# IFA Introduces a New Interactive Chart on the Predictability of Returns

Does knowing what happened in the recent past with returns of index fund portfolios help you predict the future? We explore that question in the new interactive chart below. It allows you to choose one of four IFA Index Portfolios and one of six time period lengths for a total of twenty-four possible combinations. Each data point corresponds to a different starting date, and mousing over it will show you the dates as well as the two returns. Recall that the IFA Index Portfolio number corresponds to the percentage of equities in the portfolio. The X-axis plots the return in the initial period, and the Y-axis plots the return in the subsequent period.  The R-squared number shown in the lower right-hand corner tells us the percentage of the subsequent period return that is explained by the initial period return. For example, for Index Portfolio 100, 3.23% of the current month return is explained by the prior month return, which is another way of saying that monthly returns have no predictive value.

The combination that yields the highest R-squared is the 20-year returns of Index Portfolio 100 for which the R-squared is 24.53%. This still leaves over 75% of the return unexplained, and while there appears to be a negative relationship between the first 20-year period and the second 20-year period, we must note that all of the data points lie in the upper right quadrant (no negative 20-year returns). Even if an investor was so unlucky as to get the lowest 20-year return of Portfolio 100 over the last sixty years  (7.86% annualized from 1/1/1955 to 12/31/1974), he or she still would have been better off than staying out of the market. An investor would have also been better off in Portfolio 100 compared to the S&P 500 Index which had an annualized return of 6.88%. As the chart below shows, in about seven of every eight monthly rolling periods over the last fifty years, Portfolio 100 got a higher return than the S&P 500 Index.

A question we may ask is whether the outperformance of Portfolio 100 compared to the S&P 500 Index is reliable to the degree that we would rule out chance as the explanation. For answering that question, we have a statistical test known as the t-test, which is fully explained here and here. As shown in the calculator below, there are three required inputs - the average of the yearly differences in returns, the standard deviation of returns, and the number of years. For IFA Index Portfolio 100 compared to the S&P 500 Index over 86 calendar years from 1928 to 2013, the average difference has been 2.53% (net of IFA's maximum 0.9% advisory fee) with a standard deviation of 11.92%. Plugging all three of those numbers into the calculator yields a t-statistic of 2.0, which means that we are about 95% confident that the historical outperformance of Portfolio 100 is not explained by chance.

We encourage you to try out different combinations of portfolios and time periods in the interactive chart above, and if you have any questions, please leave them in the feedback section below.