Bottom-up beta analysis OfBankex and its listed institutionsDate: March 22,2015

Business Communication Group 3Abhishek GhoshAkshat GargChitra SharmaSreejith A.SUdhayarajan

INTRODUCTIONBanks are a major part of any economic system. They provide a strong base to Indian economy too. Even in share markets, the performance of bank shares is of great importance. This is justified by the proof that in both BSE and NSE we have separate index for Banking Sector Shares. But for our study we have taken only BSE BANKEX. Thus, the performance of share market, the rise and the fall of market is greatly affected by the performance of Banking Sector Shares and this paper revolves around some of those factors, their understanding and a theoretical and technical analysis of the same. By declaring that, we have made a thorough understanding of the factors through the Beta estimation.

Risk measurement and analysis has been a critical issue for any investment decision because risk can be transferred but cannot be eliminated from the system. The nature and degree of risk varies from industry to industry. The risk can be categorized into two parts:

a> Risk-Free Rateb> Market Risk Premium

Beta is used by all categories of investors for measurement of market risk of individual companies, portfolios and sectors.

In finance, the beta () of an investment is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors. The market portfolio of all investable assets has a beta of exactly 1. A beta below 1 can indicate either an investment with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market. An example of the first is a treasury bill: the price does not go up or down a lot, so it has a low beta. An example of the second is gold. The price of gold does go up and down a lot, but not in the same direction or at the same time as the market.

A beta above one generally means that the asset both is volatile and tends to move up and down with the market. An example is a stock in a big technology company. Negative betas are possible for investments that tend to go down when the market goes up, and vice versa. There are few fundamental investments with consistent and significant negative betas, but some derivatives like equity put options can have large negative betas.

Beta is important because it measures the risk of an investment that cannot be diversified away. It does not measure the risk of an investment held on a stand-alone basis, but the amount of risk the investment adds to an already-diversified portfolio. In the capital asset pricing model, beta risk is the only kind of risk for which investors should receive an expected return higher than the risk-free rate of interest.

Internal or External conditions both are involved in measuring the sensitivity of returns of stocks. Industrial Production, money Supply ,Foreign Exchange Rate, Interest rate, Gold prices, GDP and oil prices in the world economy are involved in external conditions whereas dividend policy, earning per share, etc. are the contributors of internal factors. The paper studies the impact of Macro (External) factors on BSE BANKEX. Macroeconomic indicators are already exhibiting signs of deterioration as Rupee is depreciating against dollar, inflation is mounting, interest rates and gold prices are increasing and industrial production has started to decline. The study which measures the impact of macroeconomic forces on various sectors of stock exchange index is rare in the literature so this study provides a new way in the extending line of literature.

BANKEX

BANKEX Index Bombay Stock Exchange Limited launched "BSE BANKEX Index" on 23 June 2003. This index consists of major Public and Private Sector Banks listed on BSE. The BSE BANKEX Index is displayed online on the BOLT trading terminals nationwide. Objective:

a. An Index to track the performance of listed equity of Banks.

b. A suitable benchmark for the Central Government to monitor its wealth on the bourses.

Features:

BANKEX tracks the performance of the leading banking sector stocks listed on the BSE

BANKEX is based on the free float methodology of index construction

The base date for BANKEX is 1st January 2002

The base value for BANKEX is 1000 points

BSE has calculated the historical index values of BANKEX since 1st January 2002.

14 stocks which represent 90 percent of the total market capitalization of all banking sector stocks listed on BSE are included in the Index

The Index is disseminated on a real time basis through BSE Online Trading (BOLT) terminals.

Stocks forming part of the BANKEX along with the particulars of their free-float adjusted market capitalization are listed below.

Script Selection Criteria for BSE BANKEX: Eligible Universe Scripts classified under the banking sector which are present constituents of BSE-500 index form the eligible universe.

Trading Frequency Scripts should have a minimum trading frequency of 90% in preceding three months. Market capitalization Scripts with minimum market capitalization coverage of 90% in banking sector based on free-float final rank form the index. Buffers Buffer of 2% both for inclusion and exclusion in the index is considered so that movements in and out of the index are minimized.

For example, a company can be included in the index only if it falls within 88% coverage and an existing index constituent cannot be excluded unless it falls above 92% coverage. However, the above buffer criterion is applied only after the minimum 90% market coverage is satisfied.

