CAPM model: calculation formula

Regardless of how diversified investments are, it is impossible to get rid of all risks. Investors deserve a rate of profit that would compensate for their adoption. The capital asset valuation model (CAPM) helps to calculate the investment risk and the expected return on investment.

Sharpe's Ideas

The CAPM evaluation model was developed by the economist, and later by the Nobel Prize winner in economics, William Sharpe, and is set out in his 1970 book Portfolio Theory and Capital Markets. His idea begins with the fact that individual investments include two types of risks:

1. Systematic. These are market risks that can not be diversified. Their examples are interest rates, recessions and wars.
2. Non-systematic. Also known as specific. They are specific for individual stocks and can be diversified by increasing the number of securities in the investment portfolio. Technically speaking, they are a component of the exchange profit, which does not correlate with the general market movements.

Modern portfolio theory suggests that a specific risk can be eliminated through diversification. The problem is that it still does not solve the problem of systematic risk. Even a portfolio consisting of all stock market shares can not eliminate it. Therefore, when calculating a fair income, the systematic risk most bothers investors. This method is a way to measure it.

Model CAPM: formula

Sharpe found that the return on a particular stock or portfolio should equal the cost of raising capital. The standard calculation of the CAPM model describes the relationship between risk and expected return:

R _a = r _f + β _a (r _m - r _f ), where r _f is the risk-free rate, β _a is the beta value of the security (the ratio of its risk to risk in the market as a whole), r _m is the expected yield, ( R _m - r _f ) is an exchange premium.

The starting point of CAPM is the risk-free rate. This is, as a rule, the yield of 10-year government bonds. To it, a premium is added to investors as compensation for the additional risk that they are incurring. It consists of the expected profit from the market as a whole, minus the risk-free rate of return. The risk premium is multiplied by a factor that Sharpe called "beta."

Risk measure

The only measure of risk in the CAPM model is the β-index. It measures relative volatility, that is, shows how much the price of a particular stock fluctuates up and down compared to the stock market as a whole. If it moves exactly according to the market, then β _a = 1. The CB with β _a = 1.5 will grow by 15% if the market rises by 10% and falls by 15% if it drops by 10%.

"Beta" is calculated using a statistical analysis of individual daily indicators of the return on shares compared with the daily market return for the same period. In his 1972 classic study, "CAPM Financial Asset Valuation Model: Some Empirical Tests," economists Fisher Black, Michael Jensen, and Myron Scholes confirmed the linear relationship between yields of securities portfolios and their β-indices. They studied the price movements of shares on the New York Stock Exchange in 1931-1965.

The meaning of "beta"

"Beta" shows the amount of compensation that investors must receive for assuming additional risk. If β = 2, the risk-free rate is 3%, and the market rate of return is 7%, the excess market yield is 4% (7% - 3%). Accordingly, the excess return on shares is 8% (2 x 4%, the product of the market yield and the β-index), and the total required return is 11% (8% + 3%, excess yield plus risk-free rate).

This shows that risky investments should give a premium over the risk-free rate - this amount is calculated by multiplying the premium of the securities market by its β-index. In other words, it is entirely possible, knowing the individual parts of the model, to assess whether the current price of a share is its probable profitability, that is whether the investment of capital is profitable or too expensive.

What does CAPM mean?

This model is very simple and provides a simple result. According to her, the only reason for the investor to earn more, buying one share, and not another, is her greater risk. Not surprisingly, this model began to dominate the modern financial theory. But does it really work?

This is not entirely clear. The big stumbling block is "beta". When professors Eugene Fama and Kenneth French investigated the profitability of shares on the New York and American stock exchanges, as well as NASDAQ in 1963-1990, they found that differences in β-indices during such a long period did not explain the behavior of different securities. Linear dependence between the coefficient of "beta" and individual profitability of shares for short periods of time is not observed. The data obtained suggest that the CAPM model may be erroneous.

A popular tool

Despite this, the method is still widely used in the investment community. Although it is difficult to predict by the β-index how individual stocks will react to certain market movements, investors can probably safely conclude that a portfolio with a high "beta" will move more strongly than the market in any direction, and with a low Will fluctuate less.

