Category Archives: Stock Market

The following report provides an update on some of the metrics I use to classify market risk. The word classify is more appropriate as I think that in essence you cannot forecast risk but rather attempt to adjust to it into a timely fashion. Clearly risk would not be a risk if you could forecast it accurately. However as there is generally some degree of persistence in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE China ETF Volatility Index (VIX China) as a measure of stock market risk for China . The same methodology can be successfully applied to other inputs. Feel free to contact me at pollux@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two other measures. The VIX Volga, a measure of uncertainty of risk and the ShockIndex a measure of market dislocation. VIX Volga is simply the volatility of the VIX China over a given period. This measure highlights how uncertain and unstable the level of risk has become. Though positively correlated to the level of the VIX China the VIX China Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX China is trading at rather innocuous levels. This is not a trivial observation as the leverage undertaken by market participants tends to be an inverse function of market volatility which implies a greater vulnerability when volatility becomes uncertain at low levels and therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report are evaluated over a period of 14 days. The medians and 95% confidence intervals are calculated over the full history going back to 1990 though the charts shows only the recent years.

At close of business the 2015-06-08 the VIX China was trading at 32.3 at the 86.9 percentile. The 14-day VIX China Volga was estimated at 12.3 its 42.5 percentile and the China shockindex at 0.4 or its 19.8 percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full VIX history going back to 1990 as this would make the charts unreadable. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. To answer this I use a mapping technique developed by Kohonen in the 1980′. It uses an unsupervised neural network to re-arrange data around meaningful clusters. Though computationally complex is a practical way to summarise multidimensional data into a low (usually 2) dimensional system.

The below chart shows how the VIX price history was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX China traded 55 % of the time in Cluster 1, 31 % in Cluster 2, 9 % in Cluster 3 and 5 % in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded 77 % of the time in Cluster 1, 23 % in Cluster 2, 0 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned risk metrics. The data has been grouped and colored as a function of four clusters of increasing market risk regimes. Obviously as shown on the map, the minimum level of volatility pertains to cluster 1 and the highest to cluster4. The current regime and its progression from 21 days ago is also highlighted on the map.

Always happy to discuss any of the above, feel free to reach me at: pollux@argonautae.com

Whatever the market being traded, there always will be a a question being asked at one moment: How far can this thing go ? Clearly not an easy question to answer as this will invariably depends on factors that are partly unknown or difficult to estimate, such as fundamentals, market positioning or market risk amongst others. The first part is obviously to assess how atypical the move experienced in the given instrument is. This report aims to contribute to this.

The below chart shows the S&P 500 over the period of January 1950 to June 2015 . On the 08 June 2015 it was trading around 2079.28003.

In the below I plot the previous 125 days against other similar historical periods that would have closely matched the recent history. The data has been normalised so as to be on the same scale. The chart shows the latest 125 days in black, and overlay similar historical patterns in grey. It Also shows what has been the price path for the following 125 days as well as the observed quartiles.

Finally I plot the last 125 days and a trend forecast derived from an ARIMA(3,0,2) model as well as the 95% confidence intervals. The ARIMA model is fitted to the past 625 historical values whilst ignoring the last 125 days, therefore we can look at the recent price path against the trend forecast and its confidence intervals to gauge how (a)typical the recent move has been.