Here is a description of the studies I am doing on Value Line. FVL is an ETF which uses the Value Line timeliness system. Instead of using VL service to pick stocks individually, you can own FVL and obtain VL returns (of course other screens could be applied).

Using daily closes of FVL and SP500 ETF SPY, I did a linear regression:

For each day's change in SPY (X), what is the same day's change in FVL (Y). The actual equation for this line is:

FVL = - 0.000109 + 0.791 SPY  (Y = alpha + beta*X)

The regression does a least-squares fit of a line to the data (minimizing the sum of squares of errors in Y direction), and the slope and Y-intercept of this line describes how FVL's daily change is related to SPY's.

The slope ("beta") of 0.8 means that when SPY goes up 1%, on average FVL went up 0.8%, etc.  The intercept alpha) shows, on average, whether FVL gives higher or lower daily return than SPY, by checking where the line crosses when SPY is zero.

Both slope and intercept are tested for statistical significance (assuming error residuals are normally distributed), that is whether they were likely to have occurred by chance alone.  

(Better descriptions welcomed)

Here is the study:

FVL; Value Line timeliness ETF.

From inception in 2003, regressed daily return of FVL vs SPY:

Regression Analysis: FVL versus SPY

The regression equation is
FVL = - 0.000109 + 0.791 SPY

Predictor        Coef         SE Coef        T      P
Constant   -0.00011       0.00023    -0.48  0.630
SPY          0.79111        0.01640    48.24  0.000

S = 0.00906282   R-Sq = 59.3%   R-Sq(adj) = 59.2%

>> Conclusion: alpha (with respect to SPY) for FVL is negative, though N.S.  Beta is 0.8, and highly significant.

A scatter diagram is also available.

Charles Pennington writes:

For my curiosity, could you (if convenient) try reversing it and regressing SPY vs the VL fund, for comparison?

Kim Zussman replies:

No problem, Charles. Here's what happens when you reverse the independent and dependent:

Regression Analysis: SPY versus FVL

The regression equation is
SPY = 0.000173 + 0.749 FVL

Predictor       Coef    SE Coef               T      P

Constant   0.0001734  0.0002204   0.79  0.432
FVL          0.74920      0.01553       48.24  0.000

S = 0.00881953   R-Sq = 59.3%   R-Sq(adj) = 59.2%

Analysis of Variance

Source            DF       SS       MS        F      P
Regression         1  0.18099  0.18099  2326.84  0.000
Residual Error  1599  0.12438  0.00008
Total           1600  0.30537


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