is dividend adjusted into the price of a bond or not ?

Discussion of the Bond portion of the Permanent Portfolio

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johntaylor
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is dividend adjusted into the price of a bond or not ?

Post by johntaylor » Wed Jan 23, 2019 10:03 pm

I am still very uncertain about how to calculate returns of potential portfolio's. Last year I had my bonds in an etf and I could calculate return by just looking what my broker showed me on actual delivered prices and dividends. But now I consider switching to real LT german bonds I have to use data from historic charts to calculate returns:
2017 / 2048
https://www.deutsche-finanzagentur.de/d ... 001102432/
coupon=1.25%
The close prices:
2017-12-29: 99.96
2018-12-28: 110.08
return 2018: (109.95-100.1)/100.1 = 9.8%
2014 / 2046
https://www.deutsche-finanzagentur.de/d ... 001102341/
coupon=2.5%
Close prices:
2017-12-29:131.55
2018-12-28: 141.06
return 2018: (141.06-131.55)/131.55 =7.2%

My uncertainty is: Is the dividend already calculated into these prices or not ? I think they are not, why ?
  • If I add the coupon rate to the return both bonds get a return which are (more) similar, which is what I would expect:
    9.8%+1.25%=11.05%
    7.2%+2.5%=9.7%
  • I learned from my etf fund that dividend was not adjusted into the prices on the chart
But I am not sure. How can I find out if dividend is adjusted into the price or not ?
brownehead
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Re: is dividend adjusted into the price of a bond or not ?

Post by brownehead » Thu Jan 24, 2019 3:09 am

Bond prices never include interest payments, therefore you have to consider them to calculate historical returns. However, you must consider also the price paid for the bond to calculate the real interest (dividend) received with the coupons:

In your examples, if you bought the first bund (2048) on 2017-12-29 at 99.96, with a coupon of 1.25% the real yield for that year would be (100/99.96)*1.25=1.2505%. With the previous bund (2046), (100/131.55)*2.5=1.9004%. Then, the 2018 return for the 2048 bund would be approximately (110.08/99.96-1)*100+1.25=11.37%. And with the 2046 bund: (141.06/131.55-1)*100+1.9=9.13%.

This is an estimation, because when you buy the bond you also pay the accrued interest since the last coupon payment, and when you sell it you get your accrued interest too; moreover the annual payment is made in the middle of the year and you could reinvest it with a different bond price and so on... For simplicity I use the previous calculation for historical returns: http://www.carterapermanente.es/evoluci ... ermanente/
johntaylor
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Re: is dividend adjusted into the price of a bond or not ?

Post by johntaylor » Thu Jan 24, 2019 7:20 pm

brownehead wrote:
Thu Jan 24, 2019 3:09 am
Bond prices never include interest payments, therefore you have to consider them to calculate historical returns. However, you must consider also the price paid for the bond to calculate the real interest (dividend) received with the coupons:

In your examples, if you bought the first bund (2048) on 2017-12-29 at 99.96, with a coupon of 1.25% the real yield for that year would be (100/99.96)*1.25=1.2505%. With the previous bund (2046), (100/131.55)*2.5=1.9004%. Then, the 2018 return for the 2048 bund would be approximately (110.08/99.96-1)*100+1.25=11.37%. And with the 2046 bund: (141.06/131.55-1)*100+1.9=9.13%.

This is an estimation, because when you buy the bond you also pay the accrued interest since the last coupon payment, and when you sell it you get your accrued interest too; moreover the annual payment is made in the middle of the year and you could reinvest it with a different bond price and so on... For simplicity I use the previous calculation for historical returns: http://www.carterapermanente.es/evoluci ... ermanente/
Thanks again. I made a more detailed list with close prices of each month. I calculated (backward) adjusted close prices like this
Image
This way I get 9.25% return for the 2046 bund and 11.18% for the 2048 bund.

On your website I see that you also use 30yr german bonds with a return of 10.68%. I am curious which bond you used in 2018, so I can check my calculations.
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Re: is dividend adjusted into the price of a bond or not ?

Post by brownehead » Fri Jan 25, 2019 5:36 am

johntaylor wrote:
Thu Jan 24, 2019 7:20 pm
On your website I see that you also use 30yr german bonds with a return of 10.68%. I am curious which bond you used in 2018, so I can check my calculations.
I use the information published by the Bundesbank about 30 year bond yields, which are estimated from the yield curve of listed German bonds:

https://www.bundesbank.de/dynamic/actio ... it03b&id=0

With those yields I use the PRICE function to estimate the returns, which I've found quite consistent with market price changes on real listed bonds.
johntaylor
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Re: is dividend adjusted into the price of a bond or not ?

