or VFITX instead, the interest pay out of the bonds and the distributions of VFITX should also come out equal (except not, the fund has the advantage that it can change its composition from buying/selling bonds, but also has the overhead of selecting and performing those transactions).

(In reference to your below comment, yes, fund != holding bonds. The fund is closer to you buying the bonds, but also buying/selling as bonds mature or you anticipate changes in rates)

As mvilim noted in his response to my comment, the outcome is actually not equal, and VFITX underperformed bonds over the same period, by a larger amount than can be explained by its expense ratio.

You're simply not marking your losses to market - not having a loss here is an accounting fiction, not a real financial difference. In both situations, you have less money than if you'd bought the bonds at a later time instead.

> In both situations, you have less money than if you'd bought the bonds at a later time instead.

But this is not the situation I described. My point is that buying the bonds in January would have been better than buying the bond fund in January.

If you look at mvilim's response to my comment you will see that the fund underperformed bonds between January and today.

In theory that's true if you hold the fund forever but take the example of VGSH from another comment thread. If you bought that fund exactly 1 year ago and sold today you would have realized a return of less than 2% because while the yield is currently about 2.5% the price decrease over that time was about 1.5%. Your return would have been less than buying a single treasury yielding 2% a year ago and letting it mature.

I don't think this has anything to do with how long you hold the fund. In essence, the original comment was using bond ladders as a proxy for holding bonds till expiration and using bond funds as a proxy for always liquidating your bonds and reinvesting at the new rate on any rate change. The question is really about holding vs liquidating bonds, not funds vs ladders (which theoretically could hold or liquidate, depending on their implementation). If the market is fairly priced, then there is no expected value difference between holding and liquidating.

In the example I gave above, the value of the fund in a year is still $102 (independent of whether they hold the bonds to maturity or whether they sell at the fair market value and reinvest at the higher rate). In your example, buying and holding a treasury would only be better than VGSH if the market on average underestimated the future interest rate over that time period (so that as VGSH rolled (i.e. liquidated and reinvested) its bonds at an average rate of less than 2%). This has less to do with holding vs liquidating than it has to do with fair pricing of the interest rate. The main difference between holding to maturity and rolling the bonds is this: if you hold to maturity you make a single large bet on the interest rate; if you roll your bonds, you make several smaller bets on the interest rate.

Yes, as you say, holding a bond instead of rolling it can lead to a different return (when the market expectation of the future rate is wrong). But for most people this is irrelevant, as they won't be better at valuing interest rates than the rest of the market.

I added a note in my article to clarify this. My strategy here is short-term. You want to withdraw your capital eventually, not hold forever. Maybe you are saving for a house in a few years. If you suspect that rates are still rising when you let your ladder burn down then this can be a good approach. I agree that for long term investments (ex. a retirement account) this is probably not the right approach. Thoughts on how I can make it more clear?

I think your key point is this: "If you suspect that rates are still rising when you let your ladder burn down then this can be a good approach." I agree with this statement.

If you disagree with the market pricing of interest rates, then yes, you should do something other than the market (i.e. what the bond fund would do). Letting the ladder burn down (as opposed to continuing to roll, as the fund would) is claiming that the rates will be higher than the market is currently pricing them.

If you agree with the market pricing of bonds, then the ladder is equivalent to the bond fund (because the bond fund is simply managing the ladder for you by proxy).

From the article:

> Bond prices fall as interest rates rise. You can avoid this by buying individual bonds and holding them until they mature (pay out their full value).

You can avoid selling the bond at a loss; however, you are still holding a bond that earns less interest than current bonds are earning. As far as I know, holding to maturity doesn't improve your returns in the face of rising interest rates despite what the author seems to be implying.

What holding does is lock your returns and sets a floor. When you buy a bond and hold it you will be guaranteed to receive the return. Sure if rates rise afterwards you have opportunity cost because you can't invest that money at a higher rate, but that's what ladders help you do. You get the current rate when you add new bonds to the end. What alternatives exist? You can buy a bond fund which might decline in value if rates rise or just sit on cash but those don't seem optimal.

Don’t forget transaction fees. If you sell bond X that pays out 100$ in 1 year for bond Y which pays out 100$ in one year you gained nothing.

Yeah, the idea is that at any give price, holding any bond or selling it and using the proceeds to purchase bonds at the current rate are equivalent from a return perspective.

You are correct in rising interest rate environments where you believe the rates will continue to rise.

With bond funds you can get the same yield as the ladder (interest payments) if you hold forever and never sell, but if you sell you may take a hit because the price has gone down. That doesn't happen with ladders since you always get paid out the face value.

When you buy the bonds directly, you're choosing an explicit exit date and you know exactly what your return will be.

When you buy a bond fund, your principal is going to be reinvested, so there's a risk of interest rates going up right before you sell.

Some firms offer target maturity bond funds which will is the best of both worlds.

Liability matching is strictly more optimal. If you know when you need money you can take that portion of the risk out of the equation. On the other hand, with reinvested funds, you are paid to take the risk of interest rates going up and the lack of a fixed maturity date, by the possibility that interest rates might go down (the so-called roll-yield).

> Some firms offer target maturity bond funds which will is the best of both worlds.

These are great for corporate bonds. Check out iShares iBonds if you want to include corporate bonds in your portfolio without building a ladder or taking on interest rate risk.

You don't want to include corporate bonds in your portfolio. Generally speaking, buying equities gets you a better price for the risk you take; a slightly higher equity percentage with government-backed bonds will generally outperform at the same level of risk.

Is there a good link to learn more about that?

Not that I can easily find or remember.

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