When we have a job, we are trading our time for money, and the more we work, the more we are expecting to be paid. Therefore, we are paying more attention to the hourly pay instead of the total salary. When we invest, we are actually trading risk for money. Similarly to our job, the higher is the risk we are taking the higher is the money we want to make. The reason is that when there is a success, we need to have enough profits that will cover also the losses that we incur when the investment fails.

It is easy to calculate the hourly rate of your salary, unfortunately it is much more difficult to calculate the return of investment per unit of risk of your investment, because many investors don’t know the right tool for assessing the risk/reward ratio. This is especially true for retail investors who don’t have access to advanced software or to professional wealth manager.

In this article, I will explain you how to calculate the Sharpe Ratio, which is one of the key metric that assess risk/reward ratio of an investment, fund, or eToro popular investor.

## The Sharpe Ratio

Briefly, the Sharpe Ratio is the profit made for each unit of risk taken by the investment. From the profit, we also need to subtract the profit that we would have normally made without taking any risk. For example if we invest in short term US bonds, that is typically considered a risk-free investment. Let’s look at the steps in detail.

### 1. Retrieve investment returns

The Sharpe Ratio is typically calculated on monthly returns. Therefore, you need to take all investment returns for the time window you want to use. This is the easy part.

### 2. Retrieve the risk free returns

There are two ways of doing that. The simple way is to assume a 2% risk-free return, however that might not be true in very high or very low interest rate environment, and because we want to do things correctly we need to take the 3 months treasury bill rate (Symbol: TB3MS). This is the annualized 3 month rates, but we are calculating the Shapre Ratio on monthly returns, not the annual return. Therefore, we can convert the annual risk-free return into monthly using the formulas explained in this blog post on compound interest. This is an example assuming TB3MS=5

MonthlyRiskFreeReturn = (1.05^(1/12))-1 = 0.4%

Because TB3MS value change every day, we need to take the average for the month and calculate the monthly risk free for each month.

Finally for each month we subtract the risk-free rate from the corresponding monthly investment returns (part 1). From this we calculate the expected monthly return which is the product of all (return – risk free return)^(1/number of months)

### 3. Calculate standard deviation

Volatility is often used as an indicator of risk therefore it is used in the Sharpe Ratio calculation as denominator to normalize the profits. As a measure of volatility we simply use the standard deviation.

Finally we calculate the monthly Sharpe ratio by dividing the number calculated in point 2 with the standard deviation. The monthly shapre ratio is usually annualized by multiplying it by the square root of 12 as explained here awgmain.morningstar.com/webhelp/glossary_definitions/mutual_fund/mfglossary_Sharpe_Ratio.html

## Calculate Sharpe Ratio in Excel

Let’s start by adding the monthly return to a spread sheet.

Next we download the risk free rates from https://fred.stlouisfed.org/series/TB3MS

We first pick the right time interval then we download the data as excel format and we just copy and paste the data in our spread sheet and modify them in %.

As explain in part 2, we need to convert to the monthly yield like this

Next step is to calculate the return – the risk free return

Now we have everything to calculate the Sharpe Ratio. First we calculate the total return

From that we calculate the expected monthly return (above the risk free rate).

We can use Excel formula for the Standard deviation

The monthly Sharpe ratio is simply the division of the last 2 cells we calculated

Finally, we can annualize the Sharpe ratio as explained above by multiplying by SQRT(12)

And with this we have successfully calculate the Sharpe Ratio of our investment!

## Calculate Sharpe Ratio with pi-screener.com

If you want to calculate the Sharpe ratio of an eToro popular investor, the easiest way is to use **pi-screener.com** and add the name of the investor you want to analyze together with the starting date. The Sharpe ratio will appear in the cards below.

Furthermore, **app.pi-screener.com** can also calculate the rolling 12-month Sharpe ratio of a popular investor, which can be found in the “Other statistics” box.

## Find popular investors with high Sharpe Ratio

When searching for popular investor, it is a good idea to search by Sharpe ratio instead of overall performance for the reason explained in the introduction. Unfortunately, eToro doesn’t provide this functionality yet, but we can use PI ranking on www.pi-screener.com to rank investors by Sharpe Ratio.

## Conclusion

We often forget about risk when deciding which investment is the best. This is especially true for retail investors like eToro users who wants to copy popular investors. Sharpe Ratio is a key metric to help us deciding the right investment.