Risk Measurement & Portfolio Theory

Investment advisers use various statistical measures and theoretical frameworks to quantify risk, evaluate performance, and construct portfolios. The Series 65 exam tests these key concepts.

Standard Deviation: Measuring Total Risk

Standard deviation measures the dispersion of returns around the average—it represents total risk (both systematic and unsystematic).

Interpreting Standard Deviation

In a normal distribution (bell curve), approximately:

• 68% of returns fall within ±1 standard deviation
• 95% of returns fall within ±2 standard deviations
• 99.7% of returns fall within ±3 standard deviations

Example: A fund with 10% average return and 15% standard deviation:

• 68% of annual returns between -5% and +25%
• 95% of annual returns between -20% and +40%

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Beta: Measuring Systematic Risk

Beta (β) measures a security's sensitivity to market movements—its systematic risk only.

Beta vs. Standard Deviation

A stock can have high standard deviation but low beta (company-specific volatility), or low standard deviation but beta near 1.0 (moves with market, low unique volatility).

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Alpha: Measuring Manager Skill

Alpha (α) measures the difference between actual returns and expected returns given the level of risk (beta):

Alpha = Actual Return − Expected Return (based on beta)

Example:

• Fund return: 12%
• Market return: 10%
• Fund beta: 1.0
• Expected return (based on beta): 10%
• Alpha: 12% − 10% = +2% (manager added value)

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Sharpe Ratio: Risk-Adjusted Performance

The Sharpe Ratio measures excess return per unit of total risk (standard deviation):

Sharpe Ratio = (Portfolio Return − Risk-Free Rate) / Standard Deviation

Example:

• Portfolio return: 12%
• Risk-free rate: 3%
• Standard deviation: 18%
• Sharpe Ratio: (12% − 3%) / 18% = 0.50

Use: Compare funds with different risk levels—higher Sharpe ratio = better risk-adjusted performance.

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Modern Portfolio Theory (MPT)

Modern Portfolio Theory, developed by Harry Markowitz (1952), is the foundation of portfolio management.

Key Concepts

Correlation and Diversification

Key Insight: The lower the correlation between assets, the greater the diversification benefit.

The Efficient Frontier

The efficient frontier is the set of portfolios that:

• Maximize expected return for a given level of risk, OR
• Minimize risk for a given level of expected return

Portfolios below the efficient frontier are inefficient—they could achieve higher returns without additional risk.

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Capital Asset Pricing Model (CAPM)

CAPM explains the relationship between expected return and systematic risk:

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

CAPM Example:

• Risk-free rate: 3%
• Market return: 10%
• Stock beta: 1.2
• Expected Return: 3% + 1.2 × (10% − 3%) = 3% + 8.4% = 11.4%

Security Market Line (SML)

The Security Market Line is the graphical representation of CAPM:

• X-axis: Beta
• Y-axis: Expected return
• Slope: Market risk premium

Securities above the SML are undervalued (expected to outperform). Securities below the SML are overvalued (expected to underperform).

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Risk-Return Trade-off

Fundamental principle: Higher expected returns require accepting higher risk.

Risk Spectrum

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In Practice: How Investment Advisers Apply This

Using these measures:

• Standard deviation: Compare total volatility across investments
• Beta: Match systematic risk to client tolerance
• Alpha: Evaluate whether active managers add value
• Sharpe ratio: Compare risk-adjusted performance across funds

Portfolio construction:

• Use MPT principles to build diversified portfolios
• Seek low-correlation assets for diversification
• Plot client portfolios against efficient frontier
• Use CAPM to set return expectations

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On the Exam

The Series 65 exam tests:

1. Standard deviation as a measure of total risk
2. Beta as a measure of systematic risk only
3. Alpha as a measure of manager value-added
4. Sharpe ratio formula and interpretation
5. Modern Portfolio Theory concepts (diversification, correlation)
6. CAPM formula and components
7. Risk-return trade-off

Expect 3-4 questions on these topics. You need to understand concepts but likely won't calculate complex formulas.

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Key Takeaways

• Standard deviation measures total risk (systematic + unsystematic)
• Beta measures systematic risk only (market sensitivity)
• Alpha = Actual return − Expected return (measures manager skill)
• Sharpe Ratio = (Return − Risk-free rate) / Standard deviation
• Modern Portfolio Theory: Diversification reduces risk; lower correlation = better
• CAPM: Expected Return = Risk-free + Beta × Market premium
• Higher expected returns require accepting higher risk
• Use correlation to maximize diversification benefits