Sharpe Ratio | Definition and Formula easily explained
What is the Sharpe Ratio? How does it work? When should you use it?
The Sharpe Ratio is a value that measures the performance of a financial instrument or the ratio between risk and return. The higher the Sharpe Ratio, generally indicates a high degree of expected return relative to the risk taken on.
How does this measure work? How is it calculated? What are the advantages and disadvantages?

What is the Sharpe Ratio

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.

How to calculate the Sharpe Ratio

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:
Sa = (Ra-Rb) / (σa)
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

When to use the Sharpe Ratio

The Sharpe Ratio seeks to characterize how efficiently the return on an asset compensates the investor for the risk taken. For example, when comparing two assets, the one with a higher Sharpe Ratio generally provides a better return for the same risk and is therefore more attractive to investors.
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.

How to interpret the Sharpe ratio

Generally, the best way to evaluate if the financial instrument we are analyzing has a good Sharpe Ratio is to compare it with the Sharpe Ratio of some other instrument. For example, if you want to evaluate the performance of your investment portfolio consisting mainly of US equities, it may be advisable to compare the Sharpe Ratio of your portfolio with the Sharpe Ratio of the S&P500 or some other index.
However, sometimes it can be interesting to evaluate the Sharpe ratio in absolute terms. Here are some details on how to define “what is a good Sharpe Ratio”:
  • 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.

Limits of the Sharpe Ratio

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)

Alternatives to the Sharpe Ratio

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".