Asset Allocation Confidence Intervals in Retirement
13 Pages Posted: 18 Oct 2015
Date Written: October 16, 2015
Treating the premium of stocks over bills as a statistical phenomenon, and based on almost a century of historical data, I estimate asset allocation confidence intervals for the optimal retirement investment problem in the presence of guaranteed income. The confidence intervals arise as a result of uncertainty in the true value of the equity premium given the limited historical data and its considerable volatility. The confidence intervals are substantial. For the scenario I study the 95% confidence interval for a 65 year old retiree with $400k in assets allocated between stocks and bonds is 10 to 82% stocks. Larger confidence intervals apply to retirees with small or large portfolio sizes. I explore the reasons for this. When I add in the uncertainty in the retirees own situation, namely their risk aversion and mortality, I find the confidence intervals only change slightly. Unlike asset allocation, confidence intervals for the optimal level of consumption are found to be reasonably tight except for large portfolios in the presence of uncertainty regarding mortality.
Keywords: asset allocation, confidence interval, stochastic dynamic programming, equity premium, equity risk premium
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