Value of an asset
- The value of an asset with expected cash flows, CFt, at times, t=1,2,…,n, with required rate of return, r:
Value of a bond
- The value of a bond with coupon interest payments of I per year, maturity value (or par value) of M, maturity of n years, and a required rate of rd:
Portfolio (Br): The beta coeddicient of an N-asset portfolio with xi invested in asset i with beta equal to Bi :
Capital Asset Pricing Model (CAPM)
In equilibrium, the expected return (as well as the required return) (E(Ri)) on asset i having a beta coefficient, βi, is given by:
Where Rf is the rish-free rate of return, and E(Rm) is the expected return on the market portfolio. The term [E(Rm) – Rf] is the expected market risk premium.
- Single Asset: The risk of a single asset held in isolation is equal to the variance of the returns on the asset, σ2.
- Portfolio: The risk of aportfolio of assets is given by the variance of the returns in the portfolio, σp2.
- Single Asset in a Portfolio: The risk of a single asset held as a part of a portfolio of assets is given by the beta coefficient for that asset.
- Systematic Risk: The portion of the total risk that cannot be eliminated through diversification. The risk is also known as “market” risk. The systematic risk of an asset or portfolio is given by their beta coefficients.
- Diversifiable Risk: The portion of the total risk of a portfolio that can be eliminated through diversification. Note that:
Total Risk = Systematic Risk + Diversifiable Risk
Security Market Line (SML)
Definition: A graphical representation of the CAPM.
The slope of the SML is equal to [E(Rm)-Rf].