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Portfolio ManagementModule 2 of 3

Portfolio Risk and Return: Part II

5

Concepts

5

Formulas

1

Decisions

4

Quiz Questions

Key Concepts

5 concepts covered in this module.

Capital Market Line (CML)

CAL using the MARKET portfolio as the optimal risky portfolio. E(R) = Rf + [(Rm-Rf)/σm]σp.

Systematic vs Unsystematic Risk

Systematic (market/non-diversifiable): β measures sensitivity. Unsystematic (company-specific): eliminated by diversification.

CAPM

E(Ri) = Rf + βi(E(Rm) - Rf). Only systematic risk (β) is rewarded. Security Market Line (SML) plots this.

Beta

β = Cov(Ri, Rm) / Var(Rm). Market β=1. β>1: more volatile than market. β<1: less volatile.

Performance Measures

Sharpe (total risk), Treynor (systematic risk), Jensen's Alpha (excess return above CAPM), M² (risk-adjusted RAP).

Formulas

5 essential formulas for this module.

CAPM / SML

E(Ri) = Rf + βi[E(Rm) - Rf]

Where: Rf = risk-free, β = beta, E(Rm)-Rf = market risk premium

Beta

βi = Cov(Ri, Rm) / σ²m

Where: σ²m = variance of market returns

Treynor Ratio

Treynor = (Rp - Rf) / βp

Where: Excess return per unit of systematic risk

Jensen's Alpha

α = Rp - [Rf + β(Rm - Rf)]

Where: Positive α = outperformance vs CAPM

M-squared

M² = (Sharpep - Sharpem) × σm

Where: Risk-adjusted performance in return units

Decision Frameworks

1 decision frameworks to guide your analysis.

Which performance measure to use?

  • Sharpe: for well-diversified portfolios (total risk matters)
  • Treynor: for portfolios that are part of a larger diversified portfolio (β matters)
  • Jensen’s Alpha: for measuring active manager skill

Mind Map

Visual overview of how concepts connect in this module.

Portfolio Risk & Return II
Capital Market Theory
CML: Rf to Market
Only efficient portfolios on CML
Slope = market Sharpe
CAPM & SML
E(R) = Rf + β(Rm-Rf)
β measures systematic risk
All assets on SML in equilibrium
Above SML = undervalued
Beta
β = Cov(i,m)/Var(m)
β>1: aggressive
β<1: defensive
β=1: market
Performance
Sharpe (total risk)
Treynor (β risk)
Jensen's Alpha
M²
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Capital Market Line (CML)

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Answer
CAL using the MARKET portfolio as the optimal risky portfolio. E(R) = Rf + [(Rm-Rf)/σm]σp.
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Portfolio Management Overview and Planning