💼 Portfolio Management

Sharpe Ratio Formula — How to Calculate & Interpret

Sharpe ratio formula: (portfolio return - risk-free rate) / standard deviation. How to calculate, interpret, and compare Sharpe ratios for investments.

Key Concepts

Risk-Return Tradeoff

Higher expected return requires accepting higher risk. Historical data: stocks > bonds > T-bills in return and risk.

Utility Theory

U = E(R) - ½Aσ². Risk-averse investors (A>0) require compensation for bearing risk. Indifference curves slope upward.

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Formulas

From this module

Utility Function

U = E(R) - ½ × A × σ²

Where: A = risk aversion coefficient (A>0 for risk-averse)

CAL Equation

E(RC) = Rf + [(E(RP) - Rf)/σP] × σC

Where: Slope = Sharpe ratio of optimal portfolio

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Master Formula Sheet -- Portfolio Management

Utility Function

U = E(R) - ½ × A × σ²

A = risk aversion (A>0: risk-averse)

CAL Equation

E(Rᶜ) = Rᶠ + [E(Rₚ)-Rᶠ]/σₚ × σᶜ

Slope = Sharpe ratio

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Decision Frameworks

How does risk aversion affect portfolio choice?

Use when:

  • More risk-averse (higher A): more allocation to risk-free asset, less to risky portfolio
  • Less risk-averse (lower A): more in risky portfolio, may use leverage

Avoid when:

  • Assuming all investors want the same portfolio — risk preferences differ

Test Your Understanding

The Sharpe ratio measures:

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