trying to understand relationship between bonds, interest rates and valuation

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capran
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trying to understand relationship between bonds, interest rates and valuation

Post by capran »

I have read some leading me to think that as interest rates rise, it drives bond values lower. But I am trying to wrap my head around the relationship between the upcoming rise in interest rates versus the actual rate of interest the bond pays versus the value of that bond. Last year I had several corporate bonds that were paying 7.6% and 7.8% get involuntarily redeemed, which was easy to understand as corporate cash increased and interest rates decreased. But trying to increase my understanding of some current holdings.

CUSIP---------Company------------------ interest rate/yield-----------------------------------------------------------------yr end value
156700AMB--Century Link SR NOTE CPN 7.6% est yield 7.09% corporate/($380)taxable due 9-15-39------------------------$5362
685869EW5--Oregon hltSci UNIV REV SERB/E--3.54% est yield 3.1 ($168.75tax free) due 7/1/38 call 7-1-26@100---------$5440
250336ED2--Deschutes Cnty hsp-------4% est yield 3.63% ($1,000tax free) due 1-1-35 call 1-1-26@100-----------------$27,566
83309AFA4--Snohomish Cnty Wa HSG CPN 3.25% est yield 3.24% ($325)tax free --due 5/1/41 call 5-1-22@100----------$10,037

My assumptions: 1) From the recent declines, I am guessing that the values will continue to decline, and maybe even accelerate when interest rates actually start to rise. 2) It looks like Snohomish could call this May, and Deschutes and Oregon Health could call (redeem) in 2026, and by then the value for all three will likely decline to $100 per share by the callable date, which will bring possible CG's to zero.

One last bond holding issue:
LEO (AKA BNY) A municipal bond fund yield is 4.25% (currently$1,885 tax free) in 2020 it was 5.02% They did just cut the monthly tax free dividend from 183 to 157 November 2021, and it seems the valuation is in an accelerating decline, with just the talk of increasing interest rates(and recent cut in dividend/int. ) My assumption is that there is no such thing as an involuntary redemption or call with this kind of fund, but the valuation could fall below the cost basis of 7.12

Am I missing anything?
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by grabiner »

There is more than one interest rate. The rate that the Fed targets is the very-short-term rate. Longer-term rates are based on long-term expectations, and may not move at the same time. In particular, bond traders already know about the planned Fed moves, so the risk premium they demand for long-term bonds over short-term bonds, which determines the interest rate, includes the higher future returns on short-term bonds.
capran wrote: Thu Jan 20, 2022 11:56 am LEO (AKA BNY) A municipal bond fund yield is 4.25% (currently$1,885 tax free) in 2020 it was 5.02% They did just cut the monthly tax free dividend from 183 to 157 November 2021, and it seems the valuation is in an accelerating decline, with just the talk of increasing interest rates(and recent cut in dividend/int. ) My assumption is that there is no such thing as an involuntary redemption or call with this kind of fund, but the valuation could fall below the cost basis of 7.12
The fund itself cannot be called, but it holds bonds which can be called. When a bond is called, the fund will have to replace it with a new bond. And since the reason a bond issuer calls a bond is that it can issue new bonds at a lower yield, the called bond will usually be replaced by one with a lower yield.

The number to use for comparing muni funds is the SEC yield, which is based on the yield to maturity (or to call if a call is likely) of the bonds in the fund. If the distribution is higher than the SEC yield, this implies that the prices of bonds in the fund will decline as they approach maturity.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

grabiner wrote: Thu Jan 20, 2022 10:07 pm There is more than one interest rate. The rate that the Fed targets is the very-short-term rate. Longer-term rates are based on long-term expectations, and may not move at the same time. In particular, bond traders already know about the planned Fed moves, so the risk premium they demand for long-term bonds over short-term bonds, which determines the interest rate, includes the higher future returns on short-term bonds.
capran wrote: Thu Jan 20, 2022 11:56 am LEO (AKA BNY) A municipal bond fund yield is 4.25% (currently$1,885 tax free) in 2020 it was 5.02% They did just cut the monthly tax free dividend from 183 to 157 November 2021, and it seems the valuation is in an accelerating decline, with just the talk of increasing interest rates(and recent cut in dividend/int. ) My assumption is that there is no such thing as an involuntary redemption or call with this kind of fund, but the valuation could fall below the cost basis of 7.12
The fund itself cannot be called, but it holds bonds which can be called. When a bond is called, the fund will have to replace it with a new bond. And since the reason a bond issuer calls a bond is that it can issue new bonds at a lower yield, the called bond will usually be replaced by one with a lower yield.

