ATReturn.deferred: Calculation of after-tax return in a deferred account
In rexmacey/TaxAwareAA: Tax Aware Asset Allocation

The after-tax returns in a deferred account are pretty simple. An investment will grow to $(1+pre_tax_geometric_return)^horizon$ and that value will be subject to tax. After tax the investor will have this amount less what was paid in federal and state taxes. We convert this dollar amount into a return by raising it to the (1/horizon) and subtracting 1. The after-tax geometric return is then transformed into an arithmetic return. Most investors think of the value of their deferred account before taxes. If someone has $100 in an IRA, they think it's worth $100 which ignores the deferred tax liability. By maintaining the fiction that the account today is worth $100, we understate the after-tax return by dividing an after-tax terminal value with a before-tax starting value. Since the final dollars are correct the allocation is correct which is our goal.

1 2	ATReturn.deferred(yld, growth, valChg, foreigntaxwithheld, Expense, taxROrdInc, risk, horizon = 10)

`yld`	Yield on the investment
`growth`	Growth rate of the income paid on the investment
`valChg`	Change in valuation of the investment
`foreigntaxwithheld`	is the percent of income withheld for foreign taxes
`Expense`	Annual expense rate
`taxROrdInc`	Tax rate on ordinary income
`risk`	Standard deviation of asset class.
`horizon`	Number of year in forecast horizon