Effective Capital Gains Tax

Hey All, First time poster here. I wanted to ask about this because neither Schweser nor the CFA curriculum deemed it necessary to explain this further. Clearly they thought a smart Level 3 candidate should be able to figure this out, but this apparently isn’t the case for me. The formula (taking Schweser’s notation): Tecg = Tcg * ((1 - Pi - Pd - Pcg) / (1 - (PiTi + PdTd + PcgTcg)) Numerator is investment income percentage from unrealized capital gains. Denominator is 1 minus the total realized tax rate. I may be missing something obvious here, but how does this formula lead to the effective capital gains tax rate? Thanks in advance for any insight, HoJoon

because the cg in the above formula relates to actual REALIZED capital gains taxes already paid, like if you sold something that had appreciated. You are trying to arrive at the effective capital gains tax rate, which will incorporate deferred capital gains as well (there are some assets that have appreciated in value but have yet to be sold). Given that you have already paid taxes on realized capital gains, the rate that incorporates deferred taxes should be lower. The more you defer an outflow to the future, the more beneficial it is.

markCFAIL, thanks for your response. I understand conceptually that the effective cap gains tax rate should be lower than the stated cap gains tax rate because we’re not counting the taxes that’s already been realized/paid. But my question is more specific to the formula, how does dividing the income percentage from unrealized capital gains by 1 minus the total realized tax rate and multiplying by stated cap gains rate equal the effective cap gains rate? I think maybe I’m getting tripped up by the denominator 1 minus the total realized tax rate, struggling to grasp what that means conceptually. Thanks again.

I see it like this: Breaking this formula down into simpler terms you get Effective Tcg = Unrealized cg Income / (1 - Realized tax rate) Now, whenever you divide a net number by (1 - some percentage) you get the gross number. I do this with my paycheck all the time… I get the net amount put into my bank account and I estimate the gross by taking that amount and divide by (1 - my assumed tax rate). so to rearrange the equstion above you have: Effective Tcg * (1 - realized tax rate) = Unrealized cg Income or expanding the parenthases: Effective Tcg - Effecive Tcg*Realized tax rate = Unrealized cg Income or Whole cg - cg already taxed = Unrealized cg

what does it matter? just memorize it, then forget it after the test. If a conceptual question happens to be asked you should be able to back out the answer by knowing the formula