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What is the Sharpe Ratio? How does it work? When should you use it?

In finance, the Sharpe Ratio (also called Sharpe index) measures the performance of a single financial instrument (stocks, mutual funds, etc.) or of a portfolio compared to a risk-free (usually US government bonds) normalized with respect to volatility.

**The Sharpe Ratio represents the additional amount of return an investor receives per unit of increased risk.**

The Sharpe Ratio is defined as the difference between the investment returns and the risk-free return, divided by the standard deviation of the returns.

The**formula of the Sharpe Ratio** is:

The

Sa = (Ra-Rb) / (σa)

Where:

Sa is the Sharpe Ratio of the asset under analysis

Ra is the return of the asset whose Sharpe Ratio we want to calculate

Rb is the return of the risk-free asset

σa is the standard deviation (a measure of price volatility) of the yield of the asset for which we want to calculate the Sharpe Ratio

Sa is the Sharpe Ratio of the asset under analysis

Ra is the return of the asset whose Sharpe Ratio we want to calculate

Rb is the return of the risk-free asset

σa is the standard deviation (a measure of price volatility) of the yield of the asset for which we want to calculate the Sharpe Ratio

However, as we will see in the following chapters, it is not always so easy to evaluate the quality of an investment just by looking at the Sharpe ratio.

However, sometimes it can be interesting to evaluate the Sharpe ratio in absolute terms. Here are some details on how to define “

- A Sharpe Ratio between 0 and 1 is considered suboptimal.
- A Sharpe Ratio between 1 and 2 is considered acceptable
- A Sharpe Ratio between 2 and 3 is considered very good.
- A Sharpe Ratio of 3 or higher is considered excellent.
- A negative Sharpe Ratio means that the return of the risk-free asset is higher than the return on the instrument under analysis.

The **limits of the Sharpe Ratio** are:

- Does not take into account the temporal distribution of gains and losses (having a completely negative and a completely positive period has a different psychological impact than continuous fluctuations)
- Assumes returns have a normal distribution, which is unrealistic
- The result depends on the observation period, the length of the observation period and the frequency of measurement of the returns
- Does not distinguish between positive and negative fluctuations (takes into account the volatility in general, without evaluating its direction)

Given the limits of the Sharpe Ratio in assessing volatility, often the performance of an asset is measured using the Sortino Ratio (link to Sortino page).

The Sortino Ratio in fact measures the risk in a different way than the Sharpe Ratio. As we have seen, the Sharpe Ratio uses the standard deviation of returns as a measure of risk. This means that upward fluctuations are somehow qualified as "risk".

The Sortino Ratio, on the other hand, has been created specifically to take into account only negative fluctuations. In practical terms, the Sortino Ratio measures risk by evaluating the distribution of returns that are below a target or required return.

Hence the**Sortino Ratio**** is more effective as a tool for measuring the risk / return ratio**.

Another variation of the Sharpe Ratio is the Treynor Ratio. This indicator uses the Beta (a measure of the volatility and risk of an investment relative to the general market) of a portfolio as a benchmark for risk.

**The Treynor Ratio is particularly useful in determining whether an investor is compensated for taking a higher risk than "market risk".**

The Sortino Ratio in fact measures the risk in a different way than the Sharpe Ratio. As we have seen, the Sharpe Ratio uses the standard deviation of returns as a measure of risk. This means that upward fluctuations are somehow qualified as "risk".

The Sortino Ratio, on the other hand, has been created specifically to take into account only negative fluctuations. In practical terms, the Sortino Ratio measures risk by evaluating the distribution of returns that are below a target or required return.

Hence the

Another variation of the Sharpe Ratio is the Treynor Ratio. This indicator uses the Beta (a measure of the volatility and risk of an investment relative to the general market) of a portfolio as a benchmark for risk.