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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          Why should you buy the code?

Dr. Attaullah Shah

Created by an Expert

The code is written by Dr. Prof. Attaullah Shah, an experienced finance professional with over 20 years of experience in coding and quantitative modeling. He has published many Stata programs demonstrating his expertise.
Stata Code is cutomizable

Customizable and Extensible

While implementing the core model, the code is structured and commented in a way that makes it easy to customize and extend for your own purposes. Adapt it to your specific needs.
Save time with our Stata code

Save Time and Effort Developing Your Own Code

The code on the page implements the complex KMV Merton model for calculating distance to default and default probabilities. Developing this from scratch would take considerable time and effort.
Our Stata code is tested and validated

Accurate and Well-Tested Implementation

The code has been thoroughly tested and validated to ensure it accurately implements the published KMV Merton model. You can trust it to produce correct results.
Our Stata code is optimized for efficiency

Efficient and Optimized

The code has been optimized to run efficiently on large datasets. It leverages vectorization and other techniques to maximize performance.
We provide support for our Stata code

Expert Support

The code comes with expert support to help you implement and customize it for your needs. Get answers and guidance from the creator.
Our Stata code is affordable

Affordable Pricing

For a very reasonable price, you get reliable, optimized code plus support. Far more affordable than building it yourself.

References

 

Barillas, M., Robotti, C., & Shanken, J. (2020). Statistical tests for comparing asset pricing models. Journal of Financial Econometrics, 18(2), 397-437.

Hwang, S., & Satchell, S. E. (2014). Testing linear factor models on individual stocks using the average F-test. The European Journal of Finance, 20(5), 463-498.

Kan, R., Robotti, C., & Shanken, J. (2013). Pricing model performance and the two‐pass cross‐sectional regression methodology. The Journal of Finance, 68(6), 2617-2649.

Rahman, S., & Schneider, M. J. (2019). Tests of alternative asset pricing models using individual security returns and a new multivariate F-test. Review of Pacific Basin Financial Markets and Policies, 22(01), 1950001.

 

 

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