Introduction

The main objective is to identify and understand cross-sectional patterns in expected stock returns in PSX(Pakistan Stock Exchange). Our reasons for doing so are simple. First, to effectively execute empirical asset pricing research, it is important to have a deep understanding of the characteristics of the sample and data being used. The main objective of this blog is to empirically investigate the size and value premium in Pakistan Stock Exchange. Specifically, we will demonstrate that size has negative relation while book-to-market ratio has a positive relation with the expected stock returns.

The Size Effect

The size effect refers to the observation that stocks with large market capitalizations (large stocks) tend to have lower returns than stocks with small market capitalizations (small stocks). This result has become one of the cornerstone findings in empirical examinations of stock return predictability. The main size-related result of Fama and French (1992) is that market capitalization has the ability to predict the cross section of future stock returns.

Our investigation of the relation between market capitalization and future stock returns begins with the graph below showing average returns for Size portfolio i.e Large, Medium and Small. The average returns for Small and Medium Portfolio ranges from -20% to +20%. However, the large stock portfolio has witnessed more volatility and the average returns ranges from -25% to +25%.

However, it get a better understanding as how the Size portfolio performed over the year, the cumulative stock returns plot is shown below

This figure plots the cumulate returns of the size factor for the period from January 2004 through December 2017. The compounded excess return for month t is calculated as 100 times the cumulative product of one plus the monthly return up to and including the given month.

The graph showns, stocks with small market capitalizations have historically realized significantly higher average returns than large market capitalization stocks in Pakistan Stock Exchange. Building upon this finding, Fama and French (1993) create a portfolio designed to have returns that mimick the returns associated with the size effect and propose using the returns of this portfolio as a risk factor, known as SMB for small minus big which wil shown in the section namely Fama and French’s Size and Value Factor.

Value Premium

Fama and French (1993) claim that the value premium indicates that book-to-market ratio is a proxy for a stock’s sensitivity to a distress-risk factor. The value premium refers that value stocks, generates higher long-run returns than growth stocks, or stocks with high prices relative to these measures of fundamental value. We empirically investigate the value premium by examining the relation between book-to-market ratio and stock returns.

We begin by plotting the average retruns for the value premium portfolio as shown below. It cant be inferred anything concrete from the the graph below.

However, it get a better understanding as how the value premium factor portfolio performed over the year, the cumulative stock returns plot is shown below

This figure plots the cumulate returns of the value factor for the period from January 2004 through December 2017. The compounded excess return for month t is calculated as 100 times the cumulative product of one plus the monthly return up to and including the given month.

The results are consistent with the claims of Fama-French(1993). The cumulative returns are higher for high book-to-market ratio than low book-to-market ratio.

Fama and French’s Size and Value Factor

As discussed earlier, the superior long-run returns generated by size and value stocks is one of the central findings of empirical asset pricing research.

Taking the point of view that market capitalization proxies for a stock’s exposure to a priced but previously undefined risk factor, Fama and French (1993) create a long-short zero-cost portfolio designed to generate returns that approximate the returns associated with taking one unit of risk of this unknown size factor with little sensitivity to other factors. To create the size factor mimicking portfolio, Fama and French (1993) form a portfolio that is long small stocks and short large stocks in equal dollar amounts. They name this portfolio SMB, for small minus big.

Simlarly, Fama and French (1993) claim that the value premium indicates that book-to-market ratio is a proxy for a stock’s sensitivity to a distress-risk factor. To approximate the returns associated with taking exposure to this risk factor, Fama and French (1993) create a zero-cost factor mimicking portfolio holding long positions in stocks with high book-to-market ratios and short positions in stocks with low book-to-market ratios. This portfolio is referred to as the HML portfolio, for high minus low.

We developed the SMB and HMB factors based on the above methodology and plotted the results as shown below

This figure plots the cumulate returns of the SMB and HML factor for the period from Jan 2004 through December 2017. The compounded excess return for month t is calculated as 100 times the cumulative product of one plus the monthly return up to and including the given month. The graph shows that the value facor HMB has been a better performer in Pakistan Stock Market Compared to the Size factor

Conclusion

To summarize, we have examined the size and value premium by empirically investigating the relation between Market capitalization, book-to-market ratio (BM) and stock returns. Our analyses are in line with the hypothesis and therefore can be inferred that

The github link to the analyses is here