At Eqira we believe that factor analysis is one of the best tools for evaluating financial time series. The rationale is simple: if we can reasonably approximate an asset’s underlying factor structure, we can better understand that asset’s past and future behavior and open the door for an extraordinary number of advanced analyses. Some of the possibilities include: projecting future risk and return, divining hidden relationships between securities, running stress tests, and, as in the case of our Factor-Based Projections, estimating real-time returns for illiquid securities such as hedge funds. In this report, we discuss how to interpret the factor attribution tables that appear in many of our reports.
Factor Analysis: What is It?
At its most basic level, a factor is a descriptive feature, like a characteristic or trait. Much as we might describe a person by his or her features (e.g., physical characteristics, personality type, behavior, beliefs, etc.), we can describe financial securities in terms of attributes that affect their performance. A stock, for example, might behave like other equities, equities of similar market capitalization, equities with comparable yield, and so on. It might be sensitive to things like changes in interest rates, GDP, or the US Dollar.
Factor analysis is a statistical technique that aims to describe a time series in terms of one or more factors. If we can identify an appropriate set of factors and determine a security’s sensitivity to those factors, then we can generate predictions for the security’s behavior based solely on the performance of those factors.
Performing a Factor Analysis
The simplest method of factor analysis is a linear regression, where we model the series that we want to explain as a linear combination (i.e., a weighted sum) of related time series.
One of the first practical uses of factor analysis in the financial arena was the Capital Asset Pricing Model (CAPM), which was independently introduced by Treynor, Sharpe, Lintner and Mossin during the mid-1960s. The CAPM, also known as the market model, attempts to explain asset returns using a single factor: market risk. Despite its simplicity and empirical flaws, the CAPM is still widely used today to estimate equity betas, which measure sensitivity to the broader equity market. If we run a simple linear regression of historical stock returns on historical market returns, then the coefficient we obtain represents the stock’s beta over that period. Stocks with beta greater than 1.0 tend to be more volatile than the market, producing greater returns in bull markets and more sizable drawdowns in bear markets, while stocks with betas below 1.0 tend to be more stable.
The single factor assumption underlying the CAPM may be theoretically appropriate under certain conditions, but in the real, non-theoretical world, the CAPM has struggled to explain actual returns. It has has led researchers to propose new models. Perhaps the most famous and widely followed of these is the Fama-French three-factor model, which introduces two additional factors: size and value. It likely gave rise to the style boxes that you have no doubt seen at Morningstar or in mutual fund literature. Like its name suggests, the three-factor model attempts to decompose equity returns into three factors: the overall equity market return, the return of small capitalization stocks relative to large capitalization stocks, and the return of value stocks relative to growth stocks. The Fama-French model has certainly improved upon the CAPM, but has not discouraged others from seeking better alternatives
How Does Eqira Perform Factor Analysis?
Eqira has developed its own proprietary database of Market Factors, which we use in many of our analyses. Our Market Factors attempt to systematically describe all commonly used investment techniques, both passive and active.
Although we use more advanced statistical and machine learning techniques than simple linear regression to build our models, our approach is broadly similar to that of the CAPM and Fama-French models. We use historical data to estimate the sensitivity of an asset to a wide variety of explanatory variables, and then use those exposures to yield new insights.
Interpreting Eqira’s Factor Attribution Tables
Two of the more interesting insights we produce are our return and variance attribution analyses, which decompose the sources of an asset’s return and risk, respectively. They appear in many of our reports. The tables below, for example, are taken from our most recent Strategy Analysis report for the Eqira Hedge Fund Composite Index. The full report is available in the Clients section. Please request access if you are not already registered.
|EQ: Developed Spread||-6.83|
|VOL: Short Volatility||3.10|
|EQ: Emerging Spread||-1.69|
|CR: High Yield Spread||1.55|
|EQ: Sector Momentum||0.75|
|Factor Group||Risk Share|
|EQ: Developed Spread||13.2|
|VOL: Short Volatility||4.3|
|CR: High Yield Spread||2.0|
|EQ: Regional Spread||-1.7|
The tables decompose the index’s return over the past five years into factor groups (groups of similar factors which we’ve aggregated for simplicity and clarity; you can find a summary at the end of this report). They are telling us that equity beta, or sensitivity to the general equity market, has contributed 21.96% towards the index’s total return over the period. It has also contributed 57.5% of the risk as measured by variance. The magnitude of these values may prove disappointing for those looking to hedge funds for portfolio diversification. The alpha numbers (the portion of return and variance not explained by our factors, and most commonly attributed to manager skill) of 5.39% for return and 3.8% for risk are also much lower than most would desire. In total, the most significant 11 factors contributed 28.09% towards the index’s total return of 30.36%. They also contributed 94.9% of its variance.
