Index models - Estimating the single-index model

7 important questions on Index models - Estimating the single-index model

What is the security characteristics line?

The regression estimates describe a straight line with intercept Alpha HP and slope Beta HP, which we call the security characteristic line (SCL) for HP.

What does a high multiple R mean?

That the correlation (with the S&P 500) is quite high, that the changes (in the S&P500) are fairly closely tracked. 

What does the R square say?

Variation in the S&P excess returns explains about 52% of the variation in the HP series. 

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What is the adjusted R square?

The adjusted R-square (which is slightly smaller) corrects for an upward bias in R-square that arises because we use the fitted values of two parameters,6 the slope (beta) and inter- cept (alpha), rather than their true, but unobservable, values. With 60 observations, this bias is small.

What is the sum of squares?

The sum of squares (SS) of the regression (.3752) is the portion of the variance of the dependent variable (HP’s return) that is explained by the independent variable (the S&P 500 return); it is equal to betahp^2 stdev sp500^2.

What does the MS column say?

The MS column for the residual (.0059) shows the variance of the unexplained portion of HP’s return, that is, the portion of return that is independent of the market index. The square root of this value is the standard error (SE) of the regression (.0767) reported in the first panel. 

What is the p-value or probability or level of significance?

From a table of the t-distribution we can find the probability that the true alpha is actually zero or even lower given the positive estimate of its value and the standard error of the estimate.

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