Sharpe ratio formula: (portfolio return - risk-free rate) / standard deviation. How to calculate, interpret, and compare Sharpe ratios for investments.
Higher expected return requires accepting higher risk. Historical data: stocks > bonds > T-bills in return and risk.
U = E(R) - ½Aσ². Risk-averse investors (A>0) require compensation for bearing risk. Indifference curves slope upward.
Set of portfolios offering maximum return for each level of risk. Rational investors choose portfolios ON the frontier.
Portfolio with lowest possible risk. Starting point of the efficient frontier.
Line from risk-free rate tangent to efficient frontier. Slope = Sharpe ratio. Optimal risky portfolio at tangent point.
All investors hold the same optimal risky portfolio; they differ only in allocation between it and the risk-free asset.
Utility Function
Where: A = risk aversion coefficient (A>0 for risk-averse)
CAL Equation
Where: Slope = Sharpe ratio of optimal portfolio
Sharpe Ratio
Where: Excess return per unit of total risk
Portfolio Risk (2 assets)
Where: Diversification benefit when ρ < 1
Utility Function
A = risk aversion (A>0: risk-averse)
CAL Equation
Slope = Sharpe ratio
Portfolio Variance (2 assets)
Diversification when ρ < 1
CAPM
Only systematic risk rewarded
Beta
Systematic risk measure
Treynor Ratio
Return per unit of beta risk
Jensen's Alpha
Excess return above CAPM
M-squared
Risk-adjusted in return units
Use when:
Avoid when:
The Sharpe ratio measures:
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