Listed below are the today's Top Scrips traded in ``S&P BSE BANKEX`` with respect to Total Turnover. (20th March, 2015).

Scrip CodeScrip NameScrip GroupOpenHighLowLTPNo. of Shares TradedTotal Turnover (Lac)No. of Trades

532215.00AXISBANKA562.70565.00553.20556.75881262.004921.2328760.00

532174.00ICICIBANKA329.00329.50318.00319.101248169.004032.4928423.00

500112.00SBINA281.55282.30277.00278.351401237.003921.6627980.00

532648.00YESBANKA827.90841.25816.90832.25398049.003303.8219513.00

500180.00HDFCBANKA1052.001059.051045.251055.55309916.003262.7610223.00

532461.00PNBA162.00163.75159.40162.951078868.001750.6710717.00

532149.00BANKINDIAA214.80217.90210.65212.80598411.001280.4611560.00

500247.00KOTAKBANKA1334.901343.851308.501339.2585431.001130.847523.00

532187.00INDUSINDBKA871.50895.05871.50887.45106642.00945.748029.00

532134.00BANKBARODAA177.30177.30172.00172.90504686.00879.269952.00

532483.00CANBKA390.00390.00380.30382.05167195.00641.976851.00

500469.00FEDERALBNKA138.65140.30137.00137.65100876.00139.252623.00

Macro factors

This paper studies the impact of Macro (External) factors on BSE BANKEX and some of the factors that are considered are explained below:

Inflation

The control of inflation has become one of the dominant objectives of government economic policy in many countries. Monetary policy can control the growth of demand to tame inflation through an increase in interest rates and a contraction in the real money supply. This higher interest rates reduce aggregate demand by discouraging borrowing by both households and companies and by increasing the rate of saving (the opportunity cost of spending has increased) Inflation is usually measured based on certain indices. Broadly, there are two categories of indices for measuring inflation i.e. Wholesale Prices and Consumer Prices.

Exchange rate

Exchange Rate is the price of one country's currency expressed in another country's currency. If there is depreciation in the exchange rate, this depreciation will cause cost-push inflation and demand pull inflation. Controlling inflation will lead to increase in interest rates by RBI thereby affecting the profitability of banks.

GDP

GDP represents the total Rupee value of all goods and services produced over a specific time period. If the GDP growth rate is speeding up too fast, RBI may raise interest rates to stem inflation or the rising of prices for goods and services. As GDP growth slows down, and, in particular, during recessions, credit quality deteriorates, and defaults increase, thus resulting into reduced bank returns. Unlike nominal GDP, real GDP can account for changes in the price level, and provide a more accurate figure.

Gold prices

Of all the precious metals, gold is the most popular as an investment. Investors generally buy gold as a hedge or harbour against economic, political, or social fiat currency crises (including investment market declines, burgeoning national debt, currency failure, inflation, war and social unrest). The gold market is subject to speculation as are other markets.

LITERATURE REVIEWAswath Damodrans textbook on valuation with security analysis for investment and corporate finance, helped the report with in-depth coverage of different distinct valuation approaches and key models within reach, the beta estimation with the support of regression model paved a way for better understanding and furthermore to analyse the firm as levered or unlevered.

Manisha Luthra and Shikha Mahajans journal (2014), The Impact of Macro Factors on BSE BANKEX, cemented the report with elaboration of Macro- Economic factors like Inflation, GDP rates, Gold Prices and Exchange Rates, helped us to understand the effect on overall Beta in the BANKEX.

Reddy and Prasad (2011) analyses the effect of announcements made by RBI and S&P ratings on public and private bank stocks and BANKEX respectively. After the announcement of RBIs credit policy, the stock price of BANKEX is affected more, when compared to public or private sector banks individually. There is no impact of S&P ratings on public sector banks.

Ghosh et al. estimates the relationship between BSE Sensex and some importantEconomic factors like Oil prices, Gold price, Cash Reserve Ratio, Food price inflation, Call money rate, Dollar price, FDI, Foreign Portfolio Investment andForeign Exchange Reserve (Forex) using multiple regression model and FactorAnalysis.

