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Notes on the Current State of the Muni Bond Market

by Annette Thau

Notes On The Current State Of The Muni Bond Market Splash image

Are you worried about your bonds (or your bond funds)?

The fixed-income markets are currently getting very bad press. No less an oracle than Warren Buffett recently dubbed bonds “instruments of mass destruction.” The perception that risk is high is primarily due to the fact that interest rates remain at historic lows. The consensus seems to be that interest rates can only go up and this creates interest rate risk: When interest rates rise, the price of a bond (or a bond fund) declines. The extent of the decline is directly related to maturity length. The other face of interest rate risk, of course, is that when interest rates decline, the price of bonds rises. Again, the extent of the increase is tied directly to maturity length.

Interest rate risk affects all fixed-income securities, including Treasuries. Discussions of interest rates and interest rate risk all start with Treasury bonds. More precisely, these discussions focus on the bellwether 10-year Treasury bond, since interest rates in other sectors of the bond market typically follow Treasury rates, either up or down. If interest rates rise on Treasuries, so will those of municipal and corporate bonds.

A second factor for the current bond market worries is the constant drumbeat about the shaky finances of bond issuers—in other words, concerns about credit quality. Perception of credit risk differs for different sectors of the bond market and varies over time. Treasuries are deemed to have the highest degree of safety. Municipal bonds are next. The credit quality of corporate bonds varies widely but, on the whole, it is not nearly as high as that of municipals. Approximately 50% of all corporate bonds are now rated below investment grade—these comprise the so-called high-yield, or “junk,” bond sector.

This article focuses on the municipal bond (“muni”) market. It discusses to what extent current concerns seem justified, and it makes some suggestions about how to handle both bond funds and individual bonds.

The Municipal Bond Market: 2010–2012

For the past two years, the municipal bond market has been on a roller-coaster ride. The winter of 2010 saw several months of panic selling, due in part to the now infamous prediction by bank analyst Meredith Whitney that in 2011 there would be hundreds of muni defaults and hundreds of billions of dollars lost. Well, of course, this did not happen. Indeed, a recent study by Standard & Poor’s found that in 2011, there were a total of 10 defaults, with a total par value of about $1 billion.

The panic selling of the winter of 2010, however, resulted in massive losses across every sector of the municipal bond market. The traditional metric for determining whether municipal bonds are cheap or expensive is the ratio of yields of municipal bonds to those of Treasuries. Historically, yields of AAA (highest-rated) 10-year to 30-year muni bonds have been somewhere between 85% and 90% of Treasury yields. If the ratio is lower than 85%, muni bonds are considered expensive. Above 85% to 90% of Treasuries, muni yields are considered relatively cheap. But at the peak of the panic selling in the winter of 2010, municipal bonds with maturities ranging from 10 to 30 years were yielding 150% to 200% of Treasuries with comparable maturities on an absolute basis. Yields of long-term munis were anywhere from 5% to as high as 8% for lower-quality credits. Given the tax exemption of munis, for individual investors in the 25% tax bracket these yields were equivalent to taxable yields of 8% to 12%.

This set the stage for a significant rally in the municipal market, and munis rallied for most of 2011 and into 2012. Buyers included not only muni funds and individual investors, but also so-called crossover buyers such as large banks and taxable bond funds: They bought munis not only for their unusually high yield but also in anticipation of capital gains when ratios of munis to Treasuries returned closer to historical norms. For 2011, this strong rally translated into average total returns of 10.6% for general muni bond funds. The rally continued into the first quarter of 2012 as yields of munis continued to decline, following those of Treasuries.

But, of course, as a result of the recent rally, ratios of muni bond yields to Treasury yields have declined significantly. The ratios of 10-year muni yields to Treasury yields are at about 95%. The yields of 30-year munis remain at, or slightly above, 100% of Treasuries. Still, the yield ratios, while not as high as they were during the panic of 2010, remain reasonably attractive.

How Safe Are Municipal Bonds?

