For the example, it’s looking for the real after tax return.

First Approach:

Apply tax to the nominal pre tax return

Deduct inflation

Wouldn’t I be deducting too much?

I.e., 9%(0.75) - 2% = 4.75% real after tax return.

If I gross up the above to get the real pre tax value it’s 4.75%/0.75 it’s 6.33%

Second Approach - the reverse is to:

Deduct inflation

Apply tax to the real pre tax return

I.e., (9%-2%) * 0.75 = 5.25% real after tax return.

If I gross up the above to get the real pre tax value it’s 5.25%/0.75 it’s 7%.

Final comparison - if I take the given 9% (the nominalpre tax value) and get the realpre tax value , all I need to do is deduct 2% = 7%

Conclusion:

In this example, I need to use the second approach (take the nominal pre tax return, deduct inflation, and then apply tax) to get the real after tax return.

BUT! Schweser Mock AM Q 12 uses the first approach!

@roebftb: What you wrote makes sense, but I can’t translate that into this example, because I don’t know the return values. Effectively your example shows X(1 + a)(1 + b) = X(1 + b)(1 + a).

@Edbert: Sorry for my thoughts being all over, but the question asked to go from nominal pre-tax to real after-tax return, which is consistent with your first statement. My comparison was just making an example of the 2 methods to get there.

For the formula you wrote: I guess I’m now just confused lol. Is the equation below correct too? If so, the first component equals the nominal pre-tax, hence my decision to subtract inflation first.

Thanks - I think I’m just being thrown off by this corner case. I understand the logic from real pre-tax to nominal after-tax. I just going to remember the route to nominal after-tax and adjust from there. E.g., below: