3.6 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).

5-10%: Risk Level Low. Typical Investment: Money market, short-term bonds

10-15%: Risk Level Moderate. Typical Investment: Balanced funds, investment-grade bonds

15-20%: Risk Level High. Typical Investment: Large-cap stocks

20-30%: Risk Level Very High. Typical Investment: Small-cap stocks, emerging markets

30%+: Risk Level Extreme. Typical Investment: Individual stocks, commodities

Interpreting Standard Deviation

In a normal distribution (bell curve), approximately:

- 68% of returns fall within plus/minus 1 standard deviation

- 95% of returns fall within plus/minus 2 standard deviations

- 99.7% of returns fall within plus/minus 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%

Beta: Measuring Systematic Risk

Beta measures a security's sensitivity to market movements - its systematic risk only.

Beta = 0: No market relationship. Example Securities: T-bills

Beta = 0.5: Half as volatile as market. Example Securities: Utilities, some REITs

Beta = 1.0: Moves with market. Example Securities: S&P 500 index fund

Beta = 1.5: 50% more volatile. Example Securities: Tech stocks

Beta = 2.0: Twice as volatile. Example Securities: Aggressive growth stocks

Beta less than 0: Moves opposite. Example Securities: Gold (sometimes)

Beta vs. Standard Deviation

Standard Deviation: What It Measures - Total risk (systematic + unsystematic). Diversifiable? Partially

Beta: What It Measures - Systematic risk only. Diversifiable? No

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).

Alpha: Measuring Manager Skill

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

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

Positive alpha: Manager outperformed expectations (added value)

Zero alpha: Returns matched expectations for risk level

Negative alpha: Manager underperformed expectations

Example:

- Fund return: 12%

- Market return: 10%

- Fund beta: 1.0

- Expected return (based on beta): 10%

- Alpha: 12% - 10% = +2% (manager added value)

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

Less than 0: Underperformed risk-free rate

0.0-0.5: Below average

0.5-1.0: Good

1.0-2.0: Very good

Greater than 2.0: Excellent

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.

Modern Portfolio Theory (MPT)

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

Key Concepts

Risk-averse investors: Prefer lower risk for same return

Diversification: Combining assets reduces total risk

Correlation: How assets move together

Efficient frontier: Set of optimal portfolios

Correlation and Diversification

Perfect positive: Value Range +1.0. Diversification Benefit: None

Positive: Value Range 0 to +1.0. Diversification Benefit: Some

Zero: Value Range 0. Diversification Benefit: Good

Negative: Value Range -1.0 to 0. Diversification Benefit: Better

Perfect negative: Value Range -1.0. Diversification Benefit: Maximum

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.

Capital Asset Pricing Model (CAPM)

CAPM explains the relationship between expected return and systematic risk:

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

Risk-Free Rate: Return on T-bills

Beta: Security's systematic risk

Market Return - Risk-Free Rate: Market risk premium

CAPM Example:

- Risk-free rate: 3%

- Market return: 10%

- Stock beta: 1.2

- Expected Return: 3% + 1.2 x (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).

Risk-Return Trade-off

Fundamental principle: Higher expected returns require accepting higher risk.

Risk Spectrum

T-bills: Risk Level Lowest. Expected Return approx. 3-5%

Government bonds: Risk Level Low. Expected Return approx. 4-6%

Investment-grade corporate bonds: Risk Level Low-Moderate. Expected Return approx. 5-7%

Large-cap stocks: Risk Level Moderate-High. Expected Return approx. 8-10%

Small-cap stocks: Risk Level High. Expected Return approx. 10-12%

Emerging markets: Risk Level Very High. Expected Return approx. 12%+

Private equity: Risk Level Highest. Expected Return approx. 15%+

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

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

You need to understand concepts but likely won't calculate complex formulas.

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 x Market premium

- Higher expected returns require accepting higher risk

- Use correlation to maximize diversification benefits