A reader writes in, asking:

“I am aware that bonds and bond funds with longer duration have greater price changes in response to interest rate moves than shorter-term bonds do. And given that, I understand that longer-term bonds generally have higher yields because of that higher risk. That makes perfect sense.

What I have never been able to wrap my head around is why do the prices of longer duration bonds fluctuate more severely?”

A bond’s market price is really just the result of a net present value calculation. That is, the price of a bond at any given time is the sum of the present values of each of the cash flows from the bond (i.e., the present value of each interest payment plus the present value of the payment upon maturity).

(See this article if you haven’t encountered the concept of present value before. It’s worth a read, as it’s one of the most fundamental concepts in finance.)

As a reminder, the present value of a given cash flow is calculated as follows:

PV = FV / (1 + r)^n

where:

PV = present value
FV = future value (i.e., the dollar amount of the cash flow in question)
r = annual discount rate
n = number of years before the cash flow is received

The greater the number of years, the greater the impact of the discount rate. Compare the two following examples.

Example 1: Given a discount rate of 2%, the present value of a $1,000 cash flow to be received one year from now is $980. If we raise the discount rate to 3%, the present value falls to $971, a change of $9.

Example 2: Given a discount rate of 2%, the present value of a $1,000 cash flow to be received five years from now is $906. If we raise the discount rate to 3%, the present value falls to $863, a change of $43.

Point being, a 1% increase in the discount rate had a much larger effect on the cash flow that was further in the future.

When we’re calculating the present value of a bond, the discount rate is the return that investors could expect to earn from other bonds with similar risk (i.e., other bonds with the same credit rating and same duration).

So when interest rates change, the discount rate changes. And the further in the future the cash flow is to be received, the greater the change in present value (i.e., market price).

So, the longer the duration of a bond (i.e., the further in the future its cash flows will be received, on average), the greater the change in present value (i.e., market price) when interest rates change.

A reader writes in, asking:

“Do bond prices work like stock prices in that interest rate expectations are “priced in” in the same way that expectations for the company are “priced in” to the price of the stock? I guess what I’m asking is if everybody expects interest rates to rise and then they do rise, should I still expect my bonds to go down in value? Or does the change in interest rates have to be unexpected or bigger than expected in order for my bond prices to fall?”

As a bit of background for readers unfamiliar with the concept, a stock’s price at any given time reflects the market’s expectations for the underlying company. For example, if everybody expects a given company to have huge growth in profits over the foreseeable future, those expectations are built into the price of the stock. And the stock will only earn above average returns if the company’s profits turn out to be even greater than the market had expected.

In other words, the performance of a stock is not a function of how well the underlying company performs, but rather how well the company performs relative to the market’s expectations.

With regard to the reader’s question (i.e., whether it needs to be an unexpected change in interest rates in order to change bond prices), the answer is “it depends.” Specifically, it depends which interest rates we’re talking about.

A Bond’s Yield and Price Are Mathematically Linked

For typical nominal bonds, short of defaulting, there is no way for the interest rate to change without the price changing. A change in the price is how that the interest rate changes.

Example: If a bond with a $1,000 face value pays $40 of interest per year, that $40 is fixed. It doesn’t change. So the only way that the bond’s yield can be higher or lower than 4% is if the price is different from $1,000. In other words, the only way for the interest rate to change is for the price to change. Said yet another way, a change in the interest rate on this bond is literally the same thing as a change in its price (e.g., the bond price has gone up to $1,020 and now therefore has a yield of less than 4%, because you have to pay $1,020 to get that $40 of annual interest rather than just paying $1,000).

So if you own, for example, a 5-year Treasury bond and interest rates go up for 5-year Treasury bonds, the price of your bond will go down at the same time.

Expectations about Other Rates Might be “Priced in”

Bonds come with a variety of credit ratings and maturities, and there are different interest rates for each of those rating/maturity combinations. In addition, there are other interest rates that play important roles in the economy, such as the prime rate or the federal funds target rate.

And the interest rate on any given type of bond is based, to some extent, on expectations about various other interest rates (i.e., interest rates for other types of bonds or interest rates for things other than bonds). For example, bonds may at any given time be priced on the assumption that the Federal Reserve will raise the federal funds target rate by a certain amount. And therefore if the Fed does raise the rate by that amount, it won’t have much effect on bond prices, because that change was already “priced in.”

A reader writes in, asking:

“I was recently reading an article on Investopedia, about using Vanguard ETF to build a commission free portfolio.

What was interesting to me is this author based his article on Vanguard Target Date Funds. One of the conclusions he suggested is that a portfolio that has a stock allocation of 65% and above doesn’t need inflation protected bonds in it at all. This seems to be validated by Vanguard when you check the Target Date Funds they offer, anything with an allocation of 65% stocks indeed has no inflation protected bonds. However Vanguard’s Life Strategy Funds have no allocation to inflation protected bonds no matter the stock allocation. Was just curious about your thoughts on this.”

The purpose of Treasury Inflation-Protected Securities (TIPS) is to provide a specific, predictable after-inflation return. And they are very effective at doing this, provided that you hold them to maturity.

This makes them a super neat tool for funding a specific expense in the future, or for funding a series of expenses over time (e.g., everyday living expenses in retirement, funded via a TIPS ladder). For this purpose, they’re pretty clearly preferable to regular nominal Treasury bonds.

As a part of a portfolio, they’re perfectly fine, but not nearly so powerful. That is, they still reduce the inflation risk to which you’re exposed, but they can’t provide your overall portfolio with a predictable after-inflation return if they’re only a small part of your portfolio.

Imagine, for example, that I have a 70/30 stock/bond allocation, and 15% of the portfolio (i.e., half of the bonds) is in TIPS. Sure, that 15% of the portfolio has a predictable after-inflation return. But who really cares? I’m concerned about the return on my entire portfolio, and the uncertainty that comes from the 70% stock allocation will absolutely dwarf the uncertainty (or lack thereof) that comes from switching 15% of the portfolio between TIPS or nominal bonds.

I often think it’s instructive to look at mutual fund return charts from Morningstar — not for showing which funds are better than others, but for showing how similar or different various funds are.

The following chart plots:

• Vanguard Inflation-Protected Securities Fund (in blue),
• Vanguard Intermediate-Term Treasury Fund (in orange), and
• Vanguard Total Stock Market Index Fund (in yellow)…

…since the TIPS fund was first created in June of 2000.

Sure, you could make a case for picking one of the bonds funds over the other. But if the portfolio primarily consists of that stock fund, it wouldn’t have made a heck of a lot of difference which of the bond funds was used.

In other words, I don’t think it’s a bad idea at all to include TIPS (rather than just nominal bonds) in a mostly-stock portfolio. Rather, I just don’t think it’s likely to make that much of a difference.

This is markedly different from a situation in which the portfolio is mostly (or entirely) bonds. A nominal Treasury ladder and a TIPS ladder provide two very different levels of certainty in terms of the spending they can support.

A reader writes in, asking:

“What are your thoughts on bond diversification? Is it ok to just do something simple like a treasury bond ladder or is it necessary to diversify bonds like you do with stocks?”

No, I really don’t think that diversification is necessary for the bond portion of an investment portfolio.

Several years ago, prior to switching to a LifeStrategy fund, the bond portion of my portfolio included nothing but Treasury bonds (via a single bond fund). And that didn’t bother me at all.

The goal for the bond part of my portfolio was (and still is, for the most part) simply to act as something that is unlikely to go down (by much) during a stock market downturn. CDs or Treasury bonds (regardless of whether or not they’re held in a mutual fund, and provided they aren’t long-term bonds) achieve that goal very well without any need for additional fixed income holdings.