The number to use for comparing muni funds is the SEC yield, which is based on the yield to maturity (or to call if a call is likely) of the bonds in the fund. If the distribution is higher than the SEC yield, this implies that the prices of bonds in the fund will decline as they approach maturity.
Thank you for your reply. So, are you saying the interest rate on the individual bond holding will fluctuate? I don't see any SEC yield on the individual bonds (Deschutes, Oregon Health or Snohomish, nor on the one Century Link), just the info reported in my post, although when I look closer, it says CPN 4%, or CPN 3.375%, or CPN 3.25%, rather than INT rate or SEC Yield. With the Century Link says "SR NOTE SER P CPN 7.6% Due 9/15/39 DTD 9/21/09 FC 3/15/10 " Am I correct in assuming the price will continue to go down, at least until it reaches the call date and price on all three tax free individual bonds? the one callable this May isn't much above that 100 anyway, (100.378 December 31st). I don't see anything about callable on the Century Link holding, so don't know if that means it is not callable. (It's lower grade, -BB, compared to the other tax free bonds that have ratings of AA-, A+ and AA+).

On the LEO (BNY MELLON Strategic Municipal fund) it makes sense if they are replacing higher returning holdings as they drop off with lower return holdings, which would explain why the monthly income went from 183.33 to 157 recently. And I guess that would explain the decrease in valuation. In the info I get from Vanguard, it only lists "estimated annual income" and "Est yield" which went from 5.02% in October to 4.25% in December. I 'll dig out the prospectus to see what it might say about the SEC yield. I sure appreciate the help in trying to understand it. I thought the LEO was better than it sounds like it is, based on the fact that it will likely continue to decline in both return and valuation.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by grabiner »

capran wrote: Thu Jan 20, 2022 10:59 pm
grabiner wrote: Thu Jan 20, 2022 10:07 pm The number to use for comparing muni funds is the SEC yield, which is based on the yield to maturity (or to call if a call is likely) of the bonds in the fund. If the distribution is higher than the SEC yield, this implies that the prices of bonds in the fund will decline as they approach maturity.
Thank you for your reply. So, are you saying the interest rate on the individual bond holding will fluctuate? I don't see any SEC yield on the individual bonds (Deschutes, Oregon Health or Snohomish, nor on the one Century Link), just the info reported in my post, although when I look closer, it says CPN 4%, or CPN 3.375%, or CPN 3.25%, rather than INT rate or SEC Yield.
The SEC yield is officially computed for bond funds. The relevant number for an individual bond is yield to maturity (or yield to call). This number changes as the bond's market value changes, as it is the rate of return you would get if you bought the bond for its current market value. See SEC Yield on the wiki for an example of how this is computed; the yield to maturity is equal to the coupon rate for a bond at par, and less than the coupon rate for a bond at a premium.

The "yield" quoted on your bonds is the ratio of the coupon payment to the current price, which is not an estimate of the return. In the example on the wiki, Bond B, with a $1000 par and a current value of $1090.23, has a 2.75% coupon yield because it pays $30 every year in coupons. However, the yield to maturity is only 2.00%, because your return from holding the bond includes the loss of buying it for $1090.23 and receiving $1000 at maturity.
With the Century Link says "SR NOTE SER P CPN 7.6% Due 9/15/39 DTD 9/21/09 FC 3/15/10 " Am I correct in assuming the price will continue to go down, at least until it reaches the call date and price on all three tax free individual bonds? the one callable this May isn't much above that 100 anyway, (100.378 December 31st).
Since these bonds are at a premium, the price must go down to the par value over time, as you will receive the par value when the bonds are called, or when they mature without being called.

The reason that the bond callable in May isn't much above 100 is that it is probably going to be called; it has a 3.25% coupon rate, which is much higher than the current yield on high-quality municipal bond If you buy this bond now, you will receive the par value of the bond in May, and only four months of interest. Therefore, the bond should be worth close to the par value.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

grabiner wrote: Fri Jan 21, 2022 4:06 pm
capran wrote: Thu Jan 20, 2022 10:59 pm
grabiner wrote: Thu Jan 20, 2022 10:07 pm The number to use for comparing muni funds is the SEC yield, which is based on the yield to maturity (or to call if a call is likely) of the bonds in the fund. If the distribution is higher than the SEC yield, this implies that the prices of bonds in the fund will decline as they approach maturity.
Thank you for your reply. So, are you saying the interest rate on the individual bond holding will fluctuate? I don't see any SEC yield on the individual bonds (Deschutes, Oregon Health or Snohomish, nor on the one Century Link), just the info reported in my post, although when I look closer, it says CPN 4%, or CPN 3.375%, or CPN 3.25%, rather than INT rate or SEC Yield.
The SEC yield is officially computed for bond funds. The relevant number for an individual bond is yield to maturity (or yield to call). This number changes as the bond's market value changes, as it is the rate of return you would get if you bought the bond for its current market value. See SEC Yield on the wiki for an example of how this is computed; the yield to maturity is equal to the coupon rate for a bond at par, and less than the coupon rate for a bond at a premium.