Post by johntaylor » Fri Jan 25, 2019 1:30 pm

brownehead wrote:
Fri Jan 25, 2019 5:36 am
https://www.bundesbank.de/dynamic/actio ... it03b&id=0

With those yields I use the PRICE function to estimate the returns, which I've found quite consistent with market price changes on real listed bonds.
Okay, I found the 'PRICE' function in my spreadsheet ;) And I could recalculate your 10.68% return for 2018.

My problem with this kind of sources often is, how did they come to these yields ? I prefer to be able to calculate numbers from the base numbers myself, so that if I notice something 'strange' I can check back until the base numbers. I was thinking myself to always use the youngest available LT bond to calculate year returns. So for 2018 I use bund 2017/2048, for 2015-2017 I use bund 2014/2046, for 2013-2014 I use bund 2012/2044, etc.
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Re: is dividend adjusted into the price of a bond or not ?

Post by brownehead » Sat Jan 26, 2019 2:49 am

That's great, you shouldn't invest in anything you don't understand, checking the sorces and making your own calculation is part of the understanding process!

About using real bonds and prices for calculations I agree is a better option to find real results. However, my aim in the blog was to show a benchmark of the ideal European Permanent Portfolio, like an index, something more theoretical which can be used as a guide.
johntaylor
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Re: is dividend adjusted into the price of a bond or not ?

Post by johntaylor » Fri Feb 01, 2019 5:54 pm

brownehead wrote:
Sat Jan 26, 2019 2:49 am
That's great, you shouldn't invest in anything you don't understand, checking the sorces and making your own calculation is part of the understanding process!
Thanks, it encouraged me ;)

I told you earlier I could reproduce your results for 2018, which was grosso modo true:
your return 2018: 10.68%, my return 2018: 10.98%
But I now realize that other years differ quite a bit, for instance 2017:
your return 2017: - 5.96%, my return 2017: -28.9%
For the whole period 1999-2018 the total return differs a lot:
your return 1999-2018: 322%
my return 1999-2018: 102%
(startdate: 1998-12-30, enddate:2018-12-28)

My feeling is that I made big errors in my calculation and I hope you can help me on to find where. For instance with the data of 2017 where the returns differs the most. My calculations of the end-of-year-prices:
2016/12:..=price(date(2014,2,26),date(2046,8,15),2.5%,0.99%,100,1) = 141.75
2017/12:..=price(date(2017,9,20),date(2048,8,15),1.25%,1.27%,100,1) = 99.49
Unadjusted return 2017: (99.49-141.75)/141.75) = - 29.8%
Adjusted return 2017: (99.49-141.75+1.25)/141.75) = - 28.9%
(your return 2017: - 5.96%)

Most values (except yield) I got out of this bundesbank doc:
https://www.deutsche-finanzagentur.de/d ... sanleihen/

month...............bond........settlement.........maturity.......rate..........yield..........frequency...price calc.
....................................(=emissionstart?)..................(=coupon?).................................................
2016/12............14/46.......2014-2-26...........2046-8-15....2.5%........0.99%......1................141.75
2017/12............17/48.......2017-9-20...........2048-8-15....1.25%......1.27%......1..................99.49

About using real bonds and prices for calculations I agree is a better option to find real results. However, my aim in the blog was to show a benchmark of the ideal European Permanent Portfolio, like an index, something more theoretical which can be used as a guide.
The good news is that I made progress on making a combined and adjusted data collection on all german LT bonds, in such a way that I step over to the newest bond every moment it is published. The year returns of this collection gets quite near to the results of your calculations. Total return over 1999-2018: 333% (yours: 322%)
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Re: is dividend adjusted into the price of a bond or not ?

Post by brownehead » Sat Feb 02, 2019 5:06 am

Price function is a bit confusing, moreover we have to make some assumptions for the calculations: I assume initial bond price is allways 100 with a coupon (rate) equal to last year ending price, then with Price function I calculate the ending price of a hypothetical 30 year bond (which equals price returns) and add coupon.

For instance:

2016 ending yield = 0.99%
2017 ending yield = 1.27%
2017 initial bond price = 100
2017 ending bond price = PRICE(date(2017;12;31);date(2047;12;31);0,0099;0,0127;100;1;0) = 93.05
2017 return = 93.05 + 0.99 - 100 = -5.96%

Notice this is just an estimation, I make some tricks with dates and don't reinvest coupons, however as you have seen returns with real bonds are quite similar. Moreover, your higher returns are also explained with sometimes longer maturities of real bonds (31-32 years).
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