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How Beta, Correlation and Volatility Relate: This Year’s Data

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Since 2008, equity sector correlations have remained consistently high. As broad equity markets rallied, most, if not all, of the equity sectors moved higher in tandem with the overall market. Even then, some sectors certainly performed better than others. Traditional high beta sectors like Industrials, Financials and Technology led the market higher while traditionally low beta sectors such as Healthcare, Utilities and Consumer Staples performed well, but in line with their historical beta measures. 

In early 2013, however, sector correlations decreased and historical betas started to break down. While the broad markets continued to move higher, certain high beta sectors began to lag while lower beta sectors raced higher. A significant change in a sector’s historical beta is unusual. Looking at the chart of year-to-date sector returns below, defensive sectors such as Healthcare, Consumer Discretionary and Consumer Staples were three out of the four top-performing sectors while traditionally higher beta sectors such as Materials and Technology can be found at the bottom of the list. Keep in mind this performance dispersion is within the framework of a higher trending broad market.  

This decline in sector correlations and changing betas certainly creates opportunity to outperform (and underperform) for the average long-only active equity manager. One of the factors that has separated top-performing managers from others is their ability to own enough of the traditionally defensive sectors as the market has rallied. This flies in the face of traditional convention as many managers tend to overweight Industrials, Technology and Materials as markets rally and overweight Healthcare, Utilities and Consumer Staples as markets decline. 

This phenomenon has had a big impact on the options market, especially for portfolio managers and traders who typically write call options in the quest to generate alpha through options writing. Why? In a word, volatility.  

Taking a step back, the equity options market has been a predictor of how far certain securities and sectors should move over a particular time frame. By looking at the historical volatilities of sectors, for example, options traders could develop an educated guess about the range of outcomes for a sector and factor that into the pricing of a particular option. Of all variables in option pricing models, volatility is the only unknown variable. Traders must estimate the volatility to come up with a theoretical price and compare that to the prevailing market price. This is a significant factor dictating whether an options trader or portfolio manager buys or sells a particular option. 

Returning to the example of recent outperformance of some typically low-beta sectors, as option traders factored in traditional volatility measures for these sectors, they turned out to be much too low.  The result was writing an option that was way too cheap, and as the market rallied, the short call positions were called away. Traders were then forced to buy the stock that got called away, which forces the stock price even higher if they still want or need exposure to a security or sector. 

Within the Healthcare sector, a portfolio manager that wrote a call at the beginning of the year on one of the Healthcare sector ETFs, thinking it was a low volatility/low beta sector, was forced to purchase the call back, and in essence, buy high. As the Healthcare sector continued to move higher and exhibit significant upside volatility, the negative convexity environment potentially exacerbated the move. This was all a result of “selling” volatility that was far too low. 

Based on the formula, Beta = correlation (between sector and market) x volatility of sector/volatility of the market, if sector betas are rising and sector correlations are falling (discussed above), the relative volatility of the sector has to be rising based on the mathematical relationship above. Conversely, if sector volatility is rising and sector betas are also rising, the correlation of the sector has to be falling, if the market volatility is constant or decreasing (as in 2013). 

The relationship between the beta, correlation and volatility is complex, but very important.  For long-only equity managers, underestimating any of these statistics can lead to relative underperformance in a rising market as the wrong sectors are under- and over-weighted. For options traders and portfolio managers, a significant deviation from historical measures can lead to an under- or over-estimation of volatility, which can lead to the same conundrum, by potentially over- or under-weighting one’s exposure at an inopportune time.


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