Neha Sainis Measuring The Profitability And Productivity Of Banking Industry: A Case Study Of Selected Commercial Banks In India is used as a reference to understand the profitability and productivity of banking industry.

RESEARCH PROBLEM1. Responsiveness of the stock to its Sectorial Index rather than BSE/NSE?

2. Classification of those stock into aggressive or defensive stock as per their responsiveness as per their responsiveness to Sectorial Index?

3. Calculation of Alpha (Abnormal Return) whether it prevails in any of the stocks?

4. Whether the market (S&P BSE BANKEX) performed in accordance to the expected return of the investors (Expected return as per the CAPM)?

5. Bottom-Up Beta i.e., convert the Raw Beta into Adjusted Beta to take both systematic and the unsystematic risk?

VARIABLE IDENTIFICATION

Estimating BetaThe standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -Rj = a + b Rm where a is the intercept and b is the slope of the regression.The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.This beta has three problems:1. It has high standard error2. It reflects the firms business mix over the period of the regression, not the current mix3. It reflects the firms average financial leverage over the period rather than the current leverage.

Solutions to the Regression Beta Problem Modify the regression beta by:

Changing the index used to estimate the beta

Adjusting the regression beta estimate, by bringing in information about the fundamentals of the company

Estimate the beta for the firm using: The standard deviation in stock prices instead of a regression against an index

Accounting earnings or revenues, which are less noisy than market prices.

Estimate the beta for the firm from the bottom up without employing the regression technique. This will require:

Understanding the business mix of the firm

Estimating the financial leverage of the firm

Steps involved in estimating bottom-up betas

There are four steps:

Step 1:Break your company down into the businesses that it operates in. A firm like GE operates in 26 businesses but Walmart is a single business company. Do not define your business too narrowly or you will run into trouble in step 2.

Step 2:Estimate the risk (beta) of being in each business. This beta is called an asset beta or an unlevered beta.

Step 3: Take a weighted average of the unlevered betas of the businesses you are in, weighted by how much value you get from each business.

Step 4: Adjust the beta for your company's financial leverage (Debt to equity ratio)

Using beta as a measure of relative risk has its own limitations. Most analyses consider only the magnitude of beta. Beta is a statistical variable and should be considered with its statistical significance (R-Squarevalue of the regression line). HigherR-Squarevalue implies highercorrelationand a stronger relationship between returns of the asset and benchmark index

Comparable firms

While the narrow version of comparable firm defines it to be another firm in the same business that the firm is in, the broader definition of comparable firm includes any firm whose fortunes are tied to the firm's success and failure (or vice versa). i. Define comparable more broadly (all software as opposed to entertainment software).

ii. Look for global listings of companies in the same business; all entertainment companies listed globally would be an example.

iii. Look up and down the supply chain for other companies that feed

into your company and that your company feeds into. Thus, you may start looking for software retailers that get the bulk of their revenues from entertainment software.

How big a sample of firms required?

Any sample size greater than one is an improvement on a regression beta. However, the more firms that we have in the sample, the greater the potential savings in error. With a sample of 4, the standard error will be cut by half; with a sample of 9, by two-thirds; with a sample of 16, by 75%.

Its better to get to double digits for the sample size, if you can. If you cannot, settle for 6-8 firms and you are still saving a substantial amount in terms of estimation error.

There is clearly a trade-off between how tightly defining "comparable firm" and the sample size. If the comparable narrowly (firms like just like in terms of size and what they do), one will get a smaller sample. If one can get to double digits with a narrow definition, stay with it.

.After having comparable firms, how do we estimate the unlevered (asset) betas?

Simply average their regression betas and cleaning up those betas for financial leverage and cash holdings. In practical terms, here are some issues that one will face:

Do the regression betas for the comparable firms all have to be over the same time period and against the same index?

In a perfect world, YES! However, as the sample size increases, one can afford to get sloppy with these details, hoping that the law of large numbers bails you out. Thus, if we have 100 global firms in the sample, with betas estimated against local indices, one can get away using an average of these 100 betas since some are likely to be over-estimated and some under-estimated.

Once we have the regression betas for the firms, should we use simple or weighted averages?

Use simple averages. Otherwise, one will be attaching the beta of the largest firm or firms in the group to all of the firms in the sample.

