Purpose: The purpose of this paper is to examine three different forms of returns based on the price difference, percentage change, and difference in logarithm price from moving average buy-sell trading rule. Statistical linear correlation, the means of returns from buy/sell days, and the flexibility of long-term moving periods are examined. Design/methodology/approach: Traditional linear correlations, pairwise student t-test, and ϕ coefficient for two binary buy/sell decision variables are studied from the simple block bootstrap (convenience) sampling from S&P, Dow Jones, and NASDAQ price indices from January 29, 1985 to January 6, 2016. Findings: The authors find that different forms of returns from MA(1-50) are strongly linearly correlated via 150 simple block bootstrap (convenience) samples from S&P, Dow Jones, and NASDAQ price indices from January 29, 1985 to January 6, 2016. In other words, the price differences, the percentage returns, and logarithmic returns are exchangeable for returns from S&P, Dow Jones, and NASDAQ. The authors refute the claims from Metghalchi et al.’s (2005, 2011) papers and Brock et al.’s (1992) paper. The authors conclude that the market is efficient and investors cannot gain benefits from moving average technical trading rule. Lastly, the authors find that the decisions from MA(1-50) and MA(1-200) are highly correlated; therefore, the length of periods used in long-period moving average is flexible. Originality/value: It is one of the first studies about different forms of returns, their conclusions on the market efficiency, and the flexibility of long-term moving period for moving average buy/sell technical rules.