The "yield" quoted on your bonds is the ratio of the coupon payment to the current price, which is not an estimate of the return. In the example on the wiki, Bond B, with a $1000 par and a current value of $1090.23, has a 2.75% coupon yield because it pays $30 every year in coupons. However, the yield to maturity is only 2.00%, because your return from holding the bond includes the loss of buying it for $1090.23 and receiving $1000 at maturity.
With the Century Link says "SR NOTE SER P CPN 7.6% Due 9/15/39 DTD 9/21/09 FC 3/15/10 " Am I correct in assuming the price will continue to go down, at least until it reaches the call date and price on all three tax free individual bonds? the one callable this May isn't much above that 100 anyway, (100.378 December 31st).
Since these bonds are at a premium, the price must go down to the par value over time, as you will receive the par value when the bonds are called, or when they mature without being called.

The reason that the bond callable in May isn't much above 100 is that it is probably going to be called; it has a 3.25% coupon rate, which is much higher than the current yield on high-quality municipal bond If you buy this bond now, you will receive the par value of the bond in May, and only four months of interest. Therefore, the bond should be worth close to the par value.
Got it! Thank you for that additional clarification.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by bhwabeck3533 »

capran wrote: Thu Jan 20, 2022 11:56 am I have read some leading me to think that as interest rates rise, it drives bond values lower. But I am trying to wrap my head around the relationship between the upcoming rise in interest rates versus the actual rate of interest the bond pays versus the value of that bond.

One last bond holding issue:
LEO (AKA BNY) A municipal bond fund yield is 4.25% (currently$1,885 tax free) in 2020 it was 5.02%
I was hoping this thread would help me to the "promised land" of understanding how bond investments work. Unfortunately, I have a ways to go. What would really help me would be to see a table/spreadsheet with column headings (Year, Value, Yield, Dividend, Interest Rate, plus other pertinent variables) for one individual bond. The table would be populated with the data for each criteria for a five or ten year period. I could then see what the value of the holding would be year-after-year and what caused the variance in the investment.

I have a spreadsheet tracking the value of my bond holdings (VFIDX, VFSUX, VTABX, VBTLX) since they were purchased in Nov 2015. I have done some rebalancing in some funds, but am pretty sure my VFSUX has been untouched and these are the balances since the this bond index fund was purchased:
Nov 2015 $ 100,304
Dec 2016 $ 102,458
Dec 2017 $ 104,702
Dec 2018 $ 104,939
Dec 2019 $ 111,617
Dec 2020 $ 107,355
Dec 2021 $ 107,336

Relatively small fluctuations, but what were the factors that drove the value up and down?
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

bhwabeck3533 wrote: Sun Jan 23, 2022 8:16 am
capran wrote: Thu Jan 20, 2022 11:56 am I have read some leading me to think that as interest rates rise, it drives bond values lower. But I am trying to wrap my head around the relationship between the upcoming rise in interest rates versus the actual rate of interest the bond pays versus the value of that bond.

One last bond holding issue:
LEO (AKA BNY) A municipal bond fund yield is 4.25% (currently$1,885 tax free) in 2020 it was 5.02%
I was hoping this thread would help me to the "promised land" of understanding how bond investments work. Unfortunately, I have a ways to go. What would really help me would be to see a table/spreadsheet with column headings (Year, Value, Yield, Dividend, Interest Rate, plus other pertinent variables) for one individual bond. The table would be populated with the data for each criteria for a five or ten year period. I could then see what the value of the holding would be year-after-year and what caused the variance in the investment.

I have a spreadsheet tracking the value of my bond holdings (VFIDX, VFSUX, VTABX, VBTLX) since they were purchased in Nov 2015. I have done some rebalancing in some funds, but am pretty sure my VFSUX has been untouched and these are the balances since the this bond index fund was purchased:
Nov 2015 $ 100,304
Dec 2016 $ 102,458
Dec 2017 $ 104,702
Dec 2018 $ 104,939
Dec 2019 $ 111,617
Dec 2020 $ 107,355
Dec 2021 $ 107,336

