Beta
Now that you understand the distinction between systematic and unsystematic risk, you can learn how systematic risk is measured. The answer is beta, one of the most frequently tested concepts in portfolio theory.
Definition and Interpretation
- Beta measures the sensitivity of a security's returns to the overall market's returns
- Beta quantifies systematic risk only; it does not measure unsystematic risk
- The benchmark market (S&P 500) has a beta of 1.0 by definition
| Beta Value | Interpretation | Example |
|---|---|---|
| Beta = 1.0 | Moves in line with the market | If the market rises 10%, the stock is expected to rise approximately 10% |
| Beta > 1.0 | More volatile than the market (aggressive) | A stock with beta 1.5 is expected to rise 15% when the market rises 10% (and fall 15% when the market falls 10%) |
| Beta < 1.0 | Less volatile than the market (defensive) | A stock with beta 0.6 is expected to rise 6% when the market rises 10% |
| Beta = 0 | No correlation with the market | Returns are independent of market movements (e.g., T-bills) |
| Negative beta | Moves inversely to the market | Rare; gold stocks and certain hedge strategies may exhibit negative beta |
Exam Tip: Gotchas
- Beta 1.5 amplifies both gains AND losses. A stock with beta 1.5 rises 15% when the market rises 10%, but also falls 15% when the market falls 10%. The exam tests that higher beta cuts both ways.
- T-bills have a beta of approximately 0. They are risk-free with no market correlation, making them the baseline for zero systematic risk.
Suitability Implications
- High-beta stocks (>1.0) are suitable for aggressive investors seeking above-market returns and willing to accept above-market risk
- Low-beta stocks (<1.0) are suitable for risk-averse investors or those seeking to reduce portfolio volatility
- Beta helps match securities to the customer's risk tolerance, a direct application of the customer-specific suitability factors
Portfolio Beta Calculation
- Portfolio beta is the weighted average of the betas of all holdings in the portfolio
- Formula: Portfolio beta = sum of (each holding's weight x its beta)
Example:
A portfolio is 60% Stock A (beta 1.2) and 40% Stock B (beta 0.8):
- Portfolio beta = (0.60 x 1.2) + (0.40 x 0.8)
- Portfolio beta = 0.72 + 0.32 = 1.04
- This portfolio is expected to be slightly more volatile than the market
What the result tells you: A portfolio beta of 1.04 means that if the market rises 10%, this portfolio is expected to rise approximately 10.4%. If the market falls 10%, the portfolio is expected to fall approximately 10.4%.
Exam Tip: Gotchas
- Portfolio beta is a weighted average, not a simple average. A portfolio that is 90% in a beta-1.5 stock and 10% in a beta-0.5 stock has a beta of 1.40, not 1.0. The exam may give you weights and betas to calculate.
Beta vs. Standard Deviation
This is a frequently tested distinction:
| Metric | What It Measures | Risk Type |
|---|---|---|
| Beta | Sensitivity to market movements | Systematic risk only |
| Standard deviation | Dispersion of returns from the average | Total risk (systematic + unsystematic) |
- A well-diversified portfolio has eliminated most unsystematic risk, so its beta is the primary risk measure
- A concentrated portfolio still carries significant unsystematic risk, so standard deviation provides a more complete picture
Exam Tip: Gotchas
- Beta measures systematic risk, NOT total risk. Standard deviation measures total risk (systematic + unsystematic). The exam may ask which metric measures market risk (beta) vs. which measures total risk (standard deviation).