Treynor Ratio Calculator

1. What is the Treynor Ratio Calculator?

Definition: The Treynor Ratio Calculator computes the Treynor Ratio, a risk-adjusted performance metric that measures the return of a portfolio per unit of systematic risk (beta).

Purpose: It helps investors evaluate the portfolio's return relative to its market risk, aiding in comparing investments with different levels of systematic risk.

2. How Does the Calculator Work?

The calculator uses the following formula:

$ \text{TR} = \frac{\text{PR} - \text{Rf}}{\text{B}} $

Where:

$ \text{TR} $: Treynor Ratio (%);
$ \text{PR} $: Portfolio Return (decimal, $ \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} $);
$ \text{Rf} $: Risk-Free Rate (decimal);
$ \text{B} $: Portfolio Beta.

Steps:

Enter the beginning portfolio value.
Enter the ending portfolio value.
Enter the risk-free rate as a percentage.
Enter the portfolio beta.
Calculate the portfolio return and then the Treynor Ratio using the formula.
Display the result as a percentage, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Treynor Ratio Calculation

Calculating the Treynor Ratio is essential for:

Risk-Adjusted Performance: Measures return per unit of systematic risk, focusing on market-related volatility.
Portfolio Comparison: Enables comparison of portfolios with different beta values.
Investment Strategy: Guides adjustments to optimize risk-adjusted returns.

4. Using the Calculator

Example: Calculate the Treynor Ratio for Company Alpha with a beginning portfolio value of $2,000,000, ending value of $2,200,000, risk-free rate of 1.5%, and portfolio beta of 1.25:

$ \text{Beginning Value} $: $2,000,000;
$ \text{Ending Value} $: $2,200,000;
$ \text{PR} $: $ \frac{2,200,000 - 2,000,000}{2,000,000} = 0.10 $ or 10%;
$ \text{Rf} $: 1.5% or 0.015;
$ \text{B} $: 1.25;
$ \text{TR} $: $ \frac{0.10 - 0.015}{1.25} \times 100 \approx 6.8000\% $.

5. Frequently Asked Questions (FAQ)

Q: What is a good Treynor Ratio?
A: A Treynor Ratio above the market average (e.g., 5-10%) is generally considered good, depending on the industry.

Q: How is portfolio beta determined?
A: Beta is calculated as the weighted average of the betas of the portfolio's holdings, reflecting sensitivity to market movements.

Q: Can the Treynor Ratio be negative?
A: Yes, if the portfolio return is less than the risk-free rate, the Treynor Ratio will be negative.