Webcast replay: Investing in today's municipal bond market
June 17, 2014
Replay and transcript from a recent Vanguard webcast
From credit quality to the yield curve and problems in Puerto Rico and Detroit, there's much to consider when evaluating municipal bonds. In this live webcast aired May 22, 2014, Vanguard fixed income and investment experts Chris Alwine and Daniel Wallick detailed the challenges and opportunities of investing in today's municipal bond market.
Rebecca Katz: Well, good afternoon and welcome to this live Vanguard webcast. I'm Rebecca Katz, and whether you're joining us from your computer, your smartphone, or your tablet, we're really glad that you could join us today.
So today, we are talking about the challenges and the opportunities of investing in municipal bonds. You know, there've been some recent headline-level stories about different areas, such as Detroit and Puerto Rico that demonstrate just how important it is to hold high-quality muni bonds. Munis have also been an attractive investment when you look at their tax-free yields relative to taxable-bond yields.
So, after viewing this webcast, we hope you'll have a better understanding of the role that munis can play in your portfolio, the problems in Detroit and Puerto Rico—do they set a precedent—and then implications if the tax advantages of municipal bonds are ratcheted back. You know, the government needs more taxes. What is that implication?
So joining me today are two of Vanguard's senior investment experts. First, we have Chris Alwine. He heads the municipal bond team in our Fixed Income Group, and second, we have Daniel Wallick of our Investment Strategy Group who has also worked in public-sector financing. Thank you for being here, guys.
Chris Alwine: It's great to be here today.
Rebecca Katz: So, for those of you who watch a lot of our webcasts, you know these shows are about you and your questions. We get lots and lots of questions in advance. We'll get through as many of those as we can. But you can continue to send questions our way, either through your computer or you can even tweet us using the #VGLive, and I'll see them here on my screen, and we'll plow through as many questions as we can.
I actually think rather than do a lot of upfront chit-chat, we should just jump right into questions because we have so many good ones. Is that okay with you?
Daniel Wallick: Yes.
Chris Alwine: That'd be great.
All right, so our first question is actually from Kathy in Urbana, Illinois, and Kathy says, "My question is really a request. Would you please begin your discussion with an overview of muni bonds for those of us who have zero experience with them?" So, Daniel I'm going to throw that one to you.
Daniel Wallick: Sure. So, you can think of them as a contract between a local or state government and people that lend them money. And what state and local governments are trying to do typically is fund capital projects, and what we mean by capital projects are projects that take a lot of money, a lot of capital. And so that could be a road, or that could be a school, or that could be a hospital, or that could be an electric system, or that could be a sewer. It could be any one of a number of things that just takes a lot of money. So what governments do, is they go out and borrow that money, pay for it up front to fund the project, and then repay that over a long period of time.
Rebecca Katz: Okay, and I did mention that there's some tax advantages to munis. Want to touch on that quickly?
Daniel Wallick: Sure and so municipal bonds in particular since they affect state and local governments, they tend to have a tax advantage. So they're not subject to federal, state, or local taxes depending on the jurisdiction. And so there's this difference you'll see in the yields that accommodates for that difference in the tax impact.
Rebecca Katz: Okay, great. So we talked a little bit about what a muni is. It's a good level set, I think. Chris, maybe you can level set us on what the current landscape in the muni market is like. I mentioned a couple of states and a city—what's going on there?
Chris Alwine: Well, a lot has happened in the past year or so, so if we could just bring up the yield chart that we have. When we look at how the muni market performed, it might be surprising that it's done reasonably well, considering the ominous headlines that we've been reading about over the past year, whether it's Puerto Rico, whether it's the Detroit bankruptcy, and even the Fed taper talk has really, I think, raised some investors' anxieties about the performance or security of municipal bonds.
And the graph that we have up here, this is the yield of a 30-year AAA-rated muni, and it goes back over 5 years. Just a quick primer, as the yield goes down, the prices go up, and vice versa—so rising yields, falling prices. And what we can see there in 2013 is that the yields were at a quite low level. And estimates would say that interest rates in general might have been about 1% too low based on economic fundamentals.
And what occurred during the summer months was the Fed, who's been purchasing assets, talked about tapering—slowing down the rate of purchases— and we saw reversion back to fair value, at the same time of the Detroit bankruptcy and Puerto Rico fiscal stress, and we saw underperformance. What ultimately happened is we ended the year at a fairly high rate; go back to the yield chart, please.
And then entering the year with the heightened tax advantages from the higher marginal income taxes, lower supply, and a relatively cheap asset class, we saw a strong performance. So now we've rallied about 70 basis points or 0.7%, creating returns of about 6% in munis.
Rebecca Katz: Wow, that seems very strong for bond funds.
Chris Alwine: And I think what's important about this is that the headlines can sometimes force investors to do the wrong thing at the wrong time and that long-term perspective, riding through a little bit of short-term volatility to really realize the value of the investment over a longer time period.
Rebecca Katz: I think we're going to hear a lot of that. That's very much keeping with Vanguard's investment principles.
Chris Alwine: Exactly.
Rebecca Katz: All right. Well, typically—we've answered a couple questions— typically, I like to find out a little bit more about our audience so that we can tailor our questions as we go through the webcast. So, on your screens, you should see our first polling question on the right-hand side. If you don't see it, check and see if your browser's zoom setting is set to 100%. It's usually down in the right-hand corner.
And our first poll question is, "Please rate your knowledge of municipal bonds or municipal bonds funds: Somewhat knowledgeable; Very knowledgeable; Not knowledgeable at all." And we'll get those results in just a few seconds and share them and that'll help us gauge how to answer all the questions you've sent in.
So, why don't we take another question? We actually have one just in who's asking—this is from Arthur in Massachusetts—asking, "What is the true risk between AAA- and A-rated muni bonds?" So, either of you could talk about that. Both are very high-quality, AAA and A ratings.
Chris Alwine: Right, exactly. Well let me just take a step back. The rating agencies—Moody's and S&P and Fitch, the three primary rating agencies—will assign a rating to indicate the likelihood of default, okay, and AAA being the highest rating has historically had a very low probability of default, down to BBB, AA, A, BBB, and they're the investment-grade ratings, and then below that would be speculative-grade, or non-investment-grade ratings.
So, what we're really talking in that question is AAA to A—and I think it would be good if we could pull up the default chart—to say relative the rates of default have been quite low in terms of investment-grade securities. If we look back, the top part of the bar shows investment-grade-rated default rates based on a Standard & Poor's time series, we're only talking one or two a year over the past ten years or so.
