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Well it's late and I haven't messed around with numbers like this in three years so forgive any mistakes but I came up with...
effective tax rate= 100*[(I*PsubscriptN*(1+N))-(((I*(1-T))*(1+(PsubscriptN*N)*(1-T)))]/(I*PsubscriptN*(1+N))
where N is the % increase/decrease in value of a security, PsubscriptN is the probability of N for all N, and T is the nominal tax rate.
The basic intuitive thing is that losses up to $3000 offset equivalent gains for tax purposes because of the benefit in tax deduction but I'm not sure exactly how to represent it in the equation (can't think right now how to do it so it's not represented in the equation except as a constraint relating to N I suppose). Beyond that though, obviously, the disadvantages of tax become apparent and the ETR approaches or exceeds the nominal TR.
Fooling around with it, assuming a 20% tax rate (including on capital gains), with a $3000 capital loss maximum deduction, and a $10,000 initial investment (well, it's taxed at 20% so $8000 investment), the security can dip to a loss of 38% (8000*(1-.38)=~5000) before hitting the $3000 capital loss wall. That leaves an ETR of 10.4% or a mere 52% of the nominal TR. If the value increases by 38%, the ETR is 24.4% (122% of the NTR). So at these points, I can pay 52% of my initial tax if I lose $3000 or 122% of my initial tax if I make $3000.
At higher tax rates, this disparity in the % of the nominal that the ETR is between a 38% loss and a 38% gain closes (at 50% nominal TR, the ETR as % of NTR becomes 70% and 113% respectively). So higher nominal TR results in weakened tax benefits from capital losses but also ETR's closer to the nominal TR on the positive gain side. Makes sense, as you approach 100% NTR, ETR should approach 100%. Kind of funny. At higher tax rates, ETR approaches NTR. Higher tax rates!
Now, at higher gains, all else being equal, ETR as a % of NTR increases but at a decreasing rate (1%->2% gain, ETR as % of NTR increases by 0.77 or 0.7% increase, 40%->41% ETR as % of NTR increases by 0.40 or 0.3%). These changes in the ETR as % of NTR get smaller overall and more narrow between different gain levels as the tax rate increases (At 40% tax rate, 1%->2% gain, 0.58 or 0.57%; 40%->41%, .30 or 0.25%).
I know I'm rambling sorry it's late. The point is, I think, could be wrong, tired, but if you put in the probabilities of different investment outcomes then you have a handy little tool for determining the most tax efficient allocation of investments in a portfolio at different tax rates (too bad you can't really control this variable legally). haha not really relevant to this thread i guess. God it's been a long time since I did anything financial. I feel like I'm overlooking something d'uh.
effective tax rate= 100*[(I*PsubscriptN*(1+N))-(((I*(1-T))*(1+(PsubscriptN*N)*(1-T)))]/(I*PsubscriptN*(1+N))
where N is the % increase/decrease in value of a security, PsubscriptN is the probability of N for all N, and T is the nominal tax rate.
The basic intuitive thing is that losses up to $3000 offset equivalent gains for tax purposes because of the benefit in tax deduction but I'm not sure exactly how to represent it in the equation (can't think right now how to do it so it's not represented in the equation except as a constraint relating to N I suppose). Beyond that though, obviously, the disadvantages of tax become apparent and the ETR approaches or exceeds the nominal TR.
Fooling around with it, assuming a 20% tax rate (including on capital gains), with a $3000 capital loss maximum deduction, and a $10,000 initial investment (well, it's taxed at 20% so $8000 investment), the security can dip to a loss of 38% (8000*(1-.38)=~5000) before hitting the $3000 capital loss wall. That leaves an ETR of 10.4% or a mere 52% of the nominal TR. If the value increases by 38%, the ETR is 24.4% (122% of the NTR). So at these points, I can pay 52% of my initial tax if I lose $3000 or 122% of my initial tax if I make $3000.
At higher tax rates, this disparity in the % of the nominal that the ETR is between a 38% loss and a 38% gain closes (at 50% nominal TR, the ETR as % of NTR becomes 70% and 113% respectively). So higher nominal TR results in weakened tax benefits from capital losses but also ETR's closer to the nominal TR on the positive gain side. Makes sense, as you approach 100% NTR, ETR should approach 100%. Kind of funny. At higher tax rates, ETR approaches NTR. Higher tax rates!
Now, at higher gains, all else being equal, ETR as a % of NTR increases but at a decreasing rate (1%->2% gain, ETR as % of NTR increases by 0.77 or 0.7% increase, 40%->41% ETR as % of NTR increases by 0.40 or 0.3%). These changes in the ETR as % of NTR get smaller overall and more narrow between different gain levels as the tax rate increases (At 40% tax rate, 1%->2% gain, 0.58 or 0.57%; 40%->41%, .30 or 0.25%).
I know I'm rambling sorry it's late. The point is, I think, could be wrong, tired, but if you put in the probabilities of different investment outcomes then you have a handy little tool for determining the most tax efficient allocation of investments in a portfolio at different tax rates (too bad you can't really control this variable legally). haha not really relevant to this thread i guess. God it's been a long time since I did anything financial. I feel like I'm overlooking something d'uh.
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