## What is the Treynor Ratio?

The term “Treynor ratio” refers to the financial metric that helps assess how much excess return has been generated for each unit of portfolio level risk. The Treynor ratio has been named after its developer Jack Treynor, an American economist and one of the developers of another remarkable finance theory – the Capital Asset Pricing Model CAPM.

**Formula**

The formula for the Treynor ratio is expressed as the portfolio’s excess rate of return as compared to the risk-free rate of return divided by the beta or systematic risk of the portfolio. Mathematically, it is represented as below,

**Treynor Ratio = (r**

_{p}– r_{f}) / β### Example of Treynor Ratio (With Excel Template)

Let’s take an example to understand the calculation in a better manner.

#### Example #1

**Let us take the example of a mutual fund portfolio to illustrate the Treynor ratio concept. During the last year, the portfolio generated a rate of 6.6%, while the government treasury bills generated a return of 3.0% during the same period. First, calculate the Treynor ratio of the portfolio if its systematic risk is 0.20.**

**Solution:**

It is calculated using the formula given below

**Treynor Ratio = (r _{p} – r_{f}) / β**

- Treynor Ratio = (6.6% – 3.0%) / 0.20
- Treynor Ratio =
**0.180**

Therefore, the portfolio of mutual funds generated a risk-adjusted return of 0.180 per unit of systematic risk.

#### Example #2

**Let us take the example of two portfolios, A and B, to illustrate the use of the Treynor ratio in selecting better investment options. Portfolio A consists of mutual fund investments with higher returns and higher risk, while portfolio B is mostly of government bonds with stable returns and lower risk. The return and systematic risk of portfolio A are 8.5% and 1.2, respectively, while portfolio B’s and systematic risk are 4.5% and 0.15, respectively. Calculate whether portfolio A or B is a better investment option if the risk-free rate of return is 4.0%.**

**Solution:**

It is calculated using the formula given below

**Treynor Ratio = (r _{p} – r_{f}) / β**

**For Portfolio A**

- Treynor Ratio = (8.5% – 4.0%) / 1.2
- Treynor Ratio =
**0.038**

**For Portfolio B**

- Treynor Ratio = (4.5% – 4.0%) / 0.15
- Treynor Ratio =
**0.033**

Therefore, based on the Treynor ratios, it can be concluded that portfolio A offers better risk-adjusted returns than portfolio B. So, out of the two portfolios, A is the better investment option.

### Explanation

The formula can be calculated by using the following steps:

**Step 1:** Firstly, determine the return of the given portfolio over a specific period, say a year. The computed rate of return of the portfolio is denoted by r_{p}.

**Step 2:** Next, ascertain the return for the risk-free rate of return, which is usually the return of long-term government treasury bills. The risk-free rate of return is denoted by r_{f}.

**Step 3:** Next, calculate the rate of return generated by the portfolio more than the risk-free rate of return, computed by subtracting the risk-free rate of return (step 2) from the portfolio’s rate of return (step 1).

**Excess rate of return = r _{p} – r_{f}**

**Step 4:** Next, determine the portfolio’s beta (β), which measures its systematic risk. The beta indicates how the portfolio’s return changes in responding to the change in overall market return.

**Step 5:** Finally, the formula is derived by dividing the portfolio’s excess rate of return (step 3) by the portfolio’s beta (step 4).

**Treynor ratio = (r _{p} – r_{f}) / β**

### How does it work?

This risk-adjusted return metric is adjusted based on the portfolio’s systematic risk. The financial ratio helps assess whether or not an investment portfolio generates an adequate rate of return that is proportional to its inherent risk. The investment portfolio can be stocks, mutual funds, or exchange-traded funds. In other words, It measures the excess rate of return generated by the investment for each unit of assumed systematic risk, a risk that can’t be eliminated even by diversification of investment. Therefore, an investor desires a higher ratio value as it indicates a better return per unit of assumed risk.

### Treynor Ratio vs. Sharpe Ratio

The significant differences between the both are as follows:

- It is based on the systematic risk or beta of the portfolio, while the Sharpe ratio is based on the portfolio’s risk or standard deviation.
- It is helpful for a well-diversified portfolio, while the Sharpe ratio can be used in any investment portfolio.

### Advantages and Disadvantages

Below are the points that explain the advantages and disadvantages:

#### Advantages

- It provides ease of comparing performance across the portfolio in terms of return generated per unit of assumed risk.
- It explains the relationship between portfolio return and volatility, hence the reward-to-volatility ratio.

#### Disadvantages

- Its accuracy is subject to selecting a benchmark for calculating systematic risk. For instance, one will not get the correct outcomes if one uses a large-cap index for measuring the volatility of a portfolio of small-cap stocks.
- It can’t be used for an undiversified investment portfolio as it would carry risks other than the inherent systematic risk.
- It is a backward-looking financial ratio.

### Conclusion

So, This is one of the critical performance metrics that analysts and investors widely use for calculating returns generated by investment portfolios.

### Recommended Articles

This is a guide to the Treynor Ratio. Here we discuss how to calculate along with practical examples. We also provide a downloadable excel template. You may also look at the following articles to learn more –