Calcady™
Home / Financial / Treynor Ratio Calculator

Treynor Ratio Calculator

Calculate the Treynor Ratio to measure a portfolio's risk-adjusted performance relative to its systematic market risk (Beta).

Portfolio Performance

%

The total return generated by the portfolio over the measurement period.

%

Typically the current 3-month US Treasury Bill yield (currently ~4.5–5.3%).

Market sensitivity coefficient. S&P 500 = 1.0. Above 1.0 = more volatile, below 1.0 = less volatile.

Excellent Risk-Adjusted Returns

Treynor Ratio

6.25
Excess return earned per unit of Beta
Portfolio Return:12%
Risk-Free Rate:-4.5%
Excess Return:7.50%
Divided by Beta:÷ 1.2
Email LinkText/SMSWhatsApp

What is Treynor Ratio?

The Treynor Ratio, developed by economist Jack Treynor in 1966, measures how much excess return a portfolio generates for each unit of systematic (market) risk taken, as measured by the portfolio's Beta. It is a key metric for comparing portfolios that are part of a larger, diversified strategy.

Mathematical Foundation

Treynor=Rp−Rfβp\text{Treynor} = \frac{R_p - R_f}{\beta_p}
RpR_p= Portfolio Return — actual return generated over the period
RfR_f= Risk-Free Rate — typically the 3-month US Treasury Bill yield
βp\beta_p= Portfolio Beta — sensitivity to market movements (S&P 500 Beta = 1.0)

Laws & Principles

  • Treynor vs. Sharpe: The key difference is the risk denominator. The Sharpe Ratio uses total standard deviation (both systematic and unsystematic risk). The Treynor Ratio uses only Beta (systematic risk). Treynor is the preferred metric when a portfolio is only one slice of a larger, fully-diversified allocation, because unsystematic risk is already eliminated by diversification.
  • Beta Interpretation: A Beta of 1.2 means the portfolio historically moves 20% more than the market — up or down. A Beta of 0.7 means the portfolio is 30% less volatile than the market.

Step-by-Step Example Walkthrough

" A fund manager reports a 12% portfolio return. The risk-free rate is 4.5%. The portfolio's Beta is 1.2. "

  1. 1. Excess Return: 12% - 4.5% = 7.5%
  2. 2. Treynor Ratio: 7.5% / 1.2 = 6.25
Final Result: The Treynor Ratio is 6.25. If a comparable fund has a Treynor of 4.0, this manager is generating substantially better risk-adjusted returns per unit of market risk taken.

Quick Answer: How does the Treynor Ratio Calculator work?

The Treynor Ratio Calculator evaluates a portfolio's risk-adjusted returns based strictly on market volatility. Input your portfolio return, the current risk-free rate, and your portfolio's Beta coefficient. The calculator instantly derives the excess return generated per unit of systematic risk. A higher ratio indicates superior risk-adjusted performance, allowing you to accurately compare funds or managers operating within a broader diversified portfolio strategy.

Treynor Ratio Formula

The Core Equation

Treynor Ratio = (Portfolio Return − Risk-Free Rate) ÷ Beta

  • Numerator— Excess Return: The return generated above what you could have made holding risk-free Treasury Bills.
  • Denominator— Beta: The measure of systematic (market) risk. It isolates the volatility that cannot be diversified away.

Real-World Scenarios

✓ Maximum Capital Efficiency

Comparing two funds where the lower-returning fund is actually superior

  1. Fund A: Return 15%, Beta 1.5
  2. Fund B: Return 12%, Beta 0.8
  3. Risk-Free Rate: 4%
  4. Fund A Treynor: (15 - 4) / 1.5 = 7.33
  5. Fund B Treynor: (12 - 4) / 0.8 = 10.00

→ Fund B is mathematically superior. Although its raw return is lower, it generates dramatically more excess return per unit of market risk it exposes you to.

✗ The Leverage Trap

A fund manager taking extreme risks to artificially pump returns

  1. Market Return: 10% (Beta 1.0)
  2. Fund Return: 18%
  3. Manager's Beta: 2.8 (Extreme leverage)
  4. Risk-Free Rate: 4%
  5. Fund Treynor: (18 - 4) / 2.8 = 5.00

→ The manager is underperforming. The market's Treynor is 6.0. The manager's massive 18% return was achieved through reckless leverage, destroying risk-adjusted value.

Treynor Ratio Performance Benchmarks

Treynor Value Performance Rating Action
< 0 Destructive Liquidate capital
0.1 − Market T.R. Sub-Par Switch to passive index funds
Matches Market Indexed Acceptable for core holdings
> Market T.R. Alpha Generated Retain manager/strategy
* Note: Treynor benchmarks are purely relative. Always compare a fund's Treynor Ratio against a relevant benchmark index (like the S&P 500) during the exact same timeframe.

Pro Tips & Common Pitfalls

Do This

  • ✓Use Treynor for diversified sub-portfolios. If you are evaluating a single mutual fund that forms just 10% of your total diversified portfolio, use the Treynor ratio. Since the overall portfolio handles diversification, you only care about compensating for the systematic risk (Beta) of the individual fund.
  • ✓Compare against equivalent peers. A high-yield bond fund will naturally have a different Treynor ratio than an emerging markets equity fund. Rank funds strictly against peers within their specific asset class.

Avoid This

  • ✗Don't use Treynor for your entire net worth. If you are evaluating your entire, undivided portfolio, use the Sharpe Ratio instead. Treynor ignores unsystematic (specific) risk, which you are fully exposed to if your total portfolio is poorly diversified.
  • ✗Be cautious with negative Betas. The Treynor ratio relies on positive Beta. If evaluating a hedging strategy or short fund with a negative Beta, the formula breaks mathematically (yielding a negative ratio for positive returns) and alternate metrics must be used.

Frequently Asked Questions

What is a 'good' Treynor Ratio?

Unlike absolute metrics, there is no fixed "good" Treynor Ratio. The number is dimensionless and only has meaning when compared directly to the Treynor Ratio of an appropriate market benchmark (like the S&P 500) over the exact same time period. If an active fund's Treynor is higher than the index's Treynor, the manager added value.

What is the difference between Treynor and Sharpe Ratio?

Both measure risk-adjusted return, but they use different definitions of risk. The Sharpe ratio divides excess return by standard deviation (total volatility, both market and stock-specific). The Treynor ratio divides excess return by Beta (only market-driven systemic volatility). Use Treynor when comparing a single fund that fits inside a broader, diversified portfolio.

What does a negative Treynor Ratio mean?

Assuming a positive Beta, a negative Treynor ratio means the portfolio actually underperformed the risk-free rate. You took on equity market risk but generated less return than you would have by sitting in completely safe US Treasury Bills. It indicates a destructive investment strategy.

Why do highly volatile tech stocks often have good Treynor Ratios?

Because the Treynor ratio ignores specific, idiosyncratic risk. A highly volatile single tech stock might swing wildly on earnings reports (huge standard deviation), which would ruin its Sharpe ratio. But if its market-correlated Beta is standard (e.g., 1.2), the Treynor ratio ignores those earnings swings, making it look highly efficient. This mathematical blind spot is why Treynor must only be applied to diversified mutual funds or ETFs, not single stocks.

Related Calculators