Key Takeaways

  • Modern Portfolio Theory (MPT) by Harry Markowitz focuses on portfolio risk, not individual security risk.
  • Diversification reduces UNSYSTEMATIC (company-specific) risk but NOT systematic (market) risk.
  • The efficient frontier represents portfolios with the highest return for each level of risk.
  • Correlation measures how securities move together: +1 (same), 0 (unrelated), -1 (opposite).
  • For best diversification, add securities with NEGATIVE correlation to existing portfolio.
  • Systematic risk (market risk) affects ALL securities and cannot be diversified away.
  • Beta measures systematic risk; a beta of 1.0 equals market risk.
  • CAPM: Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate).
Last updated: December 2025

Modern Portfolio Theory

Modern Portfolio Theory (MPT), developed by Harry Markowitz in 1952, revolutionized investment management by focusing on portfolio-level risk rather than individual security risk. MPT provides the mathematical framework for building diversified portfolios.

Key Concepts of MPT

Core Principles

PrincipleDescription
Portfolio FocusEvaluate risk and return at portfolio level, not individual securities
Risk-Return TradeoffHigher expected returns require accepting higher risk
DiversificationCombining assets reduces overall portfolio risk
Efficient PortfoliosMaximize return for given risk level

The Goal of MPT

MPT seeks to construct efficient portfolios that provide:

  • Maximum expected return for a given level of risk, OR
  • Minimum risk for a given level of expected return

Correlation

Correlation measures how two securities move in relation to each other. It is measured by the correlation coefficient, ranging from -1 to +1.

Correlation Scale

CorrelationMeaningDiversification Benefit
+1.0Perfect positive - move exactly togetherNone
+0.5 to +0.9Strong positive correlationLimited
0No relationshipGood
-0.5 to -0.9Strong negative correlationBetter
-1.0Perfect negative - move exactly oppositeMaximum

Correlation Examples

Asset PairTypical CorrelationReason
Two tech stocksHigh positiveSame industry, similar risks
Stocks and bondsLow or negativeDifferent risk factors
U.S. and foreign stocksModerate positiveDifferent economies
Gold and stocksLow or negativeGold as safe haven

Application for Diversification

To further diversify a portfolio, add securities with negative correlation to existing holdings:

  • When portfolio declines, negatively correlated assets should increase
  • This reduces overall portfolio volatility
  • Perfect diversification would require correlation of -1 (rare in practice)

Exam Tip: For MAXIMUM diversification, add assets with NEGATIVE correlation. A correlation of -1.0 provides the greatest diversification benefit.

The Efficient Frontier

The efficient frontier is a curve showing all optimal portfolios that offer the highest expected return for each level of risk.

Characteristics

PositionDescription
On the frontierOptimal - cannot improve return without adding risk
Below the frontierSuboptimal - same risk with less return
Above the frontierNot achievable - would require impossible return/risk combination

Building Toward the Frontier

ActionEffect
Add diversificationMoves portfolio toward frontier
Reduce correlationImproves risk-adjusted returns
Eliminate unnecessary riskMoves closer to efficient

Types of Risk

All investment risk falls into two categories:

Systematic Risk (Market Risk)

CharacteristicDescription
Also CalledMarket risk, non-diversifiable risk
AffectsALL securities in the market
Can Be Diversified?NO
Measured ByBeta

Examples of Systematic Risk

Risk TypeDescription
Interest Rate RiskChanges in interest rates affect all securities
Inflation RiskPurchasing power erosion
Market RiskOverall market declines
Political RiskGovernment policy changes
Economic RiskRecessions affect all companies

Unsystematic Risk (Company-Specific Risk)

CharacteristicDescription
Also CalledDiversifiable risk, company-specific risk, unique risk
AffectsIndividual company or industry
Can Be Diversified?YES
Measured ByStandard deviation (for individual security)

Examples of Unsystematic Risk

Risk TypeDescription
Business RiskCompany operations, management decisions
Financial RiskCompany's use of debt
Default RiskCompany may not pay obligations
Industry RiskSector-specific challenges
Event RiskLawsuits, recalls, labor disputes

Exam Tip: Diversification ELIMINATES unsystematic risk. Systematic risk CANNOT be diversified away—investors are compensated for bearing this risk.

Beta

Beta measures a security's systematic risk relative to the overall market.

Beta Interpretation

BetaMeaningExpected Movement
β = 1.0Same risk as marketMoves with market
β > 1.0More volatile than marketAmplified movements
β < 1.0Less volatile than marketDampened movements
β = 0No market correlationMoves independently
β < 0Inverse relationshipMoves opposite to market

Beta Examples

Security TypeTypical Beta
Utility stocks0.4 - 0.7
S&P 500 Index1.0 (by definition)
Technology stocks1.3 - 1.8
Treasury bills0 (risk-free)

Portfolio Beta

Portfolio beta is the weighted average of individual security betas:

Portfolio Beta = Σ (Weight × Security Beta)

Example: 60% stocks (beta 1.2) + 40% bonds (beta 0.3)

  • Portfolio Beta = (0.60 × 1.2) + (0.40 × 0.3) = 0.72 + 0.12 = 0.84

Capital Asset Pricing Model (CAPM)

CAPM determines the expected return of a security based on its systematic risk (beta).

CAPM Formula

Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)

Or: E(R) = Rf + β × (Rm - Rf)

Where:

  • Rf = Risk-free rate (T-bill rate)
  • β = Beta of the security
  • Rm = Expected market return
  • (Rm - Rf) = Market risk premium

CAPM Example

Given: Risk-free rate = 3%, Market return = 10%, Beta = 1.5

E(R) = 3% + 1.5 × (10% - 3%) = 3% + 1.5 × 7% = 3% + 10.5% = 13.5%

CAPM Interpretation

ScenarioExpected Return
Higher betaHigher expected return (more risk)
Lower betaLower expected return (less risk)
Beta = 1.0Expected return equals market return
Beta = 0Expected return equals risk-free rate

Exam Tip: CAPM only compensates investors for SYSTEMATIC risk (beta). Unsystematic risk is not rewarded because it can be diversified away.

Loading diagram...
Types of Investment Risk
Diversification Benefit by Correlation (% Maximum Benefit)
Test Your Knowledge

Which of the following risks can be eliminated through diversification?

A
B
C
D
Test Your Knowledge

To achieve the GREATEST diversification benefit, an investor should add assets with what correlation to existing holdings?

A
B
C
D
Test Your Knowledge

A stock has a beta of 1.5. If the market rises 10%, the stock would be expected to:

A
B
C
D
Test Your Knowledge

Using CAPM, if the risk-free rate is 2%, the market return is 9%, and a stock has a beta of 1.2, what is the expected return?

A
B
C
D