Estimation of the CAPM model for 25 CRSP portfolios and 30 Industry Portfolios. Fama-Macbeth estimation of the standard errors for the coefficients

The aim of this analysis is the estimation of the Capital Asset Pricing Model (CAPM) for 25 CRSP portfolios and for 30 Industry portfolios (see Fama and French (1992)), as well as the estimation of the Fama-Macbeth standard errors of the coefficients for each asset contained in the 25 CRSP portfolio and 30 Industry portfolio (see Fama and Macbeth (1973)). The data sets span the period of time going from Jan 1959 to Dec 2010 at a monthly frequency. 

The following links provide the files needed to obtain all results:

• code: EstimationCAPM
• data sets: data_factors, data_returns, data_industry

A. Estimation of the CAPM model for the 25 CRSP portfolios

This data set was created by CMPT_ME_BEME_RETS using the 201107 CRSP database. It contains value- and equal-weighted returns for the intersections of  5 ME portfolios and  5 BE/ME portfolios.   

The portfolios are constructed at the end of Jun.  ME is market cap at the end of Jun.  BE/ME is book equity at the last fiscal year end of the prior calendar year divided by ME as of  6 months before formation.  Firms with negative BE are not included in any portfolio.

The annual returns are from January to December.

The data set is formed on the size of the portfolio (from small to big) and on the book-to-market index (from low to high).

Each portfolio is regressed on three factors: Rm-Rf (difference between returns of the portfolios and the risk free rates of return), SMB (book-to-market), and HML (size).

The excel file containing the estimated coefficients for each portfolio is provided here.


Medians
Constant: 0,0033

Rm-Rf: 1,0134
SMB: 0,5239
HML: 0,3737
Adjusted R^2: 0,9064

Fig.1 depicts the values of the coefficients and the R_squared's (against their respective median values) of the model across the 25 CRSP portfolios.

Fig.1

B. Fama-Macbeth standard errors

The Fama-Macbeth standard errors for the 25 CRSP portfolios are provided below:
Constant: 0.1328

Rm-Rf: 0.0613
SMB: 0.4848
HML: 0.3988

C. Estimation of the CAPM model for the 30 Industry portfolios

The data set is formed on the industry of reference. 

Each portfolio is regressed on three factors: Rm-Rf (difference between returns of the portfolios and the risk free rates of return), SMB (book-to-market), and HML (size). 

The excel file containing the estimated coefficients for each portfolio is provided here.

Medians

Constant: 0.3884

Rm-Rf: 1.0944
SMB: 0.1712
HML: 0.2432

Adjusted R^2: 0.6579

Fig.2 depicts the values of the coefficients and the R_squared's (against their respective median values) of the model across the 30 Industry portfolios.

Fig.2

The Fama-Macbeth standard errors for the 30 Industry portfolios are provided below:
Constant: 0.2503
Rm-Rf: 0.1565
SMB: 0.2492
HML: 0.2812

GMM Estimation of the coefficient of Relative Risk Aversion in a standard DSGE model with two different assets

In a standard DSGE model, a relevant issue is the estimation of the coefficient of relative risk aversion (RRA), i.e. the intertemporal elasticity of substitution of consumption in two subsequent periods.

In order to estimate the mentioned parameter, it is possible to use the Generalized Method of Moments (GMM). Below, the link to a MATLAB file (.m) provides a code for the GMM estimation of the RRA.
GMMestimationRRA.m

The following files have to be saved in the same working directory as the previous file:
GMM.m
optweighmat.m

The data set spans 50 years (1961-2010) and is provided below:
data1.txt (durables, non-durables, services)
data2.txt (CRSP returns, 10-year bond returns)


Model

1. Consumption is the only argument for the utility function of the representative agent
2. Gamma ('gam' in the code) is the RRA
3. U'(C) = (C)^(-gamma)
4. there are two different assets

Results

a) Graph for deflated returns on CRSP and 10-year bonds
b) Estimates of RRA:

 Consumption = Durables:

• RRA(monthly frequency) ~ 51
• RRA(quarterly frequency) ~ 66
• RRA(annual frequency) ~ 111
• RRA(5-year frequency) ~ 176

c) Test of overidentification: the p-value for the test statistic, which is distributed as a chi-square (see Hansen (1982)),  is remarkably low and close to zero. At a 5% significance level, we may not reject the null hypothesis. Hence, the model is overidentified, i.e. the different restrictions (orthogonality conditions) do not provide a unique solution for the coefficient of RRA.