Jan

6

The stocks of the first three days of 2007 have been interesting. How does the H/L range for these three days compare with prior years, and do they have any predictive value?

By using SPY daily since 1993, I checked the H/L mean for the first three days, the return of the first three days, the return of the next three days, and the standard deviation of the subsequent 241 trading day returns (starting at day four of each year through late December).

The H/L mean of the first three days of 2007 is relatively tame compared to other years, which is in keeping with the current low-volatility regime. Here is the data by year, with the second column being the average H/L for the first three days of each year:

year   average H/L
2001   0.040
2000   0.031
2003   0.022
1999   0.020
1997   0.017
1996   0.015
2005   0.015
2002   0.014
1998   0.013
2007   0.011
2006   0.011
2004   0.009
1994   0.005
1995   0.004

Concerning prediction, here is the multiple regression with the dependent variable as the second three day return, and the independent variables as the first three day H/L average and the first three day return:

Regression Analysis: second three day return versus the first three day H/L average and the first three day return

The regression equation is the second three day return = 0.0052 - 0.189 first three day H/L average - 0.359 first three day return

  Predictor         Coef.      SE Coef.    T        P
  Constant         0.0052    0.0123    0.42   0.681
1st 3 day avg.  -0.1891    0.6244   -0.30   0.768
1st 3 day ret.   -0.3588    0.2444   -1.47   0.173

S = 0.0215894   R-Sq = 18.0%   R-Sq(adj) = 1.6%

The range of the first three days had no predictive value for the second three days, but there was a slight tendency (N.S) for the return of the first three days to be reversed by the second three days.

More interestingly is what the first three days had to say about the standard deviation of the rest of the year. In the multiple regression, the return of the first three days didn't matter, but the average H/L range did (see graph).

Regression Analysis: the year's standard deviation versus the first three day average

The regression equation is the year's standard deviation = 0.00645 + 0.233 first three day average

      Predictor       Coef     SE Coef    T        P
      Constant     0.0065   0.0018    3.61   0.004
1st 3 day avg.    0.2325   0.0929    2.50   0.029

S = 0.00322239   R-Sq = 36.3%   R-Sq(adj) = 30.5%

The significant slope coefficient says that the average range of the first three days has a positive correlation with the subsequent year's (daily return) standard deviation. 2007's average first three day range of 0.011 (1.1%) predicts another year of low volatility.

This probably relates to the persistence of volatility regimes, such that high (low) range early Januaries come amidst high (low) volatility years.


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