Relatively small fluctuations, but what were the factors that drove the value up and down?
Not sure I can help, other than my initial premise from reading that bonds go down as interest rates rise, and vice versa. We only have one muni bond fund. (LEO but now BNY Mellon)
Dec 31, 2018 $37,346 monthly taxfree div/int 183.33
June 30, 2019 $42,794
Dec 31, 2019 $44,575
June 30,2020 $40,646
Dec 31, 2020 $44,470
June 30, 2021 $46,984
Dec 31, 2021 $44,365 in Nov 2021 reduced tax free div/int to 157.14
As Grabiner wrote, as higher paying bonds in the fund are redeemed or expire, they are replaced with lower paying bonds. I would think that the reduced dividend/interest paid our would add to the reduced demand for the fund, therefore driving the price down. I have felt getting 2,199.96 every year tax free was a decent return on only 37,346 investment, especially being solidly in the 22% tax bracket. Even with the decline two months ago, still getting 1,885.68 per year isn't bad. (Especially when you look at a Vanguard Admiral Money Market that earned 37.23 div and a 30 SH CG distribution on $350,000!) It will be interesting once rates really do start to rise what will happen to LEO, especially if they have another cut in Div. My other bond holdings were straight up bonds rather than a bond fund. At least now, I understand that basically they will go down to close to my basis as maturity nears, which means they really were not going down because of a potential rise in interest rates.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

I will try to find a nice simple bond pricing primer. I have advanced to a level where I just don’t anything so basic so I am nit sure where to start.

The short answer is that there is a mathematical relationship between price and yield. If you know the price of a bond you know the yield. Know the yield you know the price.

On my systems at work I can switch bond quotes between price and yield because they are absolutely interchangeable.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

alex_686 wrote: Sun Jan 23, 2022 12:45 pm I will try to find a nice simple bond pricing primer. I have advanced to a level where I just don’t anything so basic so I am nit sure where to start.

The short answer is that there is a mathematical relationship between price and yield. If you know the price of a bond you know the yield. Know the yield you know the price.

On my systems at work I can switch bond quotes between price and yield because they are absolutely interchangeable.
Is there a formula you would be willing to share. I went back and looked up quarterly statements on LEO for the last few years, with statement balance as well as the "est. yield" that Vanguard reports. Unfortunately, that's all I get. There is no SEC yield provided by Vanguard.
quarter date--balance---est. yield
30-Jun-19-----$42,794 ----5.14% monthly tax free div/int 183.33
9/30/2019----$44,942 ----4.90%
31-Dec-19 ----$44,575 ----4.94%
3/31/2020----$39,023 -----5.64%
6/30/2020----$40,646 -----5.41%
9/30/2020----$43,370------5.07%
31-Dec-20----$44,470 ------5.02%
3/31/2021----$44,732 -----4.92%
30-Jun-21-----$46,984 -----4.68%
9/30/2021----$45,570 -----4.83%
31-Dec-21-----$44,365 -----4.25% in Nov 2021 reduced tax free div/int to 157.14
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

capran wrote: Sun Jan 23, 2022 5:57 pm
alex_686 wrote: Sun Jan 23, 2022 12:45 pm I will try to find a nice simple bond pricing primer. I have advanced to a level where I just don’t anything so basic so I am nit sure where to start.

The short answer is that there is a mathematical relationship between price and yield. If you know the price of a bond you know the yield. Know the yield you know the price.

On my systems at work I can switch bond quotes between price and yield because they are absolutely interchangeable.
Is there a formula you would be willing to share. I went back and looked up quarterly statements on LEO for the last few years, with statement balance as well as the "est. yield" that Vanguard reports. Unfortunately, that's all I get. There is no SEC yield provided by Vanguard.
quarter date--balance---est. yield
30-Jun-19-----$42,794 ----5.14% monthly tax free div/int 183.33
9/30/2019----$44,942 ----4.90%
31-Dec-19 ----$44,575 ----4.94%
3/31/2020----$39,023 -----5.64%
6/30/2020----$40,646 -----5.41%
9/30/2020----$43,370------5.07%
31-Dec-20----$44,470 ------5.02%
3/31/2021----$44,732 -----4.92%
30-Jun-21-----$46,984 -----4.68%
9/30/2021----$45,570 -----4.83%
31-Dec-21-----$44,365 -----4.25% in Nov 2021 reduced tax free div/int to 157.14
So the problem is that something like this is my natural domain:

https://www.amazon.com/Handbook-Fixed-I ... nk+Fabozzi

Which is not where you should start.

First, master the NPV function on the TI BA II calculator. I think he calculator had practice problems.

Or maybe this:

http://pages.stern.nyu.edu/~adamodar/Ne ... primer.htm

Or this:

https://people.duke.edu/~charvey/Classe ... ondval.htm

Or come back if this is not for you.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

Let me take another crack at this.

For NPV calculations you need the following.

PV, or Present Value, or the bond price
I, or the interest rate
CPT, or the coupon
FV, or Future Value, or the maturity value of the bond.
N, or number of periods, or time.

You need 4 of the inputs to solve for the 5th.

Thus if you know the bond’s price you must know the interest rate. If the yield increases than the price must fall.

There is not a clean formula for it is a open solution, a iterative process that best fits the required curve.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

alex_686 wrote: Sun Jan 23, 2022 7:38 pm Let me take another crack at this.

For NPV calculations you need the following.

