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Over the years, several methods have been devised by statisticians, economists and mathematicians to measure the performance of tradable assets such as equities, commodities, stocks and currencies. One such measure is the Sharpe Ratio that **was introduced in 1966 by William F. Sharpe**: Professor Emeritus of Finance at Stanford.

The ratio has since proven to be a** valuable tool** used by investors to **gauge the return on investment compared to its risk**. The Sharpe ratio is popular with traders and fund/portfolio managers due to its simplicity. Another reason for its popularity is the fact that Professor Sharpe won the 1990 Nobel Prize in Economic Sciences. For this reason, retail investors regularly use it when buying shares.

## Sharpe Ratio: Defined

The Sharpe Ratio is a measure used by investors to better understand the return of an investment per unit of risk. This ratio provides a way for investors to determine **how much in returns they will receive** in relation to the volatility they will endure for holding the asset. This means that **an asset or portfolio with a higher Sharpe Ratio is seen as a better choice** when compared to other investments in the same category. Such a higher ratio simply translates to high returns while taking minimal risks on the investment.

## Calculating a Sharpe Ratio

When calculating the Sharpe Ratio, the following formula is used.

Sharpe Ratio = (R_{x }– R_{f}) / StdDev (R_{x})

The full definition of the terms used is as follows:

x = The investment being analyzed

R_{x} = Expected return of the investment

R_{f} = Risk-free rate of return

StdDev (R_{x}) = The standard deviation of R_{x}

We can further elaborate on the terms as follows. The investment can be a security, portfolio, currency or a new asset class. **The expected return of the investment **is what the investor expects to gain in a set time frame. This can be determined using various time periods such as daily, weekly, monthly or annually.

**The risk-free rate of return** is the theoretical rate of return of an investment with zero risk. In most cases, users of the Sharpe Ratio like to use the returns on the shortest-dated government T-Bill. When performing such calculations, investors consider a T-Bill as the safest asset in the financial markets as it is backed by the Treasury department.

The final term in the Sharpe Ratio equation is **the Standard Deviation of the asset being analyzed**. As with all standard deviations, this is a measure of the amount of variation in the value of the asset over a set time period. The Standard deviation gives a clear picture of the historical volatility of the asset being analyzed.

### Ex-Ante vs Ex-Post Sharpe Ratios

One benefit of the Sharpe Ratio is the maneuverability when choosing the type of performance data to input in the calculations.

On one hand, the Sharpe Ratio can be used to evaluate** the past performance** of an investment or portfolio. In this case, actual returns are used in the formula. Such a Sharpe Ratio is **referred to as Ex-Post**. The term ‘Ex-Post’ simply means ‘after the fact’. Such a Sharpe Ratio can additionally be used to forecast future earnings of an investment choice with sufficient past data.

In the case of an investment or portfolio **without adequate past data of performance**, the investor can **use its expected performance** to calculate what is known as an** Ex-Ante Sharpe Ratio**. The term ‘Ex-Ante’ simply means ‘before the fact’ and such a Sharpe Ratio is based on estimates and/or predicted performance.

## What does the Sharpe Ratio Tell us?

Through the shared formula and its individual constituents, we further understand that the Sharpe Ratio gives us a **quantitative measure of the performance of an investment choice** in relation to the risk undertaken when owning the asset. Once the Sharpe Ratio has been determined, the potential of an investment can be graded as follows:

- A value of less than 1 translates to a bad investment
- A Sharper Ratio of 1 – 1.99 translates to an adequate or good investment
- 2 – 2.99 is a very good investment
- Greater than 3 is regarded as an excellent choice of investment

**For example**, let us assume we are analyzing two different portfolios that constitute different stocks. After the necessary calculations, **the first portfolio is determined to provide a return of 14%**. However, with such high returns, there is the usual high volatility associated with them. In this case, **the volatility has been determined to have a value of 9%**.

The second portfolio has also been assessed and** has the potential to provide 8.5% in returns with a lower volatility of 4%**. Using a hypothetical Treasury Bill with a risk-free return of 3%, we get the following comparisons between the two portfolios.

1st Portfolio | 2nd Portfolio | |

Rate of Return | 14 | 8.5 |

Risk-free rate of return | 3 | 3 |

Volatility | 9 | 4 |

Sharpe Ratio | (14-3)/9 = 1.22 | (8.5-3)/4 = 1.375 |

All investments are all about maximizing returns while at the same time reducing the risk. In this case, the second portfolio is desirable. Additionally, by using these two examples, we further understand the exponential relationship between the volatility of an asset and the Sharpe Ratio. The lower the volatility, the higher the Sharpe Ratio. Conversely, the higher the volatility, the lower the Sharpe Ratio.

## Limitations

One weakness of the Sharpe Ratio, is its use of the standard deviation of returns to provide a measure of return on investment. A standard deviation functions on the premise that the returns are evenly distributed. However, traders and investors are aware that price movements in financial markets are not always evenly distributed over a period of time. On some trading days, there is a major spike up due to some random event such as a news announcement by a world leader. On other days the market is in the red due to traders capitalizing on a clear opportunity to go short based on Technical Indicators.

A second weakness of the Sharpe Ratio is the simple ability of some portfolio managers to manipulate their inputs to strengthen their reputation. This can be done by using a longer time period to measure the volatility thus resulting in a lower value. A portfolio manager can decide to use the standard deviation over several months rather than a few days. The former data set provides a lower estimate of volatility compared to the latter.

Thirdly, the portfolio manager can decide to sample data from a time period where the volatility was uniform or non-existent. By intentionally picking a data set, the portfolio manager can thus skew the final value of the Sharpe ratio for his benefit.

## Sharpe Ratio Vs Sortino Ratio

It is due to some of these limitations of the Sharpe Ratio that some fund managers and traders prefer to use the Sortino Ratio. Unlike the Sharpe Ratio, the Sortino Ratio does not consider the total volatility of the investment. It measures the performance of the investment relative to the downward risk of the investment. The Sortino Ratio is thus preferred by retail investors who are more concerned about the potential for the investment to incur losses.

Sortino Ratio = (R_{x }– R_{f}) / StdDev_{d}

A full definition of the terms used is as follows:

x = The investment

R_{x} = Expected return of the investment

R_{f} = Risk-free rate of return

StdDev_{d} = The standard deviation of the downside or negative asset return

## Concluding Thoughts

Summing it up, retail and institutional investors need a proper method to quantify returns in relation to risk when selecting an investment choice. Projecting potential returns is not enough when gauging the viability of an investment over a set period of time. The Sharpe Ratio provides a better representation of the attractiveness of an investment due to its inclusion of risk in its calculation. It allows investors to better understand returns in relation to the risk undertaken when holding the asset.

However, as with all ratios, the Sharpe Ratio has its limitations. It uses a standard deviation on the premise that returns are evenly distributed. With this regard, some traders and investors prefer to use the Sortino Ratio which uses only the downward standard deviation in its calculation.

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