Capital Market Line (CML), the market portfolio consists of the combination of all risky assets and the risk-free asset, using market value of the assets to determine the weights. The CML line is derived by the CAPM, solving for expected return at various levels of risk.Markowitz' idea of the efficient frontier, however, did not take into account the risk-free asset. The CML does and, as such, the frontier is extended to the risk-free rate as illustrated below:

Systematic and Unsystematic Risk: Total risk to a stock not only is a function of the risk inherent within the stock itself, but is also a function of the risk in the overall market.Systematic risk: is the risk associated with the market. When analyzing the risk of an investment, the systematic risk is the risk that cannot be diversified away.Unsystematic risk: is the risk inherent to a stock. This risk is the aspect of total risk that can be diversified away when building a portfolio.Formula: Total risk = Systematic risk + Unsystematic riskWhen building a portfolio, a key concept is to gain the greatest return with the least amount of risk. However, it is important to note, that additional return is not guaranteed for an increased level of risk. With risk, reward can come, but losses can be magnified as well.

Capital Market Line: (CML) is the tangent line drawn from the point of the risk-free asset to the feasible region for risky assets. The tangency point M represents the market portfolio, so named since all rational investors (minimum variance criterion) should hold their risky assets in the same proportions as their weights in the market portfolio.

Formula:

The CML results from the combination of the market portfolio and the risk-free asset (the point L). All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, the portfolio M is composed entirely of the risky asset, the market, and has no holding of the risk free asset, i.e., money is neither invested in, nor borrowed from the money market account. Points to the left of and above the CML are infeasible, whereas points to the right/below are attainable but inefficient.

Addition of leverage (the point R) creates levered portfolios that are also on the CML.

Capital Market Line, Sharpe Ratio and Alpha

All of the portfolios on the CML have the same Sharpe ratio as that of the market portfolio, i.e.

In fact, the slope of the CML is the Sharpe ratio of the market portfolio.

A stock picking rule of thumb is to buy assets whose Sharpe ratio will be above the CML and sell those whose Sharpe ratio will be below. Indeed, from the efficient market hypothesis it follows that it's impossible to beat the market. Therefore, all portfolios should have a Sharpe ratio less than or equal to the market's. In consequence, if there is a portfolio (or asset) whose Sharpe ratio will be bigger than the market's then this portfolio (or asset) has a higher return per unit of risk (i.e. the volatility  ), which contradicts the efficient market hypothesis.

This abnormal extra return over the market's return at a given level of risk is what is called the alpha.

Tangent Line: A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line. Note: A line tangent to a circle is perpendicular to the radius to the point of tangency.

Risk Free Assets: An asset whose future return is known today with certainty. The risk-free asset is commonly defined as short-term obligations of the US government.

Feasible Region: A feasible region is an area defined by a set of coordinates that satisfy a system of inequalities. The region satisfies all restrictions imposed by a linear programming scenario. The concept is an optimization technique.

Risky Assets: A risk asset is any asset that carries a degree of risk. Risk asset generally refers to assets that have a significant degree of price volatility, such as equities, commodities, high-yield bonds, real estate and currencies.

Market Portfolio: A market portfolio is a theoretical bundle of investments that includes every type of asset available in the world financial market, with each asset weighted in proportion to its total presence in the market.

Rational Investor: A rational behavior decision-making process is based on making choices that result in the most optimal level of benefit or utility for the individual. Most conventional economic theories are created and used under the assumption all individuals taking part in an action/activity are behaving rationally.