Chapter 13, Problem 8PS

Summary Introduction

To determine: The first-pass regression as worked out by Chen, Roll and Ross is to be performed and the relevant summary statistics is to be tabulated along with the estimation of the 12 stocks on the two factors.

Introduction: First pass regression is a time series regression to calculate the betas of retreats portfolios.This is generally tested implication of the CAPM. The early simple tests involved 3 basic steps as mentioned below:

1. Establishing sample data,

2. Estimating the SCL (security characteristic line), and

3. Estimating the SML (security market line).

Answer to Problem 8PS

The table given below depicts the first pass regressions.

	A	B	C	D	E	F	G	H	I
R-Square	$\begin{array}{l}0.07\hfill \end{array}$	$\begin{array}{l}0.36\hfill \end{array}$	$\begin{array}{l}0.11\hfill \end{array}$	$\begin{array}{l}0.44\hfill \end{array}$	$\begin{array}{l}0.24\hfill \end{array}$	$\begin{array}{l}0.84\hfill \end{array}$	$\begin{array}{l}0.12\hfill \end{array}$	$\begin{array}{l}0.68\hfill \end{array}$	$\begin{array}{l}0.71\hfill \end{array}$
Observations	$12$	$12$	$12$	$12$	$12$	$12$	$12$	$12$	$12$
Intercept	$\begin{array}{l}9.19\hfill \end{array}$	$\begin{array}{l}-1.89\hfill \end{array}$	$\begin{array}{l}-1\hfill \end{array}$	$\begin{array}{l}-4.48\hfill \end{array}$	$\begin{array}{l}0.17\hfill \end{array}$	$\begin{array}{l}-3.47\hfill \end{array}$	$\begin{array}{l}5.32\hfill \end{array}$	$\begin{array}{l}-2.64\hfill \end{array}$	$\begin{array}{l}5.66\hfill \end{array}$
Beta M	$\begin{array}{l}-0.46\hfill \end{array}$	$\begin{array}{l}0.57\hfill \end{array}$	0.41	$\begin{array}{l}1.38\hfill \end{array}$	$\begin{array}{l}0.9\hfill \end{array}$	$\begin{array}{l}1.8\hfill \end{array}$	$\begin{array}{l}0.65\hfill \end{array}$	$\begin{array}{l}1.91\hfill \end{array}$	$\begin{array}{l}2.08\hfill \end{array}$
Beta F	$\begin{array}{l}-0.35\hfill \end{array}$	$\begin{array}{l}2.33\hfill \end{array}$	$\begin{array}{l}0.68\hfill \end{array}$	$\begin{array}{l}-1.05\hfill \end{array}$	$\begin{array}{l}1.03\hfill \end{array}$	$\begin{array}{l}-1.96\hfill \end{array}$	$\begin{array}{l}1.15\hfill \end{array}$	$\begin{array}{l}0.43\hfill \end{array}$	$\begin{array}{l}0.49\hfill \end{array}$
t- intercept	$\begin{array}{l}0.71\hfill \end{array}$	$\begin{array}{l}-0.13\hfill \end{array}$	$\begin{array}{l}-0.08\hfill \end{array}$	$\begin{array}{l}-0.37\hfill \end{array}$	$\begin{array}{l}0.01\hfill \end{array}$	$\begin{array}{l}-0.52\hfill \end{array}$	$\begin{array}{l}0.29\hfill \end{array}$	$\begin{array}{l}-0.28\hfill \end{array}$	$\begin{array}{l}0.59\hfill \end{array}$
t- Beta M	$\begin{array}{l}-0.78\hfill \end{array}$	$\begin{array}{l}0.86\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}2.46\hfill \end{array}$	$\begin{array}{l}1.4\hfill \end{array}$	$\begin{array}{l}5.8\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}4.35\hfill \end{array}$	$\begin{array}{l}4.65\hfill \end{array}$
t- intercept	$\begin{array}{l}0.71\hfill \end{array}$	$\begin{array}{l}-0.13\hfill \end{array}$	$\begin{array}{l}-0.08\hfill \end{array}$	$\begin{array}{l}-0.37\hfill \end{array}$	$\begin{array}{l}0.01\hfill \end{array}$	$\begin{array}{l}-0.52\hfill \end{array}$	$\begin{array}{l}0.29\hfill \end{array}$	$\begin{array}{l}-0.28\hfill \end{array}$	$\begin{array}{l}0.59\hfill \end{array}$
t- Beta M	$\begin{array}{l}-0.78\hfill \end{array}$	$\begin{array}{l}0.86\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}2.46\hfill \end{array}$	$\begin{array}{l}1.4\hfill \end{array}$	$\begin{array}{l}5.8\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}4.35\hfill \end{array}$	$\begin{array}{l}4.65\hfill \end{array}$
t- Beta F	$\begin{array}{l}-0.35\hfill \end{array}$	$\begin{array}{l}2.06\hfill \end{array}$	$\begin{array}{l}0.7\hfill \end{array}$	$\begin{array}{l}-1.08\hfill \end{array}$	$\begin{array}{l}0.94\hfill \end{array}$	$\begin{array}{l}-3.7\hfill \end{array}$	$\begin{array}{l}0.78\hfill \end{array}$	$\begin{array}{l}0.57\hfill \end{array}$	$\begin{array}{l}0.63\hfill \end{array}$

Explanation of Solution

Given Information: Information provided in the question that are used to perform first-pass regression as din Chen,Roll and Ross by estimating the betas of the $12$ stocks on the two factors.

