Fat Tails and Asymmetric Shocks Part 1: Finance

By Julius Probst

This time the blog is split into two parts, where I will have a look at statistical distributions and outliers using Macrobond, and I will put some of the key assumptions of modern macroeconomic and financial theory to the test.

The benchmark macro model used by most economists and Central Bankers is the workhorse new-keynesian DSGE model, which are fully microfounded.

While since the financial crisis of 2008, a lot of progress has been made to make this model more realistic, I do believe that it still has a lot of shortcomings that are not easily overcome (see my own criticism here).

In finance, many models also still rest on the assumption of normal distributions, including some option pricing models and risk models. And these assumptions have caused havoc as severe miss-pricing of risk occurred prior to 2008, and risk managers were utterly unprepared for the once-in a lifetime events that occurred during the Financial Crisis. However, they should not have been. As the French mathematician Benoit Mandelbrot has taught us, finance is dominated by fat tails. Daily returns of asset prices certainly do not follow the Gaussian distribution and people already knew that way before 2008 (remember LTCM, anyone?).

I highly doubt, for example, that financial analysts had on the radar that oil futures would go negative in April due to the Corona shock. And I am sure that some traders got burnt pretty badly when this crazy event roiled financial markets two months ago.   

As the chart below shows, asset prices behave very different from the standard normal distribution according to which a 6-Sigma event should happen only about 3.4 out of a million. However, as the chart for the Dow Jones shows, they occur much more frequently, about once or twice every decade.

Commodities like gold, silver, and oil also display significant price volatility. And more exotic financial assets like Bitcoin even more so. As one can see, volatility was extreme some 10 years ago when crypto currencies were still a novelty. The historical standard deviation for the daily rate of change lies between +6% and -5%.

Not only stock and commodity prices display fat tails and significant outliers, but exchange rates as well, especially since erratic and/or unexpected policies by Central Banks can be the underlying cause. The graph below displays the daily change in Swiss Franc-Euro exchange rate.

Remember the “Franken shock” caused by the Central Bank of Switzerland (SNB) in January 2015? After facing significant upward pressure because of its status as a safe currency, the SNB stunned currency markets in 2011 as it introduced a peg to the euro in order to prevent further appreciation. While the Franc was heading towards euro parity, the SNB announced a new target of 1.20 CHF per Euro, which led to one of the largest intraday plunges for a mature currency ever, and stunning currency traders. As one can see above, the decline of more than 7% was way above the “6 sigma band” that I have added to the time chart.

In 2015, I was an intern in a small regional bank in Germany and was able to observe firsthand that the SNB had pulled another one on financial markets. After 2011, the SNB had to buy a pretty insane amount of financial assets in order to prevent further appreciation and keep the exchange rate at the stated peg. This had the consequence that the Central Bank’s balance sheet started to exceed 80% of GDP by 2015. Back then, it was decided that an appreciating currency would be the lesser evil than to continue asset purchases at an unprecedented scale. At the same day the SNB announced it would abandon the peg, the Swiss Franc appreciated by 14% to the Euro (roughly a 35 sigma event, which basically should never ever happen!).

This meant that any foreigner holding Swiss Franc assets was overnight suddenly some 14% richer whereas anybody who was holding Swiss Franc liabilities suddenly got burnt, including some currency traders.

Of course, the bigger irony in all of this is that as a result of secular stagnation, the pressure on the Franc never subsided and the SNB and had to continue to intervene in the currency market to keep the CHF at a reasonable level with the consequence that the balance sheet is now exceeding Switzerland’s annual GDP.

Macrobond Moment: I have used Macrobond ratios to transform the SNB’s balance sheet into a GDP ratio.

Besides asset prices themselves, the underlying volatility also displays extreme outliers, see the histogram of the VIX below. There is a significant skew and long tail for high volatility levels that is very different from the standard normal distribution.

Macrobond Moment: Our histogram tool allows you to easily include a normal distribution based on the underlying data.

As the histogram report in Macrobond shows, the VIX displays significant skewness and excess kurtosis, both measures of the asymmetry of the underlying probability distribution.

Histogram report
Time seriesUnited States, Volatility Indices, CBOE, S&P 500 Volatility Index (VIX), Close
Nr of observations7945
Mean19,33366
Median17,30000
Variance65,56406
Skewness2,23493
Excess kurtosis8,42879
Percentile
10%11,93000
20%13,01000
30%14,27000
40%15,76600
50%17,30000
60%19,29000
70%21,35800
80%24,18000
90%28,75000
Tail 1%
Lower tail10,03880
Lower tail expectation9,72388
Upper tail48,92880
Upper tail expectation61,13388
Tail 5%
Lower tail11,27000
Lower tail expectation10,55962
Upper tail33,70000
Upper tail expectation43,68521

More importantly, the outliers are not distributed randomly across time. As any keen observer of financial markets knows, tail events and price volatility tend to cluster. The VIX exceeded 40 only a few times before 2008 while during the financial crisis itself there were more than 100 days in 2008 and 2009 when this threshold was breached. And now in early 2020 again as a result of the Corona shock.

Given that financial asset prices behave fundamentally different than what standard risk models suggest, it becomes even more important to diversify financial portfolios. However, globalization also had the unintended consequence of leading to a higher synchronization of business cycles and asset prices across countries. The chart below shows that daily returns of the Dax and the S&P500 are significantly higher since the early 2000s (close to 60%) compared to previous decades. Ironically, this means that just as international diversification has gotten a whole lot easier thanks to globalization, the benefits of diversifying across countries have gone down because correlation of asset prices has gone up. 

Macrobond Moment: Using ”change region”, one can easily switch from the German index to the French index in this Macrobond document and test the correlations between the S&P and other countries.

Keep an eye out for Part 2: Fat tails and asymmetric shocks: In economics, Where among other things, I discuss one of the key assumptions in modern macroeconomics theory, that shocks are symmetric.

Disclaimer: We don’t usually have views and opinions about economic and financial states of affairs, (not ones that we express publicly as a company, anyway). We do believe, however, that people can and do appreciate a variety of perspectives. What you’ve just read is the perspective of the author. While we think our writers are very smart, Macrobond Financial does not expressly endorse the views presented here. And, as the old adage goes, you shouldn’t believe everything you read (not without finding the data, performing a few analyses and presenting it in a nice chart). We want to make it clear that we are not offering this information as investment advice. That being said, if you have Macrobond, you can easily check everything that’s mentioned here, and decide for yourself. If you don’t have Macrobond, now you have a great reason to get it.
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