Expected Shortfall and Value at Risk as Alternative of Market Beta to Explain Cross-Sectional Stock Returns

Expected Shortfall and Value at Risk


  • Adeel Nasir Assistant Professor, Department of Management Sciences, Lahore College for Women University, Pakistan
  • Umar Farooq Assistant Professor, FAST School of Management National University of Computer and Emerging Science (FAST-NUCES), Faisalabad, Pakistan
  • Kanwal Iqbal Khan Department of Management Sciences, University of Engineering and Technology, Lahore, Pakistan




Risk Management; Expected Shortfall; Value at Risk CAPM; Three-factor model; Five-Factor Model


The objective of this study to risk return model with Value at Risk (VaR) and Expected Shortfall (ES) as the systematic risk factors. Notably, it is tested whether VaR and ES can be used as an alternative of market beta in the traditional Capital Asset Pricing Model (CAPM), three and five-factor model. Data is collected for non-financial companies listed at the Pakistani Stock Exchange. VaR and ES are calculated at two levels of significance, i.e. 95% and 99%. Results showed that the traditional market beta of CAPM, three and five-factor model is not following risk-averse behaviour of investors. Conversely, VaR and ES showed a positive relationship with stock returns supporting the 'high-risk, high return' theory. Furthermore, investment, profitability and size factors become redundant with VaR and ES as systematic risk factors. Therefore, it is recommended that VaR and ES may be used the alternative to market beta to predict the cross sections of stock excess returns.


Ameer, D. (2013). A Test of Fama and French Three Factor Model in Pakistan Equity Market. Global Journal of Management And Business …, 13(7), 12–16.

Asad, H., & Khalid Cheema, F. (2017). An Empirical Assessment of the Q-Factor Model: Evidence from the Karachi Stock Exchange. The Lahore Journal of Economics, 22(2), 117–138. https://doi.org/10.35536/lje.2017.v22.i2.a5

Aziz, T., & Ansari, V. A. (2017). Value-at-risk and stock returns: evidence from India. International Journal of Emerging Markets, 12(2), 384–399. https://doi.org/10.1108/IJoEM-04-2015-0076

Basu, S. (1983). The relationship between earning yields, market value and return for NYSE common stock: further evidence? Journal of Financial Economics, 12(1), 129–156.

Benz, R. (1981). The relationship between returns and market value common stocks. Journal of Financial Economics, 9(1), 3–18.

Black, F. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45, 444–455.

Chen, D. H., Chen, C. Da, & Wu, S. C. (2014). VaR and the cross-section of expected stock returns: An emerging market evidence. Journal of Business Economics and Management, 15(3), 441–459. https://doi.org/10.3846/16111699.2012.744343

Chen, S. X. (2008). Nonparametric Estimation of Expected Shortfall. Journal of Financial Econometrics, 6(1), 87–107. https://doi.org/10.1093/jjfinec/nbm019

Chiah, M., Chai, D., Zhong, A., & Li, S. (2016). A Better Model? An Empirical Investigation of the Fama–French Five-factor Model in Australia. International Review of Finance, 16(4), 595–638. https://doi.org/10.1111/irfi.12099

Diamandis, P. F., Drakos, A. a., Kouretas, G. P., & Zarangas, L. (2011). Value-at-risk for long and short trading positions: Evidence from developed and emerging equity markets. International Review of Financial Analysis, 20(3), 165–176. https://doi.org/10.1016/j.irfa.2011.02.009

Fama, E. F. (2015). Cross-Section Versus Time-Series Tests of Asset Pricing Models. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2685317

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56. https://doi.org/10.1016/0304-405X(93)90023-5

Fama, E. F., & French, K. R. (1998). Value versus growth: The international evidence. Journal of Finance, 53(6), 1975–1999. https://doi.org/10.1111/0022-1082.00080

Fama, E. F., & French, K. R. (2014). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010

Fama, E. F., & French, K. R. (2017). International tests of a five-factor asset pricing model. Journal of Financial Economics, 123(3), 441–463. https://doi.org/10.1016/j.jfineco.2016.11.004

Fatima, N., Waqas, M., Hassan, R., Fraz, A., & Arif, M. (2017). Cash to Price Ratio & Stock Returns: Evidence from Emerging Markets. International Journal of Economics and Finance, 9(11), 153–162. https://doi.org/10.5539/ijef.v9n11p153

Griffin, J. M. (2002). Are the Fama and French Factors Global or Country Specific? In Review of Financial Studies (Vol. 15, Issue 3, pp. 783–803). https://doi.org/10.1093/rfs/15.3.783

Huang, W., Liu, Q., Ghon Rhee, S., & Wu, F. (2012). Extreme downside risk and expected stock returns. Journal of Banking and Finance, 36(5), 1492–1502. https://doi.org/10.1016/j.jbankfin.2011.12.014

Iqbal, J., & Azher, S. (2014). Value-at-Risk and expected stock returns : evidence from Pakistan. The Lahore Journal of Economics, 2(19), 71–100.

