Author Topic: TLT carnage  (Read 1879 times)

force majeure

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TLT carnage
« on: October 23, 2022, 03:25:52 AM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

MustacheAndaHalf

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Re: TLT carnage
« Reply #1 on: October 23, 2022, 05:14:01 AM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
Down -35% YTD.  Why did you buy it, and why did you keep holding it?

force majeure

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Re: TLT carnage
« Reply #2 on: October 23, 2022, 05:20:04 AM »
Bought as a bond holding, insurance against equity market sell-offs.
I am sure it will turn upwards, but not until rate cycle changes, or markets indicates this will happen.

MustacheAndaHalf

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Re: TLT carnage
« Reply #3 on: October 23, 2022, 06:03:12 AM »
Bought as a bond holding, insurance against equity market sell-offs.
That's why most people buy bonds, but it doesn't explain why you picked TLT instead of BND.  If you had a bond holding previously, you sold that and bought TLT.

This could be performance chasing (+15% 2019, +17% 2020), which I bring up because -35% YTD is a pretty good lesson against it.

I've been watching inflation, bond yields and the Fed, all of which lead me to invest against TLT.  There's an ETF providng -300% the return of TLT that I have bought and sold a few times this year and made a decent profit.

vand

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Re: TLT carnage
« Reply #4 on: October 23, 2022, 10:08:00 AM »
Reality check for people who think you can't lose money on bonds, or that, as disastrous as TLT has done over the kast year it can't fall a lot more:

(I wish someone with the data would do an update to these charts)

5yr Treasuries


Long term Treasuries


taken from https://awealthofcommonsense.com/2018/10/the-worst-kind-of-bear-market/

Given their starting point and that real yields are still deeply negative, I fully expect this to turn out to be the worse bond bear market in history.  Yes there will be rallies along the way, but inflation will continue to destroy the real purchasing power of fixed income investors until prices adjust to offer real positive returns.   

Talking heads in the media are touting fixed income as an option now given that you can get 4% or so, but this is still useless when inflation is 8%.
« Last Edit: October 23, 2022, 10:10:20 AM by vand »

mistymoney

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Re: TLT carnage
« Reply #5 on: October 23, 2022, 11:05:23 AM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?


vand

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Re: TLT carnage
« Reply #6 on: October 23, 2022, 06:18:23 PM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen
« Last Edit: October 23, 2022, 06:46:29 PM by vand »

Radagast

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Re: TLT carnage
« Reply #7 on: October 23, 2022, 11:40:47 PM »
What was your original plan? Why did you like 20-30 year bonds more at 2.2% yield than at 4.2%? I personally prefer 4.2% yield to 2.2%.

Full disclosure I allocate 7% to ZROZ which is down almost 50% YTD and I am unfazed. I've seen the history of these, and I expect it ALL to happen again, in an unpredictable fashion. Yup, I'm in even though I am full of forum stories about all the currencies which have gone to 0, taking bonds with them, or where the bonds just went to zero and the currency carried through. Two years ago I was like "bond bear market 1941-1981, bond bull market 1981-2021, 2021-2061 repeat?" and that narrative was right as of 2022. Humans are a species which looks at a cloud and sees a unicorn, you can't trust any of us to accurately form a narrative about a pattern, so I don't actually think that 40 year cycle will repeat though it could, it is just an example about the stuff I was saying to people who expected deflation forever. I actually have no opinion on where we are headed next.

Why own ZROZ? Deflation. Basically 93% of my investments are targeted to assets which to some extent or another should be good to OK at fighting inflation (mostly good), and more if you consider real estate. But I lack deflation protection. ZROZ is a concentrated deflation hedge, it takes up in 7% of my investments what regular bonds would require 30% to accomplish. Bonds are on average not that great an investment (often terrible), and this allows me to keep my bond allocation as small as possible. I also use savings bonds, which are another concentrated form of bond. I am dollar cost averaging in to ZROZ rather than rebalancing, because that is an effective method for an ignorant person to catch the bottom. It is possible that we are in the 1950's for long term bonds and it will take the rest of my life for my investment to recover, but I don't trust people who say inflation to forever either. For all I know we will be back to deflation in 2 years and this is the time to buy. I just don't know, and I don't believe anybody who says they do. Also, even in inflationary times there can be a flight to safety during stock crashes which causes long term treasuries to rise at an opportune time.

