# Capital Asset Pricing Model (CAPM)

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## Valuing stocks, securities, derivatives and/or assets by relating risk and expected return. Explanation of Capital Asset Pricing Model (CAPM) of William Sharpe.

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The Capital Asset Pricing Model (CAPM) is an economic model for valuing stocks, securities, derivatives and/or assets by relating risk and expected return. CAPM is based on the idea that investors demand additional expected return (called the risk premium) if they are asked to accept additional risk.

### Description of CAPM. The Capital Asset Pricing Model is explained.

CAPM was introduced by Treynor ('61), Sharpe ('64) and Lintner ('65). By introducing the notions of systematic and specific risk, it extended the portfolio theory. In 1990, William Sharpe was Nobel price winner for Economics. "For his contributions to the theory of price formation for financial assets, the so-called Capital Asset Pricing Model (CAPM)."

The CAPM model says that the expected return that the investors will demand, is equal to: the rate on a risk-free security plus a risk premium. If the expected return is not equal to or higher than the required return, the investors will refuse to invest and the investment should not be undertaken.

CAPM decomposes a portfolio's risk into systematic risk and specific risk. Systematic risk is the risk of holding the market portfolio. When the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique for an individual asset. It represents the component of an asset's return which is not correlated with general market moves.

According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk. But through diversification, the investor's net exposure is just the systematic risk of the market portfolio.

### CAPM formula

The CAPM formula is:

Expected Security Return = Riskless Return + Beta x (Expected Market Risk Premium)

or:
r = Rf + Beta x (RM - Rf)

{      Another version of the formula is: r-Rf = Beta x (RM - Rf)      }

where:
- r           is the expected return rate on a security;
- Rf         is the rate of a "risk-free" investment, i.e. cash;
- RM       is the return rate of the appropriate asset class.

Beta is the overall risk in investing in a large market, like the New York Stock Exchange. Beta, by definition equals 1,00000 exactly.

Each company also has a Beta. The Beta of a company is that company's risk compared to the Beta (Risk) of the overall market. If the company has a Beta of 3.0, then it is supposed to be 3 times more risky than the overall market. Beta indicates the volatility of the security, relative to the asset class.

### Investing in individual securities

A consequence of CAPM thinking is that it implies that investing in individual stocks is useless, because one can duplicate the reward and risk characteristics of any security just by using the right mix of cash with the appropriate asset class. This is why die-hard followers of CAPM avoid securities, and instead build portfolios merely out of low-cost index funds.

### Assumptions of the Capital Asset Pricing Model

Note! The Capital Asset Pricing Model is a ceteris paribus model. It is only valid within a special set of assumptions. These are:

• Investors are risk averse individuals who maximize the expected utility of their end of period wealth. Implication: The model is a one period model.
• Investors have homogenous expectations (beliefs) about asset returns. Implication: all investors perceive identical opportunity sets. This means everyone has the same information at the same time.
• Asset returns are distributed by the normal distribution.
• There exists a risk free asset and investors may borrow or lend unlimited amounts of this asset at a constant rate: the risk free rate.
• There is a definite number of assets and their quantities are fixated within the one period world.
• All assets are perfectly divisible and priced in a perfectly competitive marked. Implication: e.g. human capital is non-existing (it is not divisible and it can't be owned as an asset).
• Asset markets are frictionless and information is costless and simultaneously available to all investors. Implication: borrowing rate equals the lending rate.
• There are no market imperfections such as taxes, regulations, or restrictions on short selling.

Normally, all of the assumptions mentioned above are neither valid nor fulfilled. However, CAPM anyway remains one of the most used investments models to determine risk and return.

Book: William F. Sharpe - Portfolio Theory and Capital Markets -

Book: Harry M. Markowitz - Mean-Variance Analysis in Portfolio Choice and Capital Markets -

Book: Mary Jackson - Advanced modelling in finance using Excel and VBA -

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