Partly because of Meredith Whitney’s forecasts, and partly because of increasing concern about the strained finances of many issuers of municipal bonds, the media continues to focus on the presumed riskiness of municipal bonds. Following the declines of late 2010, I discussed the safety of muni bonds in the March 2011 AAII Journal (“How Safe Are Municipal Bonds?”; available at AAII.com). To summarize what I wrote:

  • The main deterrent to default is that issuers of muni bonds cannot just go out of business and liquidate themselves. Large issuers of municipal bonds depend on those bonds to fund critical continuing operations and capital budgets. A default that would shut off access to capital markets is simply not an option.
  • Issuers of municipal bonds set aside very clear sources of revenue for debt service. For most issuers, debt service is paid off over long periods of time (as long as 30 years); in addition, debt service constitutes a relatively small portion of total expenditures (4% to 8%).
  • Only 26 states allow municipalities to file for bankruptcy. Moreover, municipal bankruptcy is a very complex process.
  • Default rates among issuers of municipal bonds are extremely low—about one-third of 1%.
  • In general, riskier bonds fall into several well-known and clearly defined sectors. Two examples are private-purpose bonds, such as developments for nursing homes, and tobacco bonds.

Analogies between the credit quality of muni issuers and the debt problems of European sovereign countries or corporations are totally misplaced. And while there will no doubt continue to be some individual defaults, the perception among industry veterans is that the credit quality of the muni sector is likely to remain high. Clearly, if you are buying individual bonds, you need to investigate sources of revenue and credit quality. But given the overall low default rate of the sector and the diversified nature of bond funds, for most muni bond funds, credit quality ought not to be a major concern.

Buying Individual Bonds in the Current Environment

How would individual bonds be affected by a rise in interest rates? As stated, a rise in interest rates would cause the price of a bond to decline. But that would affect you only if you want to sell the bond. If you are a buy-and-hold investor, a rise in interest rates need not be a major concern. When the bond matures, it will be redeemed at par (the value of the bond at maturity—typically $1,000). If you bought bonds more than three years ago, when interest rates were higher, then consider yourself lucky and hold onto them until they mature.

Note that if your bonds were insured by any of the major bond insurance firms (MBIA, FGIC or AMBAC), which have been downgraded to below investment grade, then your AAA bonds have also lost their rating, since it was based on the rating of the insurer. But check the underlying rating of the issuer (that is, its own rating, without insurance, based on its own financial position). If it is at least investment grade, then credit quality need not be a major concern.

When Does Paying a Premium Make Sense?

The key to determining whether a premium bond is a good value is to compare the yield to the first call date (typically anywhere between 2018 and 2021) to yields quoted for bonds maturing on those dates. The yield of many premium bonds to the first call date is often as much as 100 basis points higher. So even if the premium bond is called on the first call date, the realized return will be higher than that currently available on bonds maturing on the same date. (Note also that if interest rates do rise, the bond is unlikely to be called.)

Be aware that brokers now quote the yield to worst (the lowest yield that could be earned by purchasing the bond) rather than the yield to maturity when they list a bond. The yield to worst may be the yield to the first call date. The yield to maturity may be as much as 100 basis points higher than the yield to worst. So in the event interest rates rise and the bond is not called, then too you would earn the higher return.

In the event you decide to buy premium bonds, however, check call provisions very carefully. Avoid bonds that are subject to extraordinary calls (primarily housing bonds) and that could be called early. Such a call might result in a loss of principal.

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If, on the other hand, you would like to replace bonds that have matured, or that have been called, then the current interest rate environment is not nearly as attractive as it was a year ago. General obligation bonds rated AAA or AA that are maturing in seven to 10 years yield anywhere between 2% and 2½%; those maturing in 15 years yield around 3%. You can pick up another 50 basis points by going out further on the yield curve (to 20 years, for example) or by buying bonds with lower credit ratings. But because investors have been doing this, yield spreads have narrowed. There is now less reward for taking on more risk.

Here are some strategies for navigating the current environment:

