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William Sharpe winner of the 1990 Nobel Prize in Economics

The Sharpe Ratio is an indicator created by William Sharpe, winner of the Nobel Prize in Economics in 1990, which allows assessing the risk-return ratio of an investment. 

relates the return on an investment in a given period to the return on another investment that is considered risk-free. And what does it mean?

This index measures the efficiency of a given investment considering its risk, comparing it with an asset that has no risk. In other words, it measures how much more you earn for the risk you take. The higher the index, the more you earn for a lower risk. The lower the index, the lower the profitability for a higher risk.

What is a risk-free investment?

A risk-free asset is one whose issuer offers absolute guarantee in fulfilling the obligation assumed in the security – that is, that it is an asset free of credit risk. It is also a condition for an asset to be considered risk-free that it does not present reinvestment risk – that is, when the security matures, another security will be available with the same conditions or it can be predicted what future risk-free rates will be.

As no company can offer this absolute credit guarantee, no matter how traditional and solid it may be, government assets – Public Bonds – are candidates for risk-free assets. But the second condition is not fully observed. There is a risk of reinvestment. When the title expires, it is likely that the same conditions as the one that ended will no longer be available in another.

Therefore, it is not so easy to point out a risk-free asset in practice. The most purists would indicate the Term Structure of Estimated Interest Rates – ETTJ, but the Treasury Financial Bill, a Public Security, can be pointed out as a good approximation of a risk-free asset, as well as the CDI, which has a correlation very high with the LFT.

Sharpe Ratio

In the original formula, the index is constituted by the difference between the returns of the asset studied and the risk-free asset divided by the risk (volatility) of the asset studied.

Sharpe Formula Index

That is, there is a balance between the extra profitability that can be gained from this investment, and this is called the risk premium, and the risk of this asset.

For clarity, see an example :
Data from 01/01/2014 to 12/31/2014

Annual return of fund A offered by Confiança Investimentos : 13.1218%
Annual volatility of fund A offered by Confiança Investimentos : 0.0354
Annual return on CDI : 10.814%

Sharpe Index A

Annual return of fund B offered by Confiança Investimentos : 13.3434%
Annual volatility of fund B offered by Confiança Investimentos : 3.3570
Annual return of CDI : 10.814%

Sharpe B Index

In the example above, both funds have very similar returns, but with very different Sharpe ratios. For the same return, it is preferable to apply where the risk is lower. Therefore, the fund with the highest Sharpe ratio, fund A, is chosen.

But as seen, it is very difficult to find an asset that is, in the essence of the word, risk free. Therefore, some variations were created. And a very used one is the Generalized Sharpe.

Generalized Sharpe

Generalized Sharpe is a variation of the Sharpe ratio that introduces the risk of the risk-free asset into the equation.

Sharpe Generalized Formula

In this way, we bring the index closer to its definition in practice, since the weighting now takes place between the extra profitability, risk premium, and the extra risk that is taken to achieve such an advantage.

Let’s use the same data in this example :
Data from 01/01/2014 to 12/31/2014

Annual return of fund A offered by Confiança Investimentos : 13.1218%
Annual volatility of fund A offered by Confiança Investimentos : 0.0354
Annual return on CDI : 10.814%
Annual volatility of CDI : 2.06%

Generalized Sharpe A

Annual return of fund B offered by Confiança Investimentos : 13.3434%
Annual volatility of fund B offered by Confiança Investimentos : 3.3570
Annual return on CDI : 10.814%
Annual volatility of CDI : 2.06%

Generalized Sharpe B

In this example, fund A again has better Generalized Sharpe. For the same return, it is preferable to apply where the risk is lower.

A good way to increase the Sharpe of a portfolio is by diversifying its components (assets and/or funds). The more uncorrelated, the higher the Sharpe Ratio, according to Portfolio Theory, since profitability increases, reducing overall risk.

Even knowing that past profitability is no guarantee of future profitability, the behavior of a given investment in the past is a good criterion when choosing an investment. This combined with the fundamentals of investing can make the difference between a good investment and a great investment.

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Good investments!

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