This is especially important for fund managers, because they may not want (or may not be allowed to) hold money if they feel that the market is likely to fall. In this case, they can hold shares with a low β-index. Investors can form a portfolio in accordance with their specific requirements for risk and profitability, seeking to buy securities with β _a > 1 when the market is growing, and with β _a <1, when it falls.

Not surprisingly, CAPM helped to increase the use of indexation to form a portfolio of shares that mimics a particular market, those who seek to minimize risks. This is largely due to the fact that, according to the model, you can get a higher yield than the market as a whole, by going to a higher risk.

Imperfect but correct

The CAPM model is by no means a perfect theory. But her spirit is true. It helps investors to determine what profit they deserve for risking their money.

Prerequisites of the capital market theory

The basic theory includes the following assumptions:

• All investors are inherently prone to avoid risk.
• They have the same amount of time to evaluate the information.
• There is unlimited capital, which can be borrowed at a risk-free rate of return.
• Investments can be divided into an unlimited number of parts of unlimited size.
• There are no taxes, inflation and transaction costs.

Because of these prerequisites, investors choose portfolios with minimized risks and maximum yield.

From the very beginning, these assumptions were treated as unrealistic. How could the conclusions from this theory have any meaning at all under such assumptions? Although they themselves can easily cause incorrect results, the introduction of the model has also proved to be a difficult task.

Criticism of CAPM

In 1977, a study conducted by Imbaran Bujang and Annuar Nassir, broke the gap in theory. Economists sorted the shares by the ratio of net profit to price. According to the results obtained, securities with a higher rate of return, as a rule, yielded more profit than predicted by the CAPM model. Another evidence not in favor of the theory appeared in a few years (including the work of Rolf Bantz 1981), when the so-called size effect was discovered. The study showed that small market capitalization shares behaved better than predicted by CAPM.

Other calculations were carried out, the general theme of which was that the financial indicators so carefully monitored by analysts actually contain certain prognostic information that is not fully reflected by the β-index. In the end, the stock price is only the discounted value of future cash flows in the form of profit.

Possible explanations

So why, with so many studies attacking the validity of CAPM, is the method still widely used, studied and accepted around the world? One possible explanation may be found in the work of 2004 by authors Peter Chang, Herb Johnson and Michael Shill, in which the analysis of the use of the CAPM model by Fam and French was carried out in 1995. They found that stocks with a low price-to-book ratio tend to belong to companies that have recently had not very outstanding results and, perhaps, are temporarily unpopular and cheap. On the other hand, companies with a higher than market ratio may temporarily be overvalued, as they are in the growth stage.

Sorting firms by such indicators as the ratio of price to book value or to profitability, revealed a subjective reaction of investors, which tends to be very good during growth and excessively negative in the recession.

Investors also tend to overestimate past results, which leads to overvaluation of prices for shares of companies with a high ratio of prices to profits (rising) and too low in enterprises with low (cheap). After the completion of the cycle, the results often show higher yields for cheap securities and lower for growing ones.

Attempts to replace

Attempts were made to create a better method of evaluation. The Intertemporal Model for Determining the Value of Merton's Financial Assets (ICAPM) of 1973, for example, is a continuation of CAPM. It is distinguished by the use of other prerequisites for the formation of the purpose of investing capital. In CAPM, investors care only about the wealth that generates their portfolios at the end of the current period. In ICAPM, they are concerned not only with recurring incomes, but also with the ability to consume or invest their profits.

When choosing a portfolio at a time point (t1), ICAPM investors study how their wealth at time t can depend on variables such as labor earnings, consumer prices, and the nature of the portfolio's capabilities. Although ICAPM was a good attempt to solve the shortcomings of CAPM, it also had its limitations.

Too unrealistic

Although the CAPM model is still one of the most widely studied and accepted, its prerequisites have been criticized from the very beginning as too unrealistic for investors in the real world. From time to time, empirical studies of the method are carried out.

Factors such as size, different ratios and price momentum clearly indicate the imperfection of the model. It ignores too many other asset classes so that it can be considered a viable option.

It's strange that so many studies are being conducted to disprove the CAPM model as a standard theory of market pricing, and no one seems to support the model for which the Nobel Prize was awarded.