Something that may jump out to the astute observer is the negative risk share for the EQ: Regional Spread factor group. How can something have negative risk? In this case, the regional equity exposure is providing such a strong diversification benefit that increasing its weight would actually reduce the index’s standard deviation.
One of the benefits of factors is that we can aggregate them any way we’d like. In the tables below, we aggregate by each factor’s asset class to give an idea of how hedge funds are sourcing their return and risk exposure at the asset class level.
|Asset Class||Risk Share|
Again we see a large concentration in equity. Hedge funds have obtained roughly half of their return and 81.5% of their risk from equity factors, which suggests that hedge funds may be relying too heavily on stocks and neglecting other asset classes.
Now that you understand how to interpret our factor attribution tables, you should keep an eye out for them in our research. We provide daily return and risk attribution reports for each of our composite hedge fund indexes as part of our Market Insights research package. We also include attribution analyses in many of our other reports, including those from our Quantitative Due Diligence and Portfolio Insights services. If you are not already a client, please contact us to learn more.
Factor Group Descriptions
The following table summarizes the factor groups most commonly appearing in our attribution reports.
|A: Alpha||The unexplained component of an asset's return. Equivalent to the residual in a regression and often interpreted as a measure of manager skill.|
|CM: Beta||The excess return of a broad commodity index|
|CM: Gold||The excess return to gold futures|
|CM: Momentum||Long commodities that have recently outperformed and short commodities that have recently underperformed|
|CM: Oil||The excess return to oil futures|
|CM: Term Structure||Long the most backwardated commodities and short the least backwardated (or contangoed) commodities|
|CM: Trend||Long commodities that are trending upward and short commodities that are trending downward|
|CR: Developed Spread||Long foreign developed corporate bonds and short US corporate bonds|
|CR: Emerging Spread||Long emerging corporate bonds and short foreign developed corporate bonds|
|CR: High Yield Spread||Long high yield bonds and short investment grade bonds|
|CR: Inv Grade Spread||Long investment grade bonds and short government bonds|
|CR: Term Structure||Long long-dated corporate bonds and short short-dated corporate bonds|
|EQ: Beta||The excess return to US equities|
|EQ: Country Momentum||Long equity indexes of countries that have recently outperformed and short equity indexes of countries that have recently underperformed|
|EQ: Country Trend||Long equity indexes of countries that are trending upward and short equity indexes of countries that are trending downward|
|EQ: Developed Spread||Long foreign developed equities and short US equities|
|EQ: Emerging Spread||Long emerging market equities and short foreign developed equities|
|EQ: Merger Arbitrage||Long equities of companies under acquisition and short equities of their acquirers|
|EQ: MLP Spread||Long master limited partnerships and short real estate investment trusts|
|EQ: Momentum||Long equities that have recently outperformed and short equities that have recently underperformed|
|EQ: Private Equity Spread||Long listed private equities and short all other equities|
|EQ: Regional Spread||Long a region and short a broad market equity index|
|EQ: Sector||Long a sector and short a broad market equity index|
|EQ: Sector Momentum||Long sector indexes that have recently outperformed and short sector indexes that have recently underperformed|
|EQ: Size||Long small cap equities and short large cap equities|
|EQ: Value||Long value equities and short growth equities|
|FI: Developed Spread||Long foreign developed government bonds and short US government bonds|
|FI: Emerging Spread||Long emerging market government bonds and short foreign developed government bonds|
|FI: Inflation-Linked Spread||Long inflation-linked government bonds and short non-inflation linked government bonds|
|FI: Non-Treasury Spread||Long non-government/non-corporate bonds and short government bonds|
|FI: Term Structure||Long long-dated government bonds and short short-dated government bonds|
|FX: Carry||Long high yielding currencies and short low yielding currencies|
|FX: Developed||Long foreign developed currencies against the US dollar|
|FX: Emerging||Long emerging market currencies against the US dollar|
|FX: Momentum||Long currencies that have recently outperformed and short currencies that have recently underperformed|
|FX: Value||Long undervalued currencies and short overvalued currencies|
|LIQ: Autocorrelation||Lagged asset returns (a proxy for liquidity risk)|
|MAC: Momentum||Long asset classes that have recently outperformed and short asset classes that have recently underperformed|
|MAC: Trend||Long asset classes are trending upward and short asset classes that are trending downward|
|RE: Developed Spread||Long foreign developed real estate securities and short US real estate securities|
|RE: Property Spread||Long non-REIT real estate securities and short REITs|
|RE: Real Estate Spread||Long real estate investment trusts (REITs) and short the equity market|
|RF: Risk-Free Rate||Long 3-month Treasury Bills|
|VOL: Developed Spread||Long US volatility securities and short foreign developed volatility securities|
|VOL: Short Volatility||The excess return to shorting US volatility securities|
|VOL: Term Structure||Long long-term volatility securities and short short-term volatility|
Connect With Us