Total Volatility on One Side, Market Sensitivity on the Other

Standard deviation measures how widely an investment’s returns vary around their average, capturing its total risk from every source. Beta measures how much an investment’s returns move in relation to the overall market, capturing only its systematic, or market, risk.

An investment can have a high standard deviation and a low beta at the same time. A gold mining stock, for example, may swing sharply in price while moving largely independently of the stock market, so most of its volatility comes from factors specific to gold and the company.

Which measure matters depends on how the investment will be held. For a client’s only investment, total risk is what the client lives with, while for a small holding inside a diversified portfolio, market risk is what remains once diversification has done its work. For the full route from the exam to a career applying these ideas, our complete guide to how to become an investment adviser representative covers every step.

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How Standard Deviation Works

Standard deviation measures the dispersion of returns around their mean. A fund with an average return of 8 percent and a standard deviation of 15 percent has returns that typically range much more widely than a fund with the same average and a standard deviation of 5 percent.

It is calculated by finding the average return, measuring how far each period’s return is from that average, squaring those differences, averaging them to get the variance, and taking the square root. Because it uses squared differences, large swings in either direction raise standard deviation sharply.

Standard deviation treats gains and losses the same way, which is both its strength and its weakness. The Series 65 Exam Preparation course at FRC covers it alongside beta, the Sharpe ratio and the other risk measures the exam tests.

How Beta Works

Beta compares an investment’s movements with those of a market benchmark. A beta of 1.0 means the investment tends to move in line with the market, a beta of 1.5 means it tends to move 1.5 percent for each 1 percent move in the market, and a beta of 0.5 means it tends to move half as much.

Mathematically, beta equals the correlation between the investment and the market, multiplied by the investment’s standard deviation divided by the market’s standard deviation. That formula shows how the two measures are linked: beta is the part of an investment’s volatility that comes from moving with the market.

Beta is central to the capital asset pricing model, which says investors are rewarded only for market risk. Our article on alpha vs beta explains how beta sets the return an investment is expected to earn.

Standard Deviation and Beta Compared

Worked Example: Calculating Standard Deviation

A fund’s annual returns over five years were 10, minus 5, 15, 20 and 10 percent. Step one: the average return is 50 divided by 5, or 10 percent.

Step two: the differences from the average are 0, minus 15, 5, 10 and 0, and their squares are 0, 225, 25, 100 and 0, totalling 350. Step three: dividing by one less than the number of years, 4, gives a sample variance of 87.5, and its square root gives a standard deviation of about 9.35 percent.

If returns are roughly normally distributed, about 68 percent of years should fall within one standard deviation of the average, between about 0.6 and 19.4 percent. About 95 percent should fall within two standard deviations, between about minus 8.7 and 28.7 percent, which gives a client a practical sense of how bad a typical poor year could be.

Splitting Total Risk Into Market and Specific Risk

Total risk, measured by variance, can be divided into two parts. Systematic variance equals beta squared times the market’s variance, and whatever is left over is unsystematic, or company-specific, variance.

Worked example: a stock has a standard deviation of 30 percent and a beta of 1.2, and the market’s standard deviation is 15 percent. Step one: the stock’s total variance is 30 squared, or 900. Step two: its systematic variance is 1.2 squared times 15 squared, or 1.44 times 225, which is 324, equal to a systematic standard deviation of 18 percent.

Step three: the unsystematic variance is 900 minus 324, or 576, which is 64 percent of the total. Step four: the share of risk explained by the market, called R-squared, is 324 divided by 900, or 0.36, so only 36 percent of the stock’s volatility comes from market movements and the rest could be diversified away.

Study Risk Measures With FRC

Risk questions on the exam often test whether you know which measure captures which type of risk, and how each behaves when investments are combined. Our Series 65 course builds those links clearly, with worked calculations you can practise until they are automatic.

Consider studying with FRC for every exam on your route. Explore our USA exam courses, from the SIE through the Series 7, Series 63 and Series 65.