PV, or Present Value, or the bond price
I, or the interest rate
CPT, or the coupon
FV, or Future Value, or the maturity value of the bond.
N, or number of periods, or time.

You need 4 of the inputs to solve for the 5th.

Thus if you know the bond’s price you must know the interest rate. If the yield increases than the price must fall.

There is not a clean formula for it is a open solution, a iterative process that best fits the required curve.
Looks like I'm out of luck, as all I have is the present value of LEO which is a muni bond fund, as well as the share price of LEO on a daily basis. But Vanguard only gives the "annual income" and "Est Yield". Share price on 12-31-21 was 8.47 with 5,238 shares and the value of 44,470.62. Nothing in the paperwork about a CPT or coupon, nor FV. Thanks for trying. As with everything in life, it is what it is.

On the few individual bonds I own, there is a little more info, for example the Oregon Health Services is followed by UNIV REV ST CHARLES HLTH SYS SER A B/E PTC CPN 4.00% DUE 1/1/35 DTD 10/12/16 FC 01/10/17 CALL 01/01/26@100.00 Moody Rating AA3 S&P Rating AA- Est Yield 3.1% but it's all Greek to me. It looks to me like I can plan that the bonds will be called between this May on one and the other two in 2026, and that the value the bond will decrease to the call price as the call date approaches. It was sure nice while it lasted. LOL
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by grabiner »

capran wrote: Sun Jan 23, 2022 9:18 pm
alex_686 wrote: Sun Jan 23, 2022 7:38 pm Let me take another crack at this.

For NPV calculations you need the following.

PV, or Present Value, or the bond price
I, or the interest rate
CPT, or the coupon
FV, or Future Value, or the maturity value of the bond.
N, or number of periods, or time.

You need 4 of the inputs to solve for the 5th.

Thus if you know the bond’s price you must know the interest rate. If the yield increases than the price must fall.

There is not a clean formula for it is a open solution, a iterative process that best fits the required curve.
Looks like I'm out of luck, as all I have is the present value of LEO which is a muni bond fund, as well as the share price of LEO on a daily basis.
Fortunately, bond funds are required to do this calculation for you. The fund knows CPT, FV and N because it holds the bonds, and it knows PV from the bond market, so it can compute I, the yield to maturity. The reported SEC yield on the fund is the average yield to maturity of all its bonds, minus the expense ratio.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by crefwatch »

It's important to understand that each individual bond in a mutual fund behaves like one of your bonds, but the whole fund together does not, exactly. A big reason is turnover. Others are varying distributions of quality, risk, and maturity dates in a fund.

Do you understand that market sentiments affect fund prices? Periodic fears about muni bond safety, especially short term, affect muni prices without use of a formula.

I haven't seen yet that you understand why a rise in rates will cause any conventional bond to decline in value.

Do you know the credit ratings for the individual bonds you cited? Do you know how to look up a bond's history at Fidelity or Vanguard?
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by bhwabeck3533 »

crefwatch wrote: Mon Jan 24, 2022 5:37 am It's important to understand that each individual bond in a mutual fund behaves like one of your bonds, but the whole fund together does not, exactly. A big reason is turnover. Others are varying distributions of quality, risk, and maturity dates in a fund.

Do you understand that market sentiments affect fund prices? Periodic fears about muni bond safety, especially short term, affect muni prices without use of a formula.

I haven't seen yet that you understand why a rise in rates will cause any conventional bond to decline in value.

Do you know the credit ratings for the individual bonds you cited? Do you know how to look up a bond's history at Fidelity or Vanguard?
Who is the "you" this post is being directed at? If it's me, the guy who owns several Vanguard bond index funds, do your statements about bonds in this post apply to my bond investments?
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by crefwatch »

bhwabeck3533 wrote: Mon Jan 24, 2022 7:55 am
crefwatch wrote: Mon Jan 24, 2022 5:37 am It's important to understand that each individual bond in a mutual fund behaves like one of your bonds, but the whole fund together does not, exactly. A big reason is turnover. Others are varying distributions of quality, risk, and maturity dates in a fund.

Do you understand that market sentiments affect fund prices? Periodic fears about muni bond safety, especially short term, affect muni prices without use of a formula.

I haven't seen yet that you understand why a rise in rates will cause any conventional bond to decline in value.
Who is the "you" this post is being directed at? If it's me, the guy who owns several Vanguard bond index funds, do your statements about bonds in this post apply to my bond investments?
No, I was addressing the OP. I have no beef with you, but you are escalating from hijacking the thread.

All of my comments about the OP's portfolio also apply to yours. However, you apparently own only open-end bond mutual funds, so my comments about individual bonds would apply only to a study of each individual holding in one of your portfolio's funds. In the shorter term, bond mutual funds don't behave as predictably as a single bond. Of course, this depends on whether the bond fund is managed or indexed, and whether it has wide variation in rating and interest rate among its holdings.

