CAPM model: calculation formula

2024 Author: Howard Calhoun | [email protected]. Last modified: 2024-01-02 13:48

No matter how diversified an investment is, it is impossible to get rid of all the risks. Investors deserve a rate of return to compensate for their acceptance. The Capital Asset Pricing Model (CAPM) helps calculate investment risk and expected return on investment.

Sharpe's Ideas

The CAPM valuation model was developed by the economist and later Nobel Laureate in Economics William Sharp and outlined in his 1970 book Portfolio Theory and Capital Markets. His idea begins with the fact that individual investments involve two types of risks:

1. Systematic. These are market risks that cannot be diversified. Examples are interest rates, recessions and wars.
2. Unsystematic. Also known as specific. They are specific to individual stocks and can be diversified by increasing the number of securities in the investment portfolio. Technically speaking, they represent a component of stock exchange earnings that is not correlated with overall market movements.

Modern portfolio theory says thatthat specific risk can be eliminated through diversification. The problem is that it still doesn't solve the problem of systematic risk. Even a portfolio consisting of all stocks in the stock market cannot eliminate it. Therefore, when calculating a fair return, systematic risk annoys investors the most. This method is a way to measure it.

CAPM Model: formula

Sharpe discovered that the return on a single 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 the value of the security (the ratio of its risk to the risk in the market as a whole), r_m – expected return, (r_m - r _{f) – exchange premium.}

The starting point of CAPM is the risk-free rate. This is typically the yield on 10-year government bonds. Added to this is a premium to investors as compensation for the extra risk they take. It consists of the expected return from the market as a whole minus the risk-free rate of return. The risk premium is multiplied by a factor that Sharp called "beta".

Risk measure

The only measure of risk in the CAPM model is the β-index. It measures relative volatility, meaning how much the price of a particular stock fluctuates up and down.compared to the stock market as a whole. If it moves exactly in line with the market, then β_a =1. A central bank with β_{a=1.5 will rise by 15% if the market rises 10%, and falls 15% if it falls 10%.}

"Beta" is calculated using a statistical analysis of individual daily stock returns compared to daily market returns over the same period. In their classic 1972 study, The CAPM Financial Asset Pricing Model: Some Empirical Tests, economists Fisher Black, Michael Jensen, and Myron Scholes confirmed a linear relationship between the returns of security portfolios and their β-indices. They studied stock price movements on the New York Stock Exchange from 1931 to 1965.

The meaning of "beta"

"Beta" indicates the amount of compensation that investors should receive for taking on additional risk. If β=2, the risk-free rate is 3% and the market rate of return is 7%, the market's excess return is 4% (7% - 3%). Accordingly, the excess return on stocks is 8% (2 x 4%, the product of the market return and the β-index), and the total required return is 11% (8% + 3%, excess return plus the risk-free rate).

This indicates that risky investments should provide 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 quite possible, knowing the individual parts of the model, to estimate whether it corresponds towhether the current share price is likely to be profitable, that is, whether the investment 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 an investor will earn more by buying one stock and not another is because it is more risky. Not surprisingly, this model has come to dominate 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 examined the performance of stocks on the New York Stock Exchange, the US Stock Exchange, and the NASDAQ from 1963 to 1990, they found that differences in β indices over such a long period did not explain the behavior of different securities. There is no linear relationship between beta and individual stock returns over short periods of time. The findings suggest that the CAPM model may be wrong.

Popular tool

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

This is especially important for managersfunds because they may not be willing (or allowed) to hold onto money if they feel the market is likely to fall. In this case, they can hold stocks with a low β-index. Investors can build a portfolio according to their specific risk and return requirements, looking to buy at β_a > 1 when the market is up and at β_{a < 1 when it falls.}

Unsurprisingly, the CAPM has fueled the growth in the use of indexation to build stock portfolios that mimic a particular market, by those seeking to minimize risk. This is largely due to the fact that, according to the model, you can get a higher return than in the market as a whole by taking a higher risk.

Imperfect but right

The CAPM is by no means a perfect theory. But her spirit is true. It helps investors determine how much return they deserve for risking their money.

Premises of capital market theory

The basic theory includes the following assumptions:

• All investors are inherently risk averse.
• They have the same amount of time to evaluate the information.
• There is unlimited capital available to borrow at a risk-free rate of return.
• Investments can be divided into an unlimited number of parts of an unlimited size.
• No taxes, inflation and operatingcosts.

Because of these assumptions, investors choose portfolios with minimized risks and maximum returns.

From the beginning, these assumptions were treated as unrealistic. How could the conclusions of this theory have any meaning under such premises? While they can easily cause misleading results on their own, implementing the model has proven to be a difficult task as well.

Criticism of CAPM

In 1977, a study by Imbarin Bujang and Annoir Nassir made a hole in the theory. Economists have sorted stocks by net income to price ratio. According to the results, securities with higher yield ratios tended to generate more returns than the CAPM model predicted. Another piece of evidence against the theory came a few years later (including the work of Rolf Banz in 1981) when the so-called size effect was discovered. The study found that small-cap stocks performed better than CAPM predicted.

Other calculations were made, the common theme of which was that the financials so carefully monitored by analysts actually contain certain forward-looking information that is not fully captured by the β-index. After all, the price of a share is only the present value of future cash flows in the form of earnings.

Possible explanations

So why, with so many studies attackingvalidity of CAPM, is the method still widely used, studied and accepted worldwide? One possible explanation can be found in a 2004 paper by Peter Chang, Herb Johnson, and Michael Schill that analyzed the use of the 1995 Pham and French CAPM model. They found that stocks with low price-to-book ratios tend to be owned by companies that have not performed very well recently and may be temporarily unpopular and cheap. On the other hand, companies with a higher than market ratio may be temporarily overvalued as they are in a growth phase.

Sorting firms by price-to-book value or earnings-to-earnings reveals subjective investor responses that tend to be very good during upswings and overly negative during downswings.

Investors also tend to overestimate past performance, leading stocks of high price-to-earnings (rising) stocks to high prices and low (cheap) firms too low. Once the cycle is complete, the results often show higher returns for cheap stocks and lower returns for rising stocks.

Replacement attempts

Efforts have been made to create a better evaluation method. Merton's 1973 Intertemporal Financial Asset Value Model (ICAPM), for example, is an extension of CAPM. It is distinguished by the use of other prerequisites for the formation of the purpose of capital investment. At CAPM, investors only care aboutthe we alth their portfolios are generating at the end of the current period. At ICAPM, they are concerned not only with recurring returns, but also with the ability to consume or invest the profits.

When choosing a portfolio at time (t1), ICAPM investors study how their we alth at time t might be affected by variables such as earnings, consumer prices, and the nature of the portfolio's opportunities. While ICAPM was a good attempt to address the shortcomings of CAPM, it also had its limitations.

Too unreal

While the CAPM model is still one of the most widely studied and accepted, its premises have been criticized from the outset as too unrealistic for real-world investors. Empirical studies of the method are conducted from time to time.

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

It is strange that so much research is being done to disprove the CAPM model as the standard theory of market pricing, and no one today seems to support the model that was awarded the Nobel Prize.