While we are here, https://portfoliocharts.com/2019/05/27/high-profits-at-low-rates-the-benefits-of-bond-convexity/

vand

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Re: TLT carnage
« Reply #8 on: October 24, 2022, 07:04:53 AM »
What was your original plan? Why did you like 20-30 year bonds more at 2.2% yield than at 4.2%? I personally prefer 4.2% yield to 2.2%.

I guess the flippant answer is that in the days of 2.2% yield that still represented a 0.2% real yield


mistymoney

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Re: TLT carnage
« Reply #9 on: October 24, 2022, 06:55:57 PM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen

I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....

ChpBstrd

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Re: TLT carnage
« Reply #10 on: October 24, 2022, 08:45:52 PM »
I think TLT and ZROZ have further to fall considering that we're only 3.25% of the way to a 4.75% to 5% predicted terminal rate on overnight rates. Not all of that change will make it into long-duration bonds like TLT and ZROZ represent, and in fact we're likely to invert the FFR vs. the 10 year yield by about 0.5%, but that still leaves 100-125 basis points to go on longer-duration treasuries. There could be lots more pain ahead for TLT. Check out the Taylor Rule for why. The Fed is going to have to raise short term rates above the level of inflation to push inflation down. We're still in stimulative territory.

The reason to own TLT NOW is if you want to place a leveraged bet on the shit hitting the fan... hard... like 2008-style. Think banks collapsing, nobody buying anything, jobless people getting foreclosed upon, and people jumping from skyscrapers bad. In that scenario, the Fed would cut rates very fast and TLT would rocket back upward. Your stocks would lose another 30-50% but your TLT would do great.

This hedging opportunity is offset by the alternative risk that TLT keeps losing value as the Fed hikes rates to 4%, then 5%, then 6%, then 7%... trying to catch up with raging inflation. That scenario would represent a repeat of the devastation experienced in 2022.

So which scenario is more likely? I think the first one is more likely, but not by enough to justify the risk of holding TLT. If I was you and holding TLT, I'd GTF out. I might then consider buying the longest-duration LEAPS call options on TLT or ZROZ as insurance against a financial crisis that would cause rapid rate cuts. In fact I'm keeping an eye on this play as an idea if we start seeing markets freeze up, joblessness go up quickly, etc.

For TLT, I'd look at buying the January 17, 2025 call options at the $100 strike which last sold for around $12.55 (so 100/12.55= nearly 8x leverage with a firm limit on downside risk). I expect this would do well in a repeat of the 2008-2009 financial crisis scenario, or even a repeat of the aborted 2016-2018 rate hiking campaign. This option also has enough duration that you can hold it for a while, waiting for events to unfold over a span of many months, and selling the options when the rate cuts are done and there's still time value. Yes, it is possible to lose 100% of this investment, but that amount is a lot less than what remains at risk if you take a comparably-sized long position in TLT.

Radagast

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Re: TLT carnage
« Reply #11 on: October 24, 2022, 09:35:44 PM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen

I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....
Almost all bond funds sell before maturity, except for things like money markets, target maturity date bond funds (BulletShares or whatever), and maybe a few others. Most sooner, for example BND sells at 1 year left, TLT at 20 years left, etc. At that time the bonds are sold at whatever the market price is, which depends on the interest rate relative to other bonds on the market.

ETFs are kept in line in other ways too, for example whenever someone buys or sells. To encourage the price to stay strictly in line with the underlying assets even if trading is thin, certain institutional traders may create or redeem baskets of shares of the underlying securities, and trade them for profit if the exchange price is whack.

