Treynor ratio in mutual funds
The Treynor ratio (also called the reward-to-volatility ratio or Treynor measure) is a risk-adjusted performance measure that divides a fund’s excess return (return above the risk-free rate) by its beta, a measure of systematic market risk, rather than by total standard deviation as in the Sharpe ratio. Developed by Jack Treynor in 1965, it is based on the Capital Asset Pricing Model (CAPM) framework and is appropriate when the mutual fund is evaluated as a component within a larger, well-diversified portfolio.
Formula
\[ \text{Treynor ratio} = \frac{R_p - R_f}{\beta_p} \]
Where:
| Symbol | Meaning |
|---|---|
| \(R_p\) | Portfolio (fund) return (annualised) |
| \(R_f\) | Risk-free rate (91-day T-bill yield) |
| \(\beta_p\) | Fund’s beta relative to its benchmark |
The Treynor ratio is expressed in per cent per unit of beta, unlike the Sharpe ratio which is a pure dimensionless ratio.
Worked example
Two mid-cap equity funds over a 3-year period:
| Metric | Fund A | Fund B |
|---|---|---|
| Annualised return | 18.0% | 20.0% |
| Risk-free rate | 6.8% | 6.8% |
| Beta | 0.85 | 1.25 |
| Standard deviation | 18% | 28% |
Treynor ratio:
\[ \text{Fund A} = \frac{18.0 - 6.8}{0.85} = \frac{11.2}{0.85} = 13.18 \]
\[ \text{Fund B} = \frac{20.0 - 6.8}{1.25} = \frac{13.2}{1.25} = 10.56 \]
Sharpe ratio:
\[ \text{Fund A} = \frac{11.2}{18.0} = 0.62 \]
\[ \text{Fund B} = \frac{13.2}{28.0} = 0.47 \]
Fund B appears to have a higher absolute return, but both Treynor and Sharpe ratios indicate that Fund A delivers better risk-adjusted performance. Fund B’s higher return is explained by its higher beta (more market risk taken), not superior manager skill.
When to use Treynor vs Sharpe
| Investor situation | Appropriate measure |
|---|---|
| Fund is the investor’s only risky asset | Sharpe ratio |
| Fund is one of several in a diversified portfolio | Treynor ratio |
| Evaluating manager skill per unit of active risk | Information ratio |
| Absolute excess return adjusted for systematic risk | Jensen’s alpha |
The logic: in a diversified portfolio, unsystematic (stock-specific) risk is diversified away. Only systematic risk (captured by beta) matters for portfolio-level risk. The Treynor ratio correctly prices only systematic risk, making it the appropriate metric for fund selection within a multi-fund portfolio.
Treynor ratio and Jensen’s alpha
Both metrics are beta-based and rooted in CAPM. The difference:
- Treynor ratio is a ratio, excess return divided by beta. It ranks funds by efficiency of systematic risk use.
- Jensen’s alpha is an absolute measure, actual excess return minus CAPM-predicted excess return. It shows how much the manager added (or destroyed) in return terms.
A fund can have a high Treynor ratio (efficient use of systematic risk) but zero alpha (no return beyond CAPM prediction). Conversely, a fund with meaningful alpha will also show a Treynor ratio above the benchmark’s Treynor ratio.
The benchmark’s Treynor ratio is:
\[ T_m = \frac{R_m - R_f}{\beta_m} = \frac{R_m - R_f}{1.0} = R_m - R_f \]
Since the benchmark’s beta is 1.0 by definition, the benchmark’s Treynor ratio equals its equity risk premium. A fund with a Treynor ratio exceeding the benchmark’s equity risk premium has delivered superior risk-adjusted returns.
Limitations
- Beta instability: Like all beta-dependent measures, the Treynor ratio relies on a stable beta estimate. Beta can shift meaningfully across market cycles, particularly for funds with dynamic asset allocation mandates.
- Ignores unsystematic risk: In a concentrated portfolio (fewer than 20–30 stocks), unsystematic risk is material and the Treynor ratio understates total risk.
- Low-beta funds may rank artificially high: A cash-heavy or defensive fund with a low beta might show a high Treynor ratio not because of manager skill but because the beta denominator is small. Cross-check with alpha and R-squared, a high Treynor ratio is most meaningful when R² is high (fund is closely correlated with the benchmark).
- R-squared caveat: The Treynor ratio is unreliable for funds with low R² (below 0.80). For such funds, beta is a poor summary of market exposure, and the ratio loses interpretive value.
- Not standard in Indian AMC factsheets: Unlike the Sharpe ratio, the Treynor ratio is not mandated by SEBI or AMFI in monthly factsheet disclosures. It is available on third-party platforms (Morningstar India, PrimeInvestor) and is used more in institutional investment analysis than in retail fund selection.
Treynor ratio for the benchmark
The benchmark’s Treynor ratio (equal to the equity risk premium) serves as the threshold. For the Nifty 50 with a long-term equity risk premium of approximately 6–8 per cent (above the risk-free rate), any equity fund with a Treynor ratio below this range is underperforming on a risk-adjusted basis.
Typical Treynor ratios in Indian equity funds (2020–2024)
| Category | Typical Treynor ratio range |
|---|---|
| Large-cap equity | 8–14 |
| Mid-cap equity | 9–18 |
| Small-cap equity | 8–20 |
| Flexi-cap | 9–16 |
| Nifty 50 benchmark (reference) | 7–10 |
These ranges are highly sensitive to the period chosen and the prevailing risk-free rate.
See also
- Beta in mutual funds
- Sharpe ratio in mutual funds
- Alpha (Jensen’s alpha) in mutual funds
- Information ratio
- R-squared in mutual funds
- Total expense ratio
- Mutual fund
References
- Treynor, J. L. (1965). “How to Rate Management of Investment Funds.” Harvard Business Review, 43(1), 63–75.
- Jensen, M. C. (1968). “The Performance of Mutual Funds in the Period 1945–1964.” Journal of Finance, 23(2), 389–416.
- AMFI, Risk statistics in factsheets, amfiindia.com.
- Morningstar India, Fund risk-return analytics, morningstar.in.
- Bodie, Z., Kane, A., and Marcus, A. J., Investments, 12th edition, McGraw-Hill.