To take advantage of the membership, explore FRC Professional Membership, which gives you a verified Digital Profile that shows employers your real-time course progress, together with the Video Resume. Current offers are on our membership deals page.

How Each Measure Behaves in a Portfolio

A portfolio’s beta is simply the weighted average of its holdings’ betas. A portfolio half in a stock with a beta of 1.2 and half in one with a beta of 0.8 has a beta of exactly 1.0.

A portfolio’s standard deviation is different. Unless the holdings move in perfect step with each other, the portfolio’s standard deviation is lower than the weighted average of the holdings’ standard deviations, because their ups and downs partly cancel out.

Worked example: two stocks each have a standard deviation of 25 percent and a correlation of 0.3. A portfolio split equally between them has a variance of 0.25 times 625, plus 0.25 times 625, plus 2 times 0.25 times 0.3 times 625, or 406.25, giving a standard deviation of about 20.2 percent, well below the 25 percent of either stock. This difference, a weighted average for beta but not for standard deviation, is one of the most tested points on the exam.

High Volatility, Low Beta, and the Reverse

Because the two measures capture different things, they can tell very different stories. A biotechnology company waiting for a drug approval may have a standard deviation of 60 percent but a beta of only 0.8, because most of its risk depends on one regulatory decision rather than the market.

A large, diversified bank, by contrast, may have a standard deviation of 25 percent but a beta of 1.3, because its fortunes rise and fall with the economy. In a diversified portfolio, the bank adds more market risk than the biotechnology stock, even though the biotechnology stock is far more volatile on its own.

Broad index funds sit at the other end. Their standard deviation is close to the market’s, their beta is close to 1.0 and their R-squared is close to 1, meaning almost all their risk is market risk.

Which Measure Should an Adviser Use?

For a client’s whole portfolio, or an investment the client will hold on its own, standard deviation is the more complete measure, because the client experiences all of the volatility. The Sharpe ratio, which divides excess return by standard deviation, follows the same logic.

For a single holding being added to a well-diversified portfolio, beta is more relevant, because the specific risk will largely be diversified away. The Treynor ratio, which divides excess return by beta, is built for this case, as explained in our comparison of Sharpe ratio vs Treynor ratio.

Beta should only be relied on when R-squared is reasonably high. A fund with an R-squared of 0.3 against the S&P 500 has a beta that says little about its real behaviour, so standard deviation is the safer guide.

Related Measures: Coefficient of Variation and Downside Risk

The coefficient of variation divides standard deviation by the average return, showing how much risk an investment carries for each unit of return. A fund with an 8 percent average return and a 12 percent standard deviation has a coefficient of variation of 1.5, while one with a 10 percent return and a 12 percent standard deviation has a figure of 1.2, so the second offers more return per unit of volatility.

Downside deviation, also called semi-deviation, measures only the volatility of returns below a chosen target, such as zero or the risk-free rate. It answers the question most clients actually care about: how bad do the bad periods get?

Maximum drawdown, the largest fall from a peak to a trough, is another practical measure. A fund with a moderate standard deviation can still have suffered a 40 percent drawdown in a crisis, and showing that figure helps clients understand what they might have to sit through.

Using Both Measures in a Client Risk Review

A good risk review uses standard deviation and beta together. Standard deviation shows the client how much the whole portfolio is likely to swing, while the beta of each holding shows which positions are driving the portfolio’s exposure to the market.

Translating the numbers into money makes them meaningful. Telling a client with a $500,000 portfolio and a 12 percent standard deviation that a typical bad year could mean a fall of $60,000 or more is far clearer than quoting the percentage alone.

Limits of Both Measures

Standard deviation assumes returns are roughly normally distributed and treats upside and downside moves equally. In real markets, large losses happen more often than a normal distribution predicts, and investors care far more about losses than about gains.

Beta is estimated from past data and can change as a company’s business, debt or industry changes. It also depends on the benchmark and time period used, so two data providers can report different betas for the same stock.

Both measures look backwards. They describe how an investment has behaved, which is useful, but they cannot guarantee how it will behave in the next crisis.

