Does anybody agree / disagree that the geometric smoothing rule for endowmnet spending could be simplified?
this is CFAI way
Spending(t) = Smoothing rate * [Spending(t-1) * (1 + Inflation(t-1)] + (1 - Smoothing rate) * [Spending rate * Beginning market value(t-1)]
since [Spending rate * Beginning market value(t-1)] = [Spending rate * Ending market value(t-2)] = Spending(t-1), we can simplify the above formula:
Spending(t) = Spending(t-1) * [Smoothing rate * (1 + Inflation(t-1)] + (1 - Smoothing rate)]
essentially, this year spending becomes last year spending multipled by the sum of smoothing rate adjusted for inflation and 1 - smoothing rate
this is CFAI way
Spending(t) = Smoothing rate * [Spending(t-1) * (1 + Inflation(t-1)] + (1 - Smoothing rate) * [Spending rate * Beginning market value(t-1)]
since [Spending rate * Beginning market value(t-1)] = [Spending rate * Ending market value(t-2)] = Spending(t-1), we can simplify the above formula:
Spending(t) = Spending(t-1) * [Smoothing rate * (1 + Inflation(t-1)] + (1 - Smoothing rate)]
essentially, this year spending becomes last year spending multipled by the sum of smoothing rate adjusted for inflation and 1 - smoothing rate