Why do we need to correct for financial leverage?

The company can have a very different policy on how much debt to use than the typical firm in the sample. Regression betas are levered betas but they reflect the financial leverage of the companies in the sample (and not the company). Its necessary to take out the financial leverage effect (un-lever the beta) to come up with a pure play or business beta.

Unlevered beta = Levered Beta / (1 + (1-tax rate) D/E)

Should we un-lever each firm's beta and then average or average and then un-lever?

We prefer to average first and then un-lever. Individual firm regression betas are noisy (have large standard error) and un-levering them only compounds the noise. Averaging first should reduce the noise, leading to better beta estimates.

What tax rate and debt to equity ratio should be used for the sector?

To be safe, its better to go with a marginal tax rate and use either the median D/E ratio or the aggregate D/E ratio for the sector. (There are always strange outliers with D/E ratios that make simple averages go haywire.)

Is it possible to adjust the unlevered betas for operating leverage?

It is possible, but only if we want to know what costs are fixed and what are variable not only for the firm but for all of the firms in the sample. If we do have that information, one can break the unlevered beta down into a business component (reflecting the elasticity of demand for your company) and an operating leverage component:

Business Risk beta = Unlevered beta/ (1 +Fixed Costs/ Variable Costs)

The problem from a practical standpoint is getting the fixed and variable cost breakdown.

How do we weight these unlevered betas to arrive at the beta for the company?

The weights should be market value weights of the individual businesses that the firm operates in. However, these businesses do not trade (GE Capital does not have its own listing) and one have to estimate the market values. One can use weight based on revenues or earnings from each business but we are assuming that a dollar in revenues (earnings) has the same value in every business. An alternative is to apply a multiple of revenues (earnings) to the revenues (earnings) from each business to arrive at an estimated value. This multiple can be estimated for the comparable firms (from which we have estimated the betas). Since we are interested in the value of the business (and not the value of equity), we should look at EV multiples (and not equity multiples). If we use revenues, we have to use an EV/ Sales multiple.

How do we adjust for financial leverage?

The standard adjustment for financial leverage is to assume that debt has no market risk (a beta of zero) and to use what is called the "Hamada" adjustment:

Levered Beta = Unlevered beta (1 + (1- tax rate) (Debt/Equity))

We can use the current debt to equity ratio for the firm we are analysing or even a target debt to equity (if a feeling of change is on the horizon) in making this computation.

If we feel uncomfortable about the assumption that debt has no market risk, estimate a beta for debt and compute the levered beta as follows

Levered Beta = Unlevered Beta (1 + (1-t)*(D/E)) Beta of debt (1-t)*(D/E)

The tricky part is estimating the beta of debt.

Can bottom-up betas change over time for a company?

Yes, and for two reasons. One is that the mix of businesses can change over time, leading to a different unlevered beta. The other is that the debt to equity ratio for the firm can change over time, leading to changes in the levered beta.

Why is a bottom-up beta better than a regression beta?

Bottom up betas are better than a regression beta for three reasons

They are more precise. The standard error in a bottom-up beta estimate is more precise because you are averaging across regression betas. The savings will approximate 1/ Square root of number of firms in the sample. Thus, even if there is only one firm is the business and has not changed its debt to equity ratio over time, we will be better off using bottom up betas.

If a firm has changed its business mix, one can reflect that more easily in a bottom-up beta because you set the weights on the different businesses. A regression beta reflects past business mix choices.

If a firm has changed its debt to equity ratio, the bottom up beta can be easily adjusted to reflect those changes. A regression beta reflects past debt to equity choices.

Research Methodology

Objectives

To investigate the impact of Bottom-up Beta Analysis on Banking Index.

Methodology

Sample selection

The sample selection for this study will include all the banking companies listed on the BSE Bankex.

Hypothesis

There is positive relationship between the bankex and individual stocks; assuming certain risk associated with each security with respect to the market; and Return from all securities are equal, i.e. r1 = r2 = r3=..= r15; i.e. here as null hypothesis, as against the alternative hypothesis that all returnsare not equal.

H01: > 0 (Positive risk of overall Beta)H02: r1 = r2 = r3=..= r15 (Return from all security are equal)

Source and collection of the data

Data required was collected in the form of secondary data on fundamentalvariables from March 20012- March 2014 taken from BSE Index website for the analysis purposes.

