The Eight Great Misconceptions About Bonds

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UpperNwGuy
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Re: The Eight Great Misconceptions About Bonds - Allan Roth - Vanguard Reference?

Post by UpperNwGuy »

You can read more about how forum members have reacted to this article here: viewtopic.php?p=5988962#p5988962
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LadyGeek
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Re: The Eight Great Misconceptions About Bonds

Post by LadyGeek »

^^^ Thanks! I merged excel's thread into the ongoing discussion.

(Also, thanks to the member who reported the post and provided a link to the thread.)
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Re: The Eight Great Misconceptions About Bonds

Post by #Cruncher »

excel wrote: Fri May 07, 2021 12:36 pmAllan Roth recently posted: The Eight Great Misconceptions About Bonds
The article includes a chart under misconception 5 ... The chart source is claimed to be Vanguard Group. ... I sent an email to Vanguard asking for more information about the chart, but they said they had no comment on 3rd party information.
Or possibly Vanguard is embarrassed to admit it's theirs :wink:, since the chart's methodology is seriously flawed. Here it is:

Image
Allan Roth, referring to the chart, wrote:Taking a four-percentage point increase in rates over one year, this bond fund would lose an estimated 21.76% in one year. ... If rates then stabilized, the fund manager is now buying bonds yielding an average of four percentage points higher. By year six, the loss is wiped out and, by year eight, the gain is higher than it would be if rates had not risen in the first place.
The problem lies in how he is calculating the 21.76% decrease.
  1. He assumes that the 4% point jump takes place half-way through year one reducing the 6.3 year duration down to 5.8 years.
  2. He assumes that the price will fall 4% times 5.8 or 23.2% . This is the real problem.
  3. He adds the 1.44% initial yield to get a net 21.76% fall in value. (-21.76% = -23.2% + 1.44%)
The main problem is his assumption # 2. There is a rule of thumb that a bond or bond fund's price change equals the duration times the interest rate change. But this only works for small changes in interest rates. For a 4% point change it significantly overstates the effect. This error causes his conclusion to be wrong. It doesn't take 8 years until the "the gain is higher than it would be if rates had not risen in the first place". This actually would occur after about 6.3 years, the assumed duration.

The misuse of the rule of thumb is most apparent for the last row in the table where the yield increases 10% points. He calculates a drop of 56.56% percent (-10% * 5.8 + 1.44%) after one year and shows the return not quite returning to 1.44% even after 10 years. The actual effect would be a drop in value of about 38%, and the 1.44% return would actually be realized after 6.3 years.

He misses the main point: regardless of the size of the rate increase, after a period equal to the duration has passed since the rate increase, if there are no further changes in rates, one's overall return will equal what it would have been without the rate increase.

excel in same post wrote:Any sources for a spreadsheet calculating the impact of interest rate changes to NAV for various durations and yields?
I prepared a spreadsheet calculated the correct way.
  • To simplify things, I assume a single zero coupon bond that matures in exactly 6 years. (The duration of a zero-coupon bond equals its maturity. )
  • I assume that the rate increase occurs immediately. The effect of this change is shown in column "0".
  • Columns "1" to "9" show the annual return of the bond each year assuming the yield remains at the new level. (This is the same method used in Allan Roth's table.) In every case the return matches the 1.44% initial yield after 6 years.

Code: Select all

Row      Col A     Col B    Col C    Col D    Col E    Col F     Col G   Col G   Col I   Col J   Col K
  1  Init rate     1.44%
  2       Term       6.0
  3  Mat value    1.0896 = 1.0144 ^ 6.0
  4  Rate Jump       0        1        2        3        4         5       6       7       8       9

