The Future Value of Mutual Fund Investments: Average Return Standard Deviation = Annualized Return Forecasts

Abstract

Forecasts for mutual fund investments include prediction intervals derived from resampling theory and the log-normal statistical distribution. Formulas for forecasting are simple enough for many individual investors and financial advisers who do spreadsheet calculations. They replace millions of numeric simulations. Forecasts are best presented in dollars or other currency as best and worst cases. Investors use those cases to judge risk and utility based on personal preferences, especially for comparing mutual funds. Precisions of historic and forecast investment values are found using propagation of error. They are used to analyze the sampling errors of forecasts. Asset allocation based on maximizing the forecast annualized return is briefly discussed with examples.

Keywords: Annualized return, asset allocation, CAGR, compound annual growth rate, confidence interval, forecasting, investor education, log-normal distribution, Monte Carlo, mutual fund, prediction interval, propagation of error, Q-Q plot, resampling, sampling error, statistical interval

JEL Classification: G11, G17, G20, G41