Markowitz Efficient Frontier Summary

Markowitz Efficient Frontier

• Course Objectives:

  • Understand avenues of investment and security analysis.

  • Illustrate portfolio management theories for improved investment.

  • Compare investment alternatives and their outcomes.

  • Adapt portfolio models for better returns.

Steps to Form a Portfolio

• Step 1: Identify security universe.

  • Use trusted analysis resources (e.g., Value Line).

  • Create an efficient portfolio from selected stocks.

• Step 2: Compute statistics for securities.

  • Calculate mean return, variance, standard deviation, correlation coefficients.

  • Use historical averages, CAPM, APT models for risk/return calculations.

• Step 3: Interpret statistics.

  • Assess value reasonableness and sustainability of results.

Role of Uncorrelated Securities

• Expected Return Calculation:

  • Portfolio return is a weighted average of component returns.

• Risks in a Two-Security Portfolio:

  • Total risk includes variance and relationships among components.

• Diversification Goal:

  • Achieve target return with minimal risk; a portfolio dominates others if it offers better return for same risk or lesser risk for same return.

Efficient Frontier

• Concept:

  • Represents optimal portfolios that aren't dominated by others.

• Minimum Variance Portfolio:

  • Left extreme of frontier; contains least risk.

• Effect of Risk-Free Rate:

  • Risk-free asset alters efficient frontier and introduces the Capital Market Line (CML).

Borrowing and Lending Portfolios

• Borrowing Portfolio:

  • Involves financial leverage, increasing expected returns and risks.

• Naive Diversification:

  • Random selection without serious analysis; eventually leads to market risk (systematic risk, measured by beta).

Single Index Model and CAPM

• Beta Measurement:

  • Relates individual security's returns to market index; used for estimating risks in CAPM.

• Risk Statistical Functions:

  • Expected return linearly related to beta in CAPM: $E(R<em>i) = R</em>f + \beta<em>i(E(R</em>m) - R_f)$.

Arbitrage Pricing Theory (APT)

• Expands on CAPM, less restrictive but does not identify common factors affecting returns directly.

• Uses multifactor influences like GDP growth, interest rates, inflation, etc.

• General Form:

  • $R<em>i = a</em>0 + a<em>1b</em>1 + a<em>2b</em>2 + … + a<em>kb</em>k + e_i$