Stata Codes for Asset Pricing Models

Testing asset pricing models requires time-series returns of portfolios formed on firms’ characteristics such as size, book-to-market, leverage, beta, and others (also commonly known as the left-hand-side variables or the LHS). These models use factor returns, such as the market factor, SMB, HML, momentum, profitability, liquidity, and investment (commonly known as the right-hand-side variables or the RHS). One challenging task is to sort assets based on specific criteria, create portfolios, calculate portfolio returns per period, and periodically rebalance portfolios as the criteria change over time. To overcome these challenges, we use dedicated programs written in Stata. These programs not only help to reduce the risk of errors that can occur when manually analyzing data in programs like MS Excel, but they also accelerate the process, saving a significant amount of time.

We provide codes for the following:

Asset Pricing Models

1. Fama and French three-factor model

Our Stata code accurately reproduces the three factors with correlations of up to 98% with the three factors of Fama and French model. See details here.

2. Fama and French five-factor model

Our Stata code accurately reproduces the five factors with significantly higher correlations with the five factors of Fama and French model. See details here.

3. Carhart four-factor model

Our Stata code accurately reproduces the three factors with correlations of up to 98% with the three factors of Fama and French model. See details here.

4. Q-factor model

The Q-factor model, also known as the investment-based asset pricing model, is an extension of the traditional Capital Asset Pricing Model (CAPM) that incorporates additional factors (such as investment-related factors) to explain asset returns. Visit this page for our Stata code.

5. ESG as a equity factor model

It has become widely accepted that making an allowance for environmental, social, and governance (ESG) criteria within an equity portfolio enhances returns. Should ESG be considered as a unique equity factor. Our code can help you answer this question.

6. Betting against the beta

The research on “betting against the beta” suggests that low-beta stocks tend to outperform high-beta stocks in terms of risk-adjusted returns. Is it so? Explore it in your data with our Stata code.

7. Liquidity adjusted CAPM (Acharya & Pedersen)

Acharya and Pedersen (2005) presented a theoretical model to explain asset prices with four types of liquidity risks, thereby modifying the single-factor capital asset pricing model (CAPM) into a liquidity adjusted capital asset pricing model (LCAPM). See details here.

8. Fama McBeth Regression with Shanken correction

The betas (β) in the cross-sectional regressions are not fixed, but are estimated in the time-series regression. There might be a sampling error in the estimates of β. Shanken (1992) suggested a correction to the standard errors of the estimates. We provide Stata code to implement the Shanken correction, see details here.

Model Testing Tools

 

Our code library has a vast range of model testing tools that are available in the extant literature. These tools are discussed here with brief summary.

1. GRS test

The GRS (Gibbons, Ross, and Shanken) test is a statistical method to evaluate asset pricing models using cross-sectional stock return data. The GRS test examines whether a proposed multi-factor asset pricing model fully captures the variation in average stock returns. It tests the null hypothesis that the pricing model is correct – that the alphas from time-series regressions of asset returns on the risk factors are jointly equal to zero.

2. Squared Sharpe Ratio

Barillas, Robotti, and Shanken (2020) proposes several statistical tests for comparing asset pricing models. For models with traded factors, they use basic alpha test: Tests whether the alphas of the factors excluded from a nested model are jointly zero when regressed on the nested model factors.

Used for nested model comparison. Direct test: Tests whether the squared Sharpe ratios of two non-nested models are equal using the asymptotic distribution of the difference in squared Sharpe ratios.

Sequential test: First tests if a model of common factors spans the models being compared using an alpha test. If not, proceeds to the direct test of equal squared Sharpe ratios.

3. Intercept based test

The Fama and French (2015) tests of the average absolute value of the intercepts,A|a_i|, A|\alpha_i|/A|r_i|, the average absolute value of the intercept \alpha_{i} over the average absolute value of r_{i} , which is the average return on portfolio i minus the average of the portfolio returns, the average squared intercept over the average squared value of r_{i} , corrected for sampling error in the numerator and denominator. Each of these tests are available for an additional fee of $49.99.

4. The average F-test.

Hwang and Satchell (2014) developed the average F-test. 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.

References

Barillas, F., Kan, R., Robotti, C., & Shanken, J. (2020). Model comparison with Sharpe ratios. Journal of Financial and Quantitative Analysis, 55(6), 1840-1874.

Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.

Gibbons, M. R., Ross, S. A., & Shanken, J. (1989). A test of the efficiency of a given portfolio. Econometrica: Journal of the Econometric Society, 1121-1152.

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.