So, both of those would have a very low rate of default. The AAA certainly has higher credit quality in terms of looking at the financial condition of that entity, and then we look at where the yields would be between those AAA versus A. Historically the market might offer, oh, you know, 0.8% to 1% higher yield to purchase a A security compared to a AAA security.
Daniel Wallick: One of the ways you can think about it is a spectrum, and AAA is at the high end of the spectrum, A is still on that quality level, and then below BBB—so BB or less—is speculative. And there's really a range, and it's all gauging on the strength and the quality of the issuer.
Rebecca Katz: Great. Well, why don't we see if we have the results of the poll in? So, we asked you, "Please rate your knowledge of muni bonds and muni bond funds," and 60% of our audience said that they are "Somewhat knowledgeable"; about 23% said, "Not knowledgeable"; and only about 17% said, "Very knowledgeable." So, that gives us a gauge. Is that surprising to either of you?
Daniel Wallick: No, I think most people usually throw themselves right in the middle of whatever the range is, but it's pretty—you know, muni bonds—people are familiar with the word "bond" but the "municipal" part sometimes is confusing, and it can be somewhat obscure. So, it's a wonderful opportunity to have this chance to talk about it.
Rebecca Katz: Well, great, let's go back to some of our questions, and I'm looking down the list for the next question. So, we can keep going further. So, our next question in here is from Craig, and he says, "As a muni investor prepared to hold bonds until maturity, am I not better off owning bonds directly rather than through funds?" And we get this question a lot, whether it's muni bonds or just taxable bonds: "Should I just own a bond outright or own a fund?" And of course Vanguard offers both, you can buy both at Vanguard—so, let's answer in a very unbiased way.
Daniel Wallick: Sure, the way I think about that, Rebecca, is to think about, "Do you want to hold a single stock or a fund?" You can think of it the same way. There are pluses and minuses on both sides. The big challenge is when you hold a single security, whether it be a bond or a stock, you're taking more-concentrated risk. So that entity may do better than the broad diversified pool of bonds or worse.
And typically it can go either way, but you're potentially taking more risk. There's more variability in what the results can be.
Rebecca Katz: But in terms of the comparison between stocks and bonds, right, there's a big difference in the risk level of holding one's stock than a bond, right, because there's some implicit guarantees behind it?
Daniel Wallick: There may or may not be. So, the challenge with bonds is there's an asymmetric risk structure, and hopefully that word's not confusing.
Rebecca Katz: No, not at all.
Daniel Wallick: The point with asymmetry is with a bond, there's a limited amount of upside you can get, but you can go down to zero on the bottom end if you default. So taking more risk with bonds is actually challenging because there's a limited amount of additional benefit you can get from the increase in a bond.
Chris Alwine: And just to tag along on what Daniel was saying is that when you look at a portfolio of bonds, in some way it's like a mini mutual fund except it doesn't have the benefits and advantages of a large mutual fund around diversification that Daniel brought up. Execution efficiency. So, at Vanguard, we have an extensive trading desk looking to get best execution, trained experts, years of experience executing in the marketplace.
Rebecca Katz: And that marketplace is fairly opaque, right? Not like the stock market, where all of us can pretty much see what's going on with a stock price.
Chris Alwine: It's an over-the-counter market in terms of relationships with dealers and understanding the valuation. Now, what's interesting about munis is they're somewhat of a complex security, believe it or not, because of the call structures and the dollar prices and tax laws, and the lower liquidity of the marketplace. So it's certainly a market where having trained experts trading securities is quite helpful.
And the last advantage of the fund is "liquidity," meaning that if there's a need to redeem fund shares to spend money on specific purposes, it's there, as opposed to having to go into the market and sell a bond that's subject to best execution or good execution in the marketplace.
Rebecca Katz: Since we're talking about holding bonds versus funds, why don't we go to our second polling question and find out actually what our audience holds. On your screen, you should see our second polling question and what we'd like to know is, "Are municipal bonds or municipal bond funds a part of your portfolio? Yes; No; No, but I'm considering them as an investment." Maybe we'll convince you after this webcast. Just kidding. In a few moments, we'll get those responses and I'll share.
I do have another question just in asking, "What is the risk of munis versus other bonds?" So we did the stock/bond comparison, but munis relative to other government bonds, maybe, and then corporate bonds?
Chris Alwine: When you look at a risk of a bond, there's a number of factors that really drive risks in fixed income investment. The first is what we call "price sensitivity" or "duration risk," and so longer-maturity bonds, those with a final maturity date, when the principal is repaid, will be more sensitive to yield changes up and down.
The second risk is around the credit risk, and the credit risk is the risk you bear that the issuer of the bond may not be able to pay back the principal and interest.
When we look at those two risks, the duration risk will be roughly comparable if the maturity or the durations are in the same ballpark. The credit risk, if we look at the default-rate slide, you can see the number has been quite low over time. So we're thinking 70 or so defaults over the past 40 or 50 years. Even in the speculative-grade ratings, the default rates have been low. And that's a contrast to in "corporate space" where you can see quite high rates of default in below- investment-grade securities, and particularly the very low-rated rating buckets.
Daniel Wallick: Right. Muni bonds default about 1/30th of the time that corporate bonds do, so there's a distinct difference there.
Chris Alwine: And there are strong reasons for that. If you think of a municipality, it really doesn't face the competition that a corporation might face. It has taxing ability.
Rebecca Katz: It has a tax base, right, for the most part.
Chris Alwine: It's essential. You need a state or local government, and they also will have balanced-budget requirements, so that they need to have balanced budgets. Those inherent credit characteristics are a big reason why we have experienced the level of defaults that have occurred over the past 40 years.
Rebecca Katz: Okay, great. Well, why don't we see how many of our audience actually hold muni bonds today? We should do this after the webcast too, to see how it's changed. We asked you, "Are the bonds themselves or bond funds a part of your portfolio," and 60% of our audience—maybe it's the same 60% who said they're somewhat familiar—also hold muni bonds and bond funds; 28% fell into that, "No, but I'm considering them as an investment option," and 12% said, "No." So a good mix and not all that surprising.
Our next question is from Delbert in Melrose, New Mexico. And Delbert—thanks for your question—says, "Why would an investor buy any type of bond fund now that interest rates are set to rise significantly?" That's a question we've been actually hearing for quite some time. We haven't seen it happen yet.
Chris Alwine: Yes, right.
