Glossary — PM M01: Portfolio Risk and Return (Part 1)

Term	Definition
Risk aversion	Preference for lower uncertainty; a risk-averse investor requires additional expected return to accept additional risk ( $A > 0$ in the utility function).
Risk tolerance	The degree of variability in returns an investor is willing and able to accept; inverse concept of risk aversion.
Utility function	A mathematical representation of investor preferences: $U = E (R) - \frac{1}{2} A σ^{2}$ , yielding a certainty-equivalent return.
Indifference curve	A curve in $E (R)$ - $σ$ space representing all portfolios that provide the same level of utility to an investor. Higher curves = higher utility.
Capital Allocation Line (CAL)	The line in $E (R)$ - $σ$ space representing all combinations of a risk-free asset and a single risky portfolio. Slope equals the Sharpe ratio of the risky portfolio.
Optimal portfolio	The portfolio on the CAL that is tangent to the investor’s highest attainable indifference curve, maximizing utility given risk preferences.
Variance	A measure of dispersion: $σ^{2} = E [(R - E (R))^{2}]$ . Quantifies total risk of an asset or portfolio.
Covariance	A measure of the co-movement of two assets’ returns: $Cov_{12} = E [(R_{1} - E (R_{1})) (R_{2} - E (R_{2}))]$ . Can be positive, negative, or zero.
Correlation coefficient	Standardized covariance: $ρ_{12} = Cov_{12} / (σ_{1} σ_{2})$ . Ranges from $- 1$ to $+ 1$ .
Portfolio standard deviation	Square root of portfolio variance: $σ_{p} = w_{1}^{2} σ_{1}^{2} + w_{2}^{2} σ_{2}^{2} + 2 w_{1} w_{2} Cov_{12}$ for two assets.
Minimum-variance frontier	The set of portfolios with the lowest variance for each given level of expected return, formed from all combinations of risky assets.
Efficient frontier	The upper portion of the minimum-variance frontier (at or above the global minimum-variance portfolio). Only these portfolios are rational choices for risk-averse investors.
Global minimum-variance portfolio (GMV)	The single portfolio on the minimum-variance frontier with the lowest possible variance among all risky-asset combinations.
Expected return	The probability-weighted average of all possible returns: $E (R) = \sum p_{i} R_{i}$ . Represents the central tendency of the return distribution.
Risk premium	The expected return in excess of the risk-free rate: $E (R) - R_{f}$ . Compensation for bearing risk.

See Also

Portfolio Risk and Return