i was thinking if investors wanted to 1) preserve their “real” asset value and also 2) have their living expenses inflation adjusted. should we, in this case, adjust inflation twice to the norminal return, (one for the portfolio to keep up with real value, another for increased annual outflow)? i.e. R(adj) =(1+ R) * (1+i) ^ 2 - 1 ~ r + 2 * i (look weird though) comments?
Not sure, but I just did an example and it was not necessary: asset base = 100.000.000 spending = 10.000.000 before inflation required return = 10% inflation = 5% after inflation required return = (1+10%)(1+5%)-1 asset base grows to 100.000.000 x (1+10%)(1+5%) = 115.500.000 spending grows to 10.000.000 x (1+5%) = 10.500.000 new asset base = 115.500.000 - 10.500.000 = 105.000.000 which is your original 100 mio adjusted for inflation (5%) both your spending and your asset value keep up with inflation in the next period asset base grows to = 105.000.000 x (1+10%)(1+5%) = 121.275.000 spending grows to 10.500.000 x (1+5%) = 11.025.000 new asset base = 121.275.000 - 11.025.000 = 110.250.000 which is previous asset base of 105 mio adjusted for inflation (5%) agin, both your spending and asset value keep up with inflation I guess this only works if spending occurs at the end of the period (once you have “achieved” the return) and if spending growth = inflation only does it make sense? asset base 1 = 100.000.000
errata 
- change the words “before” and “after” in “inflation required return” for “without” and “with” - delete last sentence of “asset base 1 = 100.000.000”
thanks. actually, (1+R)(1+i) = (1 + i) + R(1+i) so the 1st term indeed adjusts for the principal, while the 2nd term has the return (expenses) ajusted.
yes, but it’s only relates to situation when spending is fully financed from portfolio. But if not -we should check whether income from other sources is inflation adjusted. If not in long-term it’ll lead to capital invasion.
I have a simple way to look at it: First off, you have to get the timing right. Remember the dividend discount model states that r = D(t) / P(t-1) Same concept holds here: Real return ® = expenses(t) / Portfolio (t-1) Now, factor in inflation and solve for the end of period portfolio; P(t) = P(t-1) + [P(t-1) x r)] + [P(t-1) x i)] Once you have this amount (end of period portfolio) , you pay out required expenses. In other words you subtract: [P(t-1) x r)] Which leaves: P(t) = P(t-1) + [P(t-1) x i)] The remaining portfolio, after expense-payout, has increased by the rate of inflation.
So, in a way, you’re right: there is an element of “double-counting” inflation. If you’re given current expenses and current portfolio, you have to multiple expenses by 1+i to compute expenses in one year before you can compute r. A few months ago, somebody in this forum asked why the answer to an old essay question twice counted inflation.