When Diversification *Is* Necessary for Fixed Income

Just to be clear on this point, when it comes to fixed-income investments other than FDIC-insured CDs and Treasury bonds, diversification is important. That is, if you’re putting a significant part of your portfolio into muni bonds, corporate bonds, or international bonds, yes, you definitely want to diversify those holdings.

Diversification Isn’t a Bad Idea

For many investors though, the goal of their bond holdings isn’t only to act as “something safe.” They also hope to achieve some degree of “free lunch” via diversification. The general thought process is that if something has a low enough correlation to the rest of your portfolio while providing an acceptable return, adding it to the portfolio can result in reduced risk without a correspondingly large reduction in return.

This is the argument, for instance, that Vanguard makes in favor of international bonds in their funds-of-funds.

That’s a thoroughly reasonable line of thinking. And if things go according to plan (i.e., correlations and returns behave the way you hope they will) it will improve your results.

However, it isn’t necessary. And it’s not entirely obvious that it’s a clear improvement over an all-CD or all-Treasuries fixed income portfolio, because:

• CDs offer their own sort of free lunch sometimes, if you can find longer-term CDs (that have relatively high yields due to the long term) with low penalties for early redemption, and
• Corporate bonds (i.e., the most likely candidate for adding to an otherwise-Treasury bond portfolio as a diversifier) often have higher correlation to stocks than Treasury bonds do, so it’s not a sure bet that they will have the desired result.

A reader writes in, asking:

“I know that interest rates and bond prices move in opposite directions, but I don’t honestly understand why that is the case. And while we’re at it, why do bond funds with a long duration have bigger price fluctuations than bond funds with a short duration?”

Imagine that you buy a $1,000, 10-year Treasury bond, with a 2% coupon rate. (That is, it pays $20 of interest per year.) And you hold that bond for five years, such that it is now effectively a 5-year Treasury bond with a 2% coupon rate.

And imagine that, over those five years, interest rates have risen, and newly-issued 5-year Treasury bonds are now paying 3% interest.

In such a scenario, if you wanted to sell your bond for $1,000, you’d have a very difficult (i.e., impossible) time. Nobody would want to buy your bond with its 2% interest rate, when they could just buy new 5-year bonds with a 3% interest rate instead. In order to sell your bond, you’d have to sell it for less than $1,000. That is, its price has gone down because interest rates have gone up. (Specifically, you would have to sell your bond at a sufficient discount that it would offer the same yield to maturity as newly-issued bonds of the same duration.)

And the same sort of thing happens in reverse. Imagine instead that rates on 5-year Treasury bonds had fallen to just 1%. In that case, people would be willing to pay more than $1,000 for your bond with its 2% coupon rate. That is, interest rates fell, so the value of your bond went up.

Why Do Longer-Term Bonds Have More Interest Rate Risk?

When interest rates change, the price of a bond fund will move (in the opposite direction) by an amount approximately equal to the average duration of the fund, multiplied by the percentage change in applicable interest rates. For example, if the whole Treasury yield curve were to rise by 2%, a Treasury bond fund with a 3-year average duration would fall in price by roughly 6%, and a Treasury bond fund with a 7-year average duration would fall in value by roughly 14%.

But why do longer-duration bonds experience more severe price fluctuations? Without getting into the underlying math*, I think the concept is most easily understood with an example.

Imagine that on a given day you purchase a 1-year Treasury bond and a 20-year Treasury bond, both of which you plan to hold until maturity. Then, on the very next day, the entire Treasury yield curve moves upward by 1%.

• Holding the 1-year bond to maturity means you’ll be collecting a subpar interest rate (i.e., missing out on an additional 1% yield, relative to new bonds) over the next year.
• Holding the 20-year bond to maturity means you’ll be collecting a subpar interest rate each year for the next twenty years.

Missing out on an additional 1% yield for a year isn’t great of course. But missing out on 1% per year for twenty years is a much bigger deal. And that is essentially why longer-duration bonds have larger price fluctuations when current interest rates change.

