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Articles tagged with: VaR

27 October 2014

The Return of Volatility: Which VaR Model Measured Up?

Earlier this month saw volatility return to nearly every tradable market with a serious vengeance. The long-running low volatility (or no volatility, to some) state of affairs had apparently come to an end. For those of us that construct and test risk systems, this month has provided a unique in situ series of observations with which to critically examine the performance of certain VaR models.

Defining the low-vol environment

With regards to equity markets, at least, it will certainly come as no surprise that volatility has been low and getting lower for quite some time. Below is a chart of rolling 90-day S&P500 realized volatility starting on Jan 1 of this year through September 24th (one day prior to the first large down moves seen in the US Equity markets starting on 9/25/2014):

Even taking the period's peak volatility of ~ 13%, these are historically very low volatility levels for the US Equity markets. For the purposes of this evaluation we will consider the "pre-volatility" period to be from Jan 1-September 24th of 2014.

Defining the volatility-inducing events

Starting on September 25th, the S&P500 experienced a series of several outsized, negative returns:

DateReturn %Return Points

These were certainly enough observations to make even the most ardent believer in the "endless-low-volatility-bull-market" theory question his or her convictions.

Which VaR model did best?

Using data from January 1 to September 24th, we ran the S&P500 through the Parametric, Historical Simulation, and Monte Carlo VaR models offered in RiskAPI, both under 95% and 99% confidence levels. Here are the results (in index points):

ModelConfidence VaR CVaR
Parametric95% -20.69 -31.19
Parametric99% -29.27 -39.34
Full Historical95% -18.56 -28.84
Full Historical99% -39.13 -40.05
Monte Carlo95% -22.21 -27.00
Monte Carlo99% -31.29 -38.00

The last two columns in the results table above show the output of Value at Risk (VaR) and Conditional Value at Risk (CVaR) across each of the three models and two confidence levels. While VaR shows the predicted return event based on a statistical model, CVaR shows how large the actual historical period losses that exceed this prediction were, on average.

By far, the worst day for the S&P this month was on October 9th, with a loss over 40 points, or more than 2%. As a risk manager, being able to forecast such a loss well-prior to experiencing it would clearly be advantageous. At the 95% confidence level, no model using either VaR or CVaR came close to predicting the loss on October 9th. However, this is more of a function of how rare this event was than the efficacy of 95% VaR. Remember that we fully expect a 95% VaR result to fall short 5% of the time.

Using a 99% confidence level, the Full Historical model came quite close to forecasting this event using the "low volatility" data alone, while CVaR did very well across all models. The performance of CVaR in this situation speaks very highly of this metric, showing that even with event-limited data, one is able to predict large losses by explicitly examining behavior at the "tail" loss region of a distribution.

For completeness, here is what realized volatility looks like taking events since September 24th into account:

The results above were calculated using The RiskAPI Add-In, our unique software client which allows risk practitioners, portfolio managers, and traders to access a whole spectrum of on-demand portfolio risk analysis calculations.

19 September 2014

Analyzing the Risk of the Alibaba (BABA) IPO

As with other big IPO's, the Alibaba deal has drawn a lot of attention from Wall Street - it is the single largest U.S. initial public offering ever - and with that, a likely large amount of institutional investors. As such, chances are high that there are now more than several chief risk officers and portfolio managers grappling with how, exactly, to measure the exposure of this new issue.

Ownership Structure

To begin with, it's worth spending a moment talking about what specifically shares of the NYSE-listed BABA represent. Unlike shares of common stock in a typical public corporation, which resolve to one unit of direct equity in a corporation, shares of BABA are actually units in an offshore, Cayman Islands-based trust, which has a contract to share in the profits of the local Chinese Alibaba corporate entity. This is due to legal restrictions in place by the Chinese government which prohibit direct foreign ownership in Chinese Internet service companies. To get around this restriction, something called a Variable Interest Entity (VIE) was created to allow a foreign-owned investment vehicle to experience correlated returns vs. the onshore Chinese stock. In short, everybody involved agrees that one share in the VIE will track the performance of the onshore-Chinese equity. To be clear, this agreement is only as good as all of the players decide it will be, of these most notably are Alibaba's CEO Jack Ma and the Chinese government. If the on-shore owners or the authorities decide to change or invalidate elements of this agreement, it's not clear what legal recourse foreign investors could have.