  • Ladder: Buy a mix of longer and shorter maturities. If interest rates rise, you will be able to invest the proceeds from matured bonds at higher rates. In the meantime, your longer-term bonds will provide somewhat higher income.
  • For bonds with intermediate maturities (seven to 15 years), the best values are to be found in premium bonds, which are bonds trading above their par value. These are bonds that were issued in the last few years with coupons of 4% or 5%. Because bonds with comparable maturities are now being issued with 2% to 3% coupons, older bonds with 4% and 5% coupons are currently selling at premiums to par, sometimes at steep premiums. Many individual investors avoid buying premium bonds because they believe, mistakenly, that the “premium” amount paid over par is lost when the bond matures. That is a mistake. The quoted yield to maturity is based on the purchase price and redemption of the bond at par. (See the sidebar on this page for more on premium bonds.)
  • If you scour a list of bonds for sale, the highest yields quoted are those of zero-coupon munis. These might be an attractive buy if you are saving for a particular goal at a known date, such as a child’s college education. They would also be attractive buys if you have a small amount of money to invest and would not be able to invest the interest income profitably. But a note of caution is in order. Zero-coupon bonds are approximately 2½ times more volatile than bonds with comparable maturities. If interest rates rise and you need to sell, the value of zeros tanks big time. So don’t buy a zero-coupon bond unless you are prepared to hold it to maturity. Also, check the call provisions and the yield to worst (the lowest yield that could be earned by purchasing the bond).
  • Make sure you understand the exact meaning of the phrase “material events” if it accompanies a bond listing. Material events are any events that would affect the price of a bond, for example, a downgrade by any of the credit rating agencies.
  • Keep maturities to 15 years or less. In most instances, the additional yield is too low to compensate for the additional risk of going beyond 15 years due to the longer maturity.
  • Finally, but very importantly, before you buy or sell any individual bond, by all means, check its pricing history online on either EMMA (emma.msrb.org) or InvestinginBonds.com (www.investinginbonds.com). EMMA, a service of the Municipal Securities Rulemaking Board (MSRB), now archives the prospectuses of municipal bonds and includes material events, as well as continuing disclosure.

Should you buy only highly rated bonds (AA or AAA)? I personally prefer to buy bonds that are rated at somewhat above investment grade (A or higher). That is partly because of their higher liquidity. It is also due to the fact that in any sell-off, for whatever reason, lower-rated bonds decline much more than higher-rated bonds.

Municipal Bond Funds

If you own municipal bond funds, the main risk is interest rate risk: If interest rates rise, the price of your bond fund will decline. Bear in mind that by far the greatest number of municipal bond funds are long term, and they maintain a constant maturity. So rising interest rates pose a genuine risk.

To understand that risk, you need to be aware of the composition of total returns in a bond fund. For example, suppose you invested in a muni fund quoting a yield of 4% and a total return of 11% for 2011. More than one-third of the total return (4%) consists of interest income. The additional 7% is attributed to a rise in the fund’s net asset value (NAV), due to declining interest rates.

If interest rates were to reverse in 2012, or at any time thereafter, and rise by the same amount (100 basis points, or 1%), then the fund would continue to post approximately the same interest income. But its net asset value would decline by about 7%. Total return would be –4%. If interest rates rise by a higher amount, then the decline in net asset value would be larger.

So should you sell your bond funds because of that risk?

There is no way I or anyone else can answer that question. There is no way to know when or if interest rates will rise. The Federal Reserve has publicly announced that it will keep short-term interest rates low for at least a couple of years. But long and short rates do not always move in sync. For example, during 2004, the Federal Reserve raised interest rates seven times, and interest rates on long maturities actually declined. The market viewed increases in short-term rates as signaling that inflation would remain low.

But even if you view higher rates as probable, there are a number of reasons why you might not want to rush to sell your muni bond funds. First, and most important, interest rates are notoriously difficult to predict. Rates may remain low for much longer than the current consensus. Indeed, some well-known economists are actually predicting that longer interest rates may decline during the second half of 2012, and they may turn out to be correct. Interest rates in Japan have remained significantly lower than in the U.S. for well over a decade.

Second, all muni bond funds are not equally risky; the risks vary significantly from fund to fund. If you own a bond fund, you need to investigate its portfolio. Conservatively managed funds tend to invest primarily in high-quality bonds (50% or higher above investment grade) that have intermediate maturities (weighted average maturities of eight years or lower) and low expense ratios (50 basis points or lower). More aggressive funds invest in bonds with longer maturities and lower-quality credits, as well as many riskier bonds (health care, nursing homes, tobacco bonds, unrated bonds, etc.). Such funds are much more volatile: Their net asset values may go up more in rising markets, but they decline more steeply in declining markets.

One indicator you can use to gauge the risk level of any fund you own is duration. Duration is a number, listed in years, that estimates a bond’s (or a bond fund’s) sensitivity to interest rates. A very rough rule of thumb is that a bond will rise or fall in value by the amount of its duration for every 100 basis point change in interest rates. For example, the net asset value of a bond fund with a duration of seven years would go up by 7% if interest rates declined by 100 basis points (1%). Its net asset value would decline by 7% if interest rates rose 100 basis points (1%). Most bond funds now list duration in their sales literature.