I don't own international bonds, but you would have to add consideration of region and country risks, exchange-rate fluctuation, regulatory risk, as well as US and home-country taxation issues, to thinking about funds like VTABX.

Once you get beyond widely-traded bonds from large, highly-rated US corporations, it becomes harder to rely on the hope that a bond's value can be precisely determined from a dispassionate algebraic formula. Bond pricing is not an exact science. There are bookshelves of technical books on bond pricing.
Last edited by crefwatch on Mon Jan 24, 2022 2:23 pm, edited 1 time in total.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

crefwatch wrote: Mon Jan 24, 2022 5:37 am It's important to understand that each individual bond in a mutual fund behaves like one of your bonds, but the whole fund together does not, exactly. A big reason is turnover. Others are varying distributions of quality, risk, and maturity dates in a fund.

Do you understand that market sentiments affect fund prices? Periodic fears about muni bond safety, especially short term, affect muni prices without use of a formula.

I haven't seen yet that you understand why a rise in rates will cause any conventional bond to decline in value.

Do you know the credit ratings for the individual bonds you cited? Do you know how to look up a bond's history at Fidelity or Vanguard?
If this was toward helping me, the OP, I certainly do understand that market sentiment does have an effect on everything, from stocks, to bond, (and even houses for that matter). I slightly understand how a rising rate causes a decline: I totally get if you bought a bond at 2% and bond prices go to 4%, that the 2% bond would be less desirable and less valuable. What I don't get is the scenario where you buy a bond at 3%, and interest rates decline to near, and then rates are hinting they will be going up and that 3% bond still suffers in valuation. And as you can see from the above post on Jan 23 at 8:18pm, I do know the credit rating, as I cited one example in that response. I didn't know I could look up past history of the bonds on Vanguard. I only know what it has been doing since 2018. I obviously have a lot to learn, which is why I made my original post.
alex_686
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

capran wrote: Sun Jan 23, 2022 9:18 pm Looks like I'm out of luck, ...
I think you are asking the wrong question, which is O.K.. In my opinion 90% of the work is figuring out the right question. Once you figured out what the right question is then the answer is obvious.

I have been taking your question literally - what is the relationship between a bond's price and interest rates. And that is what I have given you, in a simplified format. The math behind this is absolute.

Now you are asking about a bond fund which has thousands of bonds. And what I have given you still works. All you have to do is load all of the bonds into a spreadsheet. Then change the interest rate. Then calculate the change for thousands of bonds. Then add it up all together.

So maybe that is not practical. Bond funds are a little like a flock of starlings. If you startle the flock they will move in a mass away from you but not in a uniform or homogenous block.

So focus on 2 numbers.

The first is the SEC Yield. This is a high quality number.

The second is Duration, which is a measure of time and risk.

https://www.bogleheads.org/wiki/Bonds:_ ... s#Duration

or

https://en.wikipedia.org/wiki/Bond_duration

Generally speaking the higher the duration value the more sensitive a bond or a fund of bonds is to interest rate risk.

Generally speaking - which should be enough for the average investor. I have a whole stack worth of books, white papers, academic journals, etc. going into the nuances.

But generally speaking these 2 values are high quality numbers that can help you select a bond fund, figure out its return, and measure its risk.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
alex_686
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

capran wrote: Mon Jan 24, 2022 9:12 am What I don't get is the scenario where you buy a bond at 3%, and interest rates decline to near, and then rates are hinting they will be going up and that 3% bond still suffers in valuation.
I am not following this question. Can you restate?

Rember, a bond's price and yield and just 2 different ways of saying the same thing. You are literally saying that you don't understand the case when rates are hinting at a a downwards movement (not sure how they would hint) that a bond's rate would fall downward. Well yes, if bond rates fall than bond rates fall. So I don't think that is the question you are asking.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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capran
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

alex_686 wrote: Mon Jan 24, 2022 9:36 am
capran wrote: Mon Jan 24, 2022 9:12 am What I don't get is the scenario where you buy a bond at 3%, and interest rates decline to near, and then rates are hinting they will be going up and that 3% bond still suffers in valuation.
I am not following this question. Can you restate?

