Week 45 Day 4: Sensitivity Analysis: Which Variables Matter Most?

Sensitivity analysis results (impact on success rate when each variable changes by one unit): Spending +$10,000/year: success drops 10-20%. Retirement extends 10 years: success drops 10-15%. Returns drop 2% (decade average): success drops 15-25%. Asset allocation shifts 10% (e.g., 70/30 to 60/40): success changes 2-5%. Rebalancing quarterly vs. annually: success changes < 1%. Fund selection (VTI vs. SPY vs. SCHB): success changes < 0.5%. Lesson: spend most planning energy on spending rate, not fund selection.

Detailed sensitivity analysis for a $1,000,000 portfolio, 30-year horizon, 70/30 allocation: (1) Withdrawal rate: 3.5% ($35K): 98% success. 4.0% ($40K): 95%. 4.5% ($45K): 88%. 5.0% ($50K): 79%. 5.5% ($55K): 68%. 6.0% ($60K): 55%. Conclusion: each 0.5% increase in withdrawal rate drops success by 7-13 points. THIS IS THE MOST IMPORTANT VARIABLE. (2) Time horizon: 20 years: 99% at 4.5%. 25 years: 94% at 4.5%. 30 years: 88% at 4.5%. 35 years: 82% at 4.5%. 40 years: 75% at 4.5%. Conclusion: each 5 additional years drops success by 4-7 points. Early retirees MUST use a lower withdrawal rate. (3) First-decade returns: Average first-decade return: success approximately 88-95% at 4%. Below-average first-decade return (0-5%): success approximately 70-80% at 4%. Terrible first-decade return (-2% to 0%): success approximately 50-60% at 4%. Conclusion: the first decade determines trajectory. This is why the bond tent, cash buffer, and guardrails exist. (4) Asset allocation: 100/0 stocks/bonds: 92% at 4%. 80/20: 94%. 60/40: 93%. 40/60: 87%. 20/80: 72%. Conclusion: anywhere between 50/50 and 80/20 produces similar success rates. Extreme allocations (100/0 or 20/80) are slightly worse. The exact allocation matters less than staying in the broad range. (5) Fees: 0.03% (index funds): 95% at 4%. 0.50% (cheap active): 91% at 4%. 1.00% (advisor + funds): 85% at 4%. 2.00% (expensive): 72% at 4%. Conclusion: fees are the second-most controllable variable after spending.

Sensitivity analysis in retirement planning can be formalized as a partial derivative of the success probability with respect to each input variable: dP(success) / dX_i, where X_i is each input (withdrawal rate, expected return, volatility, time horizon, inflation rate, fees, etc.). Pfau (2013) and Blanchett (2014) performed comprehensive sensitivity analyses and consistently found the same hierarchy: (1) Withdrawal rate: dP/dWR approximately -0.15 to -0.25 per percentage point (the single most sensitive variable). (2) Expected return: dP/dER approximately 0.10-0.15 per percentage point. (3) Time horizon: dP/dT approximately -0.005 per additional year. (4) Standard deviation: dP/dSigma approximately -0.05 per percentage point. (5) Fees: dP/dF approximately -0.08 per percentage point. (6) Asset allocation (stocks vs. bonds): dP/d(equity%) approximately 0.001-0.003 per percentage point (within the 40-80% equity range). The implication: the retirement planning inputs that dominate outcomes (spending rate, expected returns, time horizon) are either controllable (spending rate, fees) or inherently uncertain (returns, longevity). The inputs that are easiest to optimize precisely (asset allocation percentages, rebalancing frequency, fund selection) have minimal impact on outcomes. This creates a planning paradox: the variables that receive the most attention in popular financial media (specific fund selection, precise allocation percentages, rebalancing triggers) are the LEAST important, while the variables that receive less attention (spending flexibility, conservative return assumptions, longevity risk management) are the MOST important.