No matter how diversified the investments are, it is impossible to get rid of all the risks. Investors deserve a rate of return that would offset their adoption. The Capital Asset Valuation Model (CAPM) helps calculate investment risk and expected return on investment.
Sharp's ideas
The CAPM valuation model was developed by an economist and subsequently Nobel Laureate in Economics, William Sharp, and is outlined in his 1970 book Portfolio Theory and Capital Markets. His idea begins with the fact that individual investments include two types of risks:
- Systematic. These are market risks that cannot be diversified. Their examples are interest rates, downturns and wars.
- 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. In technical terms, they are a component of exchange profits that does not correlate with general market movements.
Modern portfolio theory suggests that specific risk can be eliminated through diversification. The problem is that it still does not solve the problem of systematic risk. Even a portfolio of all stock market stocks cannot eliminate it. Therefore, in calculating fair income, systematic risk is most annoying to investors. This method is a way to measure it.
CAPM Model: Formula
Sharpe found 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 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 ) - exchange premium.
The starting point of CAPM is the risk-free rate. This is usually the yield on 10-year government bonds. A bonus to investors is added to it as compensation for the additional risk that they are taking. 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 coefficient that Sharpe called beta.
Risk measure
The only risk measure in the CAPM model is the β-index. It measures relative volatility, that is, it 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 in accordance with the market, then β a = 1. The Central Bank with β a = 1.5 will grow by 15% if the market rises by 10% and falls by 15% if it decreases by 10%.
Beta is calculated using a statistical analysis of individual daily stock returns compared to daily market returns for the same period. In their classic 1972 study, entitled “CAPM Financial Asset Valuation Model: Some Empirical Tests,” economists Fisher Black, Michael Jensen, and Myron Scholes confirmed a linear relationship between the yield of securities portfolios and their β-indices. They studied stock price movements on the New York Stock Exchange in 1931–1965.
The meaning of "beta"
Beta shows 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 excess market yield is 4% (7% - 3%). Accordingly, the excess return on shares is 8% (2 x 4%, the product of market returns and β-index), and the total required return is 11% (8% + 3%, excess return plus risk-free rate).
This indicates that risky investments should give a premium in excess of 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 assess whether the current price of a share corresponds to its probable profitability, 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 share, and not another, is its greater riskiness. Not surprisingly, this model began to dominate modern financial theory. But does it really work?
This is not entirely clear. A big stumbling block is beta. When professors Eugene Fama and Kenneth French examined the profitability of stocks on the New York and American stock exchanges, as well as NASDAQ in 1963-1990, they found that differences in β-indices over such a long period did not explain the behavior of different securities. A linear relationship between the beta coefficient and individual stock returns for short periods of time is not respected. The data obtained suggest that the CAPM model may be erroneous.
Popular tool
Despite this, the method is still widely used in the investment community. Although the β-index makes it difficult to predict how individual stocks will respond 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, but 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 stocks 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 grows, and with β a <1 when it falls.
Unsurprisingly, CAPM has contributed to the increased use of indexation to create a portfolio of stocks that mimic a specific market by those who seek to minimize risks. This is largely due to the fact that, according to the model, it is possible to get a higher profitability than the market as a whole by taking a higher risk.
Imperfect but correct
The financial asset return model (CAPM) is by no means a perfect theory. But her spirit is true. It helps investors determine how much they deserve for risking their money.
Preconditions of capital market theory
The basic assumptions include the following assumptions:
- All investors are inherently risk averse.
- They have the same amount of time to evaluate information.
- There is unlimited capital that can be borrowed at a risk-free rate of return.
- Investments can be divided into an unlimited number of parts of unlimited size.
- No taxes, inflation, or transaction costs.
Because of these assumptions, investors choose portfolios with minimized risks and maximum returns.
From the very beginning, these assumptions were treated as unrealistic. How could conclusions from this theory have at least some significance under such assumptions? Although they themselves can easily be the cause of incorrect results, introducing the model has also proved to be a difficult task.
CAPM criticism
In 1977, a study conducted by Imbarin Bujang and Annuar Nassir, breached the theory gap. Economists sorted stocks by the ratio of net profit to price. According to the results, securities with a higher rate of return, as a rule, yielded more profit than the CAPM model predicted. Another evidence not in favor of the theory appeared a few years later (including the work of Rolf Banz 1981), when the so-called size effect was discovered. The study found that small market-cap stocks performed better than CAPM predicted.
Other calculations were also carried out, the general theme of which was that 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 price of a share 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 can be found in a 2004 work by Peter Chang, Herb Johnson, and Michael Schill, which analyzed the use of the 1995 Fam and French CAPM model. They found that stocks with a low price-to-book value ratio, as a rule, belong to companies that have recently had not very outstanding results and may be temporarily unpopular and cheap. On the other hand, companies with a higher than market ratio may temporarily be revalued, as they are in the growth stage.
The sorting of firms by indicators such as the ratio of price to book value or to profitability revealed a subjective reaction by investors, which tends to be very good during growth and overly negative during recession.
Investors also tend to overestimate past performance, which leads to overpricing the stock prices of companies with a high price-earnings ratio (rising) and too low for companies with a low ratio (low). After the cycle ends, the results often show higher returns for cheap securities and lower returns for growing ones.
Replacement attempts
Attempts have been made to create a better assessment method. The 1973 Merton Intertemporal Asset Pricing Model (ICAPM), for example, is a continuation of CAPM. It is distinguished by the use of other prerequisites for the formation of the goal of capital investment. At CAPM, investors only care about the wealth that their portfolios generate at the end of the current period. At ICAPM, they are worried not only about recurring earnings, but also about the opportunities to consume or invest profits.
When choosing a portfolio at time point (t1), ICAPM investors study how their wealth at time t may depend on variables such as labor income, consumer prices and the nature of the portfolio. Although ICAPM was a good attempt to solve the shortcomings of CAPM, it also had its limitations.
Too unreal
Although the CAPM model is still one of the most widely studied and accepted, its premises were criticized from the very beginning as too unrealistic for investors in the real world. Empirical studies of the method are conducted from time to time.
Factors such as size, various ratios and price impulse clearly indicate the imperfection of the model. In doing so, too many other asset classes are ignored so that it can be considered a viable option.
It is strange that so much research is being done to refute the CAPM model as a standard theory of market pricing, and no one today seems to support the model for which the Nobel Prize was awarded.