Rember, a bond's price and yield and just 2 different ways of saying the same thing. You are literally saying that you don't understand the case when rates are hinting at a a downwards movement (not sure how they would hint) that a bond's rate would fall downward. Well yes, if bond rates fall than bond rates fall. So I don't think that is the question you are asking.
I likely don't know enough to even ask the right question. It really is probably a moot point anyway. The yield, or annual yield is a fixed amount on the individual bonds. And as they near the call date, the "share price" should likely go to the listed call rate, which in all three tax free bonds is $100.00. (at least, that is my assumption, based on current price and call date). So, for example, I expect the Snohomish bond to be called on 5-1-22 at $100.00 per share. It's price on 12/31 was 100.37. the price today is 100.329. The interesting thing is, if indeed it is called at 100 per share, I will have a Capital gain of $309.18 in addition to having over 5 years of 325 tax free interest per year. (10,000 shares, Basis 9690.82 Rated AA+ interestingly. Whereas the Deschutes bond has a basis of 25,842.84, and it's 25,000 shares if redeemed at the call rate in 2026 of 100 per share, will be a loss of 842.84 (cost:25842.84-proceeds at 100 share 25,000=-842.84. and it will continue to pay me 1,000 per year until called, and is rated A+. And the Oregon health 5,000 shares, basis is 4966.95, and when called in 2026 @100 a share, will give a Capital Gain of $33.05 (5000-4966.95=33.05), and is rated AA-, and pays out 168.75 until called. Currently it is priced at 109.536, but as stated earlier, I would expect that share price to decline to 100 by the callable date in 2026.
alex_686
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by alex_686 »

capran wrote: Mon Jan 24, 2022 10:55 am I likely don't know enough to even ask the right question.
So at this point I will kind of recommend that you find a used text book or find a course of edx or coursea. We are getting to intermediary to advance topics. You want to master the basic building blocks before you advance to harder topics.

Anyways, let us decompose a yield into ...

Bond Yield = Expected Interest Rate + Real Rate + Credit Spread + Option Adjusted Spread.

So Yield and Price and still firmly linked. But we need to untangle all of the little bits. The OAS is the bit where we throw in things like the call option.

Now you can consider a callable bond as 2 different bonds. One where it is held to maturity, the other one where it is called. We then determine the price under each even and the probabilities of each event happening. Multiple the probability with the price, add them together, and get the price of the bond. The more likely it will be called the more likely FV and N of the bond will be the callable price.

This is oversimplifying things. For a bit more of a taste read up on binominal bond pricing.

https://ift.world/concept1/level-ii-con ... mial-tree/

Now, this too oversimplifies things but it does work as a intellectual framework.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
wfrobinette
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by wfrobinette »

capran wrote: Sun Jan 23, 2022 5:57 pm
alex_686 wrote: Sun Jan 23, 2022 12:45 pm I will try to find a nice simple bond pricing primer. I have advanced to a level where I just don’t anything so basic so I am nit sure where to start.

The short answer is that there is a mathematical relationship between price and yield. If you know the price of a bond you know the yield. Know the yield you know the price.

On my systems at work I can switch bond quotes between price and yield because they are absolutely interchangeable.
Is there a formula you would be willing to share. I went back and looked up quarterly statements on LEO for the last few years, with statement balance as well as the "est. yield" that Vanguard reports. Unfortunately, that's all I get. There is no SEC yield provided by Vanguard.
quarter date--balance---est. yield
30-Jun-19-----$42,794 ----5.14% monthly tax free div/int 183.33
9/30/2019----$44,942 ----4.90%
31-Dec-19 ----$44,575 ----4.94%
3/31/2020----$39,023 -----5.64%
6/30/2020----$40,646 -----5.41%
9/30/2020----$43,370------5.07%
31-Dec-20----$44,470 ------5.02%
3/31/2021----$44,732 -----4.92%
30-Jun-21-----$46,984 -----4.68%
9/30/2021----$45,570 -----4.83%
31-Dec-21-----$44,365 -----4.25% in Nov 2021 reduced tax free div/int to 157.14
Give up on this. Your fund has way too many underlying securities that you don't know the specifics for. Maybe you can peruse the annual report to get an idea. https://im.bnymellon.com/us/en/document ... 53_anr.pdf

1. Not all bonds were bought at issue
2. Not all bonds are held to maturity.
3. Credit worthiness of underlying bond might have changed

https://online.hbs.edu/blog/post/how-to-price-a-bond

This is far easier when you look at 1 bond and I've simplified it more.

1. Issue amount $1000
2. Coupon Rate 3% - The rate at which the bond pays on the original principal amount.
3. Monthly payments of $2.50
4. Daily accruals = 2.50/#days in month. This is the amount you would receive daily. Lets assume 30 days 0.08333 per day

The above items are fixed and never change as long as the bond is outstanding.

1. Scenario #1 - interest rates stay the same and it's the 10th of the month.
Price of bond = $1000 + the number of days accruals = to the number of days 10 days * 0.08333 = 1000.83 is the price.

2. Scenario 2 = Interest rates are higher and it's the 10th day of the month.
Price of bond goes down by some amount. (See Harvard link for details) let's say to $950. But add the 0.83 to the price for accrued interest. The yield would be $30/950 or 3.157. The payments don't change the value lost $50. What this is saying is an investor expects to earn 3.157 on thier money moving forward. The formula is pretty strait forward but the longer the bond has to maturity the further the price would swing.