An even simpler method is to look back at the performance of your fund during the financial panic of 2010 (or further back, such as during the panic of 2008). If you are uncomfortable with the volatility, then switch at least part of your monies to a less aggressive fund.

The best argument for remaining invested in bond funds is that monthly dividends represent income. Continuing income cushions declines in net asset value, which is the value of the fund’s assets. More importantly, over long holding periods, continuing income compounds. Over long holding periods, if interest rates rise, and the net asset value of a bond fund declines, rising interest income compensates for lower net asset value. Also bear in mind that trading (buying and selling funds) has tax consequences.

At the present time, general municipal bond funds are posting average yields of about 3.8%. (Those are distribution yields—that is, comprised of actual distributed interest income. Distribution yields tend to be somewhat higher than quoted SEC yields). Based on your tax bracket, these yields are equivalent to taxable yields of anywhere between 4.5% and 6%. I would anticipate that total returns would be much more modest than those of 2011 since, unless interest rates continue to decline from current levels, there will be no capital gains. But modest as it may be, a total return of 4% beats the returns of money market funds, which are currently close to zero.

Finally, in the past, I have recommended funds with very short maturities (one to three years) as alternatives to money market funds. At the current time, such funds are not a great buy. Quoted yields are well below one-half of 1%, and any rise in interest rates would result in negative total returns.

Investing in Closed-End Municipal Bond Funds

Closed-end funds (CEFs) constitute a much smaller number of funds than traditional mutual funds. They continue to post very high average yields—approximately 5.8%, tax exempt. Nonetheless, before you rush out and buy a closed-end fund because of its posted yield, you need to be aware of the CEF risk profile.

Unlike open-end funds, which are bought from their management companies, closed-end funds are sold on stock exchanges, like any other stock. The number of shares in a closed-end fund is fixed, not open ended. Closed-end funds list two different prices per share: the NAV (net asset value), which is the market price of the shares in the portfolio; and the market price of the closed-end fund, which is the price of a share of the closed-end fund. The market price may be higher than the NAV (in that case, the closed-end fund is said to be selling at a premium to its net asset value), or lower, in which case the fund is said to be selling at a discount to NAV.

When you buy a closed-end fund at a discount, you are in effect buying the assets of the closed-end fund for less than you would if you were to buy the same portfolio on the open market. For example, if the closed-end fund is selling at a 15% discount to NAV, you are getting $100 worth of bonds for $85. That boosts the yield. But if you buy a closed-end fund at a 15% premium, then the reverse occurs. You are buying $100 worth of bonds for $115.

But in addition, many closed-end funds use leverage to boost yield further. This increases the volatility of these funds significantly. About half of all closed-end funds are muni funds, and most use leverage to boost yield.

There is not enough space in an article of this length to go into additional details, but be aware that, particularly when closed-end funds sell at a premium, they incur significant risk.

Investors buy closed-end funds for two different reasons: for the higher yield and for capital appreciation when they are selling at a discount to net asset value. Investors are hoping to realize gains as the price of the closed-end fund rises to the net asset value of the bonds in the portfolio. But when closed-end funds sell at premiums, declines in price sometimes occur very quickly and very steeply. Investors in closed-end funds are quick to sell if the market price declines. And during sell-offs, partly because of the leverage in closed-end funds, volatility is much higher than that of traditional mutual funds. For example, in March, there was a brief decline in the bond market. The net asset value of open-end bond funds declined by 2% to 3%. But the market price of closed-end funds declined by five or six times that amount. All muni closed-end funds posted declines for the month of March.

At the current time, many muni closed-end funds are selling at premiums to net asset value. A steep rise in interest rates or any sell-off can result in losses for shareholders of these funds.

For more information, use the search tool at AAII.com to find past articles on closed-end funds.

Should You Invest New Money in Bonds or Bond Funds?

There is no single cookie-cutter answer to this question. If you have a large portfolio, the best way to preserve capital over long holding periods is to buy individual bonds and ladder them. But that requires time and a certain expertise.

For many individual investors, buying bond funds is a satisfactory solution. But I would focus primarily on conservatively managed funds with a record of consistent performance. Don’t go for funds with the highest posted yields; these typically are the most aggressively managed funds, and the most volatile.

Junk Bonds

Is it possible to find tax-equivalent yields equal to those of munis in taxable bonds?