Daniel Wallick: One reason to do that, if you start with the beginning principle of investing, usually it's about asset allocation, right. What should your mix of stocks and bonds be? If you look at that from a distance, you may want to scratch your head and say, well, if the long-term history of a stock is typically 10%, just throwing that average out, and bonds has historically been 5%, why would you ever buy a bond when it's lower-yielding than stocks? And the reason you do that is because of the volatility. What we mean by "volatility" is the amount that those securities move around in their price.
The value of bonds in a portfolio, at any time, is to balance out the extreme movements that you can have in your stock portion of your portfolio. And so the value of a diversified portfolio—of having both stocks and bonds or multiple different types of securities in your portfolio—remains constant regardless of the level of bonds. That's the reason why people should think about whether or not they want to have bonds in their portfolio.
Rebecca Katz: But if you know, if you just know, like this gentleman knows, that interest rates are going up, which we will ask our experts whether they know that for sure or not, maybe it's a question of when you actually go to move to—if you're those 12% who don't have bonds—do you enter the market or not? Do you have a perspective on that, Chris?
Chris Alwine: If we go back to the yield chart, at the beginning of this year, investors were convinced that yields had to go up. And so, forward views about the performance of financial markets, whether it's the stock market or the bond market, are quite difficult. It implies a level or an ability of timing of the market, by saying, "I know when it's going to go up, I know when it's going to go down."
Now certainly, the low-yield environment, if we just do the bond math that says, "What's the expected return of a bond in this environment?" It is certainly lower than we've seen in the past by definition, since the starting yield is much lower. But we have to think what Daniel said; it's about diversifying a portfolio, building that stability in there.
It sort of reminds me of the Will Rogers quote from the Great Depression, "I care more about return of my capital, as opposed to return on my capital." Certainly, if we look historically, stocks have produced higher returns with higher risk. But at times, based on risk preferences or tolerances, more bonds may make sense for specific individuals.
Rebecca Katz: Okay, great. Our next question is from—oh, it's a good follow-on question, from Steve in Columbus, Ohio. Thanks, Steve. "What is the role of munis in the taxable portion of a diversified portfolio? How do they fit into your overall bond allocation?" So now we're getting more specific. You know you need bonds for diversification and to minimize volatility. How much muni versus taxable?
Daniel Wallick: Right. A lot of this is going to drive off of a couple things. One, what's your risk tolerance. We talked earlier about the different types of bonds. Let's just talk about the three big buckets. You can have Treasuries, which are guaranteed by the U.S. government. You can have municipals, which are guaranteed by a state or local government, or you can have corporate bonds, which are guaranteed by some private company.
The risk level is: the U.S. bonds are most secure, right, U.S. Treasuries are the most secure; munis are next; and then corporates are there. So where are you in terms of that comfort level of how much risk you're willing to take? It's really the first question to ask.
The second one is, "What's the yield on munis, what's your tax rate, and how does that relate to the other options you have, and is it a valuable investment based on that?"
Rebecca Katz: Right. I believe we have a chart we can show you on how to calculate what we call the "taxable-equivalent yield," correct?
Chris Alwine: Yeah. If we could bring up that slide to go through it. Now, it looks a little busy up there, but if you look at the top formula, the tax-equivalent yield equals your muni yield divided by one minus your tax rate. Your tax rate, though, is the combined tax rate. It would be your top marginal federal tax rate, as well as state, and then also the Affordable Care Act. This is a new tax that was instituted in 2013 for investment earnings. Now, munis are exempt from that.
What we did here is we took an example. A 10-year A-rated muni today yields about 2.80%. Someone in the top tax bracket would be paying 0.434% tax rate, so one minus that percentage. We divide that out, and we get 4.95%. Now it's important to keep in mind when we're looking at tax-equivalent yields, we need to compare them to a similar alternative in taxable space. Daniel brought up the different risk spectrums, so if we were to calculate the tax-equivalent yield of a high-yield muni to a Treasury security, that would not be a fair comparison. One has a lot more risk than the other. So A-rated to A-rated, AA to A, those types of comparisons make more sense.
Now for the mathematically inclined, I will give a differing variation for that. It's not up on the screen, but your break-even tax rate would be one minus the muni yield divided by the taxable yield. For those who want to manipulate the formula, who prefer to do algebra, it's out there to give it a try. But one minus the muni yield divided by the taxable yield gives you your break-even tax rate.
Rebecca Katz: Okay, great. Well, we actually have a good follow-up question around breakevens, actually. This is from Timothy in New York, and he says, "Analyzing breakevens between taxable and tax-exempt bonds, does it make sense sometimes for someone not in the highest marginal tax rate to invest in munis?" Daniel, why don't I throw that one to you?
Daniel Wallick: It can. One is, "What's the absolute level of muni yields?" So, where are they actually trading? The other is, "What's your tax rate, your tax level?" Again, going through the math that Chris just articulated, you can figure out if it's a benefit relative to the other options that are out there.
I will go back and just reiterate what Chris said. It's really important to be comparing apples to apples, here. There may be something that looks attractive on a yield basis, but what's underlying that that we don't recognize is there's actually more risk associated with that. That may be a perfectly rational decision to make, but you want to make that consciously, not subconsciously.
Rebecca Katz: Right. Great. Our next question, speaking of risks, is from Sheets in Seattle, Washington, who says, "What criteria does Vanguard use regarding the risks, including pension risks, of municipal governments in selecting its portfolio?" I talked about headline risk, and there have been a lot of headlines around instability of pensions. What do we look at when we're thinking about bonds for our funds?
Chris Alwine: Absolutely. It's a great question. It really gets to the heart, the essence, of what investment management is about. It was once said that investment management is the discipline of relative selection. "Relative selection" says, "Are we purchasing good opportunities," meaning that, are we compensated fairly for the risk? The analysis part is around the risk.
There's really two types of risk in muni bonds. The first is credit risk—I talked about the ability of an issuer to pay back the loan, or the debt—is a big one. For that, we're using standard financial analysis around their balance sheet, their budget, their taxing ability, the economy of the area, as well as very important, the legal structure of the deal.
Munis, unbeknownst to a lot, but the revenue streams that are pledged to service the debt can be more complicated than you think. We have a team of analysts, and this is a really important point, about having in this day and age where there's more credit stress in munis than in the past, to have that team of seasoned credit analysts to review all the holdings.
