Chip, Thank you for this link. After further research I retract my comment about contributions vs conversions. I find that the calculation for the "net Income" matches how the IRS does it in Worksheet 1-3 in Pub 590a, that I linked to above.

However, your use of it seems to have some some typos:

Chip wrote: ↑Thu Oct 05, 2017 1:06 pm

Let's take a simple example, starting with an empty Roth: You convert 10k on Jan 1. On July 1 it has dropped in value to 5k, so you convert another 10k into the same Roth. By Dec 31 the asset has recovered to its Jan 1 price, so the value of the account is now 30k.

You decide you only want to pay tax on 10k of conversions, so you tell Vanguard to recharacterize the entire Jan 1 conversion. IRS rules say that they have to calculate the gain on the conversion by comparing the ratio of the adjusted opening balance (AOB) to the adjusted closing balance (ACB).

AOB is calculated as the balance of the account the day before the conversion being recharacterized was made, plus any conversions after that date. In the example this is 0+10+10 = 20k (zero opening balance plus 2 conversions of 10k each). The ACB is the balance on the date of recharacterization,

less plus any distributions or other recharacterizations (none in this case). So the ACB is 30k.

The gain on your Jan 1 conversion is calculated as (ACB-AOB)/ACB - 1 = (30-20)/30 - 1 = 33.33%

To recharacterize your 10k Jan 1 conversion Vanguard will remove 13,333 from your Roth and send it back to your tIRA.

First, the denominator of the ratio should be Adjusted Opening Balance (AOB), not ACB.

I also don't see where the "1" comes into play as you do the arithmetic, but know it represents the Value of the Conversion/Contribution on the day it was made

.

I was also curious about calculating how much would need to go back for the second conversion instead of/along with the first conversion. So, this is how I calculate it, using your example of two $10,000 conversions into an originally empty account:

To recharacterize Conversion 1 only:
AOB = 0 + 10,000 + 10,000 = 20,000

ACB = 30,000

Net Income = (30,000-20,000) / 20,000 = 0.5000 (this is $5,000 of growth on the $10,000 conversion).

To recharacterize, 10,000 + 5,000 =

15,000 would be removed.

To recharacterize Conversion 2 only:
AOB = 5,000 + 10,000 = 15,000

ACB = 30,000

Net Income = (30,000- 15,000) / 15,000 = 1.0000 (this is $10,000 of growth on the $10,000 conversion).

To recharacterize, 10,000 + 10,000 =

20,000 would be removed.

To recharacterize both Conversions at the same time:
This implies you would have to withdraw 15K + 20K out of a 30K Roth. But the reference link to Cornell (in the section that defines "Computation Period") says that:

If more than one contribution was made as a regular contribution and is being returned from the IRA, the computation period begins immediately prior to the time the first contribution being returned was contributed.

So if we were going to recharacterize both of them at the same time, they would both use the day before the first conversion. The calculation to recharacterize Conversion 1 would stay the same, but Conversion 2 would change to:

AOB = 0 + 10,000 + 10,000 = 20,000

ACB = 30,000

Net Income = (30,000-20,000)/ 20,000 = .5000 (this is $5,000 of growth on the $10,000 conversion).

To recharacterize, 10,000 + 5,000 =

15,000 would be removed.

So 15,000 removed from the 30,000 Roth for Conversion 1 and 15,000 removed from the Roth for Conversion 2, leaves the IRA empty.

Now let's see what happens if we

recharacterize Conversion 1 and a few days later, we recharacterize Conversion 2 (keeping share values stable, to not confuse the examples)

Conversion 1 will have

15,000 removed as originally discussed. But the since the recharacterization date for Conversion 2 is now different,

Conversion 2 has these calculations:

AOB = 5,000 + 10,000 = 15,000

ACB = (30,000-15,000 (Conversion 1 withdrawal)) + 15,000 (Conversion 1 withdrawal) = 30,000

Net Income = (30,000 - 15,000) / 15,000 = 15,000 / 15,000 = 1.0 (this is $10,000 of growth on Conversion 2)

To recharacterize, 10,000 + 10,000 =

20,000 would be removed for Conversion 2

So, to remove Conversion 1 followed by Conversion 2, 15,000 + 20,000 needs to be removed.

Now, let's reverse it and

recharacterize Conversion 2 and a few days later, we recharacterize Conversion 1 (again, keeping share values stable).

Conversion 2 will have

20,000 removed per its original calculation.

Conversion 1 will have these calculations:

AOB = 0 + 10,000 + 10,000 = 20,000

ACB = (30,000-20,000 (Conversion 2 withdrawal)) + 20,000 (Conversion 2 withdrawal) = 30,000

Net Income = (30,000-20,000) / 20,000 = 0.5000 (this is $5,000 of growth on Conversion 1)

To recharacterize $10,000 + $5,000 =

15,000 needs to be removed.

So, to remove Conversion 2 followed by Conversion 1 on different days, 20,000 + 15,000 needs to be removed.

Conversion into new (empty) Roths
Before we close out this example, lets see what it would have looked like if each conversion had been put into a separate Roth. The first number is for Roth A, the second for Roth B. These Roths will have no co-mingling with each other.

(to keep some alignment of the numbers, periods will be used, but they represent spaces)

.........0 .........0 opening account values

10,000 .........0 contribution day for Roth A

..5,000 .........0 Really Bad Day(s)

..5,000 10,000 contribution day for Roth B

10,000 20,000 value of the asset returned to its original value (ie, it doubled)

At this point, if Conversion 1 would be recharacterized,

10,000 would need to be removed.

If Conversion 2 would be recharacterized,

20,000 would need to be removed.

Let me know if I did something wrong in my calculations. I know it is possible that the calculations could make more than 100% of the value of the conversions be removed. I know that if you covert into a new (empty) Roth and want to recharacterize it, no calculations are done and all of it is withdrawn. But if you convert into an account that has assets in it, it is possible to withdraw some of those pre-existing assets during the recharacterization.

Edit: Fixed the error in the calculations for recharacterizing Conversion 1, then Conversion 2.

Edit: Changed the text in the example for recharacterizing Conversion 2, then Conversion 1.

Edit: Added an example of doing each conversion into a new (empty) Roth.