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).
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
| Principle | Description |
|---|---|
| Portfolio Focus | Evaluate risk and return at portfolio level, not individual securities |
| Risk-Return Tradeoff | Higher expected returns require accepting higher risk |
| Diversification | Combining assets reduces overall portfolio risk |
| Efficient Portfolios | Maximize 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
| Correlation | Meaning | Diversification Benefit |
|---|---|---|
| +1.0 | Perfect positive - move exactly together | None |
| +0.5 to +0.9 | Strong positive correlation | Limited |
| 0 | No relationship | Good |
| -0.5 to -0.9 | Strong negative correlation | Better |
| -1.0 | Perfect negative - move exactly opposite | Maximum |
Correlation Examples
| Asset Pair | Typical Correlation | Reason |
|---|---|---|
| Two tech stocks | High positive | Same industry, similar risks |
| Stocks and bonds | Low or negative | Different risk factors |
| U.S. and foreign stocks | Moderate positive | Different economies |
| Gold and stocks | Low or negative | Gold 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
| Position | Description |
|---|---|
| On the frontier | Optimal - cannot improve return without adding risk |
| Below the frontier | Suboptimal - same risk with less return |
| Above the frontier | Not achievable - would require impossible return/risk combination |
Building Toward the Frontier
| Action | Effect |
|---|---|
| Add diversification | Moves portfolio toward frontier |
| Reduce correlation | Improves risk-adjusted returns |
| Eliminate unnecessary risk | Moves closer to efficient |
Types of Risk
All investment risk falls into two categories:
Systematic Risk (Market Risk)
| Characteristic | Description |
|---|---|
| Also Called | Market risk, non-diversifiable risk |
| Affects | ALL securities in the market |
| Can Be Diversified? | NO |
| Measured By | Beta |
Examples of Systematic Risk
| Risk Type | Description |
|---|---|
| Interest Rate Risk | Changes in interest rates affect all securities |
| Inflation Risk | Purchasing power erosion |
| Market Risk | Overall market declines |
| Political Risk | Government policy changes |
| Economic Risk | Recessions affect all companies |
Unsystematic Risk (Company-Specific Risk)
| Characteristic | Description |
|---|---|
| Also Called | Diversifiable risk, company-specific risk, unique risk |
| Affects | Individual company or industry |
| Can Be Diversified? | YES |
| Measured By | Standard deviation (for individual security) |
Examples of Unsystematic Risk
| Risk Type | Description |
|---|---|
| Business Risk | Company operations, management decisions |
| Financial Risk | Company's use of debt |
| Default Risk | Company may not pay obligations |
| Industry Risk | Sector-specific challenges |
| Event Risk | Lawsuits, 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
| Beta | Meaning | Expected Movement |
|---|---|---|
| β = 1.0 | Same risk as market | Moves with market |
| β > 1.0 | More volatile than market | Amplified movements |
| β < 1.0 | Less volatile than market | Dampened movements |
| β = 0 | No market correlation | Moves independently |
| β < 0 | Inverse relationship | Moves opposite to market |
Beta Examples
| Security Type | Typical Beta |
|---|---|
| Utility stocks | 0.4 - 0.7 |
| S&P 500 Index | 1.0 (by definition) |
| Technology stocks | 1.3 - 1.8 |
| Treasury bills | 0 (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
| Scenario | Expected Return |
|---|---|
| Higher beta | Higher expected return (more risk) |
| Lower beta | Lower expected return (less risk) |
| Beta = 1.0 | Expected return equals market return |
| Beta = 0 | Expected 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.
Which of the following risks can be eliminated through diversification?
To achieve the GREATEST diversification benefit, an investor should add assets with what correlation to existing holdings?
A stock has a beta of 1.5. If the market rises 10%, the stock would be expected to:
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?
8.2 Asset Allocation Strategies
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