Treynor Ratio Divides Your Return by Beta, Not Volatility. That Changes Which Portfolio Wins
6 min read
Loading...
6 min read
You are comparing two portfolios. Portfolio A bounces around more than Portfolio B, so its Sharpe ratio looks worse. Case closed, B wins, right?
Not so fast. A large chunk of Portfolio A's bounciness might have nothing to do with the market at all, it could just be noise specific to the handful of stocks it holds. Once you strip that noise out and look only at how much each portfolio moves with the market, Portfolio A can come out ahead. The Treynor ratio is the number built to make exactly that comparison, and it does not always agree with Sharpe ratio about who actually won.
The Treynor ratio divides a portfolio's excess return, how much it earned above a risk-free rate, by its beta.
(Portfolio return − Risk-free rate) ÷ Beta
Two terms worth pinning down before anything else:
Risk-free rate is the return you could get with essentially zero risk, usually approximated with a short-term government instrument like a Treasury bill, or in Indonesia, an instrument like Bank Indonesia's own rate-setting tools. It is the baseline every "excess return" is measured against.
Beta measures how much a portfolio tends to move when the overall market moves, calculated by comparing its returns against a benchmark index over time. A beta of 1.0 means the portfolio has historically moved in step with its benchmark. A beta of 0.6 means it has historically moved about 60% as much. A beta of 1.5 means it has historically moved about 50% more.
The Treynor ratio was introduced by the economist Jack L. Treynor in his 1965 paper "How to Rate Management of Investment Funds," published in the Harvard Business Review. Treynor also co-developed the Capital Asset Pricing Model (CAPM), which is where beta itself comes from as a concept, so the two ideas share the same DNA.
Sharpe ratio divides excess return by standard deviation, a measure of how spread out a portfolio's total returns have been. That total includes every source of bounciness a portfolio has.
Beta only counts one slice of that bounciness: the part that moves together with the market. Modern portfolio theory splits a portfolio's total risk into two pieces.
Systematic risk is the part tied to the broader market, things like interest rate moves, a recession, or a market-wide selloff. You cannot diversify this away, because it affects almost everything at once. Beta measures exposure to this piece specifically.
Unsystematic risk, also called diversifiable risk, is the part specific to individual holdings, a single company's earnings miss, a factory fire, a product recall. A well-diversified portfolio spreads this kind of risk thin across many holdings, so in theory it should not be the part an investor gets compensated for carrying.
A portfolio can have high total volatility while still having a low beta, if most of that volatility comes from stock-specific noise rather than broad market swings. That is the exact gap Treynor ratio is built to see and Sharpe ratio is not.
Here are two hypothetical portfolios, used purely to show the mechanics, both earning the same 8% excess return over the risk-free rate in a given year.
Portfolio A holds a concentrated set of smaller, more idiosyncratic stocks. Its total volatility (standard deviation) is 20%, but because those stocks do not all move together with the broader market, its beta is only 0.6.
Portfolio B holds a set of large, market-tracking stocks. Its total volatility is a calmer 12%, but because those stocks move closely with the index, its beta is a full 1.0.
| Portfolio A | Portfolio B | |
|---|---|---|
| Excess return | 8% | 8% |
| Total volatility (standard deviation) | 20% | 12% |
| Beta | 0.6 | 1.0 |
| Sharpe ratio (excess return ÷ volatility) | 0.40 | 0.67 |
| Treynor ratio (excess return ÷ beta) | 13.3% | 8.0% |
By Sharpe ratio, Portfolio B wins clearly, less pain for the same return. By Treynor ratio, Portfolio A wins just as clearly, more return for every unit of market risk taken on. Neither ratio is wrong. They are answering different questions.
Treynor ratio tends to matter most when you are looking at one piece of a larger, already-diversified portfolio, rather than a standalone holding someone owns on its own. The logic behind CAPM, which Treynor ratio leans on, assumes unsystematic risk gets diversified away somewhere else in an investor's total holdings, so only the market-linked piece should earn a reward.
If a portfolio is not actually diversified, a handful of concentrated positions with real company-specific risk still sitting exposed, Treynor ratio can flatter it by ignoring risk that has not actually been diversified away yet. That is the ratio's own sharpest limitation: it assumes a condition (real diversification) that has to be checked separately, not assumed.
Treynor ratio also depends entirely on which benchmark you calculate beta against. A stock or portfolio can carry a very different beta against the IHSG than it would against the S&P 500, so a Treynor ratio computed against the wrong benchmark for a portfolio's actual exposure can mislead rather than clarify.
You need three numbers: your portfolio's return over a period, a risk-free rate for the same period, and your portfolio's beta against a relevant benchmark.
NetWort calculates beta for individual holdings from real price history against a detected benchmark, not from an assumption. You can see a stock's own beta on its asset page, for example BBCA, Bank Central Asia, one of the more heavily-weighted names on the IHSG. A stock or portfolio with a beta below 1.0 has historically moved less than its benchmark; above 1.0, more.
Your beta sits alongside Sharpe ratio, volatility and drawdown in the Portfolio Health section of your dashboard. Pull that beta and your own return, subtract a risk-free rate benchmark of your choosing, and do the division yourself to see where your own portfolio lands. For the current BI Rate and broader rate backdrop to use as a risk-free rate reference, check the macro context page.