3. Scenario 3. Interest rates dropped and it's the tenth of the month. Price increases to 1050.83 current yield is 30/1050 now yield is 2.85. Opposite of above but same premise.

This how fluctuations in prices occur. Now do that for every bond in your fund every day and you too can calculate the price.
crefwatch
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by crefwatch »

What I meant by research on Vanguard was: If you click on your holding in your portfolio, you will see some basic information about the bond. Select and copy the CUSIP number from that display. The top right has a link saying something like "Research Bonds". When I click that, I have to select which account I'm working in, maybe not if you only have one account.

In the search window that opens up, there is a CUSIP edit box, and a "Search by CUSIP" button. Paste in the CUSIP and push the button. I must say, I thought this result would show the current Yield to Maturity of the the bond, but it does not. I wanted to point out that statistic to you. It will also reveal if the bond was issued at a price other than 100. When you are buying a bond listed for sale at Vanguard, the YTM is prominently displayed during the transaction. If the bond is called, that figure is no longer accurate. Some bond sales feature Yield to First Call, but that is of course speculative.

If you click on the Buy or Sell buttons that appear in the first window (first paragraph this post), you can click a link that says Trade History. This will show a much longer trade history than you saw in the CUSIP search just above. I doubt it's the entire lifetime of the bond, however. Of course, you now click "Cancel" on the Buy or Sell, and exit back to the bond list.

Fidelity is even more noted for bond data, but I haven't searched there lately. Originally, non-customers could do research at Fidelity.

I trust you know that bonds are bought and sold at an unrevealed markup by the dealer, as well as having a sort of commission charge by Vanguard, and an adjustment for accrued interest. This spread is much larger for small retail customers, but probably never less than 2%. So it's often better to hold a bond near maturity until maturity, since there is no "charge" for redemption.
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capran
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

crefwatch wrote: Mon Jan 24, 2022 2:39 pm What I meant by research on Vanguard was: If you click on your holding in your portfolio, you will see some basic information about the bond. Select and copy the CUSIP number from that display. The top right has a link saying something like "Research Bonds". When I click that, I have to select which account I'm working in, maybe not if you only have one account.

In the search window that opens up, there is a CUSIP edit box, and a "Search by CUSIP" button. Paste in the CUSIP and push the button. I must say, I thought this result would show the current Yield to Maturity of the the bond, but it does not. I wanted to point out that statistic to you. It will also reveal if the bond was issued at a price other than 100. When you are buying a bond listed for sale at Vanguard, the YTM is prominently displayed during the transaction. If the bond is called, that figure is no longer accurate. Some bond sales feature Yield to First Call, but that is of course speculative.

If you click on the Buy or Sell buttons that appear in the first window (first paragraph this post), you can click a link that says Trade History. This will show a much longer trade history than you saw in the CUSIP search just above. I doubt it's the entire lifetime of the bond, however. Of course, you now click "Cancel" on the Buy or Sell, and exit back to the bond list.

Fidelity is even more noted for bond data, but I haven't searched there lately. Originally, non-customers could do research at Fidelity.

I trust you know that bonds are bought and sold at an unrevealed markup by the dealer, as well as having a sort of commission charge by Vanguard, and an adjustment for accrued interest. This spread is much larger for small retail customers, but probably never less than 2%. So it's often better to hold a bond near maturity until maturity, since there is no "charge" for redemption.
I have known the CUSIP, as it's on the monthly printout. But didn't know you might get additional info other than what is printed. I have not voluntarily redeemed any bond, but two years ago had several 7.8% bonds called, which was a bummer. No fee on a called bond. At one point bond income was over 8k. Now the only three tax free, which will be called one this year and two in 2026. I have one lower rated Corporate 156700AMB Century link inc, that says CPN 7.6% with an est yield of 7.09% 5,000 shares at currently 107.25, paying 380 per year. BB-. I don't see any Call on it, and it's scheduled for 2039.
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by crefwatch »

Didn't you pay more than "100" for the individual bonds you bought?
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capran
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Re: trying to understand relationship between bonds, interest rates and valuation

Post by capran »

crefwatch wrote: Tue Jan 25, 2022 7:12 am Didn't you pay more than "100" for the individual bonds you bought?
Looking through paperwork to see if there was a points type charge from Vanguard, but that must be listed somewhere else. All I can find so far is: Oregon Health Sci 5,000 shares -- Cost per share .99 -- total cost 4967.03 -- value as of 1/20/22 5301.90 with the call info I posted earlier
Snohomish Cnty Wa HSG 10,000 shares --Cost per share .97 -- total cost 9691.21 -- current value 1/20/22 10,034.80
Deschutes CNTY OR HSP 25,000 shares -- cost per share 1.03 -- total cost 25,832.86 --- current value 1/20/22 27,460.50
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