The following fundamental variables were collected and computed (with Natural Logarithm and Regression Model):

Market prices of the stock (Close Price) Beta of Stock Daily Return on Stock Daily Return on Sensex Risk free rate Average Daily Market Return Annualised Market returns

Period of the study

The present study is an attempt to test the impact of various macro factors on the BSE BANKEX during the period from 2012 to 2014.

Tools used for analysis

In this research, linear regression model has been used to determine the explanatory power of each valuation model. A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

Tests include the estimation of linear regressions with dependent variable the bank stock price and several components of financial statements as the independent variables. For comparing the explanatory power of research models in valuing the stock of companies listed on Indian stock exchange, we use adjusted R-square of the models.

In another expression, we can show that which valuation models, results arecloser to real stock prices. To do so, different regression models must be tested. In this section, first the significance of impacts of independent variables on thedependent variable and determining R in each model will be regarded and in the second place the relative importance of each independent variable will be discussed.

The integrity of regression assumptions can be determined by considering residuals distribution and its relationships with other variables. Residuals include the difference between the observed values of a dependent variable and the predicted values by regression line. The assumptions of these models should be regarded. In regression analysis considering linearity, normality, stability of variance and independence of observations is of vital importance. In this research, these assumptions were considered, but not mentioned here for brevity.

Since in this research we intend to review 6 valuation modelsa. Levered Betab. Unlevered Betac. Cost of Equity d. Total Unlevered Betae. Levered Total Betaf. Total Cost Unlevered Betag. Debt-Equity Ratio

Individual Firms: Alpha Value, Beta Estimation, P-Value & R-SquareNameType of BankIntercept (Alpha)X - Variable (Beta)P - ValueR - Square

Axis BankPrivate Sector0.001.210.000.70

Bank of BarodaPublic Sector-0.061.100.000.53

Bank of IndiaPublic Sector-0.141.220.000.47

Canara BankPublic Sector-0.161.190.000.50

Federal BankPrivate Sector-0.340.910.000.04

HDFC BankPrivate Sector0.040.790.000.67

ICICI BankPrivate Sector0.021.120.000.81

IndusInd BankPrivate Sector0.041.100.000.61

Kotak Mahindra BankPrivate Sector0.810.810.000.54

Punjab National BankPublic Sector-0.091.120.000.56

State Bank of IndiaPublic Sector-0.060.940.000.63

Yes BankPrivate Sector-0.041.450.000.63

Note: Federal Bank has a R-Square of 0.03820428, which is quite not acceptable. This is because of Stock-Split. Debt Equity Ratio of the Firms

