The capital asset pricing model – CAPM for short – is a model that explains price formation on stock markets. It was developedby William F. Sharpe and others in the 1960s. It is based on the portfolio theory developed a decade earlier by Harry M. Markowitz. Until today, the CAPM is considered a trend-setter for the market-compliant valuation of securities.
In contrast to other equilibrium models in economics, which explain the price as a dependency on supply and demand, the CAPM relates the yield – as the price for a securities investment – to the (market) risk. In this sense, it is a one-dimensional explanatory model. By now, there are several further developments, such as the three-factor model by Fama/French, which also takes other influencing variables into account. However, those models usually only represent a refined verison of the CAPM.
Some ideal-typical assumptions
Like many models in economics, the CAPM is based on ideal-typical assumptions in order to be able to derive its statements. These include in particular
- the existence of a complete capital market
- normally distributed returns on securities;
- homogeneous investor expectations;
- risk aversion – i.e. for two investment alternatives with the same expected return but different risk, investors always prefer the lower-risk option.
The model further assumes that there is a risk-free investment option in addition to risky securities investments. In reality, these could for example be short-term government bonds with a first-class solvency.
Ideal market portfolio in a market equilibrium
The idea of the CAPM is that there is an ideal market portfolio in a market equilibrium in which all traded securities are included according to their relation to the market risk and are “correctly” valued. Investors then hold a combination of the risk-free investment and the market portfolio according to their personal risk propensity or aversion. The yields that can be achieved with different combinations depending on the market risk can be shown graphically with the help of the capital market line.
The valuation of an individual security
The valuation of an individual security is then based on the relationship between the individual security risk and the general market risk using the following formula:
ERi = Rf + ? X (ERm – Rf)
ERi = expected return of the security
Rf = return on risk-free investment
ERm = expected return of the market portfolio
? = Beta factor
This correlation can also be represented graphically via the so-called security market line.
The formula can be interpreted as follows: if the valuation is in line with the market, the expected return on a security is composed of the interest rate for risk-free investments plus an individual risk premium for each security. This risk premium is determined on the one hand by the risk premium for the general market risk (ERm – Rf) and on the other hand by the so-called Beta factor ?. It is security-dependent and reflects the extent of the statistical correlation between the securities risk and the general market risk. Only the so-called systematic risk is taken into account in the Beta factor; the so-called unsystematic risk, on the other hand, can be eliminated by portfolio diversification and is therefore not compensated via the market. The higher the beta factor, the higher the risk premium. The risk-free investment has a ? of zero, the market portfolio a ? of one.
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