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Articles tagged with: Beta

02 October 2020

Factor Analysis Part I

Using RiskAPI to calculate Factor sensitivities

Factor analysis of equity portfolios represents a significant portion of the equity investment sector. The ability to measure and decompose portfolio factor exposure is key to this group.

In addition to multi-model VaR and Stress-Testing, Factor analysis is also available in the RiskAPI Add-In. Using the system's exposure analysis functionality, generating factor sensitivities is both simple and fast. In this post we will examine a factor analysis process using a portfolio composed of all 102 Nasdaq 100 components against a collection of popular US Equity factors:

The above image shows the output of the "Multiple Regression" keyword via the RiskAPI Add-In's "Market Macro" feature. This feature allows users to quickly generate API calculations by simply entering in a table with the appropriate column headings. For simplicity, this example uses the S&P 500 index, as well as 5 "off-the-shelf" factor index equity ETF's:

  • VLUE - the value factor
  • QUAL - the quality factor
  • MTUM - the momentum factor
  • SIZE - the small cap factor
  • STLG - the growth factor

The "Coefficients" row, generated by the Add-In, represents the OLS regression beta coefficients of the portfolio vs. all of the included factor symbols under the "Index" keyword. The regression is run using YTD daily data, as specified by the "start date" and "end date" keywords. Weekly and Monthly periodicities are also available via the Add-In, including rolling versions of all of the above.

An important detail produced alongside the beta coefficients is the row labeled "T-stats", indicating how significant the regression coefficients are. Values further away from zero suggest more valid beta coefficients. From the results above, we can see that this Nasdaq 100 portfolio has a beta of 1.88, nearly twice the S&P 500. What's more, the t-stat is quite high, at 13.73, telling us this is a beta that is quite valid. This is not a surprise given the existence of many SPX components in the Nasdaq 100, such as AAPL, MSFT, and AMZN.

In contrast, the momentum factor has a low t-stat of 0.94, suggesting that the low beta coefficient of 0.05 is both not explanatory or statistically significant. The "Multiple Regression" feature also produces several other metrics to help the practitioner gain insight in the validity of all factors used as well as the underlying data the analysis was run on.

In the next post in this series, we will examine how the RiskAPI system's factor exposure analysis capability can be utilized to execute multi-factor stress-testing and scenario analysis.

25 August 2015

A Look at the Recent US Equity Market Drop

To say that recent activity in the US Equity market has been unprecedented would certainly be an understatement. On Friday, August 21st, and Monday, August 24th the S&P 500 index fell 3.24% and 4.02% respectively. To put these declines in perspective: based on a year's worth of data, Monday's market drop was equivalent to an over 4 standard deviation event, making these declines extreme by any statistical measure:

Date   Return   Standard Deviations
August 20   -2.13%   2.86
August 21   -3.24%   4.17
August 24   -4.02%   4.83

For some perspective, to correctly estimate last Friday's decline using a year of daily data through August 20th, a parametric VaR would require a confidence interval of 99.9984%. This equates to the probability of such an event occurring to be less than once in 10,000 observations.

On the subject of VaR, one would require using data going back to 2008 to anticipate the returns just seen on Friday, August 21st:

For Monday, August 24th's decline of 77.68 points, only a conditional VaR using 7-years of data (again, including 2008) correctly estimated the S&P 500's decline that day:

Which brings us to why stress-testing is exceedingly important as a complimentary set of exposure analysis. Here we shock an at-the-money option on the SPY's starting with data as of August 20th using a -5% move in the S&P 500 Index:

The benefit of stress-testing is its lack of reliance on statistical (historical) data. Regardless of the presence of extreme events in a given data set (or detrimentally, in this case, the lack thereof), stress-testing allows for simulation of market shocks in all environments, volatile, extreme, or not.


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.

23 April 2015

Highest (and Lowest) S&P 500 Components by Beta

Current top 10 highest beta components of the S&P 500 index:

First Solar IncFSLR1.9034
TripAdvisor Inc.TRIP1.8698
United Rentals IncURI1.8450
Newfield Exploration CoNFX1.8196
Micron Technology IncMU1.8081
Harman Intl Industries IncHAR1.7811
Skyworks Solutions IncSWKS1.7116
Allegheny Technologies IncATI1.6592
LyondellBasell Industries N.V.LYB1.6427
Freeport-McMoRan IncFCX1.6155

Current top 10 lowest beta components of the S&P 500 index:

Sigma-Aldrich CorpSIAL0.0244
Pepco Holdings IncPOM0.2402
HCP IncHCP0.2414
Family Dollar Stores IncFDO0.2892
Health Care REIT IncHCN0.3474
Newmont Mining CorpNEM0.3502
Ventas IncVTR0.3719
Southern CoSO0.4073
Duke Energy CorpDUK0.4118
AvalonBay Communities IncAVB0.4400

All calculations are as of 4/22/2015, executed on 1-year of daily data, adjusted for corporate actions.

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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