Second pass regression

Second pass regression

A cross-sectional regression of portfolio returns on betas. The estimated slope is the measurement of the reward for bearing systematic risk during the period analyzed.
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Fan and Liu (2005) examine the relationship of size and BTM to explain the future expected returns of US equity market for the period of 1965 to 1998 by using second pass regression. The study reports that size and the BTM ratio contain distinct and significant components of financial distress, growth options, the momentum effect, liquidity, and firm characteristics.
Table 4 presents the results of cross-sectional Fama and Macbeth (1973) second pass regression. Average portfolio returns are regressed on factor loading estimated for first pass regression (market premium, size premium, value premium and information efficiency premium).
The empirical results also documented that Fama and Macbeth (1973) second pass regression found that past betas can explain current returns.
The empirical results also documented that Fama and Macbeth (1973) second pass regression report that past betas can explain current returns.
Estimating Security Market Line is a cross sectional regression procedure in testing linearity of risk and return so called second pass regression. Previously, we employed regression in equation (3) for every single stocks analyzed; then, calculate sample averages of the excess return on each of the stocks from the full sample, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] sample estimates of beta coefficients o each of the stocks, [[beta].sub.i], sample average of the excess return of the market index, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and following regression is conducted:
To test second pass regression (5) null hypotheses, we simple employ t-test as follows:
Second pass regression (5) results do not support well the linear relationship between average excess return which is used as a proxy for expected excess return and ex-post betas within the estimation period (in theory ex-ante betas are linked with expected return).
The important materials and instruments that can be used are: a) monthly returns extracted from the SES Journal from the immediately post reform period of the SES, covering 1986-1993, b) first pass time-series regression as in equation (III-3) to estimate beta, second pass regression, if necessary, to find the values of [[eta].sub.0] and [[eta].sub.1] as in equation (III-4), c) cross-section T-test of stocks in the sample to determine if the mean difference between estimated excess return and the actual excess return of the stocks in the year is not significantly different from zero.
They are done on a yearly basis all the time, except when the work involves the second pass regression.
Therefore my methodology to use T-test in place of the time-series second pass regression should produce results that are closer to the real situations with no more statistical problem.
The second pass regression estimates Equation 1, now including the off board volume variable, using the specialist-dominated and then the limit-order-dominated samples determined in the first pass regression.
These betas estimated using equations (1) and (6) are then used in a second pass regression to calculate estimates of the security asymptotic beta, as well as measures of the intervalling effect:
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