The obvious candidates are the so-called high-yield corporate bonds, also known as junk bonds. By definition, these bonds are rated below investment grade. The quoted yields for junk bonds are typically well above those quoted for munis, either individual bonds or bond funds. I would urge caution when dealing with high-yield bonds or bond funds for a number of reasons.

The credit quality of corporate bonds as an asset class is significantly lower than that of munis. As noted above, approximately 50% of all corporate bonds are rated below investment grade. Furthermore, while the number of defaults varies from year to year, it is a far larger number than that of munis. So buying individual high-yield bonds requires genuine expertise. If the higher yield of that sector appeals to you, bond funds provide a significant buffer against defaults by spreading the risk among many bonds. The best bet would be funds that invest in the higher-quality junk bonds: They do not quote the highest yields, but returns are more consistent.

The traditional metric for measuring how attractive junk bonds may be at any one time depends on how much more you are earning compared to Treasuries. Spreads of junk bonds compared to Treasuries reached unprecedented levels during the financial panic of 2008: 2000 to 2500 basis points higher than Treasuries. (Yes, those numbers are correct). When spreads of junk bonds to Treasuries are 200 to 250 basis points, junk bonds are considered somewhat expensive. You are not getting paid enough for the risk you are taking.

In 2009, junk bonds rallied significantly from the depressed levels of 2008. Average total returns of junk bond funds were stellar: almost 32%. Since then, returns have been more modest. At the present time, average yields (again, distribution yields) quoted for junk bond funds have fallen to approximately 5.11%, representing spreads to Treasuries of about 250 to 300 basis points (higher for funds investing in the lowest-rated junk bonds). Any rise in Treasury rates would cause the ratios to become even less attractive. Note also that corporate bonds track the stock market as much as, or more than, the bond market. Declines in the stock market would result in declines in the price of corporate bonds.

Remember also that junk bonds are taxable. For personal monies—that is, money that is not tax-sheltered—based on your tax bracket, the realized yield may not be higher than that of tax-exempt munis. Junk bond funds may make sense for tax-sheltered accounts, but investigate any fund you are considering very carefully.

U.S. Treasuries

As you may remember, during 2011, S&P downgraded U.S. Treasuries to AA+. I am not sure what motivated that downgrade, but it does not cause me to worry about the credit quality of U.S. Treasuries. The rest of the world seems to share that opinion: Over the past couple of years, U.S. Treasuries have rallied whenever there is a concern about any debt worldwide.

On the other hand, be aware that U.S. Treasuries fully share interest rate risk. Long-term Treasury zeros are very risky if interest rates rise. So-called long-duration Treasury bond funds had stellar total returns in 2012 (more than 30%) because long Treasury rates declined steeply. But year to date, long-duration Treasury funds have been among the worst-performing bond funds, posting declines of 4% to 5% through March as long-term Treasury rates rose.

Conclusion

This article has been focused on current conditions in the municipal bond market. So it is heavily focused on credit quality and interest rate risk. But bear in mind that an election is looming. Tax rates will be a major issue in the upcoming campaign: If tax rates rise on higher income earners, then that may make the entire muni sector more attractive. Conversely, a number of proposals are on the table for discussion, which might cap how much tax-exempt income can be earned. That would impact the muni market.

In addition, be aware of “headline risk.” The 2010 panic in the muni market was greatly magnified by the publicity accorded Meredith Whitney’s forecast of looming massive defaults. She is currently writing a book; when it is published, it will no doubt cause a lot more head-shaking. Also, if any highly publicized default were to occur, the entire issue of credit quality may once more cause a panic.

Nonetheless, my overall take on the fixed-income markets is that conditions are not nearly as dire as a lot of media would have you believe. True, money market funds are yielding next to nothing. And returns for all categories of bond funds in 2012 are unlikely to match those of 2011. Capital gains due to falling interest rates are not likely. If you own aggressive funds, it may be time to pocket your profits for the past year and put some money in lower-risk, less-aggressive funds or keep it in money market funds until some better opportunities arise. But you can earn modest returns by diversifying risk among maturities and credit quality. The watchword in the current environment is to remain invested, but cautiously.

The author thanks Jeff Tjornejoh, head of research for the Americas at Lipper, for data on bond funds and Cecilia Gondor, executive vice president of Herzfeld Research, for data on closed-end bond funds.


