Arithmetic mean: a bellwether for unbiased forecasting of portfolio performance

Purpose – We know that estimates of terminal value of long-term investment horizons are biased. Unbiased estimates exist only for investment horizon of one time-period. The purpose of this paper is to suggest a method based on the arithmetic mean in order to obtain unbiased estimates for the terminal value of long-term investment horizons. Design/methodology/approach – The method used for the investigation was to employ loss functions or error statistics. Namely, the mean error, the mean absolute error, the root mean squared error, and the mean absolute percentage error was used. Findings – The suggested method produced the closest values to the actual ones than any other suggested averaging method when the authors examined ten-year investment horizons for Standard & Poor's 500 index and on Dow Jones Industrial index. Practical implications – Portfolio managers and individual investors may use this paper's suggestion if they wish to obtain unbiased estimates for investment horizons greater than one time-period. Originality/value – The suggestion to equate the time-period of the observed data to the time-period of the investment horizons is novel and useful to practitioners since it produces unbiased estimates.