The Future Value of Mutual Fund Investments: A Better Bootstrap-Based Forecasting Model

Abstract

Numeric bootstrap from resampling theory is the basis for estimating the future value of mutual fund investments. It is used algebraically to derive formulas for the statistics of historic investments: sample precision; the mean and median, and their precisions. The bootstrap is also used to derive two forecasting models, including a new one. Numeric simulations determine the most accurate model. Probabilities are estimated for profitability, doubling of investments, and whether one mutual fund is likely to be more profitable than another. Investors can compare forecast outcomes using "likely", "best", and "worst" case scenarios expressed in dollars or other currency. Methods of allocating mutual funds in portfolios are reviewed, such as "minimum risk" or "maximum profit". Prediction intervals largely overlap, which makes the practical value of such optimizations doubtful for individual investors. A formula shows that annual rebalancing of mutual fund portfolios provides a small increase in profit during the early investment period compared to not rebalancing. The jackknife approach to forecasting is briefly discussed. A third appendix analyzes model variance.

Keywords: annualized return, asset allocation, bootstrap, CAGR, compound annual growth rate, confidence level, forecasting, inflation, investor education, jackknife, lognormal distribution, mutual fund, normal distribution, optimization, precision, prediction interval, resampling, statistical interval

JEL Classification: G11, G17, G20, G41