The Memory Aid

Remember “SD is the whole story, beta is the market chapter”: standard deviation captures all volatility, while beta captures only the part linked to the market.

For portfolios, remember “beta adds up, SD does not”: portfolio beta is a weighted average, but portfolio standard deviation is usually lower than the weighted average because of diversification.

For choosing, remember “alone, use SD; in a crowd, use beta”.

Exam Traps to Avoid

The first trap is saying beta measures total risk. It measures only systematic risk; standard deviation measures total risk.

The second trap is calculating portfolio standard deviation as a simple weighted average. That only works when the holdings are perfectly correlated.

The third trap is assuming a low beta means low volatility. An investment can have a low beta and a high standard deviation if most of its risk is company-specific. The fourth trap is relying on beta when R-squared is low.

A Client Scenario

A client holds a $600,000 portfolio of broad index funds and wants to add a 5 percent position in a small mining company that a friend recommended. The stock has a standard deviation of 55 percent and a beta of 0.6, and the client is worried that it is too risky.

The adviser explains that on its own the stock is extremely volatile, but because its beta is low and its returns are largely unrelated to the market, a small position adds relatively little to the overall portfolio’s risk. The adviser models the portfolio’s standard deviation before and after the purchase to show the effect.

The adviser also points out that a 55 percent standard deviation means the position could easily halve in a bad year. The client decides to limit the position to 3 percent, and the adviser documents the discussion, the risk figures and how the decision fits the client’s goals and time horizon.

The Dictionary as a Video Library

The FRC dictionary is a study tool, not just a glossary. Every entry pairs a written explanation with deep-dive video, on-page quizzes and interactive flash cards, so you can read a concept, watch it explained and test yourself in one place.

Rules are covered in the same depth: open a rule and you will find the full explanation alongside video walk-throughs of how it applies in practice. Open the standard deviation and beta entries to see each calculation worked through on video and test yourself with the quizzes.

Practice Questions to Test Yourself

Question one: Which measure captures both systematic and unsystematic risk? Standard deviation.

Question two: A portfolio holds 40 percent in a fund with a beta of 1.5 and 60 percent in a fund with a beta of 0.5. What is the portfolio beta? 0.9, because 0.6 plus 0.3 equals 0.9.

Question three: A stock has a standard deviation of 20 percent and a beta of 0.8, and the market’s standard deviation is 15 percent. What is its systematic variance? 144, because 0.8 squared is 0.64 and 0.64 times 225 is 144.

Question four: Two stocks with standard deviations of 20 percent are combined equally, and their correlation is less than 1. Is the portfolio standard deviation 20 percent? No, it is lower, because imperfect correlation reduces combined volatility.

Question five: A fund has an R-squared of 0.25 against the S&P 500. Is its beta a reliable risk measure? No, because only a quarter of its volatility is explained by the market.

Turn Analytical Skill Into Career Evidence

Explaining risk in plain language is one of the most valuable skills in client advice, especially when markets turn. FRC’s Digital Profile shows employers the courses you are actively studying and the progress you have earned through assessed learning, verified by FRC, and a QR code on your resume takes them straight to it.

The FRC Video Resume lets a hiring manager hear you before the interview. Explaining why a volatile stock can add little risk to a diversified portfolio shows the analytical judgment investment firms look for.

Related Questions

Standard deviation and beta each sit on the horizontal axis of a different line in portfolio theory, as explained in Security Market Line vs Capital Market Line. For a way to limit downside volatility on a holding without selling it, see our comparison of call option vs put option.

Key Points to Retain

Standard deviation measures the total volatility of an investment’s returns around their average, including both market and company-specific risk. Beta measures only market risk, showing how much an investment tends to move for each 1 percent move in the market.

Total variance splits into systematic variance, equal to beta squared times the market’s variance, and unsystematic variance, which diversification can remove. Portfolio beta is a weighted average of the holdings’ betas, but portfolio standard deviation is usually lower than the weighted average, and beta is reliable only when R-squared is reasonably high.

For the role the exam leads to, read our guide to what an investment advisor representative is.