### Articles tagged with: Factors

20 October 2020

# Factor Analysis Part II

In Part I of this series, we explored the ability to calculate portfolio factor sensitivities using the RiskAPI Add-In. In Part II, we will look at the application of a multi-factor portfolio stress test using the same principles.

Using the Stress-Testing feature of the RiskAPI Add-In, we can set up a multi-factor stress test, applying shocks of varying magnitudes and directions to each factor of interest. The system will evaluate the simultaneous effects of such a shock scenario both on each individual component as well as the portfolio as a whole.

As in Part I, we continue to leverage the "Market Macro" keywords-based feature of the Add-In to quickly generate RiskAPI calculations on portfolio and factor symbols and quantities. The above image shows the output of a multi-factor stress test performed on all 103 Nasdaq 100 components against the same factors used in Part I. These are presented again here:

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

The "Index" and "Index Stress" keywords allow us to specify which set of factors the stress test is being run with, as well as the magnitudes of the shocks applied to each factor. The "Stress Type" keyword defines, via the entry "Index MR", that a multi-factor stress test is being performed (also available are single-factor, underlying prices, implied volatility, and other types). The Index MR stress testing method leverages the system's multiple regression capability to calculate the portfolio's factor sensitivities over the data set and factors specified. It then applies the individual user-defined factor shock values in the process of evaluating the multi-factor shock scenario.

For the stress test in question, the large one-day changes in value experienced on March 16th, 2020 are used. These ranged from -12% in the SPX to as high as 14.6% in the SIZE factor. The system returns three pieces of information as outputs of the scenario:

- Stress Price - the price of the portfolio component under the shock scenario
- Stress Impact - the simulated P&L of the portfolio component under the shock scenario
- Total Stress Impact - the total portfolio simulated P&L under the shock scenario

The same process can be applied to a less intuitive portfolio, leveraging the options valuation capabilities of the system:

Here we see the same multi-factor scenario applied to a present-day "costless-collar" options strategy on AAPL shares. The system automatically performs the factor sensitivity analysis, shock-propagation, and options valuation required to evaluate such a scenario on the option portfolio in question.

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.