How is Beta Calculated?
Beta is a measure of volatility or systematic risk or a security or a portfolio compared to the market as a
whole. The market can be considered as an indicative market index or a basket of universal assets.
If Beta = 1, then the stock has the same level of risk as to the market. A higher beta, i.e., greater than 1,
represents a riskier asset than the market, and beta less than 1 represents risk less than the market.
Capital Asset Pricing Model: CAPM
Many techniques are available to estimate expected rate of return but most of them yield results which
are not accurate and reliable. The large errors in estimation make these techniques redundant or not
very useful for the purpose of portfolio optimization.
One of the techniques traditionally used for estimating expected returns is Capital Asset Pricing Model
or popularly known as ‘CAPM’.
CAPM is an important financial management concept that was developed by economists John Lintner,
Jack Treynor, William Sharpe etc. It is an extension of Markowitz’s diversification theory. It represents
linear relationship between required rate of return and systemic risk involved and this relationship is
represented in the following equation:
ERi = Rf + (Rm – Rf) βi
Where,
ERi = Expected return of a security or a portfolio ‘i’
Rf = Risk free rate of return
Rm = Expected return on market portfolio M.
βi = Beta of the security or a portfolio ‘i’
Rm – Rf = Market Risk Premium
Hence, effectively, CAPM considers equity risk premium, that is rate of return of the asset that is in
excess of the average return provided by the market. Further, this equity risk premium is adjusted for
the systematic risk present by considering the beta value. Beta value is nothing but
the correlation of the asset with the market. Further, the risk free rate of return is added to arrive at the
expected rate of return. Risk free rate of return is nothing but the rate of return available on short term
Bonds/Treasury Bills.
ASSUMPTIONS & CRITICISM OF CAPM
Once the assumptions of CAPM are discussed, the criticism itself will become quite clear. The following
are the main assumptions used for CAPM
1. The model assumes that the unsystematic risk can be completely eliminated through diversification in
the portfolio. It also assumes that the investor holds diversified portfolio.
2. In order to get comparable data for risk free rate of return, average rate of return in the market and
beta value, the CAPM model assumes single-period horizon for all transactions. Typically, one year
period is utilized for calculating all the inputs, although this period can be changed basis requirement.
3. The model assumes that all investors have access and knowledge of the risk free rate of return
available in the market and that they will borrow or lend in risk free it.
4. The CAPM model also assumes perfect capital market, that is, there are no transaction costs or taxes
and that all the information available is correct and can be plotted easily. Further, all of this information
is easily accessible to the investors.
Looking at the above assumptions, it is clear that while these assumptions may be necessary to create a
theoretical framework and a model, they are definitely not something that will be available in real world
market scenario where there are many hurdles such as, taxes, transaction cost, availability of
information to investors, free trading of investments, etc. Another assumption of investor holding a
diversified portfolio is difficult to envisage in the real world environment as it is not necessary that every
investor will want to replicate the entire market in the asset portfolio held by him. Another major
criticism is that not every investor can borrow and lend money at the risk free rate of return in the real
world. The rate of lending and borrowing differ, especially so for individual investors where rate of
borrowing is much higher than the risk free rate of return in the market. Despite all the criticism, CAPM
remains one of the most popular and widely used methods for calculating the expected rate of return.
Many methods were used instead of CAPM, however, CAPM still remains a favourite.
In fact, the utilization of CAPM in the investment management industry and corporate finance world has
become quire advanced and sophisticated. Further, it is used parallel with other techniques and
methods such that the results can be validated and outliers can be identified and rectified.
CAPM remains popular as it accounts for only systemic risk that cannot be diversified and also provides
the information in a standard and clear format. Further, in past 50 years, CAPM has been subjected to
frequent empirical testing and it has withstood the results. The method is also widely used to calculate
cost of equity as it accounts for systemic risk. Hence, it is superior to the dividend growth model also.
