# Introduction to Capital asset pricing model (CAPM)

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The capital asset pricing model (CAPM) is a model frequently used in financial economics to
determine the rate of return required for a particular asset when added to a well diversified
investment portfolio.

The model takes into account the sensitivity of the asset to non-diversifiable risk (also known as
market risk or systematic risk). As well as expected market return and the expected return of a
theoretically risk-free asset.

The model was introduced by Jack L. Treynor, William Sharpe, John Litner and Jan Mossin
based on earlier work of Harry Markowitz on diversification and modern portfolio theory.

The fundamental problem stems from the fact that these theories are based on the normal
distribution (Gaussian law or bell curve). Which greatly underestimates the events as crises or
crashes. An additional problem is that the assumptions on which these theories are based are
not very realistic (the rationality of investors included).

CAPM is a model to calculate the price of an asset or a portfolio of investments. For individual
assets, it makes use of the security market line (SML) which represents the expected return on
all assets in a market as a function of non-diversifiable risk. Including its relation to the expected
return and systematic risk (beta ) to show how the market should estimate the price of an
individual asset in relation to its class.

SML line is also used to calculate the proportion of reward-to-risk ratio for any asset in relation
to the overall market. The equilibrium that describes the CAPM is: E (R_i) = r_f + \ beta_ (im) (E
(R_M) - r_f) \, where: E (ri) is the expected rate of return of capital on the asset.

While (im) is the beta (amount of risk with respect to the market portfolio), or \ Beta_ (im) = \ frac
(Cov (R_i, R_M)) (Var (R_M)) \,.

E (rm - rf) is the excess return of market portfolio, (Rm) market performance and (Rf)
performance of a risk-free asset.

It is important to note that this is a beta unlevered, that is, it is assumed that if a company has
no debt in its capital structure, it therefore does not bear incorporated financial risk.

Once the expected return, E (Ri) is calculated using CAPM, the future cash flows that will
produce that asset can be discounted to their present value using this rate, in order to determine
the appropriate price of assets or securities .

In theory, an asset is properly appreciated when observed price is equal to the value calculated
using CAPM. If the price is higher than the valuation obtained, the asset is overvalued, and vice
versa.

CAPM calculates the appropriate rate of return required to produce an asset, given the risk
assessment. Beta greater than one symbolizes that the asset has a higher than average risk,
while beta below one indicates a lower risk. Therefore, an asset with a high beta should be
discounted at a higher rate as a means of rewarding the investor for taking the risk that the
asset creates.
The risk in a portfolio includes systemic risk, also known as non-diversifiable risk. This risk
refers to the risk which all assets in a market are exposed to. By contrast, the diversifiable risk is
intrinsic to each individual asset. Diversifiable risk can be reduced by adding assets to the
portfolio so they can mitigate each other. However, systemic risk can not be diminished.

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