Capital market line

The capital market line (KML, Eng. Capital Market Line CML) is a relationship from capital market theory. She is the expected (in the sense of claimed ) risk-return combination of efficient portfolios in balance. On the capital market line are all risk-return combinations that the investor is prepared to accept.

The capital market line is a component of the Capital Asset Pricing Model, which is a further development of portfolio theory. It is thereby attempted to determine a balance between several market participants, whereas the portfolio theory considers only a representative individual.

Assumptions

The concept of capital market line is based on the following assumptions:

  • It is risk-averse investors with possibly different preferences.
  • Select the investors only efficient portfolios.
  • The investors have the same expectations as a result of the same information.
  • The investors invest over the same planning horizon.
  • There is a risk-free investment and debt option, wherein the target interest rate is the lending rate.

Based on these assumptions, an equilibrium can be derived.

Derivation of the equilibrium

In individual portfolio must be included in contrast to the market portfolio, not all stocks. From Tangentialportfolio every investor holds a share.

This market clearing occurs, each share must be included in Tangentialportfolio. This is the case if the aggregate demand and the number of shares outstanding are exactly alike.

The budget condition is

  • : Share of Tangentialportfolios ( risky part )
  • : Risk-free portion of the portfolio
  • : Share of Tangentialportfolio, m k identical for each investor

Market clearing condition

  • : Budget of the investor
  • : Risk-free portion of the portfolio

Budget condition

  • : Sum of the budget
  • : Plant in Tangentialportfolio

Equation of the capital market line

  • The maximum diversification, the purchase of the market portfolio dar. This wohldiversifizierte portfolio offers the best risk / return ratio
  • Then a reduction of risk is possible only by adding a risk-free investment
  • The slope is a ratio of the excess return of the market and its risk. This means there is a normalization.

Result

  • In equilibrium, is that the market portfolio is equal to the Tangentialportfolio. This is the only empirically testable statement of the CAPM.
  • Each investor holds a risky stock portfolio, with matches its structure.
  • It is the Tobin separation, that is, the decision on the risky portion and the decision on the structure are separated.
  • All efficient portfolios are fully positively correlated, as they are composed of the risk-free rate and the market portfolio.
Security characteristic line
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