What Is the Capital Asset Pricing Model (CAPM)?
Every investor puts their money into two pots: the riskless asset and a single portfolio of risky assets. All investors hold the risky assets in same proportions.
The Capital Asset Pricing Model shows how investors’ asset demand determines the relation between assets’ risk and return in a market equilibrium.
The CAPM is an equilibrium model specifying the relationship between risk and return on assets held in well-diversified portfolios. It requires that in equilibrium total asset holdings of all investors must equal the total supply of assets.
ASSUMPTIONS OF CAPM
1. Single investment period
2. Homogeneous expectations; identical estimations of expected returns, variances, covariances among various assets
3. Investors can borrow and lend at the risk free rate; there are no restrictions on short sales of assets.
4. Stocks are perfectly divisible, and liquid
5. No taxes
6. No transactions costs
7. Investors are price takers.
8. Quantities of all assets are given are fixed.
The assumptions of the model guarantee the efficiency of the market portfolio. Such a condition is necessary for the validity of an exact linear relationship between expected return and risk for individual securities or portfolios at equilibrium.
IMPLICATIONS OF CAPM
1. The market portfolio is the tangent portfolio.
2. Combining the risk-free asset and the market portfolio gives the portfolio frontier.
3. The risk of an individual asset is characterized by its covariability with the market portfolio.
4. The part of the risk that is correlated with the market portfolio, the systematic risk, cannot be diversified away.
5. The part of an asset’s risk that is not correlated with the market portfolio, the non-systematic risk, can be diversified away by holding a frontier portfolio.
In CAPM, we can decompose an asset’s return into three pieces:
ri − rF = αi +βiM (rM − rF)+ εi
where
• E[εi] = 0
• Cov[rM, εi] = 0
Three characteristics of an asset:
• Beta (β)
• Sigma (ε)
• Alpha (α)
BETA
• Beta measures an asset’s systematic risk.
• Assets with higher betas are more sensitive to the market.
SIGMA
• An asset’s sigma measures its non-systematic risk.
• Non-systematic risk is uncorrelated with systematic risk.
ALPHA
• According to CAPM, α should be zero for all assets.
• α measures an asset’s return in access of its risk-adjusted award according to CAPM.
Different Version of CAPM
Fischer Black developed a risk –return linear relationship by considering the case where investors can neither borrow nor lend at the riskless rate of interest.Black’s model is called TWO FACTOR CAPM or Rz version of CAPM. Black’s model assumes that short selling of risky securities is permitted and uses two (minimum standard deviation) portfolios: the market portfolio and another portfolio whose rate of return has no correlation with the rate of return on the market portfolio. The return on the market portfolio is uncorrelated with the return of an infinite number of portfolios that have the same expected return but only one of them lies on the minimum standard deviation(variance) portfolio set. This is called the minimum standard deviation zero beta portfolio.Its beta is zero since it is uncorrelated with the market portfolio. Black’s CAPM can be expressed as:
E(Ri) = E (Rz) + ( E( Rm) – E (Rz) ßi
Rz = return on minimum standard deviation –zero beta portfolio
This model has two implications:
1. At equlibrium, investors hold portfolios consisting of combinations of the market portfolio and its corresponding minimum standard deviation zero beta portfolio
2. The market portfolio is expected return / standard deviation efficient because all investors choose expected return standard deviation efficient portfolios from the same efficient frontier and market portfolio is a linear combination of efficient portfolios.
THE BOTTOM LINE
The CAPM is simple, and relatively easy to implement. It distinguishes systematic risk and non systematic risk, and provides a simple pricing model. For any asset i:
E[ri] − rF = βiM (E[rM] − rF) (11.1)
where βiM = σiM/σ2M
Given the premium of market portfolio, the riskless rate and assets’ market betas, equation determines the premium of all assets.
We thus have an asset pricing model – the CAPM.
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