Mutual funds are required to "mark to market" at the end of every business day, tallying up all their assets and their values.

Radagast

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Re: TLT carnage
« Reply #12 on: October 24, 2022, 09:40:10 PM »
The reason to own TLT NOW is if you want to place a leveraged bet on the shit hitting the fan...
Or if you follow a predetermined asset allocation, and don't want to follow the market's every move, playing with options and leverage, risking more than you put in. In fact, I'm pretty sure the efficient market hypothesis says that all this dodging is a net negative among all traders, akin to betting red at roulette. It definitely won't be green, so that means you have a 50/50 chance. I could be missing something...?

BicycleB

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Re: TLT carnage
« Reply #13 on: October 25, 2022, 12:50:22 AM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen

I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....

@mistymoney, I think the reason is that changes in interest rates logically change the value of existing bonds.

I think the mechanism is that, from the viewpoint of a different investor, bonds at the new rate are available, so in the event that bonds like the old bonds are offered for sale, the price needs to change in order for the old bonds to be a mathematically reasonable purchase. The fact that most bond investors can calculate this effect means that the recognized value of the original old bonds changes. It's true that the bonds can be held to maturity, but their recognized value changes anyway due to comparison with other bonds that have the new interest rates.

Will defer to wiser commenters - still trying to understand bonds. :)
« Last Edit: October 25, 2022, 12:57:36 AM by BicycleB »

habanero

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Re: TLT carnage
« Reply #14 on: October 25, 2022, 02:28:07 AM »
I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....

Because when interest goes up in the treasury market you can buy similar no risk of principal loss pyaing higher coupons so the older, low coupon bonds fall in value as there are more attractive investment opportunities for investors wanting to own US treasuries. These older bonds is what the ETF is holding so as these securities fall in value, so must the ETF.

This effect is amplified the longer the duration, sensitivity to interest rates increase the longer the maturity of the bond. That's why half the long bond (30y UST) issued in may 2020 is gone, it was issued at a price around 100, it now trades sub-50 so over 50% loss in value. The bond will pay you its 1.25% of interest per year and you will get 100 back at maturity. But the 1.25% coupion is much lower than what you can get in the market now hence the value has been chopped hard.

So the price of "old" bonds have to match the value of buying more recently issuance with similar maturity and the newer ones pay significantly higher coupons. The current on-the-run long bond pays a coupon of 3% and was issued  in august this year at price 83.7 (it was a tap of previous issuance, hence a price different from par). The yield to maturity on that bond is now around 4,35%. So if the treasury were to issue a brand new 30y bond now with a price around 100 it would need to have a coupoin of around 4.35% otherwise noone would buy it at 100.

« Last Edit: October 25, 2022, 02:33:09 AM by habanero »

mistymoney

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Re: TLT carnage
« Reply #15 on: October 25, 2022, 01:55:42 PM »
I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....

Because when interest goes up in the treasury market you can buy similar no risk of principal loss pyaing higher coupons so the older, low coupon bonds fall in value as there are more attractive investment opportunities for investors wanting to own US treasuries. These older bonds is what the ETF is holding so as these securities fall in value, so must the ETF.

This effect is amplified the longer the duration, sensitivity to interest rates increase the longer the maturity of the bond. That's why half the long bond (30y UST) issued in may 2020 is gone, it was issued at a price around 100, it now trades sub-50 so over 50% loss in value. The bond will pay you its 1.25% of interest per year and you will get 100 back at maturity. But the 1.25% coupion is much lower than what you can get in the market now hence the value has been chopped hard.

So the price of "old" bonds have to match the value of buying more recently issuance with similar maturity and the newer ones pay significantly higher coupons. The current on-the-run long bond pays a coupon of 3% and was issued  in august this year at price 83.7 (it was a tap of previous issuance, hence a price different from par). The yield to maturity on that bond is now around 4,35%. So if the treasury were to issue a brand new 30y bond now with a price around 100 it would need to have a coupoin of around 4.35% otherwise noone would buy it at 100.

