The Capital Asset Pricing Model (CAPM) is a model for calculating the required rate of return to offset risks when an asset is added to a diversified portfolio.
$E(R)$ is the security's required rate of return.
$R_f$ is the risk-free borrowing rate.
$\beta$ is the security's expected excess return sensitivity to the market risk-premium.
The risk that $\beta$ measures is the non-diversifiable risk, or the systematic risk, because it is the risk that cannot be reduced through diversification of the portfolio.
$\alpha$ measures the risk-adjusted excess return of an asset. In other words, it measures the portion of an asset's expected return that is not accounted for by its riskiness. In an efficient market, $\alpha$ is zero.
Another way to think of this is that $\alpha$ is the value added through active investment management and $\beta$ is the market return.
The Capital Asset Pricing Model (CAPM) makes several assumptions to simplify the practice of trading securities and the preferences of investors:
To generate the efficient frontier for a given level of risk, one can plot all the optimal portfolios that yield the highest return at that risk level.
The efficient frontier plots all portfolios where $\alpha$ is zero. Here, the diversifiable or non-systematic risk is minimized since the optimal portfolio contains all available assets.
The Capital Allocation Line (CAL), which contains all the possible combinations of risky and risk-free assets, is the optimal risk-reward portfolio. The CAL is a plot of the CAPM equation with the intercept as the risk-free rate and the slope measuring the increase in expected return given an increase in risk.