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)
| Feature | Description |
|---|---|
| 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 (β)
What it measures: Sensitivity to market movements (systematic risk)
| Feature | Description |
|---|---|
| Risk Type | Systematic risk only |
| Benchmark | Market portfolio (β = 1) |
| Higher Value | More market-sensitive |
| Best For | Comparing diversified portfolios |
R-Squared (R²)
What it measures: How much of a portfolio's movements are explained by the benchmark
| R² Value | Interpretation |
|---|---|
| 100% | Perfectly tracks benchmark (index fund) |
| 80-99% | Highly correlated with benchmark |
| 50-79% | Moderately correlated |
| < 50% | Benchmark not representative of the portfolio |
Important: R² determines whether beta is meaningful. If R² is low, beta is unreliable.
Performance Measures
Alpha (Jensen's Alpha)
What it measures: Excess return above what CAPM predicts—manager skill
Formula:
Alpha = Actual Return − [Rf + β(Rm − Rf)]
| Alpha Value | Interpretation |
|---|---|
| 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(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)
Formula:
Sharpe Ratio = (Portfolio Return − Risk-Free Rate) / Standard Deviation
| Feature | Description |
|---|---|
| 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)
Formula:
Treynor Ratio = (Portfolio Return − Risk-Free Rate) / Beta
| Feature | Description |
|---|---|
| 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
| Feature | Sharpe Ratio | Treynor Ratio |
|---|---|---|
| Risk Measure | Standard deviation (total) | Beta (systematic) |
| Best For | Undiversified portfolios | Diversified portfolios |
| When to Use | Evaluating standalone investments | Evaluating portfolio components |
| Assumption | All risk matters | 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)
Formula:
Information Ratio = (Portfolio Return − Benchmark Return) / Tracking Error
Where tracking error = standard deviation of the difference between portfolio and benchmark returns
| Feature | Description |
|---|---|
| Purpose | Evaluate active managers |
| Higher Value | More consistent outperformance |
| Interpretation | How reliably does the manager beat the benchmark? |
Summary Comparison
| Measure | What It Measures | Risk Used | Best For |
|---|---|---|---|
| Standard Deviation | Total volatility | — | Risk comparison |
| Beta | Market sensitivity | — | Systematic risk |
| R-Squared | Benchmark correlation | — | Beta reliability |
| Alpha | Manager skill | Beta | Performance attribution |
| Sharpe Ratio | Risk-adjusted return | Std Dev | Undiversified portfolios |
| Treynor Ratio | Risk-adjusted return | Beta | Diversified portfolios |
| Information Ratio | Consistent outperformance | Tracking Error | 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
- Standard deviation measures total risk; beta measures systematic risk
- R-squared indicates how much the benchmark explains portfolio movements
- Positive alpha = outperformance; negative alpha = underperformance
- Sharpe uses standard deviation (total risk)—for undiversified portfolios
- Treynor uses beta (systematic risk)—for diversified portfolios
- Higher ratios = better risk-adjusted performance
A portfolio has a return of 15%, the risk-free rate is 3%, and the portfolio's standard deviation is 24%. What is the Sharpe ratio?
The Treynor ratio differs from the Sharpe ratio in that the Treynor ratio:
A positive alpha indicates that a portfolio manager:
9.5 Asset Allocation
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