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. [1] [2]
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.
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.
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Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk.
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In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk is present, in which case expected utility is maximized. Formally, exponential utility is given by:
In Finance the Treynor–Black model is a mathematical model for security selection published by Fischer Black and Jack Treynor in 1973. The model assumes an investor who considers that most securities are priced efficiently, but who believes they have information that can be used to predict the abnormal performance (Alpha) of a few of them; the model finds the optimum portfolio to hold under such conditions.
Capital allocation line (CAL) is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays the return to be made by taking on a certain level of risk. Its slope is known as the "reward-to-variability ratio".
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