Treynor ratio
Also written Reward-to-volatility ratio
Risk premium per unit of market risk — the return a scheme earned above the risk-free rate, divided by its beta rather than by its standard deviation.
In plain language
The Sharpe Ratio asks: how much excess return did this scheme earn for each unit of total risk it took? The Treynor Ratio asks a narrower question: how much excess return did it earn for each unit of market risk?
The numerator is identical — the scheme's return minus the risk-free rate, which the workbook calls the risk premium. The denominator is where they part. Sharpe divides by standard deviation, which captures every wobble the scheme had. Treynor divides by beta, which captures only the part of the wobble that came from the market moving.
Higher is better, for both.
How it works
Why would anyone want to ignore part of the risk? Because in a properly diversified portfolio the rest has already been dealt with.
Standard deviation measures total risk: systematic plus unsystematic. Beta measures systematic risk alone. If a scheme holds fifty stocks, its company-specific risk has largely been diversified away, and the risk that remains — the risk it is genuinely being paid to take — is market risk. Treynor measures the reward against precisely that.
The workbook is explicit about the consequence: since the concept of beta is more relevant for diversified equity schemes, Treynor Ratio comparisons should ideally be restricted to such schemes.
The market's beta is 1 by definition, so a scheme with a beta of 1.4 swings about 40 percent harder than the index, and one with a beta of 0.7 about 30 percent less. Dividing by beta therefore asks a fund manager who took a racier portfolio to bring back proportionately more.
Neither ratio is mandatory to disclose. The only measure of risk-adjusted return that AMCs must publish — daily, on their website, and in comparable format on AMFI's — is the Information Ratio.
The formula
Treynor Ratio = (Rs − Rf) ÷ Beta
Sharpe Ratio = (Rs − Rf) ÷ Standard deviation
where Rs is the scheme return, Rf the risk-free return (the T-Bill index is a good measure of it), and Rs − Rf the risk premium.
The workbook's illustration: risk-free return 5 percent, a scheme with a beta of 1.2 earning 8 percent.
Treynor Ratio = (8% − 5%) ÷ 1.2 = 2.5
A worked example
Two diversified equity schemes over the same three years, with the risk-free rate at 6.5 percent:
| Scheme P | Scheme Q | |
|---|---|---|
| Return | 16.0% | 14.2% |
| Risk premium | 9.5% | 7.7% |
| Beta | 1.35 | 0.88 |
| Standard deviation | 18.2% | 11.9% |
| Treynor Ratio | 9.5 ÷ 1.35 = 7.04 | 7.7 ÷ 0.88 = 8.75 |
| Sharpe Ratio | 9.5 ÷ 18.2 = 0.52 | 7.7 ÷ 11.9 = 0.65 |
Scheme P won on raw return by 1.8 percentage points and lost on both risk-adjusted measures. It earned more because it took more market risk, not because the manager was better: a beta of 1.35 in a rising market does that on its own.
Put it in rupees. An investor with Rs 10,00,000 in each finished with about Rs 15,61,000 in P and Rs 14,89,000 in Q — P ahead by roughly Rs 72,000. But when the market next falls 20 percent, P is built to fall about 27 percent and Q about 17.6 percent, a gap of some Rs 1,40,000 on the same corpus. Q gave up Rs 72,000 of upside to avoid twice that on the way down.
Why NISM asks about it
Chapter 7.4 (Concept of risk-adjusted return) presents Sharpe, Treynor and the Information Ratio together, with the worked figures above, and the examiner loves the pair. Expect the computation — (8% − 5%) ÷ 1.2 = 2.5 is in the workbook verbatim — and expect the discrimination question: which ratio uses beta (Treynor) and which uses standard deviation (Sharpe). The other reliably asked fact from the same section is that the Information Ratio is the only risk-adjusted measure mandatory for AMCs to disclose.
Common exam traps
- Treynor uses beta; Sharpe uses standard deviation. Everything else about the two is identical, and this is the whole question.
- Restrict Treynor comparisons to diversified equity schemes. Beta is meaningless for a concentrated or sectoral portfolio whose risk is mostly company-specific, and for a debt scheme.
- Never compare across scheme types. The workbook says a Sharpe Ratio of an equity scheme cannot be compared with that of a debt scheme, and the same restriction applies here.
- A negative risk premium makes both ratios nonsense. When a scheme underperforms the risk-free rate, a lower beta produces a more negative number — so ranking on the ratio inverts.
- Higher is better, but only against a comparable peer. A Treynor Ratio in isolation means nothing.
- Treynor is not mandatory to disclose. The Information Ratio is.
Where this is taught
- Series V-B · Chapter 7: Performance of Mutual Fundsintroduced here
- Series XIX-B · Chapter 6: Fees Structure, Fund Performance and Benchmarkingintroduced here
- Series XV · Chapter 12: Fundamentals of Risk and Returnintroduced here
- Series V-D · Chapter 11: Mutual Fund Scheme Performanceintroduced here
- Series V-A · Chapter 11: Mutual Fund Scheme Performanceintroduced here
- Series X-A · Chapter 16: Portfolio Performance Measurement and Evaluationintroduced here
- Series XIX-C · Chapter 9: Fee Structure and Fund Performanceintroduced here
Related terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- CAPMA model that prices the return an investor should demand from a share: the risk-free rate plus beta times the market risk premium.
- Sharpe ratioReturn earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Systematic riskThe part of an investment's risk that comes from economy-wide forces moving every asset at once — it cannot be diversified away, and it is the only risk the market pays you to carry.
- Unsystematic riskThe part of an investment's risk that belongs to one company or one issuer — a strike, a fraud, a downgrade — and which diversification can remove, unlike market-wide systematic risk.
- Information RatioExcess return over the benchmark divided by the standard deviation of that excess return — a measure of the manager's skill and of the consistency with which the excess return is produced.
- Tracking errorThe gap between the return of a passive fund and the return of the index it is trying to replicate — the measure of how faithfully an index fund or ETF does its one job.