Value at Risk (VaR) was developed by Till Guldimann, then Head of Global Research at J.P. Morgen, and has been widely used in the financial industry since the 1990s to assess risk (Jorion, 2007, p 18).

But what does VaR have to do with Neoland? VaR is a statistical method and is used to measure the amount of potential loss. It measures how big the losses can be within one trading day in your Neoland portfolio with a probability of 99%.

It shows you the statistically maximum possible loss that your AI could achieve per day. The smaller your value at risk is, the better it is.

As mentioned in a previous blog article about the Sharpe Ratio described, daily returns also play a central role in the calculation of VaR. For this purpose, we will take a look at the VaR using a practical example, the MSCI World. To do this, we will first look at the daily returns of the MSCI World in the period from 01.01.2020 - 31.12.2020.

Figure 1: MSCI World daily returns, data from Yahoo Finance, own presentation.

In total, the trading year 2020 with 252 trading days was considered. Of course, it makes sense to increase the period in order to obtain a more reliable statement about the VaR, but this was not done here for reasons of clarity. As can be seen in the figure, the price loss on March 16, 2020 was the largest at -11% (red). This means that on this day, the MSCI World fell by 11% in one day as a result of the spread of the coronavirus. This compares to a plus of 9% (green) on 24.03.2020. In the rest of the year, the daily returns fluctuated between -3% and +2%.

Now, at regular intervals, we create ranges that go from the lowest to the highest returns, and count how many days with the corresponding returns fall into each range. For example, there are 3 days where the MSCI World fell by more than 8% (orange) and again 2 days where it fell by more than 5%. And so on. If we now assign all trading days to the ranges, we get a frequency distribution for the daily returns, which is shown in Figure 2.

Figure 1: MSCI World daily returns, data from Yahoo Finance, own presentation.

The X-axis of the diagram represents the areas previously defined at regular intervals. The Y-axis indicates the frequency. For example, the chart shows that the MSCI World has fallen by - 3% to -2% on 10 trading days (green).

Now we come to the 99% probability mentioned in the introduction. For this, combine each daily return with a probability of finding a lower return from the 252 trading days. We use a confidence interval of 99%, as is common in the financial industry (Jorion, 2007, p. 19). That means we have to find the loss days which were not exceeded in 99% of the cases. These are all daily returns except the 2 worst trading days, these represent the 1% (2 out of 252 trading days). This is shown in figure 2. From this we can see that the last losing day, which is smaller than 99% of the other trading days, is -8% (red circle).

Now we can make the statement that, for example, based on a portfolio consisting of the MSCI World, there is a 99% probability that no major price decline of -8% will occur within one day. The value at risk is therefore -8%. Of course, this assumption is only based on historical returns from one year and should not be overstated. However, the VaR is a very good complement in combination with other risk measures like the Maximum Drawdown, Time under Water and Sharpe Ratio in Neoland. If we now transfer this to absolute figures, this means that with a portfolio of 3,000€ with 99% probability the daily loss will not be greater than 240€ (-8%).

The VaR can therefore be used to estimate the risk in an investment. In your Neoland Dashbaord you will see the daily VaR, which is calculated based on the historical returns of the AI. Compare the VaR of your AI with the example calculated here and estimate for yourself how much loss you could take on a day.

Sources

Wipplinger, E. Philippe Jorion: Value at Risk – The New Benchmark for Managing Financial Risk, 2007, Fin Mkts Portfolio Mgmt 21, 397–398, Available at: https://doi.org/10.1007/s11408-007-0057-3

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