## What is Treynor’s Ratio? What are its uses?

**What is Treynor’s Ratio? What are its uses?**

__Definition:__

Treynor Ratio is also called reward-to-volatility ratio measures and adjusts for systematic risk to understand the efficiency with which the manager allocates fund’s assets to compensate the investor taking a given level of Risk. Quite straight-forward, it is merely the excess of returns earned more than the Risk-free return at a given level of market risk.

Highlighting the Risk-adjusted profits generated by mutual funds and portfolio schemes, this ratio was conceptualized by Jack Treynor (who also gave birth to the idea of Capital Asset Pricing Model) expanding upon the contributions made by William Sharpe (the person behind the Sharpe Ratio) and towards Modern Portfolio Theory.

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__The Formula In-depth:__

Given following is the equation for Treynor’s Ratio:

The excess return in the numerator (calculated by Rp – Rf) represents the excess return one gets from taking up the risk. Usually, treasury bills are used to represent the Risk-free rate at which one earns – though it can be argued that no investment is risk-free.

The Risk measurement used in the formula is a measure of systematic risk – that is the beta of the portfolio. Systematic risk the unverifiable part of the total risk that is caused by factors beyond the control of the firm or firms. In simple words, it is the risk that is inherent to the market and cannot be diversified or reduced. Beta in the formula measures the tendency of the portfolio returns to change as the market returns change. The beta of the portfolio can be calculated by dividing the product of covariance of the portfolio’s return and the market returns by the variance of market returns over a specified period of time.

In essence what Treynor ratio represents is how much return an investment such as a portfolio of stocks, exchange-traded fund, a mutual fund scheme earns for the amount of risk you’ve assumed. By measuring how successful the investment is in terms of providing a measurement for compensation received by the investor for taking up risk, the investor can how to measure the Treynor’s ratio for other investment alternatives and make a better decision.

The assumption behind the ratio is that the investors must be compensated for the risk that is inherent to the portfolio in the form of systematic risk i.e. the un-diversifiable risk.

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__Example: __

Imagine a portfolio with 3 stocks, A, B, and C.

First, we need to calculate the weight of each stock in the portfolio, this can be done by:

Value of Each Stock/Total value of the portfolio

Weights:

- Stock A: 25%
- Stock B: 43.75%
- Stock C: 31.25%

Portfolio Return: Weight of each stock * return of each stock

=25% × 8% + 43.75% × 12% + 31.25% × 4%

Calculating, we get a total portfolio return as 8.5%

For Portfolio Beta, we take the average of individual stock betas

=25% × 1 + 43.75% × 1.5 + 31.25% × 0.75

Calculating, we get total portfolio beta as 1.14

Treynor’s Ratio is simply: (Rp – Rf)/Beta of portfolio

=(8.5%-3.5%)/1.14

= 4.39%

__Limitations of Treynor Ratio:__

- One of the main problems inherent with Treynor Ratio is due to the fact that it utilizes Beta of the Portfolio which is a backward-looking measure of risk. Investments may not perform similarly in the future as they did in the past and so the accuracy of Treynor’s ratio can be easily compromised if appropriate benchmarks are not used for calculation of beta measure.
- Treynor Ratio cannot be utilized if the investment has a negative beta value. The entire formula goes haywire if there is a negative beta in the formula.
- There are no dimensions for ranking the Treynor’s Ratio. If the investments are similar, higher Treynor’s Ratio would intuitively be better but it doesn’t necessarily mean that the investment would be better than others which are not very similar to the investment in question. Also, the significance of the difference cannot be evaluated – basically, 0.5 may be better than 0.25, but not necessarily twice as good.

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__Sharpe Ratio v/s Treynor Ratio:__

Sharpe Ratio is another measure in the category of ‘Return per Unit of Risk’. The main difference between the Treynor’s ratio and the Sharpe Ratio is that the former uses beta of the portfolio and the later uses Standard Deviation of the Portfolio Returns.

Though we’ve already discussed where Treynor Ratio falls short, the disadvantage of the Sharpe Ratio may present itself in cases where our investments simply don’t have a normal distribution like in the case of Hedge Funds, where returns are often skewed because of multiple options and dynamic trading strategies being utilized.

**Author: Aman Aggarwal**

**About the Author:** Aman is an Economics and Finance graduate with a budding interest in Strategic Management and Investment. An avid reader of all things Behavioral and Data Science –I strongly believe in solving problems with solutions backed up by quantitative rigor.

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