# A Tale of Two Betas

It was the bullish of times, it was the bearish of times, it was the age of hedging, it was the age of letting it all ride. In such turbulent market environments it can be helpful to revisit a cornerstone analytic of capital markets: the humble Beta.

Beta is the classic measure of how an asset behaves relative to the broad market. Although beta is a seemingly easy analytic to understand, calculating it can be quite a different exercise. Betas can be an important part of the investment process: from evaluating the riskiness of assets, to making sure one’s portfolio is beta neutral, to understanding what is driving the performance of one’s portfolio.

Discretionary managers whom are expected to deliver Alpha should always be aware that market neutrality doesn’t always equal beta neutrality. Quantifying beta and managing it can be critical to the investment management process.

This week we investigate two ways to build a beta: Historical Beta and Predicted Beta. Both measures capture the same market behavior and are analogous in terms of interpretation, but are calculated in different ways.

### Historical Beta

Historical Beta is calculated via a regression, traditionally an ordinary least squares linear regression. Given a time series of asset returns and market returns, one can calculate a regression where the slope is the asset’s beta. While in theory this process seems easy enough, there are a slew of assumptions that must be made in order to arrive at a reasonable beta, with some of the questions being:

- What market should I use?
- How much data should I use?
- What frequency of data should I use?
- How should I weight the data?
- Should I trim outliers in the returns data?
- Should I weight recent history more heavily? If so, by how much?
- What regression scheme should I use?
- How do I calculate the beta of an IPO, which doesn’t have historical returns? If I proxy returns, how should I?

All of these are important questions that need to be answered, and the beta you get out of the regression is dependent on it. Slight changes to any of these assumptions can lead to much different beta results, with some choices having a big influence on betas, and other choices having more subtle effect.

As an example, in the current environment the assumption of how much historical data to use makes a big difference. If we took a one year historical beta on a daily basis, **approximately half of the history would be pre-COVID and thus beta would be influenced by a risk regime much different than we are currently in.**

A better potential indicator of an asset’s beta today would be to only include history where the market acknowledged COVID - clearly Tech, Energy, and Retail have been performing quite differently recently than long term. Skimming over a beta’s assumptions may lead to wrong conclusions and introduce undesired market risk into one’s portfolio.

### Predicted Beta

Assuming we’re running an ordinary least squares regression in solving for an asset’s beta, we can also solve for this beta using the following equation:

Beta = Covariance(asset,market) / Variance(market)

Of course the above statistics are referring to the covariance and the variance data associated with the asset and market realized returns data, but this introduces an interesting possibility: using a factor risk model to estimate the covariance and variance.

The entire goal of risk model providers are to build better variance estimators using a structured approach - differentiating more drivers of variance than just the market, such as Style, Industry, and Country factors. When deciding how to input the returns for these models, they research all sorts of different approaches to building predictors: trading off the number of data points with the stability of the estimators, systematic approaches to trimming outliers, and precise exponential weighting schemes to make sure recent history is accurately captured in updating the estimators.

Risk model providers also apply approaches to estimating IPO returns and exposures when they are first listed, and then Bayesian adjusting them as real returns are realized, so you can always have a Beta to analyze for IPOs.

Similar to how return history choice can matter for Historical Beta calculations, the responsiveness of the risk model used for Predicted Beta can influence an asset’s Beta. Risk model providers that provide risk models for different time horizons, such as Long Horizon, Medium Horizon, Short Horizon, and Trading models will all predict different asset betas. In this case the history of the model matters less (although it definitely can matter) and is more about the exponential weighting half-life, where more recent data more heavily influences an asset’s beta.

### Conclusion

Betas are a fundamental analytic that help investors understand how an asset behaves relative to the broad market. There are many ways to calculate a beta, all of which have various pros and cons, so multiple perspectives of an Asset’s beta is likely warranted. Omega Point is dedicated to working with our risk model providers to help provide these analytics to our clients to help them make better investment decisions. Although we depart from this topic in the next few weeks to focus on Election coverage, rest assured Product enhancements and future Factor Spotlights will dig deeper into this topic.

### US & Global Market Summary

**US Market: 9/28/20 -10/2/20**

- The market gained strength in the middle of the week on optimism around impending fiscal stimulus, although news that the US president had tested positive for COVID-19 shook investors on Friday, adding more tumult to a period already fraught with uncertainty.
- Friday’s jobs report (one of the last major economic releases prior to the election) disappointed, as nonfarm payrolls increased by 661,000 last month vs. consensus estimates of 800,000. The unemployment rate fell by more than expected to 7.9%, although much of this looks to have been driven by a decline in labor force participation.
- Several companies (such as Disney, Allstate, American Airlines, and United Airlines) announced major layoffs this week, the impact of which will be seen down the road.
- US-based equity funds received $1.1B, marking the first inflow in seven weeks.

**Normalized Factor Returns: Axioma US Equity Risk Model (AXUS4-MH)**

**Growth**was again the week’s biggest winner, continuing to rise back towards the mean after hitting a trough of -1.92 SD below the mean on 9/18.**Momentum**also continued to bounce back from a recent bottom of -0.85 SD below the mean on 9/21.**Earnings Yield**headed higher into Overbought space, now sitting at +1.42 SD above the mean.**Profitability**slowly drifted deeper into Oversold territory, now at -1.07 SD below the mean.**US Total Risk**(using the Russell 3000 as proxy) declined by 51bps.

**Normalized Factor Returns: Axioma Worldwide Equity Risk Model (AXWW4-MH)**

**Growth**continued its rapid ascent from its recent bottom of -1.66 SD below the mean on 9/18, and has exitedOversold territory after its +0.47 SD move this week.**Momentum**also saw some relief, and look poised to lost its Oversold designation this week.**Value**moved further away from its recent bottom of -1.12 SD below the mean on 9/16, up +0.14 SD on the week.**Profitability**saw ongoing weakness, down -0.23 SD and heading deeper into negative space.- Unlike the US,
**Global Risk**(using the ACWI as proxy) declined by 54bps.

Regards,

Chris