Sharpe Ratio

#### Categories: Expert mode | Neoland-App Dashboard

Published: 19 July 2021
Written by: Marius Siegert

The Sharpe Ratio gives you an overview of how much return you get for the risk that your artificial intelligence (AI) takes. Simply put, you can see whether your returns are due to smart decisions by your AI or too much risk. The higher the Sharpe Ratio, the more return you get for the risk you take. In general, this allows you to compare different investment opportunities, independent of AI in the investment process, and select the appropriate investment based on the best risk-return ratio (Sharpe, 1994).

To calculate the Sharpe Ratio of your AI, the following formula with a few variables is used.

Average daily return of your AI: $$R_{KI}$$

Average daily return of a risk-free product: $$R_{rf}$$

Daily fluctuations of your portfolio: $$σ$$

$Sharpe Ratio=\frac{R_{KI}- R_{rf}}σ*√252$

In order to calculate the actual return of your portfolio, the return of a theoretically risk-free product is subtracted from the return of your AI in the numerator.

But what is a theoretically risk-free product? In portfolio management, we speak of a risk-free product if it is certain to generate returns in the future. Such a product can be, for example, a government bond or a call money account. However, because these financial products are so safe and are very likely to generate profits, these profits are correspondingly small. This is because there is always a conflict between risk and return on the financial market: high risk also tends to mean higher returns, while low risk tends to mean lower returns.

The actual return of your portfolio is therefore the return of your AI minus the return that you could have achieved with a theoretically risk-free product. To calculate the Sharpe ratio, the actual return is divided by the risk of your portfolio (Bailey, Lopez de Prado, 2012). This is where the term risk-return ratio comes from.

But what is risk now? The risk of a portfolio can also be called volatility and basically describes the standard deviation. This tells you how much the value of your portfolio fluctuates and how far it moves away from the average value. The larger the standard deviation, the more volatile and therefore risky your portfolio is. A Sharpe ratio above 1 is generally considered good, if it is higher than 2 it is very good and a Sharpe ratio above 3 is called excellent.

As an example, the MSCI World is considered on a daily closing price basis in the period from 01.01.2020 - 31.12.2020 and its Sharpe Ratio is calculated in this period.

Figure 1: MSCI World Price Development & Daily Returns, data from Yahoo Finance, own presentation.

First of all, we can see that the daily average return of the MSCI World has a value of 0.070% in the period of one year under consideration. The next step is to look at a risk-free product, e.g. the call money account. There you get 0% interest or return for your deposit at most banks at the moment. Therefore, the actual return is equal to the return of the MSCI World, because if you invest your money risk-free, you can not achieve a return in the current ECB interest rate environment.

Finally, for the calculation of the Sharpe ratio, the risk of the MSCI World or, expressed mathematically, the daily standard deviation, i.e. the fluctuation around the mean value, is missing. In the present case, this amounts to 2.064%. Taking into account that the Sharpe Ratio is usually expressed on an annual basis (hence the factor with the square root of 252 trading days per year), this results in the following calculation (Sharpe, 1994, p. 4):

$Sharpe Ratio=\frac{0.070\%-0\%}{2.064\%}*√252 = 0.54$

A Sharpe Ratio of 0.54 and thus > 0 means that historically the return of the MSCI has been higher than the return in a risk-free product. However, the risk to achieve the return was higher than the return achieved. At a Sharpe Ratio > 1, the return outweighs the risk and this is what signals a promising investment.

Compare the Sharp Ratio of the MSCI World with the current Sharpe Ratio of your AI on the Neoland Dashboard to get a first impression and directly compare the two investment options.

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