#124: Conditional Value at Risk

S2N Spotlight

This visualisation took me many hours, as I wanted to make everything adjust programmatically without any manual adjustments. I will try not to make this “spotlight” too technical. The concepts are very important to grasp from a risk management point of view, but the actual derivation of the formulae is much less so.

VaR (value at risk) in the chart below shows there is a 95% probability that the daily returns of the S&P 500 will lie between the 2 vertical red lines, which I have coloured blue. I decided to include a positive VaR as well to show upside potential or if you are shorting downside potential. The threshold of VaR on the downside is -1.50%, and 1.43% on the positive side. This means there is a 5% chance that returns will be worse than these thresholds. This is where VaR has some limitations, so let us introduce an improved metric.

CVaR (conditional value at risk) is the average of all the actual instances where returns were beyond the VaR threshold. In the S&P 500 example below, you can see that the CVaR is -2.33% relative to a VaR of -1.50 on the negative side.

I have added the most extreme bins on both the left and right tails to show you that the 5% that shoots past the VaR can shoot by a very long way. These are usually the extreme moves that blow up your account. While CVaR helps approximate the average of all the extreme moves, it still doesn’t imply that the threshold cannot or will not be breached.

To add a bit more colour, I chose 2 other assets to analyse. We will look at gold and then bitcoin. I can see that I need to improve my automated calibration of the labels as the chart sizes are inconsistent, but I am too lazy to change it today.

Gold produces a pretty normal distribution pattern. The Bitcoin chart really catches my eye. You can expect 1 out of every 20 days to experience a loss of -12.07 or a gain of 12.76%. Of course, that doesn’t mean 1 out of every 20 days; it means (excuse the pun), on average, 5% of the time you can expect such price movements. If you want to get a better grasp of statistics, you should look up the law of big numbers to understand the concept more.

I want to add that I purposely use the 1 out of 20 day example to highlight that it is important when viewing things from a risk point of view that you see things in the context of a time frame. Statistically, it is more accurate to view it in percentage terms. I personally think this abstracts the concept a little too much and prefer to be on high alert at all times, which a time frame gives you.

I guess that is why my screensaver message on my mobile says, “Calm Down.”

S2N Observations

I plotted both the headline and core inflation numbers on the chart below. I have also added the Fed Target Rate of 2% for a visual reference. Let’s be clear: while inflation seems to be coming down, it is still well above the target rate.

I came across some pretty crazy stats.

The Bank of Japan owns ~80% of the country’s ETFs and 7% of the entire Japanese stock market, according to Morningstar and Tokyo Stock Exchange data. Moreover, the BoJ holds ~55% of the Japanese government bonds.

Performance Review

Chart Gallery

News Today

The post #124: Conditional Value at Risk appeared first on Signal2Noise.