[ultimda horaf]

Now here's an aside I noted just fooling around with things at 5 am:

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.

a response to Kuci:

Kuci:

http://www.irs.gov/newsroom/article/...106799,00.html

# If your capital losses exceed your capital gains, the excess can be deducted on your tax return and used to reduce other income, such as wages, up to an annual limit of $3,000, or $1,500 if you are married filing separately.

I should know. Like I said, I took full value of the capital loss deduction for 2009 and will be using it the next two years.

Now...
From Kuci: Even if it did work, all you would have shown is that a capital gains tax provides favorable rates to people who make bad investments. ...why is this a good thing? Umm... it means that the unfavorable tax situation on the plus side is compensated by the favorable tax situation in case of loss (ie- all investments involving capital gains are made under conditions of uncertainty so you have to take your lumps with your gains) so what I'm saying is up until a loss of $3000, the plusses and minuses of a CG tax with regards to ETR balance out under conditions of uncertainty. This is a very important point.

From Kuci: edit: your 25% figure is not sensibly calculated. The $800 is pre-investment but the $600 is post-investment. Look, what you yourself was calculating was the effective tax rate. The effective tax rate by definition is the actual tax paid divided by net taxable income, expressed as a percentage. That is why using $750 is not quite accurate because he wouldn't be taxed on that (the issue is the difference in losses... he losses less money in absolute terms with a tax because he had less money to invest). He would instead be taxed on $800, which is the $1000 original minus his $200 in capital losses.

So there you go.

Could anyone else a bit more seasoned in financial modeling help out a bit. Did I make some errors? Or could you explain it in a way that a CS grad like Kuci could understand?