Now on the portfolio management side, they're looking at the structure—the call option, the dollar price, the maturity—and then they're pulling that all together to say, "Is this a good opportunity in the market?" If it is, we're looking to purchase it. At the same time, always scouring the portfolio to say, okay, this bond has run its course. The value is out of the bond. It's overpriced. Let's move that bond out and purchase a more attractive security.
Daniel Wallick: If I could just add one thing to that, Rebecca. The other thing to think about, that we talked about earlier, is we're doing that in the context of broad diversification. If you look at the long-term national fund [Long-Term Tax-Exempt fund], there's a thousand different securities in that. We're never going to make a big bet on any one name. We want to really try and diversify the risk we're taking, and we think over the long run, that's going to serve clients really well.
Rebecca Katz: Okay. Well, speaking of risk, we are actually apparently getting a ton of questions in on Puerto Rico and Detroit, and how we think about that, and those risks, and—I think it's important that we talk a little bit about that. I'm just going to open that up to both of you to talk about that. And put it in context of broad diversification, as well.
Daniel Wallick: Sure. If I could, I'm just going to say I have a long history in municipal defaults. I grew up in New York in the '70s, when Gerald Ford asked them to drop dead. Before Vanguard, I worked on the solution for Philadelphia in their coming restructuring of their debt, coming out of a problem, when Rendell took over as mayor. So I've got a lot of experience in this.
The challenge is, when we read about Detroit and we read about Puerto Rico, even if go beyond the headline and read the articles, it's pretty miserable news. I mean, it's a pretty bad situation. The challenge is, that's one of only a very few of all the issuers who are out there. There must be 70,000 different issuers out there.
The fraction of the number, even on a dollar basis, this is really, really small relative to everything. Going back to that issue of diversification and having all the different names, the impact on a fund, certainly on a diversified fund, is less. That's just to put it in context of how we think about it terms of the fund.
In terms of those specific names, there are some really serious issues. Let's start with Puerto Rico. The challenge with Puerto Rico is it's a territory, not a state. There's a whole series of legal issues you'd have to figure out, if they did actually choose not to pay back their debt. That would be an issue. Let me just pause right there.
When we look at credit for anybody, we're talking about two factors. It's, "Do you have the ability to pay," and "Do you have the willingness to pay?" You may hear this over and over again when you hear about any bond, and certainly with municipals. So, do you have the ability to pay and the willingness to pay?
Most of these entities have the ability; the question is the willingness, because there's some trade-offs they have to make. That's really assessing those becomes highly qualitative. But Puerto Rico's real challenging because it's a territory.
And then Detroit, which is going through a legal process right now, the challenge with that one is there are a lot of different people, stakeholders, involved, and everybody has a different view of what should happen. Pensioners have one view, current workers have one view, bondholders have another, and the judge and the oversight entity from the state have to figure out how they're going to slice a smaller pie.
Chris Alwine: I'll just add that if you look at Puerto Rico, it's a unique issuer in terms of the level of debt. Puerto Rico has a lot of debt relative to the underlying economic potential or growth rates of the Commonwealth.
Rebecca Katz: Naïve question: Does Puerto Rico have taxing authority?
Chris Alwine: Oh, absolutely. In Puerto Rico, absolutely.
Rebecca Katz: Oh, okay. In Puerto Rico. Making sure.
Chris Alwine: Yes, and they certainly levy taxes. The new administration is aggressively tackling the budgetary challenges, and attempting on the debt load, but they need to get some economic growth there. It's unique to the muni market. What happens, we saw the graph on the defaults, is there aren't that many, and the market tends to segment them, and say, "Okay, that's one out of 30,000; one out of 70,000 because it's not systemic." Now, Puerto Rico has a lot of debt, so if it did go through a restructuring, it could cause some volatility in the market if there was forced selling. But we would see that to be much shorter-lived than some systemic event.
A few years ago, a prominent analyst came out with a very bold prediction about very high levels of defaults. Those type scenarios, we don't see. We see a higher level of bankruptcies in the future, but still, very isolated. What's interesting about a lot of muni issuers is we often say these could be the slowest-moving train wrecks around, because if you think of Detroit, the peak Detroit, whether it was population or economic growth, was sometime in the late '70s; thirty-five years later, we got the bankruptcy. It tends to be slow. Generally predictable, you know, but it comes down to what Daniel said: a willingness and ability. That's part of the analytical process to assess that.
Rebecca Katz: A question. There's a writer and advisor, Allan Roth, who e-mailed in with a question about the $2 trillion in underfunding pension and health-care liabilities that many municipalities face. He asks if we would see additional systemic defaults if stocks don't have a great run. Can you talk about that relationship between stocks and pension liabilities?
Chris Alwine: If we take a look at pensions, the average municipal pension fund is not funded at 100%. It's going to be funded less than that. When the $2 trillion dollars is mentioned, it's assuming that the funding level is at 100%. Now, most experts would say an 80%-funded plan is adequately funded for a state or local government.
"The challenge is, when we read about Detroit and Puerto Rico, even if we go beyond the headline and read the articles, it's pretty miserable news. I mean, it's a pretty bad situation. The challenge is, that's one of only a very few of all the issuers. There must be 70,000 different issuers out there. The fraction of the number, even on a dollar basis, shows this is really, really small relative to the entire muni market."
But there are a number of plans that have funding levels much lower than that. Since they're investing the plan assets in a diversified portfolio, but with an allocation to equities, if those equities were to go down, it's going to require greater contributions.
And so when we look at entities who have pension plans, what we're really looking at is the funding level and how much of their budget is required—they're called the "actuarially required contribution," or ARC—on an annual basis. And are they making it? If they're making the ARC, that means they're closing the gap. But if the market were to fall, the ARC goes up. If that's a challenge for their budget, meaning it consumes a larger and larger portion of the budget, then there's a higher risk in those entities. Certainly entities that have pension issues we're cautious, particularly the lower-rated entities, is where we've had interest.
Now in terms of the correlation, certainly that correlation should go up over time if we see weak stock markets, which as I said before, require greater contributions.
Rebecca Katz: Especially for an extended period of time.
Chris Alwine: For an extended period of time, exactly.
Rebecca Katz: So Daniel?
Daniel Wallick: If I could just underscore, this really comes down to the willingness, the willingness to manage that issue. That's what we're really looking at. Are people willing to make the continued commitment to do that? We haven't seen a systemic relationship of that across the country, again, as Chris mentioned. Some people are very good at it, some people are really bad at it, and there's a lot of people in the middle. You really want to look at that through time.
