The price to Book ratio (P/B) ratio has been considered appropriate for valuing companies composed
primarily of liquid assets such as banking institutions.
The P/B ratio of a stock is linked to the return on equity and cost of equity. The higher the
expected return on equity on a stock, the higher is the P/B ratio, and the higher the cost of
equity of stock the lower is the P/B ratio. The justified P/B ratio can be calculated as:
Methodology
We identified all private sector banks listed on BSE. The total sample size was 17 after excluding some banks. For all these banks we collected three metrics, P/B ratio, ROE, and Capital Adequacy Ratio (CAR) as of 31st March 2021. The required rate of return of a bank depends upon the risk of a bank and we used CAR as a proxy for risk. We ran a regression taking the P/B ratio as a dependent variable and ROE and CAR as independent variables (IVs).
The below chart shows the distribution of P/B ratios of private sector banks in India. The median P/B was 1.78 and the average P/B was 1.76
31st March 2021., sample size-17 banks
Regression Output:
The results of the regression are as follows:
The R square is moderate, the coefficient of ROE is significant but not the coefficient of CAR
(at 5% level of significance), the F statistics is significant and hence I use the regression results to get the
predicted P/B ratio for each bank. This predicted P/B ratio is compared with the observed P/B ratio of
the bank to calculate whether the bank is undervalued or overvalued. The results are as follows:
Prediction Results:
Small finance banks, Yes Bank, and JK Bank (government holding 68%) have been excluded, few other banks also have significant government holding,
followed by DCB Bank and Karur Vysya Bank. IDFC First Bank is the most overvalued bank.
South Indian Bank has a relatively low P/B and Bandhan Bank has a relatively high P/B, however, their predicted
P/B is almost equivalent and hence they seem to be fairly valued. Notably, this analysis only shows how a
particular bank is valued relative to other banks in the list. Further analysis of the particular bank is
required to find out if the stock is trading below its intrinsic value.
Residual plot and Q to Q Plot
regression.
Squares (OLS) Regression.
The residuals on Q to Q plot fall reasonably on a straight line which is an important condition to using hypothesis testing to rely on the statistical significance of the model.
Limitations of the model
After excluding some of the banks from the list, the sample size for this regression is 17 banks. The sample size for running a regression with two independent variables (IVs) is at least 20 to 30. Since our sample size is small this will reduce the predictive ability of the regression.
As shown in equation -1, an input for the stable growth rate is also required to calculate justified P/B, however, we have not considered growth rate in our analysis. By ignoring the growth rate we have assumed that the growth rate is equal for all stocks.
The sample data on Return on Equity (ROE) and Capital Adequacy Ratio (CAR) are correlated (Pearson correlation coefficient, 0.65). This can introduce multicollinearity in the model. Although multicollinearity affects the coefficients of IVs, it does not affect the overall fit of the regression.
Our predicted P/B ratios are point estimates and we have not considered the prediction interval around those estimates. A prediction interval can provide more confidence in the predicted values.
All the predictions are based on past data (31st March 2021). Hence the predictions are also relevant for that period. At present, the stock prices, book value, ROE, CAR for these stocks would have changed.
Reference: Aswath Damodaran, Jim Frost
Disclaimer: The blog post should not be construed as investment advice. The blog post is written with the purpose to discuss the application of regression analysis in relative valuation. 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 views of any organization with which I am affiliated or potentially affiliated. 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. I welcome feedback on tulsyananimesh@gmail.com