Discussion

James from IL posted over 2 years ago:

Annette,

I wonder if you are underestimating the political risk of municipal bonds. For example, what happens when the market is no longer willing to buy the debt of either Illinos or California? Do you think the politicians will choose to continue to service existing debt at the expense of state pensions and retiree health care benefits, or will they stiff "rich" bond holders seeking tax exempt income in favor continuing pension and health care benfits to hard-working Americans?

Thanks.

Jim


William from FL posted over 2 years ago:

A couple of comments about the box on closed end bond funds. Another reason for holding this type of security is unrestrained liquidity. Many open ended bond funds (eg Vanguard) have frequent trading and liquidation limits that may effect one's ability to liquidate positions in down markets. Looking and the bond fund duration data will give a index of interest rate volatility. Finally many closed end funds sell at either a discount or premium for long periods. Buying a fund at a discount to NAV does not necessarily mean that it is a bargain. Looking at pricing history is a better way to figure this out.


John from CA posted over 2 years ago:

First, interest rates are at historical lows manipulated by the FEDs. This is not the time to buy bonds. Second the muni market has not changed in 50 years; the spread in 3 percent. Dont try to sell a bond, you may get a low ball bid from an un-named source who is actually your own broker. Ratings are meaningless and can change overnight by several ranks. Insurance, regulated by the NY Insurance commissioner is a fraud. Small bond buyers over the last decade have been screwed by the banks, brokers and insurance companies. Speciffically, we were sold INSURED securities in a market unregulated to control insurance company default and fraud. Yet Wall Street continues to rake in the big bucks and sidesteps regulation attempts.


Will from MA posted over 2 years ago:

Given the assumptions listed, how long would interest payments have to be reinvested in a muni bond fund for the investor to get back to par after a 1% riase in intrest rates?

Assumptions: Duration of 7 years, an expense rations of .25% and a return of 3.8% of tax-exempt income


Don from FL posted over 2 years ago:

Excellent article; thank you.


Patricia from NY posted over 2 years ago:

Being a holder of a municipal bond fund, I feel comfortable after
reading your article


Alan from NJ posted over 2 years ago:

This is an excellent example of clear financial writing. Thoughtful and measured, it is valuable for long time muni investors while being accessible to newcomers. Thank you Ms. Thau and AAII.


Douglas from AZ posted over 2 years ago:

In evaluating closed end funds its also important to make sure that the fund is earning at least as much as it is distributing and that there are unused revenues (UNII) for problem periods. Cefconnect.com has all the info you need to select muni cefs that are paying upwards of 5% tax free.


anonymous from IL posted over 2 years ago:

Great article.


Pete from NJ posted over 2 years ago:

Enjoyed the article and thanks.... Any reason why I would need to diversify my individual bonds among more than one bond shop? I am presently using Stoever Glass in NYC. As you know, they recommend and buy the bonds for me and also hold the bonds. It is a little scary not actually having a bond as proof of purchase but I am told that that is the way it is done today. I do get confirmation statements and monthly statements.

Sound kosher to you ?

Thanks again.


Asghar from CT posted over 2 years ago:

this article is the most informative presentation of bond, bond funds and munis i have ever read.exellent and honest descriptions of bond market.thank you.


Larry from CA posted over 2 years ago:

"Yield to Worst" is not as comforting as it sounds. It does not, according to my experience, take into account sinking fund redemptions scheduled prior to maturity. Such sinking fund redemptions apparently are not considered "calls" as selecting non-callable only securities does not eliminate bonds with sinking fund redemption schedules and likewise such are not considered a 'call' when yield to worst is posted.


Daljit from MD posted over 2 years ago:

Very well explained a must read for all investors.


Joseph Turney from KS posted over 2 years ago:

I did not see any referance to the fact that any premium paid for tax exempt is not considered a loss for tax purposes.


S Frank from CT posted about 1 year ago:

When are the muni bond professionals and bond buyers going to realize that yield to maturity, yield to call or yield to worst do not accurately reflect the yield on a muni bond? For example, if someone buys a bond maturing in 2030, with a 5% coupon and a YTM of 4%, they are not rally earning 4%/year. The YTM, YTC, YTW calculations assumes that the 5% coupon is invested at 4%, which is not likely. I have developed a more accuarte fomula for determing the yield on a bond. While munis still offer a good investment it's a real eye opener to calculate the "true" yields.


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