BanksEquityDebtRatio

Axis Bank38,220.492,80,944.577.35

Bank of Baroda35,985.585,68,894.3915.81

Bank of India29,923.084,76,974.0515.94

Canara Bank29,620.114,20,722.8214.20

Federal Bank6,860.7159,729.048.71

HDFC Bank43,478.633,67,337.488.45

ICICI Bank73,213.323,31,913.664.53

IndusInd Bank9,030.1960,502.296.70

Kotak Mahindra19,084.5456,929.752.98

PNB38,516.334,61,203.5311.97

SBI1,18,282.2513,94,408.5111.79

Yes Bank7,115.2274,185.6310.43

Average Beta, Average Debt-Equity Ratio & Average R-Square

BETADEBT EQUITY RATIOR SQUARE

Axis Bank1.2089588127.490.696258759

Bank of Baroda1.09826443415.320.534453942

Bank of India1.22047665315.950.468494047

Canara Bank1.19061660414.250.504452098

Federal Bank0.9080051058.820.038204284

HDFC Bank0.7935909298.320.670829371

ICICI Bank1.1224564.640.805553

IndusInd Bank1.0964986.90.611049

Kotak Mahindra Bank0.8083445.110.541481

Punjab National Bank1.11536500.561559

State Bank of India0.94448000.631300

Yes Bank1.45379400.629042

AVERAGE1.0800707797.2333333330.557723038

SQUARE ROOT OF AVG R SQUARE0.746808569

BETADEBT EQUITY RATIOR SQUARE

Axis Bank1.217.350.70

Bank of Baroda1.1015.810.53

Bank of India1.2215.940.47

Canara Bank1.1914.200.50

Federal Bank0.918.710.04

HDFC Bank0.798.450.67

ICICI Bank1.124.530.81

IndusInd Bank1.106.700.61

Kotak Mahindra Bank0.812.980.54

Punjab National Bank1.1211.970.56

State Bank of India0.9411.790.63

Yes Bank1.4510.430.63

AVERAGE1.089.910.56

SQUARE ROOT OF AVG R SQUARE0.75

Estimated Discounted Rates

Estimated Valuation ModelsRates

UNLEVERED BETA0.14

TOTAL UNLEVERED BETA0.18

LEVERED BETA1.08

TOTAL LEVERED BETA1.45

LEVERED COST OF CAPITAL0.11

TOTAL LEVERED COST OF CAPITAL 0.11

Note: Rates which are used for determination of the calculation of the above estimated valuation models

MARGINAL TAX RATE0.30MARKET RETURN (Rm)0.10RISK FREE RETURN (Rf)0.08RISK PREMIUM (Rm - Rf)0.02

The empirical tests that are applied to equity valuation for Banks in the examined banking sector are based on the following models: a) Levered Beta, b) Unlevered Beta, c) Cost of Equity, c) Total Unlevered Beta, d) Levered Total Beta, f) Total Cost Unlevered Beta, and g) Debt-Equity Ratio which captures the spirit of the value relevance of linear regression analysis. The valuation models are introduced and tested empirically, using the estimation method on a sample of 14 Indian bank stocks included in BSE BANKEX. These tests include the estimation of linear regressions with the various banks market price as the dependent variable and various components taken from the financial statements as independent variables. Overall, the results of the empirical analysis indicate that the linear accounting-based valuation model (EBO Model) that incorporates both stock and flow components, provides greater explanatory power and thus better captures the different aspects of equity values of bank stocks in the Indian banking sector .

SUGGESTION

A fairer way to compute alpha would be to add back a reasonable expense ratio (something in the 1.0% range) to the funds return. This seems only fair since a funds expected returns should actually be less than its benchmark, given the same risk level as the index. A funds expected returns should be less than its benchmark because an index has no expense ratio, does not factor in trading costs when securities are bought or sold, and does not provide shareholder services. This fairer way would be used when comparing a fund or ETF against its peer group. A potential shortcoming of alpha is it may not reflect management skill in selecting securities. Instead, a low alpha might simply mean the fund has high expensessomething largely beyond the control of the people selecting fund securities. A second flaw with alpha is that a positive or negative number could be the result of good or bad luck. By reviewing a funds alpha over several periods, the impact of luck becomes less and less. Remember, alpha is considered a valid measurement only if the portfolio has a high or very high R-squared number (75100).

If a lot of debt is used to finance increased operations, the company could potentially generate more earnings than it would have without this outside financing. If this were to increase earnings by a greater amount than the debt cost (interest), then the shareholders benefit as more earnings are being spread among the same amount of shareholders. However, the cost of this debt financing may outweigh the return that the company generates on the debt through investment and business activities and become too much for the company to handle. This can lead to bankruptcy, which would leave shareholders with nothing.

For a suggestion to have a more control debt-equity ratio then Optimal debt-to-equity ratio is considered to be about 1, i.e. liabilities = equity, but the ratio is very industry specific because it depends on the proportion of current and non-current assets. The more non-current the assets (as in the capital intensive industries), the more equity is required to finance these long term investments.

CONCLUSION

On an overall, the null hypothesis is accepted. After computation, out of 14 banks listed in BANKEX, 8 of them has a significance value of more than one, which represent the stock is aggressive and quite volatile. For example, YES BANK has an estimation of Beta around 1.45, indicates that the stock is 45 percent more volatile than the market beta of Sensex 1. The stated stock will deliver 14.5 percent return if the market has delivered 10 percent return in same time period. Its opposite is also true if Sensex delivers 10 percent negative return then the stated stock will fall by 14.5 percent in the same time period. A beta of less than 1 implies lesser volatility. But on an average after formulation and computation the overall return is 1.08 percent, therefore slightly volatile of 8 percent as the remaining banks are of less risky i.e., under 1.

