# Fama Macbeth Procedure Manual Template

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## Re: st: fama macbeth procedure

Description: Fama-MacBeth Approach. L CAPM. Review of CAPM MacBeth: use a procedure that is now known as the 'Fama-MacBeth Fama and MacBeth Tags: capm lecture macbeth testing.

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Latest Highest Rated. For each equation, we can run OLS and obtain estimates of? We could also estimate the equations jointly. Is there any advantage to doing this, that is, run the seemingly unrelated regression on the system?

As it turns out, joint estimation is useless if we only need estimates for?

However, for our joint test, its not useless. We need the covariance matrix for our joint test. This is critical for the maximum likelihood approach. Given joint normality of excess returns, the likelihood function for the cross-section of excess returns in a single period is 9 The Likelihood Function With T i.

Because if you know the distribution, MLEs are Consistent Asymptotically efficient Asymptotically normal The log of the joint pdf viewed as a function of the unkown parameters,? There are N of these as well, one for each? The variances and covariances of the estimators can be derived using the Fisher Information Matrix.

## Lecture 18: Testing CAPM - PowerPoint PPT Presentation

The information matrix is minus the matrix of second partials of the log-likelihood function with respect to the parameter vector. Now, we impose the CAPM restrictions. If we only estimate the unconstrained model, we can the Wald test. We will also consider likelihood ratio and Lagrangian multiplier tests. Note that? Substitute a consistent estimate of it into the statistic and then under the null the distribution is asymptotically chi-squared.

The MLE of? We, however, know the finite sample distribution. We can use this to do the Gibbons Ross and Shaken test. To do so, we will need the following theorem from Muirhead Theorem Let the m-vector x be distributed N 0,? We can construct J1 and J0 using only the estimators from the unconstrained model. The portfolio with the maximum squared Sharpe ratio must be the tangency portfolio.

When the ex-post q is m, J1 0. As ms squared SR decreases, J1 increases evidence against the efficiency of m.

## Fama macbeth procedure manual template

The test statistic is CLM p show that there is a monotonic relationship between J1 and J2 Therefore we can derive finite sample distribution for J2 based on the finite sample distribution of J1 23 Jobson and Korkie Adjustment which is also asymptotically distributed as a Why do we need different statistics? Because although their asymptotic properties are similar, they may have different small-sample properties.

It may looks more complicated. But if you remember from your econometrics course, all three statsistics Wald, Likelihood Ratio, Lagrangian Multiplier can easily test nonlinear restrictions.

See CLM p One alternative approach is to use quasi-maximum likelihood. Under certain regularity conditions you can estimate the model as if the returns were normally distributed, and the Wald, Likelihood ratio, and Lagrangian multiplier tests are still valid after adjusting for the covariance matrix for the errors.

However, small sample properties of QMLE are of serious concern. Another alternative is to use GMM, which only rely on a few momentum conditions. Whats the consequence of error-in-variable problem?

The maximize the power of test, group stocks into portfolios based on stocks betas.

Unsolved problems errors ei are correlated across stocks. This causes problems for estimating standard deviations of coefficient estimates.

Fama and MacBeth use a procedure that is now known as the Fama-MacBeth regression 30 Fama and MacBeth Perform the cross-sectional regression in each month, to obtain rolling estimates for a and?.

Call them at and? Then, calculate the time series means and time series t-stats for at and?

Test ave at ave Rf and ave? They also perform the test using an extended model Ri? Black version of CAPM seems more consistent with the data. Other variables, such as squared beta and the variance of idiosyncratic component of returns, do not have marginal power to explain average returns. In other words, C1 and C2 seem to hold C3 is rejected.

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