The Same Excess Return, Divided by Different Risks

The Sharpe ratio and the Treynor ratio both measure how much return an investment earned above the risk-free rate for each unit of risk taken. The difference is the risk measure: the Sharpe ratio divides excess return by standard deviation, which captures total risk, while the Treynor ratio divides it by beta, which captures only market risk.

That one difference decides when each ratio is useful. The Sharpe ratio suits an investment that will be held on its own, or a whole portfolio, while the Treynor ratio suits a holding that will sit inside an already diversified portfolio.

For both ratios, higher is better, and both can rank the same funds in a different order. For the full route from the exam to a career applying these measures, our complete guide to how to become an investment adviser representative covers every step.

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How the Sharpe Ratio Works

The Sharpe ratio, developed by Nobel laureate William Sharpe, is calculated as the portfolio return minus the risk-free rate, divided by the portfolio’s standard deviation. It answers the question: how much extra return did this investment deliver for each unit of total volatility?

Because standard deviation includes both market risk and company-specific risk, the Sharpe ratio penalises investments that are poorly diversified. A concentrated fund that swings sharply will have a lower Sharpe ratio than a diversified fund with the same return.

The Sharpe ratio is the most widely quoted risk-adjusted measure in fund reports and marketing material. The Series 65 Exam Preparation course at FRC covers it alongside the other performance measures the exam tests.

How the Treynor Ratio Works

The Treynor ratio, developed by Jack Treynor, is calculated as the portfolio return minus the risk-free rate, divided by the portfolio’s beta. It answers a different question: how much extra return did this investment deliver for each unit of market risk?

Because beta ignores company-specific risk, the Treynor ratio assumes that risk has already been diversified away. It is therefore most meaningful for well-diversified portfolios, or for a holding being added to one.

The Treynor ratio is expressed in percentage points per unit of beta, so its values look larger than Sharpe ratios. The two cannot be compared with each other, only with the same ratio for other investments.

Sharpe Ratio and Treynor Ratio Compared

Worked Example: Calculating Both Ratios

The risk-free rate is 4 percent. Fund A returned 12 percent with a standard deviation of 18 percent and a beta of 0.9, and Fund B returned 11 percent with a standard deviation of 12 percent and a beta of 1.2.

Step one: Fund A’s Sharpe ratio is 8 divided by 18, or 0.44, and Fund B’s is 7 divided by 12, or 0.58, so Fund B ranks higher. Step two: Fund A’s Treynor ratio is 8 divided by 0.9, or 8.9, and Fund B’s is 7 divided by 1.2, or 5.8, so Fund A ranks higher.

Step three: the rankings reverse because Fund A carries a lot of company-specific risk, shown by its high standard deviation relative to its beta. The Sharpe ratio penalises that risk, while the Treynor ratio ignores it.

Which Fund Should the Client Choose?

The answer depends on how the fund will be used. If the client will hold only one of these funds, total risk is what the client experiences, so the Sharpe ratio is the right guide and Fund B is the better choice.

If the fund will be a small part of an already well-diversified portfolio, much of Fund A’s company-specific risk will be diversified away. In that case, market risk is what matters, the Treynor ratio is the better guide, and Fund A adds more return per unit of the risk that remains.

This is the most important exam point about the two ratios. The question is not which ratio is better in general, but which one fits the portfolio the investment will sit in.

Worked Example: Ranking Three Funds Against the Market

The risk-free rate is 4 percent and the market returned 10 percent with a standard deviation of 16 percent and, by definition, a beta of 1.0. Fund X returned 9 percent with a standard deviation of 10 percent and a beta of 0.7, Fund Y returned 14 percent with a standard deviation of 22 percent and a beta of 1.4, and Fund Z returned 11 percent with a standard deviation of 15 percent and a beta of 1.1.

Step one: the market’s Sharpe ratio is 6 divided by 16, or 0.375, and its Treynor ratio is 6 divided by 1.0, or 6.0. Step two: the Sharpe ratios are 0.50 for Fund X, 0.45 for Fund Y and 0.47 for Fund Z, so all three beat the market on total risk, with Fund X best.

Step three: the Treynor ratios are 7.1 for Fund X, 7.1 for Fund Y and 6.4 for Fund Z, so all three also beat the market on market risk, with X and Y tied. Step four: the highest raw return, Fund Y’s 14 percent, does not make it the best fund on either measure once risk is taken into account.

This is the lesson clients most often need to hear. A fund at the top of a return league table may simply have taken the most risk, and risk-adjusted measures show whether that risk was rewarded.

Study Performance Measurement With FRC

Questions on risk-adjusted returns often give a small table of funds and ask which is best, and the right answer depends on reading what kind of portfolio the client holds. Our Series 65 course trains you to calculate each ratio quickly and choose the right one for the scenario.

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 the Ratios Connect to Portfolio Theory

The Sharpe ratio of the market portfolio is the slope of the capital market line, and the Treynor ratio of the market is the slope of the security market line, which equals the market risk premium because the market’s beta is 1.0. Our article on security market line vs capital market line explains both lines.

An investment with a higher Sharpe ratio than the market lies above the capital market line, offering more return per unit of total risk than the market itself. An investment with a higher Treynor ratio than the market lies above the security market line, which means it has positive alpha.

This link is why the Treynor ratio and alpha tell a similar story. Both judge performance against market risk, while the Sharpe ratio judges it against everything the investor has to live with.

Leverage Does Not Change the Sharpe Ratio

Mixing an investment with cash or borrowing to invest more in it changes both its excess return and its standard deviation in the same proportion. As a result, the Sharpe ratio stays the same.

