Introduction

We are excited to announce that we have developed a Stata code for the Average F-Test. This test was originally developed by Hwang and Satchell (2014). It averages the squared t-statistics on the estimated alphas of individual assets. A key advantage of the test is that it can be applied to a large number of assets N, even when N > T, unlike the GRS-test which requires T>N. It is robust to non-normality and ellipticity in asset returns. We have Stata codes for the test and also for the simulation exercise which generates the average F distribution from which the critical values of the test are derived.

Instead of the maximum pricing error of the F-statistic, Hwang and Satchell (2014) propose the average pricing error. By treating t-statistics of the estimated alphas as pricing errors of individual assets, an aggregated pricing error for N assets can be measured by averaging squared t-statistics of alphas. Therefore, the Average F-Test is defined as follows:

S^2 = \dfrac{Tc}{N} \sum_{n=1}^{N} \dfrac{\hat{\alpha_n}^2}{\hat{\sigma_n}^2}

where

\hat{\alpha}_n^2 = \sum_{t=1}^{T} (r_{n,t} - \hat{\alpha}_n - \hat{\beta}_n r_t^f)^2 /({T - K - 1})

and

  • \alpha_n^2 is the squared alpha (pricing error) of the nth asset;
  • T is the number of time periods,
  • K is the number of factors,
  • r_{n,t} is the return of the nth asset at time t,
  • \alpha_n is the alpha of the nth asset,
  • \beta_n is the beta of the nth asset, and
  • r_t^f is the risk-free rate at time t.

 

Our Stata Code Implementation

We have developed a comprehensive Stata code that replicates the methodology used in Hwang and Satchell’s paper. The code allows you to set the following parameters as per your your research design:

  • T : Number of observations
  • K : Number of factors
  • N : Number of assets
  • REPS: Number of repetitions

Our Stata code is in the form of a Stata ado program, so you can easily set the above parameters for any dataset. The ado file is not compiled code, which means you can open it in any text editor and view the source code. The program reports Average F-test critical values at confidence intervals ranging from 90% to 99.5%. It also reports the number of assets, factors, observations, and simulations.

 

Pricing

The code for the Average F-Test, which implements the methodology proposed by Hwang and Satchell, is available for purchase. You can acquire this comprehensive and user-friendly Stata code for a price of 149 GBP. This is a valuable investment for researchers and practitioners in finance looking to apply this new statistical method in their work. If you have any questions or need further information, feel free to ask! 

 

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Dr. Attaullah Shah
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