|The process described above may be expressed in algebraie terms as follows :|
|Let t =||date, measured in weeks;|
|pt =||actual market (Standard & Poor's index of 90 stocks) at date t;|
|increase or decrease (rate) in actual market from date t to date t+1 ;|
|increase or decrease (rate) in "random forecasting record," that is, one-half increase or decrease in actual market;|
|ratio of random forecasting record at date t+1 to random forecasting record at date t;|
|compounded random forecasting record at date t+1;|
|qt =||fraction of funds kept in market on advice of forecaster from date t to date t+1;|
|ratio of value of above investment (including idle cash) at date t+1 to value at date t;|
|compounded value of investment at date t+1;|
|"index of performance" of forecaster from date 1 to date t+1 that is, ratio of coumpounded value of investment to compounded random forecasting record;|
That one of the forecasters had an average annual rate 6.02 per cent better than the random forecasting record is to be discounted by the fact that it is the best of the 11 records examined. Assuming a complete lack of ability, if one had the opportunity to make 11 attempts, the best of these by chance might show a considerable degree of success. In this analysis, the least successful of the forecsters, with an average annual rate 5.62 per cent worse than the random forecasting record, was wrong almost as much as the most successful one was right.
in computing the market gain or loss on each forecast instead of the Standard & Poor's average of 90 stocks since the latter is not available prior to 1926. The resulting figure was reduced to the actual effective annual rate of gain instead of to the index of performance. The rate of gain computed as above indicated is 14.2 per cent a year, of wich about 4.2 per cent is dividend and interest income. In the same period a continuous investment in the stocks composing the Dow-Jones industrial average would have shown a return, including dividends, of 10.9 per cent a year. Following the forecasts, therefore, would have resulted in a gain of 3.3 per cent a year over the result secured by a continuous investment in the common stocks composing the Dow-Jones industrial average.
Cowles Commission for Research in Economics
The University of Chicago
(*) Cowles Commission Papers, New Series, No. 6.
(1) "Can Stock Market Forecasters Forecast ?" by Alfred Cowles, ECONOMETRICA, Vol. 1, July, 1933, pp. 309-324
(2) The author is indebted to Dickson H. Leavens, Forrest Danson, and Miss Emma Manning of the Cowles Commission for Research in Economics, The University of Chicago, for assistance in tabulating the forecasts and computing the records.
(3) For the period subsequent to 1939 only 7 of the 11 forecasting records were available.
(4) Where needed in order to preserve the continuity of this average, corrections were made to offset the effect of stock dividends and changes in the list of stocks included. (5) The word "sequence" is used here to denote when a rise follows a rise, or a decline a decline. A "reversal" is when a decline follows a rise, or a rise a decline.
(6) "Some A Posteriori Probabilities in Stock Market Action," by Alfred Cowles and Herbert E. Jones, ECONOMETRICA, Vol. 5, July, 1937, pp. 280-294.