Six-Factor Asset Pricing versus LSTM Forecasting in the Pakistan Stock Exchange
Contributors
- Malaika Nisar Research Scholar, Department of Management Sciences, COMSATS University Islamabad, Abbottabad Campus, Khyber Pakhtunkhwa, Pakistan.
- Dr. Muhammad Naveed Jan Assistant Professor, Department of Management Sciences, COMSATS University Islamabad, Abbottabad Campus, Khyber Pakhtunkhwa, Pakistan.
- Dr. Usman Ayub Professor, Department of Management Sciences, COMSATS University Islamabad, Abbottabad Campus, Khyber Pakhtunkhwa, Pakistan.
Abstract
This research examines whether the six-factor asset pricing model or Long Short-Term Memory (LSTM) recurrent neural network is better suited to forecasting the portfolio excess return in the Pakistan Stock Exchange (PSX), which is a frontier market with relatively less history. The data used is monthly for 300 PSX companies classified into 30 factor sorted portfolios (Jan 1999 – Dec 2025, 312 months), where a six-factor time-series regression with Newey-West HAC errors is estimated, followed by joint pricing error significance test using Gibbons-Ross-Shanken (GRS) statistic. A portfolio-specific LSTM is trained on the same six factors using a fixed chronological split (196 training, 42 validations, 42 test months) and compared with the regression on an identical 42-month out-of-sample window using RMSE, MAE, out-of-sample R², hit rate, and three formal tests. The six-factor model explains substantial return variation (mean in-sample R² = .758), but the GRS test rejects the null of jointly zero pricing errors (F = 12.251, p < .0001; mean |α| = 0.749%). The LSTM shows no systematic incremental forecasting value: the regression achieves lower RMSE on 28 of 30 portfolios and a higher out-of-sample R² (.590 vs. −.022), with all three formal tests rejecting equal accuracy at p < .0001. The LSTM's limited value concentrates in momentum-sorted portfolios, consistent with permutation importance ranking momentum as the dominant learnable input. We interpret this as evidence that algorithmic flexibility does not automatically yield forecasting gains under limited training data and noisy returns, not as evidence against machine learning generally.
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Corresponding Author
Dr. Muhammad Naveed Jan
Assistant Professor, Department of Management Sciences, COMSATS University Islamabad, Abbottabad Campus, Khyber Pakhtunkhwa, Pakistan.
Corresponding Author: [email protected]
