Real Returns, Drawdowns and Recovery Math

Real return is multiplicative

When both return and inflation are percentages, the exact real-return relationship is (1 + nominal return) divided by (1 + inflation), minus 1. Simply subtracting inflation is only an approximation. Keep nominal and real assumptions clearly labelled.

Loss and recovery percentages are asymmetric

After a 20% decline, the portfolio is at 80% of its former value and needs a 25% gain to return to the starting level. After a 50% decline it needs a 100% gain. This arithmetic says nothing about how quickly markets will recover; it only describes the required change from the lower base.

Contribution targets depend heavily on time

When solving for a monthly contribution, keep the goal, starting balance, horizon and return assumption visible. Test a lower-return case before increasing the expected return just to make the required contribution look easier.

Keep return, inflation and fees in compatible units

A projection is only internally consistent when the return, inflation and fee assumptions describe the same time basis and the target is expressed in either nominal or real terms deliberately. If the goal is stated in today's purchasing power, do not compare it directly with an unadjusted future nominal balance.

Stress the path as well as the average

A single average return can hide the effect of when gains and losses occur. For accumulation, test lower-return periods while contributions continue; for drawdown, test an adverse early sequence because withdrawals reduce the capital available for a later recovery. These scenarios are not forecasts, but they show whether the conclusion depends on an unrealistically smooth path.