Capital market line
Encyclopedia
Capital market line 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.
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, this portfolio 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.
Addition of leverage (the point R) creates levered portfolios that are also on the CML.
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 is above the CML and sell those whose Sharpe ratio is below. Indeed, from the efficient market hypothesis
it follows that we cannot beat the market. Therefore, all portfolios should have a Sharpe ratio less than or equal than the market's. In consequence, if there is a portfolio (or asset) whose Sharpe ratio is bigger than the market's then this portfolio (or asset) gives more return for unity 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
.
Formula
The CML results from the combination of the market portfolio
Market portfolio
Market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market, with the necessary assumption that these assets are infinitely divisible....
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
Efficient Frontier
The efficient frontier is a concept in Modern portfolio theory introduced by Harry Markowitz and others. A combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk...
, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, this portfolio 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.
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 ratioSharpe ratio
The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
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 is above the CML and sell those whose Sharpe ratio is below. Indeed, from the efficient market hypothesis
Efficient market hypothesis
In finance, the efficient-market hypothesis asserts that financial markets are "informationally efficient". That is, one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information available at the time the investment is made.There are...
it follows that we cannot beat the market. Therefore, all portfolios should have a Sharpe ratio less than or equal than the market's. In consequence, if there is a portfolio (or asset) whose Sharpe ratio is bigger than the market's then this portfolio (or asset) gives more return for unity of risk (i.e. the volatility
), which contradicts the efficient market hypothesisEfficient market hypothesis
In finance, the efficient-market hypothesis asserts that financial markets are "informationally efficient". That is, one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information available at the time the investment is made.There are...
.
This abnormal extra return over the market's return at a given level of risk is what is called the alpha
Alpha (investment)
Alpha is a risk-adjusted measure of the so-called active return on an investment. It is the return in excess of the compensation for the risk borne, and thus commonly used to assess active managers' performances...
.
See also
- Capital allocation lineCapital allocation lineCapital allocation line is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays to the investors on the return they can make by taking on a certain level of risk...
- Modern portfolio theoryModern portfolio theoryModern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
- Security characteristic lineSecurity characteristic lineSecurity characteristic line is a regression line, plotting performance of a particular security or portfolio against that of the market portfolio at every point in time. The SCL is plotted on a graph where the Y-axis is the excess return on a security over the risk-free return and the X-axis is...
- Security market lineSecurity market lineSecurity market line is the graphical representation of the Capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk .-See also:...