Code: Select all

  5         0%     0.00%    1.44%    1.44%    1.44%    1.44%     1.44%   1.44%   1.44%   1.44%   1.44% 
  6         1%    (5.72%)  (3.42%)  (0.53%)   0.45%    0.94%     1.24%   1.44%   1.58%   1.69%   1.77% 
  7         2%   (11.05%)  (7.99%)  (2.44%)  (0.52%)   0.45%     1.04%   1.44%   1.72%   1.94%   2.10% 
  8         3%   (16.04%) (12.32%)  (4.30%)  (1.47%)  (0.03%)    0.85%   1.44%   1.86%   2.18%   2.43% 
  9         4%   (20.71%) (16.40%)  (6.11%)  (2.41%)  (0.50%)    0.66%   1.44%   2.00%   2.43%   2.76% 
 10         5%   (25.08%) (20.25%)  (7.87%)  (3.33%)  (0.97%)    0.47%   1.44%   2.14%   2.67%   3.08% 
 11         6%   (29.16%) (23.89%)  (9.57%)  (4.22%)  (1.43%)    0.28%   1.44%   2.28%   2.91%   3.40% 
 12         7%   (32.99%) (27.34%) (11.23%)  (5.11%)  (1.89%)    0.10%   1.44%   2.41%   3.15%   3.72% 
 13         8%   (36.58%) (30.60%) (12.85%)  (5.98%)  (2.34%)   (0.09%)  1.44%   2.55%   3.38%   4.04% 
 14         9%   (39.95%) (33.68%) (14.42%)  (6.83%)  (2.78%)   (0.27%)  1.44%   2.68%   3.62%   4.36% 
 15        10%   (43.11%) (36.61%) (15.95%)  (7.66%)  (3.22%)   (0.45%)  1.44%   2.81%   3.85%   4.67%
Follow these steps if you want to use this spreadsheet:
  • Select All, Copy, and Paste [ * ] the following at cell A1 of a blank Excel sheet.

    Code: Select all

    Init rate	0.0144
    Term	6
    Mat value	=(1+B1)^B2
    Rate Jump	0	=B4+1	=C4+1
    0	=B$3/(1+B$1+A5)^B$2-1	=(1+B5)*(1+$B$1+$A5)-1	=((1+C5)^(D$4-1)*(1+$B$1+$A5))^(1/D$4)-1
    =A5+0.01
    =A6+0.01
    =A7+0.01
    =A8+0.01
    =A9+0.01
    =A10+0.01
    =A11+0.01
    =A12+0.01
    =A13+0.01
    =A14+0.01
  • Copy cells D4:D5 right to column K.
  • Copy cells B5:K5 down to row 15.
  • Format for readability.
  • Modify cells B1, B2, or A5:A15 as desired.
* If you have trouble pasting, try "Paste Special" and "Text".
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Re: The Eight Great Misconceptions About Bonds

Post by j.click »

I always enjoy and learn from #Cruncher's posts. As one who attended a liberal arts college so I would not have to take calculus, I am in awe of his number crunching ability. However, I HAVE mastered the 'rule of 72'.....
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Re: The Eight Great Misconceptions About Bonds

Post by LadyGeek »

While we're looking at numbers, I never really understood why a bond's price moved inversely with the yield (interest rate). Descriptions of how bonds work didn't help. What worked was looking at the fundamental bond equation.

See the wiki: Bond pricing
Since I is in the denominator of the bond price equation, increasing I will decrease the price (the other variables are fixed). Therefore, a bond's price will always theoretically move in the opposite direction to its yield.

As yields change in the marketplace, the only variable that can compensate for these changes is price (sum of PV).[4] This why bond charts show price and yield- they are the only 2 variables that are not set by the bond. Change one and the other follows.
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nedsaid
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Re: The Eight Great Misconceptions About Bonds

Post by nedsaid »

Bonds are far simpler than stocks, alternatives, hedge funds, and derivative investments.
This statement just lost me here. Bonds can actually be quite complex instruments. The basic concepts of a bond are very simple but basic concepts are not necessarily real world.

What makes bonds potentially a complex investment? Let me list a few:

1) Call dates. A 10 year bond with a call date in 5 years is in many respects a 5 year bond. If interest rates fall, the bond will most likely be called.

2) Credit ratings.

3) Bond covenants.

4) If the company defaults, in what order will bond investors be made whole in event of bankruptcy. A company might have several bond issues and those issues might vary in priority in who gets paid first. Subordinated debt vs. Senior Debt.

5) Collateralization. What backs the bond in case of default?

6) Buying at a discount vs. buying at a premium. Effective interest rates vs. coupon rates.

7) Much of the Bond Market is not very liquid. You have the effect of higher bid/ask spreads than you might have expected.
A fool and his money are good for business.
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