All 4 Topics · Complete Reference

Chapter Study Guides

Comprehensive chapter-by-chapter reference covering all concepts, formulas, and comparative analyses for the Asset Management session. Sourced from Prof. Rosu's course materials.

Chapter 1

Asset Allocation & Modern Portfolio Theory

Core MPT framework, efficient frontier, Sharpe ratio, Black-Litterman model

1. Core Concepts

Asset Allocation

The process of distributing an investor's wealth across asset classes (stocks, bonds, real estate) to achieve the optimal balance between expected return and risk.

Modern Portfolio Theory (MPT)

Introduced by Harry Markowitz. Its core insight: diversification — combining assets that are not perfectly correlated — can significantly reduce overall portfolio risk without sacrificing return.

Mean-Variance Investor

An investor who makes decisions based solely on two parameters: the expected return (mean) and the risk (variance or standard deviation) of the portfolio.

Investment Opportunity (IO) Set

The set of all feasible portfolios that can be constructed from a given set of assets, plotted in the expected return–standard deviation (E, σ) space.

Efficient Frontier

The upper edge of the IO Set. Portfolios that offer the highest expected return for a defined level of risk. Any rational investor will choose a portfolio on this frontier.

Tangency (MVE) Portfolio

The portfolio on the efficient frontier that maximizes the Sharpe ratio — the point where the Capital Market Line is tangent to the risky asset frontier.

2. Key Formulas

Portfolio Expected Return (2 Assets)

E_P = w_A·E_A + w_B·E_B

Portfolio Variance (2 Assets)

σ_P² = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_Bρ_A,B

Matrix Form (N Assets)

E_P = w'E | σ_P² = w'Ωw

Sharpe Ratio

SR = (E_P − r_f) / σ_P

MVE Portfolio Weights

w_MVE ∝ Ω⁻¹(E − r_f·1)

GMV Portfolio Weights

w_GMV ∝ Ω⁻¹·1

3. Comparative Analyses

Capital Allocation Line (CAL) vs. Capital Market Line (CML)

Feature	CAL	CML
Definition	All combinations of the risk-free asset and any specific risky portfolio	The specific CAL using the Tangency (MVE) Portfolio
Slope	Sharpe Ratio of the chosen risky portfolio	Maximum possible Sharpe Ratio
Significance	Shows risk-return tradeoff for a particular mix	The new Efficient Frontier when a risk-free asset exists

Tangency (MVE) Portfolio vs. Global Minimum Variance (GMV) Portfolio

Feature	MVE Portfolio	GMV Portfolio
Objective	Maximizes the Sharpe Ratio	Minimizes absolute portfolio variance
Location	Tangency point of CML with risky frontier	Leftmost point (nose) of the hyperbola
Formula	w ∝ Ω⁻¹(E − rf·1)	w ∝ Ω⁻¹·1

4. Black-Litterman Model

While MPT is theoretically sound, it is highly sensitive to input estimates. The Black-Litterman (BL) model addresses this by combining market equilibrium returns with an investor's subjective views.

BL Prior

Starts from the assumption that the market portfolio is efficient. Equilibrium returns: μ_eq = δΩw_M

Investor Views

The investor specifies absolute or relative views on asset returns, with a degree of confidence (matrix U).

Posterior Portfolio

Bayesian updating combines prior + views. Optimal portfolio = benchmark + weighted sum of view portfolios.