Worked example: Fund A, with a 12 percent return and an 18 percent standard deviation, is combined half and half with Treasury bills yielding 4 percent. Step one: the combined portfolio returns 8 percent with a standard deviation of 9 percent. Step two: its Sharpe ratio is 4 divided by 9, or 0.44, exactly the same as Fund A on its own.

This is why the Sharpe ratio is useful for comparing investment strategies: a fund cannot improve it simply by taking more risk. It can only improve it by earning more return for the risk it takes.

Other Risk-Adjusted Measures

Several other ratios build on the same idea. The Sortino ratio replaces standard deviation with downside deviation, penalising only volatility below a target return, which many investors see as the risk that really matters. It is popular with clients who care more about avoiding losses than about volatility in general.

The information ratio divides a manager’s return above the benchmark by tracking error, the standard deviation of that excess return. It measures how consistently an active manager beats the benchmark, and a figure of around 0.5 or higher sustained over several years is generally regarded as strong.

Jensen’s alpha measures return above the level the capital asset pricing model predicts, in percentage points rather than as a ratio. Our article on alpha vs beta works through that calculation.

Limits of Both Ratios

Both ratios rely on past returns, and results can change a great deal depending on the period chosen. A fund that looks excellent over three years may look very different over ten.

The Sharpe ratio treats upside and downside volatility as equally bad, and it can be misleading for investments whose returns are not normally distributed, such as strategies that sell options and occasionally suffer large losses. The Treynor ratio is only as reliable as the beta behind it, and beta means little for funds with a low R-squared against their benchmark.

Negative ratios, which arise when returns fall below the risk-free rate, are also hard to interpret. In those cases, a fund with more risk can appear to have a better ratio, so advisers should compare negative values with caution.

Using the Ratios in Client Fund Reviews

Advisers rarely rely on a single number. A sound fund review looks at the Sharpe and Treynor ratios over several periods, such as three, five and ten years, alongside alpha, beta, R-squared, fees and the consistency of the manager’s approach.

The ratios should also be compared with an appropriate peer group. A bond fund’s Sharpe ratio should be judged against other bond funds with similar duration and credit quality, not against an equity fund, because the risk and return patterns are so different.

Finally, risk-adjusted performance has to be translated into language the client understands. Saying that a fund earned more return for each unit of risk it took, and showing how much it fell in the last downturn, is usually more useful to a client than quoting the ratio itself.

The Memory Aid

Remember “Sharpe sees everything, Treynor sees the market”: the Sharpe ratio uses total risk, the Treynor ratio uses only market risk.

For when to use each, remember “solo, use Sharpe; in a team, use Treynor”: the Sharpe ratio for stand-alone holdings, the Treynor ratio for holdings within a diversified portfolio.

For the formulas, remember “same top, different bottom”: both use excess return on top, with standard deviation or beta on the bottom.

Exam Traps to Avoid

The first trap is using the Treynor ratio to judge a client’s only investment. Because the client bears all of its risk, the Sharpe ratio is the right measure.

The second trap is comparing a Sharpe ratio with a Treynor ratio. They use different units and can only be compared with the same ratio for other investments.

The third trap is forgetting to subtract the risk-free rate. Both ratios use excess return, not total return. The fourth trap is assuming a fund can raise its Sharpe ratio simply by adding leverage; doing so raises return and risk in the same proportion.

A Client Scenario

A client with a well-diversified $1.5 million portfolio wants to add one actively managed equity fund for 5 percent of the total and asks the adviser to choose between two candidates. The adviser is shown fund factsheets highlighting each fund’s Sharpe ratio.

The adviser explains that because the new fund will be a small part of a diversified portfolio, most of its company-specific risk will be diversified away, so the Treynor ratio and alpha are the more relevant measures. The adviser calculates both for each fund over several periods and checks that each fund’s beta is reliable.

The adviser recommends the fund with the higher and more consistent Treynor ratio, explains why it ranks second on Sharpe ratio, and documents how the choice fits the client’s goals and existing holdings.

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 Sharpe ratio and Treynor ratio entries to see each formula worked through on video and test yourself with the quizzes.

Practice Questions to Test Yourself

Question one: A portfolio returned 10 percent with a standard deviation of 15 percent, and the risk-free rate was 4 percent. What is its Sharpe ratio? 0.40, because 6 divided by 15 is 0.40.

Question two: The same portfolio has a beta of 0.8. What is its Treynor ratio? 7.5, because 6 divided by 0.8 is 7.5.

Question three: A client will hold only one fund. Which ratio should guide the choice? The Sharpe ratio, because the client bears the fund’s total risk.

Question four: Which ratio ignores company-specific risk? The Treynor ratio, because it uses beta, which measures only market risk.

Question five: A fund is mixed 50 percent with Treasury bills. What happens to its Sharpe ratio? It stays the same, because excess return and standard deviation both fall by half.

Turn Analytical Skill Into Career Evidence

Choosing between funds on a risk-adjusted basis is part of everyday advisory work, and clients notice when an adviser can explain the choice clearly. 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 two ratios can rank the same funds differently shows the analytical depth investment firms look for.

Related Questions

Risk-adjusted returns matter just as much in fixed income, where higher yields usually mean more credit risk. Our comparison of investment grade vs high yield bonds shows how that trade-off works for bond investors.

Key Points to Retain

The Sharpe ratio is excess return divided by standard deviation, measuring return per unit of total risk, and is the right measure for stand-alone investments and whole portfolios. The Treynor ratio is excess return divided by beta, measuring return per unit of market risk, and suits holdings within a well-diversified portfolio.

The two ratios can rank funds differently when a fund carries a lot of company-specific risk. Leverage does not change the Sharpe ratio, both ratios depend on the period measured, and related measures include the Sortino ratio, the information ratio and Jensen’s alpha.

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