We all use the term Beta quite frequently in the stock markets saying that stock X has a beta of more than 1 or stock Y has a beta of less than 1. Let us look at what this concept of Beta is all about?

Beta

Risk is an important consideration in holding any portfolio. The risk in holding securities is generally associated with the possibility that realised returns will be less than the returns expected. Risks can be classified as Systematic risks and Unsystematic risks.

· Unsystematic risks

These are risks that are unique to a firm or industry. Factors such as management capability, consumer preferences, labour, etc. contribute to unsystematic risks. Unsystematic risks are controllable by nature and can be considerably reduced by sufficiently diversifying one's portfolio.

· Systematic risks

These are risks associated with the economic, political, sociological and other macro-level changes. They impact the entire market as a whole and cannot be controlled or eliminated merely by diversifying one's portfolio.

What exactly is Beta?

The extent to which different portfolios are affected by these systematic risks as compared to the effect on the market as a whole is different and is measured by Beta. To put it differently, the systematic risks of various securities differ due to their relationships with the market. The Beta factor describes the movement in a stock's or a portfolio returns in relation to that of the market returns. For all practical purposes, the market returns are measured by the returns on the index (Nifty, Sensex, Mid-cap etc.). The assumption is that the index is a good reflector of the market.

Methodology / Formula

Beta is calculated as:

Covariance (X,Y) / Variance ((X)

where,

Y is the returns on your portfolio or stock - DEPENDENT VARIABLE

X is the market returns or index - INDEPENDENT VARIABLE

Variance is the square of standard deviation.

Covariance is a statistic that measures how two variables co-vary, and is given by:

Total Returns Index

What exactly do we understand by Total Returns Index? Most of the regular indices are price indices and hence reflect the returns one would earn if investment is made in the index portfolio. However, a price index does not consider the returns arising from dividend receipts. Only capital gains arising due to price movements of constituent stocks are indicated in a price index. Therefore, to get a true picture of returns, the dividends received from the constituent stocks also need to be factored in the index values. Such an index, which includes the dividends received, is called the Total Returns Index. Total Returns Index reflects the returns on the index arising from (a) constituent stock price movements and (b) dividend receipts from constituent index stocks.

Methodology for Total Returns Index (TR) is as follows

The following information is a prerequisite for calculation of TR Index:

· Price Index close

· Price Index returns

· Dividend payouts in Rupees

· Index Base capitalisation on ex-dividend date

Dividend payouts as they occur are indexed on ex-date.

First calculate Indexed Dividend as under:

Indexed Dividend = Dividend Payout / Base capitalization of the Index

Indexed dividends are then reinvested in the index to give TR Index.

Base for both the Price index close and TR index close will be the same. An investor in index stocks should benchmark his investments against the Total Returns index instead of the price index to determine the actual returns versus the index

Investible Weight Factors (IWFs)

Free float methodology is globally regarded as an ideal methodology for calculation of equity indices. As per this methodology, free-float market capitalization of all index constituents is considered for calculation of the index. Free-float market capitalization of the index constituents is derived by applying IWFs on full market capitalization of respective companies in the index. This approach aims to limits the influence of a particular company in the index to the extent of its actual free float and reduces influence of large promoter/ strategic holding (which generally is not available for trading) on the index, thus making it truly investable.

Free float methodology in index calculation aids both active and passive investment strategies. Active managers are able to compare their portfolio return vis-à-vis the investable index and at the same time passive fund managers are able to offer low tracking error by introducing passive funds such as index funds, exchange traded funds linked to investable indices calculated based on free-float methodology.

IWF as the term suggests is a unit of floating stock expressed in terms of a number available for trading and which is not held by the entities having strategic interest in a company. Higher IWF suggest greater number of shares held by the investors as reported under public category within a shareholding pattern reported by each company.

The IWFs for each company in the index are determined based on the public shareholding of the companies as disclosed in the shareholding pattern submitted to the stock exchanges on quarterly basis.

The following categories are excluded from the free float factor where identifiable separately:

· Shareholding of promoter and promoter group

· Government holding in the capacity of strategic investor

· Shares held by promoters through ADR/GDRs.

· Strategic stakes by corporate bodies

· Investments under FDI category

· Equity held by associate/group companies (cross-holdings)

· Employee Welfare Trusts

· Shares under lock-in category

Take the case of XYZ Ltd with total outstanding paid up share capital of 1 crore shares

Shares

%

Shareholding of promoter and promoter group

19,75,000

19.75

Government holding in the capacity of strategic investor

50,000

0.50

Shares held by promoters through ADR/GDRs.

2,50,000

2.50

Equity held by associate/group companies (cross-holdings)

12,575

0.13

Employee Welfare Trusts

1,45,987

1.46

Shares under lock-in category

14,78,500

14.79

Now let us look at how the IWF is calculated?

IWF = [1,00,00,000 – (19,75,000 + 50,000 +2,50,000 +12,575 +1,45,987 +14,78,500)] / 1,00,00,000

= 0.61 or 61%. That will be the free float considered for the index weighting.