Recently, the IT sector has been in news with major IT companies announcing their quarterly results (Q2, FY 21). Infosys reported a 20.5% growth in its consolidated net profit (after minority interest) for the second quarter ended September 30th, over the same period last year. For HCL tech it was a growth of 18.5% in net profit during the same period, while for Wipro and TCS it was a decline of 3.4% and 7.05% respectively. In the first week of October TCS also became the second Indian firm after Reliance Industries to cross the Rs 10 lakh crore mark. With the announcement of financial results and with stock market moves, investors and analysts look to gauge the performance of stocks based on various metrics.
In this blog post, I will be doing the same i.e. try to analyze the performance of top Indian IT stocks (by market cap), however, the metric I will be using is Jensen’s alpha. This measure was first used by Michael Jensen in 1968 to evaluate mutual fund managers.
Jensen’s Alpha
Simplistically putting, Jensen’s alpha is the return on a stock that is above (or below) its’ expected return based on the Capital Asset Pricing Model (CAPM). In general, Capital Asset Pricing Model (CAPM) is the model used to find the expected return on a stock based on its’ systematic risk (Beta). Any return (positive or negative) that is not explained by this model is the Jensen’s alpha of a stock.
Calculation of Jensen’s Alpha
Both equation-1 and equation-2 are used in the calculation of Jensen’s alpha. Equation-2 shows how Jensen’s alpha can be calculated through regression analysis. Equation-2 shows that, if we run the regression of the excess return on a stock (Ri -Rf) (dependent variable or “Y”) over the excess return on market (Rm-Rf) (independent variable or “X”), the slope of the line will be the Beta (β) while the intercept of the line will be Jensen’s alpha (∝). This line is also known as Security Characteristic Line (SCL).
Comparison of IT stocks based on Jensen’s alpha.
I calculated Jensen’s alpha of top Indian IT stocks by market cap. For this, I ran a regression of excess returns on these stocks over the excess returns on market. I collected monthly returns for these stocks (listed on BSE) for the period between January 2015 to August 2020. I assumed a monthly risk-free rate of 0.096% over the period of regression. Excess returns over the risk-free rate were calculated for each month, by subtracting 0.096% from the monthly return of a particular stock over the period of regression. Excess returns on market were calculated by subtracting 0.096% from the monthly returns of S&P BSE 500, over the period of regression. The results of the regression for these 4 stocks are summarized below.
Regression Results
Interpretation of Jensen’s Alpha
As discussed earlier the intercept of these regression lines will be Jensen’s alpha (∝) for these stocks. Infosys had an ∝ of approx. 0.81%. This means that on average Infosys made approx. 0.81% extra each month over the period of regression. This extra return is over and above the return as predicted by CAPM. Since CAPM takes into consideration the riskiness of the stock with respect to the market (i.e. Beta), it can be said that this extra return was over and above, the expected, risk-adjusted return of Infosys. This extra return was earned on an average each month, so, it can be estimated that on an annual basis, Infosys earned an extra, 0.808% X 12= 9.70%.(approx). This calculation shows that Infosys earned the highest Jensen’s alpha over the period of regression and Wipro the lowest. However, based on this it would be difficult to conclude that the performance of these stocks was significantly different from the prediction as per CAPM.
Statistical Significance of Jensen’s Alpha (Intercept)
All four stocks have a high p-value of intercept which means that for all these four stocks we cannot reject the null hypothesis that intercept or Jensen’s alpha is zero. In other words, in none of these stocks, Jensen’s alpha is statistically significant and hence it cannot be concluded that the performance of these stocks was significantly different from the prediction as per the CAPM.
Statistical Significance of differences between Jensen’s alpha
I tried to compare the regression lines of each stock with one another (i.e. a total of six pairs) to check the null hypothesis that the difference in intercepts of these stocks is equal to zero. The process involved (although I am not an expert in running such regressions), combining the data of two stocks together and creating, categorical variables (0 and 1) for the two stocks. Then, I ran a regression on the combined dataset and checked for the significance of the difference in intercepts. All the six regressions show a high p-value for the difference in intercepts which means we cannot reject the null hypothesis that the difference in intercepts was equal to zero.
This means that we can not conclude that any of these stocks earned a Jensen’s alpha which was significantly different from Jensen’s alpha of the other 3 stocks.
To summarize we cannot conclude that any of these stocks, performed significantly different from the prediction as per the CAPM, and any of these stocks significantly outperformed each other on a risk-adjusted basis.
Limitations of Jensen’s Alpha.
The analysis is based on CAPM and is subject to the limitations of the CAPM. There are limitations of the linear regression model also (such as the presence of outliers) which can impact the precision of this analysis. Moreover, the analysis is based on past data and there is no guarantee that the past performance of stock would be repeated in the future. The future performance of a stock is likely to depend on several other factors (for example, growth in the number of clients which will further drive revenue growth) rather than relying only on past data.
Disclaimer: This blog post is not a stock or investment recommendation. It is not meant to provide any professional advice and is written with the purpose to discuss an analytical methodology. The methodology has various limitations and some of them have been discussed above. Any investment action you take based upon the analysis presented here is strictly at your own risk. The analysis and views presented here do not reflect the ideologies or points of view of any organization, I am affiliated with, or potentially affiliated with. Despite best efforts to present authentic information, the blog post is likely to suffer from errors and omissions. I am eligible to modify, update, or delete the information on this blog post.
