DefinePK

Research Objective

To test whether Value at Risk (VaR) and Expected Shortfall (ES) can be used as alternative systematic risk factors to market beta in traditional Capital Asset Pricing Model (CAPM), three-factor, and five-factor models for explaining cross-sectional stock returns in the Pakistani Stock Exchange.

Methodology

The study collected daily stock price data for 527 non-financial firms listed on the Pakistan Stock Exchange (PSX) from 1998 to 2015. VaR and ES were calculated at 95% and 99% significance levels. The research employed Ordinary Least Squares (OLS) regression and quantile regression to compare the explanatory power of CAPM, three-factor, and five-factor models with modified models using VaR and ES as systematic risk factors.

Methodology Flowchart

                        graph TD
    A["Data Collection: 527 non-financial firms, PSX 1998-2015"] --> B["Calculate VaR & ES at 95% & 99%"];
    B --> C["Apply OLS Regression: CAPM, 3-Factor, 5-Factor Models"];
    C --> D["Modify Models: Replace Beta with VaR/ES"];
    D --> E["Apply Quantile Regression"];
    E --> F["Compare Model Performance"];
    F --> G["Analyze Results & Draw Conclusions"];                    

Discussion

The study argues that market beta is an inappropriate proxy for systematic risk in the Pakistani stock market, likely due to the presence of cyclical stocks leading to negative beta. VaR and ES, which focus on the tail of the distribution, provide a more accurate representation of risk and a positive risk-return relationship. The findings suggest that VaR and ES can effectively control for the effects of size, investment, and profitability factors, making them potentially superior alternatives to market beta for explaining cross-sectional stock returns, especially in volatile emerging markets like Pakistan.

Key Findings

- Traditional market beta in CAPM, three-factor, and five-factor models showed a negative relationship with stock returns, contradicting the risk-averse behavior of investors and the 'high-risk, high return' theory.
- VaR and ES demonstrated a positive relationship with stock returns, supporting the 'high-risk, high return' theory.
- Investment, profitability, and size factors became redundant when VaR and ES were used as systematic risk factors.
- ES-based models showed the highest explanatory power, with an adjusted R² of 0.62 in the single-factor model.
- VaR and ES-based models better predicted stock returns compared to market beta across different quantiles of excess returns.

Conclusion

Value at Risk (VaR) and Expected Shortfall (ES) are recommended as effective alternatives to market beta for explaining cross-sectional stock returns in the Pakistan Stock Exchange. These measures align better with the 'high-risk, high return' theory and offer superior explanatory power compared to traditional asset pricing models, particularly in volatile emerging markets.

Fact Check

- Data was collected for non-financial companies listed on the Pakistani Stock Exchange from 1998 to 2015.
- VaR and ES were calculated at two levels of significance: 95% and 99%.
- The study found a negative relationship between market beta and stock returns in the Pakistani market.

Mind Map