Rebecca Katz: We need to go vote in our local elections, which always have low turnout. We've had a couple of clarifying questions come in. We had a question from Patrick in Massachusetts, who says, "Can you explain what duration means," since we've mentioned that a few times. Then we also had a request to see that equation again, so you can write it down. We could certainly send it out later. First, explain duration risk. Many people are familiar with maturity of a bond but not duration.
Chris Alwine: The duration is a measure of the price-sensitivity. That means for a change in interest rates—we had that first graph I talked about when rates fall, prices go up, rates rise, prices go down—duration is a way to give you an estimate of how much prices go up or down. It's typically shorter than maturity, so a 10-year bond might have an 8-year duration.
The standard formula—we don't have it up on the screen—would say take the duration, –1 times the duration, multiplied by the yield change will give you an approximation of the rate change. So a 5-year bond with a 4-year duration, if interest rates go up 1%, we could see that price of the bond fall about 4%.
Daniel Wallick: Rebecca, I think next time we should give Professor Alwine a whiteboard.
Rebecca Katz: I agree.
Chris Alwine: Oh, a whiteboard. That would be fun.
Daniel Wallick: He can walk us through.
Rebecca Katz: We have to tell people when they register to bring their calculators.
Daniel Wallick: The other way to think about it is the weighted average of the bond. You have bonds at a certain maturity, and they have payments throughout time. If you weight that and average, where does it fall out? It gives you the length of the bond.
Rebecca Katz: Because in a bond fund, you have 10-year bonds and 20-year bonds, and they all have different maturities.
Daniel Wallick: Yeah, correct.
Rebecca Katz: So some of them are at 6, and 4, and 3—
Daniel Wallick: So you take the weighted average of that, where do you fall down on that sort of scale and that spectrum? The impact is still the same. As Chris said, the longer duration you have, the more you're going to move around with the interest rates. The shorter you have, the less it's going to move around.
Rebecca Katz: People can find that on our website for our funds.
Chris Alwine: It's absolutely on the website. The average-weighted maturity as well as the average-weighted duration are out there.
Rebecca Katz: Okay, great. Our next question is from—well, we've answered some of these—from Charles in Mitchellville, Maryland, who says, "General obligation bonds are considered safe, since the taxing authority of the issuer backs the bond payments and principal. With the current political mania for no new taxes, just how safe are these bonds?" It's interesting, I mentioned local politicians, and you've talked about willingness. How do politics affect muni bonds? Does it change your views on willingness?
Daniel Wallick: Let me just start with, I think the question's really a helpful one for clarification. We haven't talked about it yet, but we probably should. There are a variety of different types of security. How is the government going to pay you back? General obligation is, "I'm going to pay you back with whatever money I have from all different sources, every possible source," which generally means income or property taxes. Those are the key ones.
But there are other sources. You can have revenue sources, which is based on sewer fees, or turnpike fees, or any of those. So there's a variety of sort of revenue-based issues that people can use to sort of have that, so understanding that there are different types of security that are being pledged to pay back your bonds.
Historically, general obligations have been the most secure. If you look at Moody's, 71 defaults over the last 41 years. Only five of them have been general obligation bonds. Most of them are these, what we call "revenue bonds." Some source of an individual project is providing the revenue to pay back the bonds. There's definitely a spectrum there.
In terms of the "no new taxes," people talk about that a lot, but when it comes to push or shove, when they look at the trade-off of not paying back your bonds or paying back your bonds, it is most often always beneficial to pay back your bonds so you can go back to the market again.
Chris Alwine: Exactly, yeah. Most issuers are going to require market access to fund capital projects or to roll over existing debt. The cost of bankruptcy in the few that have taken place, if you go back and ask those officials, oftentimes they're questioning whether it was actually worth going through the bankruptcy process.
Rebecca Katz: It must take a long period of time before they can regain that trust to get funding.
Chris Alwine: Yeah, absolutely. Absolutely.
Daniel Wallick: Also, Rebecca, we typically see, when you sort of poll voters, they don't want new taxes. But if you ask them something specific, "Yes, I would like a new road." They're typically willing to pay for something that they think is prudent. If you connect those with the capital projects, typically there is that opportunity of repaying.
Rebecca Katz: Okay, great. Well, another question about different types of muni bonds. Richard from Chester, Connecticut, says, "Does buying an insured municipal bond guarantee that your investment will be protected even in the case of a municipal bankruptcy?" Daniel, maybe, since you're talking types of bonds.
Daniel Wallick: Right. What bond insurance is, is a third-party entity, a private company, that is saying, "For a fee we will guarantee that you get paid." If the issuer, say the "city of someplace," decides not to pay, we, the insurance company, will come in and pay. There's no absolute guarantee. That's another contractual relationship you have. That company has to be in business, the legal issues have to get worked through; you see this in Detroit right now. There's a whole series of issues. It certainly is belts and suspenders. It's another level of value, potentially. But there's a price to be paid for it, there's a trade-off. I don't know Chris, if you want to talk about how we think about—
Rebecca Katz: Do we have those in our fund portfolios?
Chris Alwine: Oh, certainly we do own insured bonds. It's really a double-barreled credit enhancement. If the underlying issuer were to default, and this happened in Detroit, there are Detroit city-owned bonds in which the bond insurer's making the principal and interest payments, you have a second layer of credit protection. But as Daniel said, they have to have the claims-paying ability at the time to pay off the bonds.
We do own, and our preference is to actually own uninsured bonds, simply because we have a team of credit analysts who can evaluate the credit risk and looking for opportunities. An insured bond will typically trade at a lower yield than an uninsured bond. Daniel talked about the fee, that's sort of the insurance premium that the issuer pays, and the bond trades at a lower yield.
Now the lower the rating—meaning, let's say, BBB rating of the underlying—the larger the gap. That insured bond will trade at a much lower yield than where it was uninsured. So a AA insurer insuring a BBB bond, there could be upwards to maybe a half-a-percent difference, a AA to AA, about the same rating quality. You're not going to get that much of a yield difference.
Rebecca Katz: Because the insurer doesn't have as much risk.
Chris Alwine: Yeah.
Daniel Wallick: If I may, Chris earlier mentioned, we have 20 credit analysts who look at all of our credits. We're happy to make those judgments about credit. I mean, that's what they get paid for, that's what we're good at. Now you can either ask somebody else to make that assessment, which is the bond insurer, or you yourself could do it. That's sort of the trade-off. We actually always look through whatever the rating agencies or the bond insurers do, to look at the underlying credit. That's what those 20 people do, regardless of how it's—
Rebecca Katz: Right. We never just use the credit-rating agency's evaluation as a rubber stamp.
