Risk And Return

### Retrun

• Expected Return (E(r)) – The expected return of an investment with n possible outcomes, ri, i=1,…,n, each with probability of pi: • Variance of Returns (σ2) – The variance of returns of an investment with n possible outcomes and with an expected return, E(r): • Standard Deviation (σ): • Coefficient of Variation (CV): • Covariance of Returns (σij): The covariance between the returns of asset i and asset j, each having n possible outcomes with joint probabilities Ps (ri, rj): • Correlation Coefficient (pij): • Two-Asset Portfolio:
• Expected Return ((E(rp) – The expected return on a two-asset porfolio with proportion xi invested in asset i, and xj invested in asset j • Variance of Returns p2): • N-Asset Portfolio:
• Expected Return ((E(rp) – The expected retrun on an N-asset portfolio having a proportion xi invested in asset i, i=1,…,N: • Variance of Returns (σp2): ### Beta Coefficient

##### Assets – 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.

### Risk

• 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].