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CAPM (Capital Asset Pricing Model) calculator, CML (Capital Market Line) form - valuation of capital assets


The CAPM calculator can be used to calculate the cost of equity, to evaluate the investment effectiveness of collective investment funds (open-end investment funds, pension funds, etc.), to study the efficiency of the stock market, etc.
The CAPM model allows to illustrate the relationship between the incurred systematic risk, otherwise known as market or non-diversifiable risk, and the expected rate of return.

The CAPM calculator in the form of CML allows you to calculate the expected rate of return from the so-called the effective portfolio (on the border of Markowitz's effective portfolios).



CAPM (capital asset pricing model) CML form - valuation of capital assets



Risk-free rate Rf =
Expected return of investment Rm =
Standard deviation of portfolio returns SX =
Standard deviation of market returns SM =











Useful information CAPM (capital asset pricing model) – a model that shows the relationship between the incurred systematic risk, otherwise known as market or non-diversifiable risk, and the expected rate of return. The CAPM model is used to calculate the cost of equity, to evaluate the investment efficiency of collective investment funds (open-end investment funds, pension funds, etc.), to study the efficiency of the stock market, etc.

The model was independently developed by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966), based on earlier work by Harry Markowitz on investment portfolio diversification. Sharpe, Markowitz and Merton Miller were jointly awarded the Nobel Prize in Economics in 1990 for their contribution to the development of the financial economy.

The CAPM model has two forms. The first is the CML (Capital Market Line) equation:
$$\displaystyle R=R_{f}+{\frac {s_{X}}{s_{M}}}(R_{m}-R_{f})\displaystyle R=R_{f}+{\frac {s_{X}}{s_{M}}}(R_{m}-R_{f})$$
where:
sX – standard deviation of portfolio returns "X",
sM – standard deviation of market returns "M".

This form is a formula for the expected rate of return from the so-called the effective portfolio (on the border of Markowitz's effective portfolios).

The second figure applies to all portfolios, not only effective ones, but also individual stocks. This is the SML (security market line) equation:
$$\displaystyle R=R_{f}+\beta \cdot (R_{m}-R_{f})\displaystyle R=R_{f}+\beta \cdot (R_{m}-R_{f})$$
where:
R – expected return of investment
Rf – risk-free rate (usually the rate of return on government securities)
Rm – market return rate
β – beta of the investment (ratio determining the share of the risk of a given security in the market risk).

The risk-free rate is the rate of return on bonds or treasury bills, as the assumption is that the state cannot be insolvent. The rate of return on the market is, for example, the rate of return on a stock index. As for Beta, this ratio is calculated by brokerage houses, the calculation of this ratio itself is quite complicated, as it is the quotient of the covariance of rates of return on the "X" security and the market portfolio M to the variance of the rates of return on the market portfolio.

The CAPM is based on a number of assumptions:
  • The financial market is in equilibrium
  • Investors have a square utility function or the return distribution is normal
  • The variance of the returns is an appropriate measure of risk
  • The model covers one period in which the model parameters remain unchanged
  • The market covers all assets, including human capital










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