Daniel Wallick: Correct.
Chris Alwine: Exactly. We're independent, thorough, and rigorous analysts. We're assigning our own independent credit-assessment opinion on all the issuers that we own in the fund, and on insured, we're still looking through to the underlying.
Rebecca Katz: Okay, great. Well, apparently, we are just being badgered for that really handy equation, so we're going to put that back up on the screen, and let you see it for a few moments. Get your pens out. Here it is. Do you want to walk us through it one more time? Maybe Daniel, you this time?
Daniel Wallick: One of the ways to think about it is one minus the muni yield over the taxable yield. That's the easiest way to think about it.
Chris Alwine: That's your break-even tax rate.
Daniel Wallick: If that comes out as, what is it, one, you're indifferent to which one you buy. I would say that this is a nice equation to have and to work through; it's not the reason to buy a muni bond or not, alone. You have to be comfortable with the underlying risks associated with that.
And as Chris mentioned earlier, owning a Treasury relative to a muni, there are very different risks associated with that, the same way there would be a corporate in here. That's the first level of comfort you have to get comfortable with, is that qualitative assessment. But then you want to look at—you can actually do the math—of how well or poorly are munis trading today, relative to comparable equivalents. This math would help you work through that.
Chris Alwine: Maybe we want to pull up the after-tax yield chart, at this point, that we have. Looking at—if you could just pull that up.
Rebecca Katz: You work with finance guys; you get lots and lots of charts.
Chris Alwine: Lots of charts, yeah. So we got two charts here.
Rebecca Katz: It's great. Getting an education today.
Daniel Wallick: This is a very good one.
Chris Alwine: This ties into one of the other issues that we'd like to discuss about tax reform. The top chart is the after-tax yield advantage of buying a AAA muni to a 30-year U.S. Treasury bond.
Daniel Wallick: Historically.
Chris Alwine: Historically, over time. The average is about 1.5%, that's the horizontal line. You can see it cycles around that, and the financial crisis in 2008 it peaked up at over 3%. Lately it's about at the long-term average, maybe a little bit through.
Daniel talked about the difference in risk between a muni and a Treasury. Well, this is an indication of what that is. That extra 150 basis points of yield, 1.5%, is really around, "Well, I'm buying something that's less liquid. I'm buying something that's a little lower credit quality. I'm buying something that has a call option attached, which has some implications on yield."
Daniel Wallick: It takes more work to figure out what it is.
Chris Alwine: What it is, and so forth. You can see, though, that it's fairly stable in a variety of tax regimes. The bottom chart shows the top marginal federal tax rate over time, and you can see it goes up, it goes down, the last blip there is the sun setting over what was known as the "Bush tax cuts." It's fairly stable, but that's an indication of the compensation investors demand for taking on the risk of owning a muni over a U.S. Treasury security.
Rebecca Katz: Great. Well, speaking of risk again, going back to Puerto Rico, Paul sends a question saying, "When a default like Puerto Rico actually happens, what happens to investors? What are they actually left with?" So, it's a bankruptcy; if you own the bond, you're a debtor. What happens?
Daniel Wallick: Okay, so we can look at history, and then we can look forward. We should look at both of those. Because, I'm going to tell you, history's just one of many possible outcomes that could have happened. We shouldn't bank everything on history.
But historically, with muni defaults, you're getting 90%+ of the dollar back. The haircut you take, that technical term, right, the amount of pain you have to suffer has historically been modest. But there's been some.
Chris Alwine: I will say—that's for general obligation bonds—but the number of observations, the instances of default have been few historically.
Daniel Wallick: Which is why we have to be careful about looking at history relative to the future. Because the future may be different. Again, let's work through a couple. We can look at both Detroit and Puerto Rico. Again, the two are different because of the organizational structure. Again, being a territory, Puerto Rico has a really different avenue or workout structure than Detroit. I think Detroit's an interesting one, and I'm going to start there.
Detroit has said, we're having trouble paying, there's an oversight coming in, there's a judge, and there are a lot of people sitting at the table saying, "I need my money that's been pledged for X." That includes bondholders. That includes the current employees. That includes the residents of the city, and that includes pensioners. The question that the judge and everybody else has to figure out is, "Who gets paid first, and how much does everybody get paid?"
Chris Alwine: The process of the bankruptcy is that the city provides a plan of adjustment. That's supposed to right-size the balance sheet, right-size the level of debt relative to the ability to service that debt. But what ultimately happens is, in this case, the financial manager will be negotiating with all the different creditors. Daniel talked about the retirees, pensioners, the bondholders, and so forth trying to strike deals that everyone can agree on.
Now what's different about Detroit is that the recovery values have been lower at this point in time. Now, that's not finalized. There's still a lot of work to be done in Detroit. The unlimited tax GO, which typically, or historically, received almost 100 cents on the dollar, negotiated about 70% on the dollar. That's lower than what we've typically seen—
Rebecca Katz: That's already happened, and that's final?
Chris Alwine: Well, there's an agreement, but the plan has not been fully blessed and signed off on, so it's not an approved plan. The lesser, sort of in a seniority ladder, the limited-tax bonds they're still negotiating, but the financial manager came out at 15 cents on the dollar, maybe part bargaining position. Ultimately, for those entities that are lower-rated, and local GO space in states that allow for bankruptcy—not all states allow a local to file for bankruptcy—we expect that the risk premium, or the yield on those types of securities, will go higher over time to reflect the higher level of risk.
Now, if we look at the muni market, most of the muni market is rated A-rated or above. It's a high-quality market. But in the BBB land where there's pension issues, that's certainly an area that we're cautious on.
Rebecca Katz: I have to ask the question that's probably on a lot of investors' minds, which is, "Do our funds have exposure to Puerto Rico or Detroit?" So, put you on the spot.
Chris Alwine: You know on Detroit, we made a decision to hold insured bonds. We own some insured bonds that were purchased a while ago. This is a great example of relative value. We could have sold them into the market, but the level we would have sold them at was too cheap. We looked at the underlying and said, "Well, it's trouble."
However, the bond insurance is on there, it was a AA-rated bond insurer, and we said, they're going to have the ability to pay if this default takes place and so we held that.
The other bonds that we hold in Detroit are—and we're talking under 0.25%, so these are very small holdings—are the water and sewer bonds. And so this is a separate legal entity owned by the city that provides water and sewer services to the city as well as the surrounding counties. That has been, at this point, an unimpaired creditor. We expect to get 100 cents on the dollar back on those bonds. Now, in terms of Puerto Rico, we've had a very cautious approach to Puerto Rico for a while.
