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The Capital Asset Pricing Model (CAPM), originated in the early to mid-1960s, was built upon the concept of modern portfolio theory and diversification. The capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset’s non-diversifiable risk.
The capital asset pricing model is a financial model to illustrate the pricing of securities and risk-free assets. This model presents an investment’s return and risk results in a weighted fashion.
The return, on the y-axis, is a random variable, which offers both variance and expected value. The risk is indicated on the x-axis as the standard deviation of return.
Capital Asset Pricing Model (CAPM) is a sophisticated mathematical method of formulating a relationship between expected risk and expected return.
In essence, the Capital Asset Pricing Model is built on a pervasive investment theory, in which the Capital Asset Pricing Model claims that higher risk justifies higher returns. Building upon that assertion, the Capital Asset Pricing Model states that the return on an asset or security is equal to a risk-free return, plus a risk premium. Thus, according to the Capital Asset Pricing Model, the projected return must be on par with or above the required return to rationalize the investment. End calculation of the Capital Asset Pricing Model is conveyed graphically by the security market line (SML). Capital Asset Pricing Model is a fairly complicated device used primarily by trained financial practitioners to calculate the pricing of high-risk securities.
The CAPM takes into account the following:
Return represents the expected value that can be paid, and is referred to as “r”.
Risk indicates the danger of losing the investment, or standard deviation (sigma).
As indicated by rf, this is the equivalent of treasury bills or bank savings. In order to be on the capital market line, one must have an investment in rf. These are considered ‘efficient portfolios’.
Portfolio M is the market portfolio, which contains all securities, each in proportion to its outstanding or market value. In practice, one must select a benchmark portfolio, such as the S&P 500 or the Russel 5000, as it is impossible to invest in absolutely everything simultaneously.
The capital market line is an element of the capital asset pricing model. The CML is used to evaluate portfolio performance.
CAPM
William Sharpe (1964) published the capital asset pricing model (CAPM). Parallel work was also performed by Treynor (1961) and Lintner (1965). The model extended Harry Markowitz’s portfolio theory to introduce the notions of systematic and specific risk. For his work on the capital asset pricing model, Sharpe shared the 1990 Nobel Prize in Economics with Harry Markowitz and Merton Miller.
The capital asset pricing model considers a simplified world where:
In such a simple world, Tobin’s (1958) super-efficient portfolio must be the market portfolio. All investors will hold the market portfolio, leveraging or de-leveraging it with positions in the risk-free asset in order to achieve a desired level of risk.
The capital asset pricing model decomposes a portfolio’s risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As 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 to an individual asset. It represents the component of an asset’s return which is uncorrelated with general market moves.
According to the capital asset pricing model, the marketplace compensates investors for taking a systematic risk but not for taking a 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.
Systematic risk can be measured using beta. According to the capital asset pricing model, the expected return of a stock equals the risk-free rate plus the portfolio’s beta multiplied by the expected excess return of the market portfolio. Specifically, let Zs and Zm be random variables for the simple returns of the stock and the market over some specified period. Let zf be the known risk-free rate, also expressed as a simple return, and let β be the stock’s beta. Then
E(Zs) = zf + β[E(Zm) – zf]
[1]
where E denotes an expectation.
Stated another way, the stock’s excess expected return over the risk-free rate equals its beta times the market’s expected excess return over the risk-free rate.
For example, suppose a stock has a beta of 0.8. The market has an expected annual return of 0.12 (that is 12%) and the risk-free rate is .02 (2%). Then the stock has an expected one-year return of
E(Zs) = .02 + .8[.12 – .02] = .10
[2]
Because [1] is linear, it generalizes to portfolios. Let Zp be a portfolio’s simple return, and let β now denote the portfolio’s beta. We obtain
E(Zp) = zf + β[E(Zm) – zf]
[3]
Formula [1] is the essential conclusion of the capital asset pricing model. It states that a stock’s (or portfolio’s) excess expected return depends on its beta and not its volatility. Stated another way, excess return depends upon systematic risk and not on total risk.
We call CAPM a “capital asset pricing model” because, given a beta and an expected return for an asset, investors will bid its current price up or down, adjusting that expected return so that it satisfies formula [1]. Accordingly, the capital asset pricing model predicts the equilibrium price of an asset. This works because the model assumes that all investors agree on the beta and expected return of any asset. In practice, this assumption is unreasonable, so the capital asset pricing model is largely of theoretical value. It is the most famous example of an equilibrium pricing model.
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This glossary post was last updated: 29th December, 2021 | 1 Views.