The calculated first-pass regression through the table given below and tabulated the relevant summary statistics are:

	A	B	C	D	E	F	G	H	I
R-Square	$\begin{array}{l}0.07\hfill \end{array}$	$\begin{array}{l}0.36\hfill \end{array}$	$\begin{array}{l}0.11\hfill \end{array}$	$\begin{array}{l}0.44\hfill \end{array}$	$\begin{array}{l}0.24\hfill \end{array}$	$\begin{array}{l}0.84\hfill \end{array}$	$\begin{array}{l}0.12\hfill \end{array}$	$\begin{array}{l}0.68\hfill \end{array}$	$\begin{array}{l}0.71\hfill \end{array}$
Observations	$12$	$12$	$12$	$12$	$12$	$12$	$12$	$12$	$12$
Intercept	$\begin{array}{l}9.19\hfill \end{array}$	$\begin{array}{l}-1.89\hfill \end{array}$	$\begin{array}{l}-1\hfill \end{array}$	$\begin{array}{l}-4.48\hfill \end{array}$	$\begin{array}{l}0.17\hfill \end{array}$	$\begin{array}{l}-3.47\hfill \end{array}$	$\begin{array}{l}5.32\hfill \end{array}$	$\begin{array}{l}-2.64\hfill \end{array}$	$\begin{array}{l}5.66\hfill \end{array}$
Beta M	$\begin{array}{l}-0.46\hfill \end{array}$	$\begin{array}{l}0.57\hfill \end{array}$	0.41	$\begin{array}{l}1.38\hfill \end{array}$	$\begin{array}{l}0.9\hfill \end{array}$	$\begin{array}{l}1.8\hfill \end{array}$	$\begin{array}{l}0.65\hfill \end{array}$	$\begin{array}{l}1.91\hfill \end{array}$	$\begin{array}{l}2.08\hfill \end{array}$
Beta F	$\begin{array}{l}-0.35\hfill \end{array}$	$\begin{array}{l}2.33\hfill \end{array}$	$\begin{array}{l}0.68\hfill \end{array}$	$\begin{array}{l}-1.05\hfill \end{array}$	$\begin{array}{l}1.03\hfill \end{array}$	$\begin{array}{l}-1.96\hfill \end{array}$	$\begin{array}{l}1.15\hfill \end{array}$	$\begin{array}{l}0.43\hfill \end{array}$	$\begin{array}{l}0.49\hfill \end{array}$
t- intercept	$\begin{array}{l}0.71\hfill \end{array}$	$\begin{array}{l}-0.13\hfill \end{array}$	$\begin{array}{l}-0.08\hfill \end{array}$	$\begin{array}{l}-0.37\hfill \end{array}$	$\begin{array}{l}0.01\hfill \end{array}$	$\begin{array}{l}-0.52\hfill \end{array}$	$\begin{array}{l}0.29\hfill \end{array}$	$\begin{array}{l}-0.28\hfill \end{array}$	$\begin{array}{l}0.59\hfill \end{array}$
t- Beta M	$\begin{array}{l}-0.78\hfill \end{array}$	$\begin{array}{l}0.86\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}2.46\hfill \end{array}$	$\begin{array}{l}1.4\hfill \end{array}$	$\begin{array}{l}5.8\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}4.35\hfill \end{array}$	$\begin{array}{l}4.65\hfill \end{array}$
t- intercept	$\begin{array}{l}0.71\hfill \end{array}$	$\begin{array}{l}-0.13\hfill \end{array}$	$\begin{array}{l}-0.08\hfill \end{array}$	$\begin{array}{l}-0.37\hfill \end{array}$	$\begin{array}{l}0.01\hfill \end{array}$	$\begin{array}{l}-0.52\hfill \end{array}$	$\begin{array}{l}0.29\hfill \end{array}$	$\begin{array}{l}-0.28\hfill \end{array}$	$\begin{array}{l}0.59\hfill \end{array}$
t- Beta M	$\begin{array}{l}-0.78\hfill \end{array}$	$\begin{array}{l}0.86\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}2.46\hfill \end{array}$	$\begin{array}{l}1.4\hfill \end{array}$	$\begin{array}{l}5.8\hfill \end{array}$	$\begin{array}{l}0.75\hfill \end{array}$	$\begin{array}{l}4.35\hfill \end{array}$	$\begin{array}{l}4.65\hfill \end{array}$
t- Beta F	$\begin{array}{l}-0.35\hfill \end{array}$	$\begin{array}{l}2.06\hfill \end{array}$	$\begin{array}{l}0.7\hfill \end{array}$	$\begin{array}{l}-1.08\hfill \end{array}$	$\begin{array}{l}0.94\hfill \end{array}$	$\begin{array}{l}-3.7\hfill \end{array}$	$\begin{array}{l}0.78\hfill \end{array}$	$\begin{array}{l}0.57\hfill \end{array}$	$\begin{array}{l}0.63\hfill \end{array}$

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