Rebecca Katz: Right. We've been talking about Puerto Rico a long time.
Chris Alwine: They've had a lot of debt. We've had a large underweight to that. Puerto Rico has about, depending on how you measure it, it could be about a 3% weight in the municipal bond market. We've been running about on average about a 1% weight in entities, because of the number of issuers within Puerto Rico, as well as securities that we feel have less downside risk in the portfolio.
Daniel Wallick: If I could, on average, our funds have less than 1% exposure to Puerto Rico.
Rebecca Katz: All the funds together.
Daniel Wallick: Right. It's the third-largest muni issuer in the market. But we have a very low exposure to that. If I could just loop back to the original question here, which was, "What happens if Puerto Rico defaults?" That's a whole other kettle of fish because it's a territory, it's not a state. There's a real question of, "Could the legislature just wake up one day and do what Argentina did and say, we're just not going to pay you back?" Let's go to court in wherever, New York, or wherever this is done. That would be a whole other way of approaching it. Because it's a territory, would the federal government come in, how would they come in? It's very complicated on what would happen there.
Chris Alwine: Exactly.
Rebecca Katz: Hopefully we will not face that decision. We have a question about ratings agencies from Loretta in Lincoln, Nebraska, who says, "Can we trust the ratings now, from the agencies that did so poorly with their ratings before the 2008 financial crisis?" So obviously we look at them, you mentioned we also look past them. How should investors consider rating-agency ratings?
Chris Alwine: If you look at where the rating agencies were criticized, it was on the subprime taxable asset-backed securities. These were a security that pooled subprime mortgages together, and they were assigning AAA ratings to issues that ended up defaulting. They were sort of roundly criticized for that. They weren't criticized for corporate bond ratings, or municipal bond ratings; you didn't see that.
Now, it doesn't—we're not going to accept a third-party rating. We value our independent judgment on the credit assessment of these issuers, and so that's the advantage of having a team of analysts. That's their job.
Daniel Wallick: I think the rating agencies as the third party is a good starting point for anybody to think about the relative value or strength of a credit. But you want to think through that and look at the specifics of what's going on.
Chris Alwine: That's a good point. It's not like you ignore them because they can have market impact. If they were to downgrade, you could see bonds widen out and so forth. But we need to have our own independent credit assessment.
Rebecca Katz: Great. So, Alan, who doesn't give us a city, says, "My financial planner says the sweet spot for muni funds is in the intermediate range. I could take some risk but wonder about the eventual rise in interest rates." We've had a few questions that were coming in about what's the sweet spot for duration. So, obviously we never give specific advice on a webcast because we have no idea what your risk profile is or how much money we're talking about, but is there a "sweet spot" or is that just too subjective?
Chris Alwine: I would call it subjective because you have to think, and Daniel brought this up earlier, "What are my objectives? Do I want a short-term bond fund because my risk tolerances could be lower, or I have a need to spend the money sooner?" Those types of things.
I think why people may talk about intermediates as being the sweet spot is that they provide more yield than a short-term bond fund but with a lot less price sensitivity in a down market than a long-term bond fund.market. So, they're stuck right in the middle of that maturity range or duration spectrum, and so individuals seem to have gravitated to that. But a sweet spot, I'm not so sure. You know, it's really based on your goals.
Daniel Wallick: Well, if you look at the yield curve, right, people talk about that "hockey stick"—
Rebecca Katz: Yeah, yield curve—you may have to define that.
Daniel Wallick: Sorry, so that's the, "What's the yield you get at every different time point on the horizon?" So, you can get paid on a 3-month, 6-month, 1-year, 2-year, 5-year, 10-year, 20-year, or 30-year maturity, and you get paid a different amount on each one of those. And the longer you go out, the more you get paid. That's because there's more risk associated with having to hold that for that long period of time. So, the sweet spot is, "Is there an optimal point on all of that where I'm paid the most for the amount of risk I'm taking?"
Given the current shape of the yield curve, a lot of people look right at that intermediate where relative to what I could buy that's shorter, I'm getting paid a lot more, but relative to what I'd have to buy that's longer, I'm getting paid close. So, that's why people look at that. Again, there are a lot of different factors that go into how you want to make a decision, but if you look at the yield curve, there definitely is a bend in it.
Chris Alwine: You do see that around 20 years, 15 to 20 years, it starts to flatten out. Think of the yield curve, you've got maturities and yields and they go up generally speaking.
Daniel Wallick: The yield is what you get for owning bonds.
Chris Alwine: Right. What you get.
Rebecca Katz: That's the interest rate.
Daniel Wallick: Right.
Rebecca Katz: So, that yield curve, that sweet spot, is going to change as interest rates fluctuate or inflation, correct?
Daniel Wallick: Well, so that's the way it looks today, right. The question is, "How's that going to impact you over the long-term?" And what matters for that is how does the yield curve shift and change. There are all these different terms. You can call it "bear flattening," "twists." We're not going to get into the technical terms, but there are umpteen different ways that the yield curve can change, and how it changes would impact what your final results are.
Chris Alwine: Absolutely.
Rebecca Katz: Interesting. Brian from Pittsburgh has a different type of question. He asks, "What are your thoughts on the lack of dealer liquidity in the municipal market and overall bond market? What kind of impact could this have on munis being less liquid than other parts of the fixed income market?"
So, generally speaking, we've talked about one of the disadvantages or difficulties in buying a muni on your own is that it's really not transparent. That marketplace is not transparent. You have to call people. So, how is that relative to other bonds that you might be buying on your desk, and how should an investor think about that?
Chris Alwine: I mean there have certainly been changes in terms of the dealer's ability or capacity to make active liquid markets in the fixed income markets. Now, the fixed income markets, we mentioned before, are over-the-counter, meaning you've got a dealer in the center and all the buy-side firms; the clients are calling in buying and selling bonds to a dealer; you could be doing electronic exchange as well. That differs from the stock market where you might have a centralized exchange with highly liquid billions of shares trading a day. Now, after the financial crisis, a number of things happened.
One, the regulatory environment got more difficult for the dealers to take risks. So, they've reduced the size of their balance sheet, and internally the dealer community has made it much more difficult for the trading desk to grow the balance sheet or to take on more risk to try to level out the volatility that's in the marketplaces.
