Treynor Ratio Calculator Online – Easily Measure Risk-Adjusted Investment Performance
Treynor Ratio Calculator
Treynor Ratio Calculator
What is Treynor Ratio
The Treynor Ratio helps us understand how much excess return a portfolio generates for every unit of systematic risk it takes. In simple terms, if your portfolio assumes 1 unit of risk, the Treynor Ratio tells you how much extra return you're earning above the risk-free rate for taking on that risk. It's also known as the "reward-to-volatility" ratio.
To grasp this better, remember there are two kinds of returns:
1. Risk-free return –
This is what you earn without taking any risk, like returns from government bonds or fixed deposits. Let’s say government securities offer a return of 7%—you earn this without any market risk.
2. Risk-based return –
This is what you earn by taking on some level of market risk. For example, if a stock offers a 12% return, and the risk-free return is 7%, then you're earning an additional 5% for taking that risk.
The Treynor Ratio quantifies this extra 5% return per unit of risk, helping investors judge whether the additional return justifies the risk taken.
Understanding Beta (The Key Risk Component)
Treynor identified two key components of risk. The first arises from fluctuations in the overall stock market, while the second comes from the specific movements of an individual security. According to Treynor, understanding the relationship between these two types of risk is crucial—and the best way to analyze and manage this relationship is through beta.
So, what exactly is beta?
Beta is a measure of a portfolio’s sensitivity to market movements. In simple terms, it helps us gauge how much a portfolio will respond to changes in the market. For instance, if your portfolio has a beta of 1.5, and the market rises by 0.2 (or 20%), your portfolio is expected to increase by 1.5 times that amount—so, 30%. However, the reverse is also true: if the market drops, your portfolio could fall 1.5 times more than the market.
This means beta deals specifically with systematic risk—the kind of risk that is tied to the entire market and cannot be eliminated through diversification. It doesn't interfere with the market itself; instead, it reflects how much your portfolio is exposed to these unavoidable market-wide swings.
Example: Which Portfolio Manager Performed Best?
Example: Imagine that over a 10-year period, the S&P 500 (representing the market portfolio) delivered an average annual return of 10%, while Treasury bills (a reliable proxy for the risk-free rate) offered an average annual return of 5%. Now, consider the performance of three different portfolio managers over the same time span:
• Manager A: Average annual return = 10%, Beta = 0.90
• Manager B: Average annual return = 14%, Beta = 1.03
• Manager C: Average annual return = 15%, Beta = 1.20
Let’s evaluate how each manager performed relative to their level of market risk.
Solution.
First, we determine the current Treynor Ratio of the market.
T(Market) = (portfolio return - risk free rate)/beta
portfolio return = 10% = 10%/100% = 0.10
risk free rate = 5% = 5%/100% = 0.05
Beta = 1
T(Market) = (0.10 - 0.05)/1
T(Market) = 0.05
This serves as a benchmark—if a portfolio delivers a return of 0.05 per unit of risk, it becomes the standard. A portfolio with a higher Treynor Ratio is considered to be performing well, while one with a lower ratio is underperforming.
Now, let’s evaluate the three portfolios.
Calculation: Manager A
T(A) = (portfolio return - risk free rate)/beta
portfolio return = 10% = 10%/100% = 0.10
risk free rate = 5% = 5%/100% = 0.05
Beta = 0.90
T(A) = (0.10 - 0.05)/0.90
T(A) = 0.056
Calculation: Manager B
T(B) = (portfolio return - risk free rate)/beta
portfolio return = 14% = 10%/100% = 0.14
risk free rate = 5% = 5%/100% = 0.05
Beta = 0.90
T(B) = (0.14 - 0.05)/01.03
T(B) = 0.087
Calculation: Manager C (and the Final Verdict)
T(C) = (portfolio return - risk free rate)/beta
portfolio return = 15% = 15%/100% = 0.15
risk free rate = 5% = 5%/100% = 0.05
Beta = 1.20
T(C) = (0.15 - 0.05)/1.20
T(C) = 0.083
Among them, Manager B delivers the highest return, followed by Manager C, and finally Manager A.
About the Author: Abhishek Lohar
B.Com Graduate and the Founder of Free Online Financial Calculator. I specialize in simplifying complex financial calculations and investment strategies. My mission is to ensure you can make confident financial decisions using our research-backed content and accurate calculators.
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Disclaimer: The information provided in this article is for educational purposes only and should not be considered financial advice. Please consult with a qualified professional before making any investment decisions.