S & P 500 P/E
Comparing Tables 4 and 2 we find considerable consistency coupled with some inconsistency. TOLSR and the inflation rate do not work in the 1960-67 time period while they do for the full period. The other variables are uniformly significant for both time periods.
Unlike the 1960-67 results, the 1968-74 results differ substantially from both the 1960-74 and 1960-67 results. The billrate and mutual fund cash variables behave similarly for all three time periods. The other variables do not. For the 12-month period the confidence index and specialist short-sale variables are consistent but are not for other adjustment periods. While TOLSR and the inflation rate do not work for the 1960-67 period, they do for the more recent period. On the other hand, secondary distribution and market PE ratio variables do not appear to have predictive content for the 1968-74 period.
REGRESSION RESULTS FOR 1960-67
1-month 3-month 6-month 9-month 12-month
These comparisons leave us with a mixed verdict. Only two of the variables appear to work consistently for all adjustment and time periods. It should be noted, however, that there was some consistency with some of the other variables. Furthermore when variables had an incorrect sign, they were generally insignificant. Is the modest amount of stability in the relationships sufficient to be useful in predicting future market movements? In an attempt to deal with this question the following test was performed: Using the coefficients of Table 4 a predicted value for (XJ was determined for the 1968-74 period and
these Xs were compared with their actual values. One with the information
available in 1967 could have actually followed such a policy. Correlation and F ratios were calculated for each adjustment period and are reproduced in Table 6.
REGRESSION RESULTS FOR 1968-74
Variable 1-month 3-month 6-month 9-month 12-month
0.292 0.505 0.895 0.415 -0.792
intercept (1.01) (1.35) (2.02) (0.77) (-1.21)
TOLSR (2.8) (2.59)
-0.002 -0.003 -0.009 -0.001 0.014
CONFIDENCE (- .67) (-0.76) (-1.77) (-0.24) (2.04)
S & P 500 P/E (0.9)
A COMPARISON OF PREDICTED AND ACTUAL PRICE PERFORMANCE
.577 42.34 1,85
.555 37.77 1,85
.497 27.87 1,85
.00000005 .00000016 .000003
The results of Table 6 are rather convincing evidence that there is sufficient stability in the relationship, for it to be meaningful. The F of the relation between the predicted and actual value of X is significant at the 1 percent level for a one-month adjustment period. For the other adjustment periods the relationship is significant at a much higher level.
Two points should be noted here. First it might well be possible to improve the correspondence by deleting variables insignificant for the earlier timeperiod and refitting the regression for each prediction. For example, the predictions for 1970 might be based on a regression fit to 1960-69 data. In this way new information would be utilized as it becomes available. On the other hand, the reader should be cautioned not to read too much into these results. By no means have they established that a trading rule based on market indicators could outperform a buy-and-hold strategy with transaction costs considered. It should, however, be pointed out that requiring a signal to pass such a comparison may be too strong a test. It is possible that, even if a trading rule can not outperform a buy-and-hold strategy, it may be useful. Consider an investor with funds to be committed. His alternatives include buying now and buying later. In either case he will incur transaction costs when he commits his funds. If there are indications that the market is about to decline (even if the expected value of the decrease is less than transactions costs), he would tend to be better off waiting. Similarly one who plans to sell but is able to wait may find useful a trading rule that is on balance correct but by less than enough to cover transactions costs. Until trading rules are formulated and such a strategy compared with a buy-and-hold approach, we will not know if these market indicators could be utilized to forecast well enough to outperform the market. Such a test, however, is not the only test of such indicators usefulness.
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