So, there's a few implications of this. The first implication would be that we're going to see higher price volatility, and particularly on the downside. So, when yields are rising and prices are falling, that may be sharper than in the past to get to the clearing level because the dealer community won't buy the bond to position it.
The second big implication here is that as a fund manager, you need to have an intentional liquidity policy, and at Vanguard we've had a long-standing policy in munis, a market with less liquidity than other fixed income markets, to hold more cash or more high-quality assets that will have liquidity when the environment gets difficult.
Rebecca Katz: I see. Anything to add to that?
Daniel Wallick: So, you can think about it as risk. So, what's happened in the dealer community is that we're less willing to take the risk of holding the bond. This is because of the items that Chris mentioned, because of regulation and because of market conditions. And so, I would say that's one of the advantages of a fund today is that what we're doing is we're looking at a lot of different securities. Again, I had mentioned 1,000 in the national fund [Long-Term Tax-Exempt fund] earlier. We're holding a lot of that. We're looking at all of that so that we're never stuck with any one big piece.
Rebecca Katz: Right.
Daniel Wallick: And again, that's the potential advantage of a fund versus holding individual securities.
Chris Alwine: That's a great point. So the trading desk is looking for those with a very diverse portfolio. Where do I get best execution in this environment? And it's in all different environments.
Rebecca Katz: And you could always wait and sell something different if you wanted to—
Chris Alwine: Sell something different—you don't have to sell one bond. You've got high levels of diversification to do that with.
Rebecca Katz: Great. Our next question is from Jim in Downingtown, Pennsylvania, so up the street from us. "If a yield on a municipal bond is greater than I can get elsewhere, is there any reason not to put some in my IRA account? I'm retired and like everyone else, I'm looking for income."
So, let's talk about muni bonds. First of all, muni bonds are tax-free, right? IRAs are tax-deferred, for the most part. So, would you ever want both—a muni bond in an IRA?
Daniel Wallick: Right, which I think it's a great question. Because you think intuitively—it's like well, that wouldn't make sense. That would never make sense because I'm already getting the tax benefit from the bond. Why do I have to put it in a tax-deferred fund? So, the question you want to get to is—there could be moments in time where muni yields are actually better than your equivalent.
But what you want to make sure you're doing is doing an apples-to-apples comparison. So, typically, when that most likely occurs is when we're looking at, say, a short-term Treasury versus a longer-term muni, and the muni might have a higher yield. You're getting that higher yield because you're actually taking on more risk.
Again, we talked about U.S. Treasuries, munis, and corporates. It's fine to do a comparison of where you want to be amongst those three buckets, but you want to make sure, as Chris said earlier, you're doing an apples-to-apples comparison in terms of—at a minimum, the duration because that's a risk you're taking. But the second one is credit—how much willingness are you willing to sort of change on your credit structure?
Rebecca Katz: Would it be a red flag if you saw, say, an intermediate-term Treasury and an intermediate-term muni and the muni—I'm sorry intermediate-term corporate is what I meant to say—and the muni was higher, but it's a "safer" investment. Wouldn't that be a red flag that there's something wrong there?
Daniel Wallick: Not necessarily. It could be the vagaries of the market. Chris showed that yield chart before; there are periods of time when the munis were really, really strong relative to certainly Treasuries or other places. It can just be where the pressure is in the market or the cash flow or a variety of things.
Chris Alwine: Usually it's short-lived so the muni market I talked about is a little lower liquidity, and so there's pockets, or brief periods of time, where the technical conditions, when we may be seeing money leave the funds at the same time, that there's heavy supply, and you can get this dislocation that takes place for a month or two or three, and then the relative value, the attractiveness of munis, takes over, and buyers come back into the market and buy what they would perceive to be a cheap asset.
Daniel Wallick: I would say most often, the prudent long-term strategy, though, as you were alluding to, why double-up on your tax advantage? Why put a tax-deferred security in a tax-deferred account? You potentially save the space in your tax-deferred account for taxable securities because you can always buy the muni outside of that.
Daniel Wallick: Right.
Rebecca Katz: Great. We just have a couple of minutes left, and there's some interesting questions coming in. So, Cheryl in Virginia, goes back to this idea between the bond and the fund. And she says, "Well, if I invest in a single bond, I know what I'm getting at the end of that maturity. You put $1,000 in, you get $1,000 back. If I buy enough fund, I'm subject to the value of all the bonds in the fund and not guaranteed the value of my principal." So, that's true.
Daniel Wallick: That's absolutely true. So, let's walk through that piece by piece. Remember, if you buy a bond, you know it's going to be until you hold it which means you have to hold it. And so if a muni bond is 30 years, you have to hold it for 30 years to capture that because if you were in need of selling it prior to that, then you're going to take the discount or the premium that goes along with that. So, there's an assumption built into that that you're going to hold for a really long period of time.
And then, let's go back to the fund. The fund actually has the diversification benefit, so you're not taking the credit risk of any one story. So that single bond could also suffer from—if it were a Puerto Rican bond or a Detroit bond—just making this up in extreme cases. If you hold one credit item, you could be impaired on that basis as well, so the diversification benefit of a fund can be there as well.
Chris Alwine: I seem to always get the more challenging technical topics here, but what happens when you have a rise in rates, the value of the bond falls. But your earnings ability when you reinvest the interest back into the markets at a higher rate, and so your expected returns actually go up over time—
Rebecca Katz: In the fund—in the fund because you're getting higher dividends into the fund?
Chris Alwine: In the fund, exactly. They're being reinvested at a higher rate and there's a break-even point—that's the duration of the bond—where you're indifferent between the two.
Rebecca Katz: Great.
Daniel Wallick: If I may, it's just sort of counterintuitive that rising rates will actually help a fund but they can.
Rebecca Katz: Yeah, over time. All right, well unfortunately, we are plumb out of time. We still have lots and lots of questions. So, we'll have to come back and do this again. I want to thank you both for being here this afternoon. This is really interesting.
Chris Alwine: It's great to be here.
Daniel Wallick: Great, thanks.
Rebecca Katz: And from all of us here at Vanguard to all of you watching out there in virtual land, thanks for joining us this afternoon and we covered a lot. We covered those equations, so we will send out an e-mail with highlights, and we'll make sure to include that calculation for you in just a few weeks.
And you should see on your screen right now, a survey popping up on the right- hand side. We would love your thoughts on this webcast and any future topics you'd like to see us cover.
So, from all of us here to all of you, thanks for tuning in and we hope to see you again next time.
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