Treynor vs Sharpe: Which ratio better measures your investment returns?

The performance of a portfolio cannot be judged solely by how much it has risen. The real question is: How much risk did you take on to achieve this level of return? This is the reason for the existence of the Treynor ratio and the Sharpe ratio.

Risk-adjusted returns sound complicated but are actually quite simple

Both ratios are doing the same thing - measuring how much you can earn for each unit of risk you take. But they look at risk in completely different ways:

Treynor Ratio only concerns itself with systematic risk (also known as market risk). This is the risk that you cannot avoid through diversification, such as a decline in the entire stock market. The calculation formula is quite straightforward:

Treynor = ( portfolio return - risk-free rate ) / Beta value

For example: with a portfolio annual return of 9%, a risk-free rate of 3%, and a Beta value of 1.2, the Treynor ratio = (9-3)/1.2 = 0.5. This means that for each unit of systematic risk, there is an excess return of 0.5 units.

The Sharpe ratio is much broader. It looks at total risk - not just market risk, but also stock-specific or industry-specific risks. Measured using standard deviation:

Sharpe = ( portfolio return - risk-free rate ) / standard deviation

In the same example, changing the data: annual return 8%, risk-free rate 2%, volatility 10%, then Sharpe ratio = (8-2)/10 = 0.6.

What are the key differences?

To be honest: If your portfolio is already well diversified, the Treynor ratio is more useful because what remains is mainly systematic risk. However, if your portfolio is not sufficiently diversified, use the Sharpe ratio, as it will account for the risks you've missed.

Which one to choose?

• Are you an institutional investor managing a large diversified portfolio? Use Treynor
• Are you comparing different things like stocks, bonds, and funds? Use Sharpe.
• Not sure? Look at both indicators, it's more comprehensive.

Remember, these two ratios are just tools. A high ratio does not necessarily mean making a profit, and a low ratio does not necessarily mean incurring a loss. They simply help you clarify whether the returns are worth it in light of the risks you are taking.