Needless to say, there are a great deal of structural risk factors in the very nature of the shares of BABA that need to be carefully considered as part of the systemic risk inherent in owning shares of BABA.

Market Risk of an IPO

Analyzing the market risk of an IPO has always been difficult. By definition, shares in an IPO do not have any historical pricing data, something ex post facto risk calculations rely on heavily to generate exposure analytics. If a stock only has one day's worth of pricing history (as is currently the case with BABA) how does one calculate return observations? How can predictions based on historical data even be made if no historical data exists? So what's a risk manager to do?

Enter data proxying. Data proxying is a mechanism whereby the original market-driven historical pricing used to analyze a financial instrument is replaced with a single or combination of adjusted or derived historical time series. There are several reasons to proxy market data. Chief among them is data scarcity- there simply isn't enough market data available. Another is a belief that the market is mis-pricing a security and that proxied data better reflects the "real" historical value and risk.

The source of proxied data can be a geographically relevant index, a sector-relevant stock, or a basket of financial instruments chosen for macro-economic or fundamental reasons. In the case of a proxy for an IPO, the idea is to come up with a replacement for the non-existent historical pricing data and provide instead a suitable time series that approximates the return behavior of the stock, pre-IPO. With the proxied data in-hand, useful exposure analytics can be derived and utilized as is the case with instruments that have abundant pricing information.

Proxying in RiskAPI

The RiskAPI system provides a built-in proxying mechanism that enables the return history of an existing data set to be mathematically joined to any available IPO data. Proxying is done via a dedicated symbol format which contains the information necessary to construct the proxy. In the case of BABA, this can be done as follows:


The result of the proxy symbol above is a data set that combines the return history of the S&P 500 Index prior to 9/19/2014 (the IPO date) and any available data for BABA since the IPO. In contrast to a wholesale replacement of BABA with a position in the S&P 500, no quantity adjustment needs to be made in order to match the position size of the proxy. The market value of 10,000 shares of BABA and 10,000 shares of SPX;BABA;09-18-2014.PRX will be equivalent.

The proxy above represents a crude approximation of pre-IPO behavior using the returns of a US equity index. This proxy would only be appropriate if one holds the view that the S&P 500 is a reasonable substitute for the behavior of BABA pre-IPO. In order to more closely approximate the economic risk of BABA shares, a more fitting proxy could use the China-based Shanghai Composite Index:


Note that even though the Shangahi Index is a China-based equity index and as such would represent a CNY-denominated asset, the RiskAPI system allows users to denominate the proxy in US Dollars (for example) allowing the proxy to sample the market returns only of the index, eliminating any currency exposure, which would not be present for holders of BABA, a stock listed in the US and denominated in dollars. Below are sample results run using the RiskAPI Add-In with both forms of proxying:

The output above shows the results of three different forms of proxying: outright substitution (note the different quantity change made to match the market value), simple US-based index proxying, and local-market index proxying. Note the significant difference in VaR as a result of the application of the Shanghai Composite index vs. the S&P 500.

The results above were calculated using The RiskAPI Add-In, our unique software client which allows risk practitioners, portfolio managers, and traders to access a whole spectrum of on-demand portfolio risk analysis calculations.

01 March 2012

Extreme Gold

Yesterday (February 29th) saw what can only be classified as an extreme downward move in gold prices: A -5.05% change in the spot price over the span of a single day. To see how this event stacked up, we ran GCY0 (the RiskAPI symbol for physical gold) through the system using a start date of December 31st, 2007. Here is what we found:

  • Largest Positive Return: 10.27% (September 17th, 2008)
  • Largest Negative Return: -7.68% (October 10th, 2008)
  • One Standard Deviation: 1.39% (as of February 28th)
  • 99% Confidence Historical Simulation VaR: 3.8% (as of February 28th)
  • By every measure, this was a very rare event. To put it in perspective, out of the 1,077 return events that occurred between 12/31/20007 and 2/28/2012, only 8 exceeded -4% in size, or about 0.083% - less than 1%.

    The results above were calculated using The RiskAPI Add-In, our unique software client which allows fund managers to access a whole spectrum of on-demand portfolio risk analysis calculations.

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