Definition
Standard Deviation
A statistical measure of the dispersion of returns for a security or portfolio. Indicates total risk (both systematic and unsystematic). Higher standard deviation means greater volatility. Under normal distribution, 68% of returns fall within 1 standard deviation, 95% within 2, and 99.7% within 3.
A fund with 12% average annual return and 8% standard deviation would have returns between 4% and 20% approximately 68% of the time (one standard deviation from the mean).
Standard deviation measures total risk (systematic + unsystematic); beta measures only systematic (market) risk. Standard deviation is not the same as variance (variance is standard deviation squared).
How is Standard Deviation tested on the exam?
- Comparing the volatility of two investments using their standard deviations
- Understanding that standard deviation measures both systematic and unsystematic risk
- Interpreting what a high vs. low standard deviation indicates about an investment
- Calculating probability ranges using the 68-95-99.7 rule (normal distribution)
- Distinguishing between standard deviation (total risk) and beta (systematic risk only)
Regulatory limits
Regulatory Limits
| Description | Limit | Notes |
|---|---|---|
| 1 standard deviation coverage (normal distribution) | 68% of returns | Approximately 68% of returns fall within 1 SD of the mean |
| 2 standard deviations coverage (normal distribution) | 95% of returns | Approximately 95% of returns fall within 2 SDs of the mean |
| 3 standard deviations coverage (normal distribution) | 99.7% of returns | Approximately 99.7% of returns fall within 3 SDs of the mean |
Remember the "68-95-99.7 Rule": Think of standard deviation as a YARDSTICK measuring how far returns wander from average. 68% of returns stay within 1 yardstick, 95% within 2 yardsticks, 99.7% within 3. Key distinction: SD measures TOTAL risk (all wobbles), while beta measures only market-related wobbles. Higher SD = wider wandering = riskier investment.
Practice questions
Test your understanding with the questions below. Pick an answer to reveal the explanation.
Jennifer, a 45-year-old investor with moderate risk tolerance, is comparing two growth mutual funds for her retirement portfolio. Fund X has an average annual return of 11% with a standard deviation of 18%. Fund Y has an average annual return of 9% with a standard deviation of 7%. Jennifer wants steady, predictable growth without significant year-to-year fluctuations. Which recommendation is most appropriate?
B is correct. Fund Y's lower standard deviation (7% vs. 18%) indicates more stable, predictable returns with less volatility, which aligns with Jennifer's stated preference for steady growth and her moderate risk tolerance. While Fund Y has a slightly lower average return (9% vs. 11%), it offers more consistency year-to-year.
A focuses only on average return while ignoring Jennifer's explicit preference for avoiding "significant year-to-year fluctuations". Fund X's 18% standard deviation means returns could range from -7% to +29% in roughly 68% of years. C is incorrect because higher standard deviation indicates more volatility, not more diversification. D is incorrect because lower standard deviation indicates lower total risk, not higher systematic risk.
The Series 65 exam tests your ability to match investment volatility (measured by standard deviation) to client risk tolerance and investment objectives. Understanding how to interpret standard deviation in the context of client suitability is critical for making appropriate recommendations and explaining risk-return trade-offs.
Under a normal distribution, approximately what percentage of an investment's returns fall within one standard deviation of the mean?
B is correct. Under a normal distribution, approximately 68% of returns fall within one standard deviation (plus or minus) of the mean return. This is a fundamental statistical concept known as the empirical rule or 68-95-99.7 rule.
A (50%) is incorrect and has no significance in standard deviation analysis. C (95%) is the percentage of returns falling within TWO standard deviations of the mean. D (99.7%) is the percentage of returns falling within THREE standard deviations of the mean.
The Series 65 exam frequently tests knowledge of the 68-95-99.7 rule for normal distributions. This knowledge is essential for interpreting standard deviation statistics, estimating probability ranges for investment returns, and evaluating the likelihood of extreme outcomes.
A mutual fund has an average annual return of 14% with a standard deviation of 10%. Assuming returns follow a normal distribution, what is the approximate range of returns that would occur 68% of the time?
B is correct. Calculate: Mean ± 1 standard deviation = 14% ± 10% = 4% to 24%. Under normal distribution, approximately 68% of returns fall within one standard deviation of the mean.
A (-6% to +34%) incorrectly uses two standard deviations (14% ± 20%), which would represent the 95% confidence interval. C (7% to 21%) incorrectly uses half of one standard deviation (14% ± 5%). D (10% to 18%) incorrectly uses a 4% range, which doesn't correspond to the given 10% standard deviation.
Calculation questions involving standard deviation and probability ranges are common on the Series 65 exam. You must understand how to apply the 68-95-99.7 rule to calculate expected return ranges, which helps evaluate investment risk and set realistic client expectations for portfolio performance.
All of the following statements about standard deviation are accurate EXCEPT
C is correct (the EXCEPT answer). Standard deviation does NOT measure only systematic risk. it measures TOTAL risk, which includes both systematic (market) risk AND unsystematic (company-specific) risk. This is a critical distinction from beta, which measures only systematic risk.
A is accurate: standard deviation captures all sources of volatility, making it a measure of total risk. B is accurate: higher standard deviation values indicate greater volatility and wider fluctuations in returns around the mean. D is accurate: standard deviation is expressed in percentage points, the same units as returns, which makes it interpretable (unlike variance, which is expressed in squared units).
The Series 65 exam tests your ability to distinguish between different risk measures. Understanding that standard deviation measures total risk (both systematic and unsystematic) while beta measures only systematic risk is essential for portfolio construction, diversification strategies, and explaining risk characteristics to clients.
Stock A has an average annual return of 15% with a standard deviation of 20%. Stock B has an average annual return of 8% with a standard deviation of 5%. Which of the following statements are accurate?
1. Stock A has higher volatility than Stock B
2. Approximately 68% of the time, Stock A's returns fall between -5% and +35%
3. Stock B is less risky than Stock A based on standard deviation
4. Stock A has a better risk-adjusted return because it has higher average returns
C is correct. Statements 1, 2, and 3 are accurate.
Statement 1 is TRUE: Stock A's standard deviation (20%) is significantly higher than Stock B's (5%), indicating greater volatility and wider fluctuations in returns.
Statement 2 is TRUE: Using the 68% rule, Stock A's returns fall within one standard deviation of the mean approximately 68% of the time: 15% ± 20% = -5% to +35%.
Statement 3 is TRUE: Stock B's lower standard deviation (5% vs. 20%) indicates it has lower total risk, making it less risky from a volatility perspective.
Statement 4 is FALSE: Risk-adjusted return cannot be determined from average return alone. Stock A has higher absolute returns but also much higher risk. To evaluate risk-adjusted returns, you would need measures like the Sharpe ratio (which considers both return and standard deviation). Stock A's higher return comes with four times the volatility.
The Series 65 exam tests your ability to analyze multiple risk and return characteristics simultaneously. Understanding how to interpret standard deviation in relation to returns, compare risk levels between securities, and recognize that higher returns don't automatically mean better risk-adjusted performance is critical for portfolio evaluation and investment selection.
What concepts relate to Standard Deviation?
This term is part of this cluster :
Where does Standard Deviation appear on the Series 65 exam?
This term is tested in the following Series 65 exam topics:
Types of Risk
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