Javid, A. Y., & Ahmad, E. (2011). Asset Pricing Behaviour with Dual-Beta in Case of Pakistani Stock Market. The Pakistan Development Review, 50(2), 95–118. https://doi.org/10.30541/v50i2pp.95-118

Kashif, M., Ilyas, A., Rehan, R., & Chhapra, I. U. (2018). Asset pricing and the size effect: Empirical evidence from Karachi Stock Exchange (KSE). Academy of Accounting and Financial Studies Journal, 22(6).

Kashif, M., Saad, S., Chhapra, I. U., & Ahmed, F. (2018). An empirical evidence of over reaction hypothesis on Karachi stock exchange (KSE). Asian Economic and Financial Review, 8(4), 449–465. https://doi.org/10.18488/journal.aefr.2018.84.449.465

Khan, K. I., Naqvi, S. M., Ghafoor, M. M., & Akash, R. S. I. (2020). Sustainable Portfolio Optimization with Higher-Order Moments of Risk. Sustainability, 12(5), 2006.

Kubota, K., & Takehara, H. (2017). Does the Fama and French Five-Factor Model Work Well in Japan? International Review of Finance, 1–10. https://doi.org/10.1111/irfi.12126

Lin, S.-Y., Chang, C.-C., & Lai, Y.-C. (2010). Applying spectral decomposition in Value-at-Risk: Empirical evidence from Taiwan stock market. Journal of Financial Studied, 18(3), 2–3.

Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13. https://doi.org/10.2307/1924119

Lohano, K., & Kashif, M. (2018). Testing asset pricing models on the Pakistan Stock Exchange. Business Review, 13, 1–19.

Mager, J. (2012). Value-at-Risk Estimation in the Basel III Framework. Technische Universit¨at M¨unchen.

Mager, J., & Klüppelberg, C. (2012). Value-at-Risk Estimation in the Basel III Framework.

Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Nasir, A., Khan, K. I., Mata, M. N., Mata, P. N., & Martins, J. N. (2021). Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall. Mathematics, 9(4), 394. https://doi.org/10.3390/math9040394

Naqvi, S. M. W. A., Khan, K. I., Ghafoor, M. M., & Rizvi, S. K. A. (2019). Evidence of volatility clustering and asymmetric behavior of returns in Asian emerging stock markets. Pakistan Economic and Social Review, 57(2), 163.

Peter, A. A., Abreo, X. D., & Ali, A. (2017). Fama and French three factor model application in the Pakistan stock exchange. Journal of Business Studies, 13(1), 1–11.

Sarykalin, S., Serraino, G., & Uryasev, S. (2008). Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization. In State-of-the-Art Decision-Making Tools in the Information-Intensive Age (pp. 270–294). INFORMS. https://doi.org/10.1287/educ.1080.0052

Scheule, H., Kellner, R., & Rösch, D. (2016). The role of model risk in extreme value theory for capital adequacy. The Journal of Risk. https://doi.org/10.21314/JOR.2016.337

Sharpe, W. F. (1964). Capital Asset Prices: a Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x

Theriou, N. G., Maditinos, D. I., & Chadzoglou, P. (2005). The cross-section of expected stock returns: An empirical study in the Athens stock exchange. Managerial Finance, 31(12), 58–78.

Totić, S., & Božović, M. (2015). Tail risk in emerging markets of Southeastern Europe. Https://Doi.Org/10.1080/00036846.2015.1109037, 48(19), 1785–1798. https://doi.org/10.1080/00036846.2015.1109037

Zada, H., Rehman, M. U., Ghani, M., Zulfikar, S., & Bhutto, A. (2018). Application of Fama and French Five Factor Model of Asset Pricing: Evidence From Pakistan Stock Market. International Journal of Economics, Management and Accounting, 26(1), 1–23.

Zhang, Q., Saqib, Z. A., Saqib, K. A., Mahmood, S., & Cao, M. (2019). Alternative three factor model for asset pricing for the investment, market and profitability premium in emerging markets: An evidence from Pakistan’s stock exchange. 2019 16th International Conference on Service Systems and Service Management, ICSSSM 2019, 1–6. https://doi.org/10.1109/ICSSSM.2019.8887691




How to Cite

Nasir, A., Farooq, U., & Khan, K. I. (2023). Expected Shortfall and Value at Risk as Alternative of Market Beta to Explain Cross-Sectional Stock Returns: Expected Shortfall and Value at Risk. South Asian Review of Business and Administrative Studies (SABAS), 5(1), 27–40. https://doi.org/10.52461/sabas.v5i1.1780