*For those who are interested in the technical explanation: The market value of a bond at any point in time is equal to the sum of the present values (i.e., discounted values) of each of the future cash flows the bond holder will receive. When market interest rates change, the discount rate we use to calculate present value changes. And a given change in discount rate (e.g., 1% higher or lower) has a much greater effect on cash flows far in the future (such as you would receive with a long-term bond) than cash flows in the near future.

A reader writes in, asking:

“Apparently Vanguard’s new Core Bond Fund is going to be similar to the Total Bond Market Index Fund, but actively managed with an eye as to upcoming interest rate hikes and cuts.

Am interested if you think this fund is worth looking at to complement the Total Bond Market Index Fund in a way to attempt to ‘time’ interest rates. Would it be a bit easier to ‘time’ interest rates than the market? There are some long term trends I think we all can agree on. For example, sooner or later interest rates will once again rise. Of course knowing when and how much rise there will be is the rub. I would also be interested if you knew what the proposed duration of this fund was, as I did not notice while doing my preliminary research.”

For those who haven’t yet heard about the new Vanguard Core Bond Fund, you can read Vanguard’s announcement here or see the fund info page here.

Here are a few of the details:

• The plan is for the new fund to be an actively managed counterpart to the Vanguard Total Bond Market Index Fund — investing in similar securities, but trying to outperform via “security selection, sector allocation, and, to a lesser extent, duration decisions.”
• The fund will have an expense ratio of 0.25% (0.15% for Admiral shares).
• The fund is supposed to have a duration ranging from “0.5 years above or below the fund’s benchmark, the Barclays U.S. Aggregate Float Adjusted Index,” which would give it an average duration roughly in the 5-6 years range.

As I’ve said before I do not necessarily have any opposition to using actively managed funds. The problem is simply that most actively managed funds cost quite a bit more than their passively managed counterparts. And lots of research (a few cases of which are mentioned here) has shown that lower-cost funds tend to outperform higher-cost funds.

And on that note, the good news is that this new fund is pretty darned cheap for an actively managed fund. It is, however, still somewhat more expensive than the Vanguard Total Bond Market Index Fund, which has an expense ratio of 0.20% (0.07% for Admiral or ETF shares).

With regard to the question of whether it’s easier to predict interest rate movements than stock market movements, I am not aware of any evidence showing that to be the case. Perhaps ironically, one of the more compelling arguments I’ve seen against trying to predict interest rates comes from a 2011 Vanguard research paper.

On pages 6-7 of the paper the authors discuss how well the market (as a whole) does at predicting both the federal funds target rate and the yield on 10-year Treasuries. In short, the predictions are terrible. (Figure 7 is particularly noteworthy. In the figure, each of the little hairs extending away from the dark line shows the market’s prediction at a given time. As you can see, it’s pretty rare for the predictions to line up with what actually occurred going forward.)

The authors also note that shortening the duration of one’s bond holdings due to an anticipated rise in interest rates means forgoing the higher yields that could have been earned on longer-duration bonds while waiting for rates to rise. In the authors’ words:

“Finally, in addition to interest rates’ unpredictability, it’s important to consider that even if a manager makes a correct call on the direction of rates, the timing and magnitude of any change are crucial, as a short-duration strategy is a “negative carry” position. In an environment characterized by a steep yield curve, this negative carry can mean a significant return forfeiture if yields do not rise as anticipated. Even then, a manager who correctly predicts a rise in interest rates could likely suffer a performance penalty if rates rise less than forecast or if the timing of the change is either too early or too late.”

So, frankly, I would be surprised if the fund is able to reliably add value by predicting interest rate movements.

In other words, if I were to buy the fund, it would be as a low-cost way to bet on the managers’ ability to exclude specific bonds that will underperform (e.g., due to credit troubles) rather than as a way to bet on somebody’s ability to predict interest rates. But personally, I’d prefer to just stick with my index funds rather than make any such bets.