Thanks so much for taking the time to explain! :)

mistymoney

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Re: TLT carnage
« Reply #16 on: October 25, 2022, 01:57:21 PM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen

I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....

@mistymoney, I think the reason is that changes in interest rates logically change the value of existing bonds.

I think the mechanism is that, from the viewpoint of a different investor, bonds at the new rate are available, so in the event that bonds like the old bonds are offered for sale, the price needs to change in order for the old bonds to be a mathematically reasonable purchase. The fact that most bond investors can calculate this effect means that the recognized value of the original old bonds changes. It's true that the bonds can be held to maturity, but their recognized value changes anyway due to comparison with other bonds that have the new interest rates.

Will defer to wiser commenters - still trying to understand bonds. :)

Thanks! we will learn together!

mistymoney

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Re: TLT carnage
« Reply #17 on: October 25, 2022, 01:59:15 PM »
What are people doing about holding TLT bond fund?
I am a holder from last year, and I am underwater quite a percentage YTD.
I either keep holding, add more to average down, or sell and cut losses.
I know its a tough call.

I had to look up this performance, and to say I am shocked is an understatement. I'm so sorry and I don't have any advice.

Looks like it is down 33% YTD....more than the sp500.....for a treasury bond ETF. I guess it is due to buying and selling within the ETF, but seems holding to maturity would be best for the fund. But they are likely selling at a loss and buying new? or so many people are selling out the fund they have to sell? Can they not just hold?

It is down because interest rates went from 0% to 3%, which in a fund where the average duration is 17yrs it means for a 1% change in interest rates you can expext the the fund to decline 17%. 
https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf

Nice when interest rates are falling, not so nice when they are going up.

Bond funds are continually selling bonds as they grow older and buying new ones to replace them with, thereby keeping average duration of the fund in line with its stated policy, but that is not the reason they have fallen

I got that part of it! I was assuming that was baked in....but if you have government securities, you can hold till redemption with no loss of capital. So I'm trying to figure out why the ETF is down over 30%, when the underlying securities wouldn't lose value if you held to maturity. Needing to keep buying and selling was the only thing I came up with....
Almost all bond funds sell before maturity, except for things like money markets, target maturity date bond funds (BulletShares or whatever), and maybe a few others. Most sooner, for example BND sells at 1 year left, TLT at 20 years left, etc. At that time the bonds are sold at whatever the market price is, which depends on the interest rate relative to other bonds on the market.

ETFs are kept in line in other ways too, for example whenever someone buys or sells. To encourage the price to stay strictly in line with the underlying assets even if trading is thin, certain institutional traders may create or redeem baskets of shares of the underlying securities, and trade them for profit if the exchange price is whack.

Mutual funds are required to "mark to market" at the end of every business day, tallying up all their assets and their values.

This is what I am missing in my treasury direct account! All I see is par value, except for TIPS - so I guess my value is changing but I just don't see it.

Thanks!

vand

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Re: TLT carnage
« Reply #18 on: October 25, 2022, 02:04:06 PM »
habernero explained it very well. It basically boils down to the rate at which you discount future cashflows, as so much of finance ultimately does.   As the income from bonds are FIXED (ie known in advance), higher inflation means that the present value of that future income isn't worth as much as it is in inflation is projected to be lower, hence the face value of the bond falls in order to compensate.

You may never notice or realise this if you buy and hold bonds directly and have no intention of selling them, but remember that you get back par value when they mature, and that will be worth less upon expiry in a high inflation environment than in a lower inflation environment.  We have said it before in various other bond threads that inflation is like kryptonite to fixed income investments.

mistymoney

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Re: TLT carnage
« Reply #19 on: October 25, 2022, 02:07:56 PM »
habernero explained it very well. It basically boils down to the rate at which you discount future cashflows, as so much of finance ultimately does.   As the income from bonds are FIXED (ie known in advance), higher inflation means that the present value of that future income isn't worth as much as it is in inflation is projected to be lower, hence the face value of the bond falls in order to compensate.

