"AOII Net" Portfolio [Return.sub.t] = (Daily Net [Holding.sub.1, t] X Daily [Return.sub.1, t]) + (Daily Net [Holding.sub.2, t] X Daily [Return.sub.2, t]) + ...
The ability of this active investing style of online investors to outperform the passive approach of buying the index fund will be measured by the calculation of the "AOII Net" advantage.
"AOII Net" [Advantage.sub.t] = "AOII Net" Portfolio Daily [Return.sub.t] - Market Index [Return.sub.t] (5)
The composition of the stocks and the corresponding returns of the online investor's portfolio and the "AOII Net" advantage will be readjusted on a daily basis until the end of the study (April 28, 2000).
The daily net holdings, or weights, were multiplied by the daily returns and summed up to find the "AOII Net" return of +0.2929%.
As one might expect in an informationally efficient market, there are periods when the "AOII Net" portfolio advantage is positive, and other periods when the advantage is negative.
The model does not include an intercept and uses a dummy variable for each quartile of the AOII index to control for differences in daily average returns that may lead to spurious autocorrelations (Higgins, Howton and Perfect (2000)).
To test this relationship, Equation 2 will be estimated by regressing daily QQQ returns on the AOII dummy variables and the lagged market returns:
Where: [R.sub.qqq,t] = Daily returns for QQQ security at time t; [R.sub.spy,t-1] = Daily returns for SPY security at time t-1; [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] = Dummy variables for the quartiles of the AOII; and [e.sub.t] = a random error term.
Where: [R.sub.qqq,t] = Daily returns for QQQ security at time t; [R.sub.qqq,t-1] = Daily returns for QQQ security at time t-1; [R.sub.spy,t-1] = Daily returns for SPY security at time t-1; [Q.sub.1t], [Q.sub.2t], [Q.sub.3t] and [Q.sub.4t] = Dummy variables for the quartiles of the AOII; and et = a random error term.
All of the returns are positive and statistically different from zero on days when the AOII fell in the first quartile.
The practical conclusion to this result is that investors should evaluate the AOII, if the index increases (decreases), implement the contrarion decision is to sell (buy).