9.4 Risk & Performance Measures

Investment advisers use various metrics to evaluate portfolio risk and performance. Understanding these measures is essential for client reporting, manager evaluation, and investment selection.

Risk Measures

Standard Deviation

What it measures: Total volatility (dispersion of returns around the mean)

- Risk Type: Total risk (systematic + unsystematic)

- Higher Value: More volatile, riskier

- Lower Value: Less volatile, more stable

- Best For: Comparing undiversified portfolios

Interpretation Example:

- Fund A: 10% return, 8% standard deviation

- Fund B: 10% return, 20% standard deviation

- Fund A is less risky with the same return

Beta

What it measures: Sensitivity to market movements (systematic risk)

- Risk Type: Systematic risk only

- Benchmark: Market portfolio (beta = 1)

- Higher Value: More market-sensitive

- Best For: Comparing diversified portfolios

R-Squared (R-squared)

What it measures: How much of a portfolio's movements are explained by the benchmark

- 100%: Perfectly tracks benchmark (index fund)

- 80-99%: Highly correlated with benchmark

- 50-79%: Moderately correlated

- Less than 50%: Benchmark not representative of the portfolio

Important: R-squared determines whether beta is meaningful. If R-squared is low, beta is unreliable.

Performance Measures

Alpha (Jensen's Alpha)

What it measures: Excess return above what CAPM predicts - manager skill

Alpha = Rp - [Rf + beta (Rm - Rf)]

Where Rp = Actual Portfolio Return

- Positive: Outperformed expectations - value added

- Zero: Performed as expected for risk level

- Negative: Underperformed expectations - value destroyed

Example:

- Actual return: 14%

- Risk-free rate: 3%

- Market return: 10%

- Beta: 1.2

Expected return = 3% + 1.2 x (10% - 3%) = 11.4%

Alpha = 14% - 11.4% = +2.6% (outperformed)

Sharpe Ratio

What it measures: Excess return per unit of total risk (standard deviation)

Sharpe Ratio = (Rp - Rf) / portfolio standard deviation

Where portfolio standard deviation = portfolio standard deviation

- Risk Measure: Total risk (standard deviation)

- Higher Value: Better risk-adjusted performance

- Best For: Undiversified portfolios (total risk matters)

- Interpretation: Return earned per unit of total risk

Example:

- Portfolio return: 12%

- Risk-free rate: 2%

- Standard deviation: 20%

Sharpe Ratio = (12% - 2%) / 20% = 10% / 20% = 0.50

Treynor Ratio

What it measures: Excess return per unit of systematic risk (beta)

Treynor Ratio = (Rp - Rf) / portfolio beta

Where portfolio beta = Portfolio Beta

- Risk Measure: Systematic risk (beta)

- Higher Value: Better risk-adjusted performance

- Best For: Diversified portfolios (unsystematic risk eliminated)

- Interpretation: Return earned per unit of market risk

Example:

- Portfolio return: 12%

- Risk-free rate: 2%

- Beta: 1.25

Treynor Ratio = (12% - 2%) / 1.25 = 10% / 1.25 = 8.0

Comparing Sharpe and Treynor

- Risk Measure: Sharpe Ratio: Standard deviation (total); Treynor Ratio: Beta (systematic)

- Best For: Sharpe Ratio: Undiversified portfolios; Treynor Ratio: Diversified portfolios

- When to Use: Sharpe Ratio: Evaluating standalone investments; Treynor Ratio: Evaluating portfolio components

- Assumption: Sharpe Ratio: All risk matters; Treynor Ratio: Only systematic risk matters

Decision Rule

- If the portfolio is the investor's ONLY holding, use Sharpe (total risk exposure)

- If the portfolio is ONE OF MANY holdings, use Treynor (only systematic risk matters due to diversification)

Information Ratio

What it measures: Active return per unit of tracking error (consistency of outperformance)

Information Ratio = (Rp - Rb) / Tracking Error

Where:

- Rb = Benchmark Return

- Tracking Error = standard deviation of the difference between portfolio and benchmark returns

- Purpose: Evaluate active managers

- Higher Value: More consistent outperformance

- Interpretation: How reliably does the manager beat the benchmark?

Summary Comparison

- Standard Deviation: What It Measures: Total volatility; Risk Used: not applicable; Best For: Risk comparison

- Beta: What It Measures: Market sensitivity; Risk Used: not applicable; Best For: Systematic risk

- R-Squared: What It Measures: Benchmark correlation; Risk Used: not applicable; Best For: Beta reliability

- Alpha: What It Measures: Manager skill; Risk Used: Beta; Best For: Performance attribution

- Sharpe Ratio: What It Measures: Risk-adjusted return; Risk Used: Std Dev; Best For: Undiversified portfolios

- Treynor Ratio: What It Measures: Risk-adjusted return; Risk Used: Beta; Best For: Diversified portfolios

- Information Ratio: What It Measures: Consistent outperformance; Risk Used: Tracking Error; Best For: Active managers

In Practice

When evaluating managers:

- Look for positive alpha (value added)

- Compare Sharpe ratios for standalone investments

- Use Treynor ratio when adding to an existing diversified portfolio

- Check R-squared before relying on beta

- Higher information ratio indicates more consistent outperformance

On the Exam

Series 65 frequently tests:

- Calculating Sharpe ratio and Treynor ratio

- Knowing which risk measure each ratio uses

- Understanding when to use Sharpe vs. Treynor

- Interpreting positive vs. negative alpha

Key Takeaways

1. Standard deviation measures total risk; beta measures systematic risk

2. R-squared indicates how much the benchmark explains portfolio movements

3. Positive alpha = outperformance; negative alpha = underperformance

4. Sharpe uses standard deviation (total risk) - for undiversified portfolios

5. Treynor uses beta (systematic risk) - for diversified portfolios

6. Higher ratios = better risk-adjusted performance