The desirable value of beta depends upon the individual risk bearing capacity. So, one can expect a high return from a stock that has a beta of 2, but will have to expect it to drop much more when the market falls.

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%: 0% indicates that the model explains none of the variability of the response data around its mean.

100% indicates that the model explains all the variability of the response data around its mean.In general, the higher the R-squared, the better the model fits the data.

Furthermore, if R-squared value is low but have statistically significant predictors, one can still draw important conclusions about how changes in the predictor values are associated with changes in the response value. Regardless of the R-squared, the significant coefficients still represent the mean change in the response for one unit of change in the predictor while holding other predictors in the model constant. Obviously, this type of information can be extremely valuable. Such in the cases of the banks which have above 0.50 r-square value, which is meeting 50 percent of the explained variation with total variation.

Higher R-Square depends on the decision-making situation, and it depends on the objectives or needs, and it depends on how the dependent variable is defined. In some situations it might be reasonable to hope and expect to explain 99% of the variance, or equivalently 90% of the standard deviation of the dependent variable. In other cases, one might consider it to be doing very well if there is a proper explanation of 10% of the variance, or equivalently 5% of the standard deviation, or perhaps even less.

The overall debt-equity ratio is high, for BOI it is around 15.94 and overall nearly 10 %. Therefore it generally means that this sector is very aggressive in financing its growth with debt. This can result in volatile earnings as a result of the additional interest expense. Only Kotak Mahindra Bank has the lowest debt in terms of equity and similarly ICICI stands seconds in terms of lower D/E ratio.

With reference to Neha Sainis article, MEASURING THE PROFITABILITY AND PRODUCTIVITY OF BANKING INDUSTRY: A CASE STUDY OF SELECTED COMMERCIAL BANKS IN INDIA, about the profitability, there is a significant difference between the selected banks of public and private sector. And when productivity is concerned, there is no significant difference between the selected banks of public and private sector. Although both sectors show increasing trend in productivity ratios but in comparison private sector banks are having high productivity and high profitability. Public sector bank shows low productivity, the reason may be high staffing. Staff needs to be managed according tothe business and forecasting of human resource planning can be done accordingly.

Alpha is one of five technical risk ratios; the others are beta, standard deviation, R-squared, and the Sharpe ratio. These are all statistical measurements used in modern portfolio theory (MPT). All of these indicators are intended to help investors determine the risk-reward profile of a mutual fund. Simply stated, alpha is often considered to represent the value that a portfolio manager adds to or subtracts from a fund's return.

A positive alpha of 1.0 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%. Most of the Firms under BANKEX is underperforming.

If a CAPM analysis estimates that a portfolio should earn 10% based on the risk of the portfolio but the portfolio actually earns 15%, the portfolio's alpha would be 5%. This 5% is the excess return over what was predicted in the CAPM model.

The cost of equity is very difficult to estimate, partly because it as an implicit cost and partly because it varies across equity investors. For publicly traded firms, we estimate it from the perspective of the marginal investor in the equity, who we assume is well diversified. This assumption allows us to consider only the risk that cannot be diversified away as equity risk, and to measure it with a beta (in the CAPM) or betas (in the arbitrage pricing and multi-factor models). We also presented three different ways in which we can estimate the cost of equity: by entering the parameters of a risk and return model, by looking and computing at return differences across stocks over long periods, and by backing out an implied cost of equity from stock prices.

The Cost of Debt is the rate at which a firm can borrow money today and will depend on the default risk embedded in the firm. This default risk can be measured using a bond rating (if one exists) or by looking at financial ratios. In addition, the tax advantage that accrues from tax-deductible interest expenses will reduce the after tax cost of borrowing.

REFERENCES

Damodaran on Valuation :Estimating Discount Rates

Manisha Luthra and Shikha Mahajans journal (2014), The Impact of Macro Factors on BSE BANKEX,

Reddy and Prasad (2011) analyses the effect of announcements made by RBI and S&P ratings on public and private bank stocks and BANKEX respectively.

Ghosh et al. paper Determinants of BSE Sensex: A Factor Analysis Approach

Neha Sainis paper MEASURING THE PROFITABILITY AND PRODUCTIVITY OF BANKING INDUSTRY: A CASE STUDY OF SELECTED COMMERCIAL BANKS IN INDIA