You may never notice or realise this if you buy and hold bonds directly and have no intention of selling them, but remember that you get back par value when they mature, and that will be worth less upon expiry in a high inflation environment than in a lower inflation environment.  We have said it before in various other bond threads that inflation is like kryptonite to fixed income investments.

Yes, thanks, need to keep this in mind.

vand

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Re: TLT carnage
« Reply #20 on: October 25, 2022, 02:15:14 PM »
It has to be said that fundamental analysis of stock investing is not all that different - you are basically valuing a business based upon your best estimate of its future cashflows, and discounting that back to the present. Both stocks and bonds are cashflowing investments whose present value is determined to a greatest or lesser extent upon the rate at which you discount future cashflows. Bonds are easier, stocks there are more variable to consider.

Buffett explains it all:
https://www.youtube.com/watch?v=Bxqre8vPYBo

habanero

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Re: TLT carnage
« Reply #21 on: October 29, 2022, 05:58:10 AM »
Here is what happens to a 6% bond bought and held until maurity for 10 years. Its assuming 6% coupon payed annual for simplicity (bonds generally pay semiannual coupons but that's not very relevant for the illustration). I have assumed three stiistic scenarios:

The first is that yield to maturity drops by 0.20% per year, this can be thought of as no change in the interest rate level, but yield to maturity (YTM) drops as you roll down the issuer's credit curve and the credit risk decreases.

The second is that yields drop by 0.50% per year due to the combined effect of rolling down the credit curve + lower interest rates in the market.

The third is that yields drop by 2% per year down to a minium of 0% and stay there for a couple of years, then increase sharply by 2% every year until maturity.

The point is to illustrate a few effects: One is that yields go down as the maturity gets shorter, but due to the shorter duration the value does not go up by much and towards the end you have a "pull to par" effect as the bond nears its maturity date. So despite yields going down, the value goes down as well.

The second is that despite a sizeable and steady drop in yields, peak value occurs in year 5, after that the pull-to-par effect starts dominating and the value drops.

The third is that when yields go down sharply and stay down, the value doesnt increase anymore as all the juice is squeezed out of the bond You had a good run on the investment, but it wont continue. Then later, even as rates go up sharply the value doesnt change that much as the remaining maturity is short.

Year   YTM           Price          YTM           Price           YTM           Price
0   6.00%   100.0   6.00%   100.0   6.00%   100.0
1   5.80%   101.4   5.50%   103.5   4.00%   114.9
2   5.60%   102.5   5.00%   106.5   2.00%   129.3
3   5.40%   103.4   4.50%   108.8   0.00%   142.0
4   5.20%   104.0   4.00%   110.5   0.00%   136.0
5   5.00%   104.3   3.50%   111.3   0.00%   130.0
6   4.80%   104.3   3.00%   111.2   2.00%   115.2
7   4.60%   103.8   2.50%   110.0   4.00%   105.6
8   4.40%   103.0   2.00%   107.8   6.00%   100.0
9   4.20%   101.7   1.50%   104.4   8.00%   98.1
10   4.00%   100.0   1.00%   100.0   10.00%   100.0

To illustrate bond convexity, assume you buy a 30y bond with a 5% coupon. Convexity is the non-linear relationship between change in yield and change in price. As yields drop towards zero this effect gets very strong.

Yield           Price          Change
5.00%   100.0   0
4.00%   117.3   17.3
3.00%   139.2   21.9
2.00%   167.2   28.0
1.00%   203.2   36.0
0.00%   250.0   46.8


This latter effect is a good chunk of the explanation for the stellar run long-dated bonds had during the pandemic when yields got slashed. Now the effect works in reverse as yeilds rise quickly and the market value of long bonds goes down really fast. This also shows the effect of duration - compared to the 10y example above, the price changes are much bigger for a 30y bond (tad apples to oranges as the 10y example also assumes the bond gets shorter, but the point is still valid).
« Last Edit: October 29, 2022, 11:34:43 AM by habanero »