Bulls, Bears and Beta

The Capital Asset Pricing Model implies that assets with high beta should provide a higher rate of return than those with low beta. High beta assets are such because of a high degree of market exposure: a large amount of correlation with the overall market and high volatility. But, is it possible that high beta assets, with their high volatility, may outperform during market booms and then underperform during times of distress (relative to low beta assets)?

I can’t take credit for this idea, but I thought it was an interesting thought and worth some exploration.


The original Capital Asset Pricing Model (CAPM) relates the expected return of an asset to the risk-free rate of return and the return premium of the overall market.

Rasset = Rfree + β*(Rmkt – Rfree)

The coefficient beta, which represents the slope of the relationship, may be solved for using the following equation(s)

β = ρasset,mkt*(σassetmkt) = covar(Rasset,Rmkt)/var(Rmkt)

Beta has two components: correlation and relative volatility, and it may be interpreted as a measure of market exposure or systematic volatility. High beta assets have a combination of high correlation and high volatility while low beta assets have lower correlations and lower volatility, usually. The basic idea here is that assets with higher amounts of systematic volatility should be rewarded with an increased rate of return.


The dot-com bubble of the late 1990s provides the starting point for this thought experiment. Consider two different sectors during this period: business equipment (computers, software and electronics) and consumer non-durables (food, textiles, apparel and toys). Both of these portfolios came from the 12 industry portfolios file provided by Ken French’s data library which is a rough approximation of US market sectors. What’s interesting about these two particular sectors is that they had very similar returns over the period from January 1995 through September 2001. While the volatility of the S&P 500 and consumer non-durables was also similar, business equipment went on a rather wild ride with a volatility of more than twice that of the overall market

Equity Performance
(Jan 1995 – Sep 2001)
CAGR Volatility Beta
S&P 500 14.8% 16.0%
Business Equip. 13.9% 34.1% 1.66
Consum. Non-Durables 14.1% 14.4% 0.54

When this period is broken down into a bull market and ensuing bear market the differences in performance become readily apparent. High beta stocks, represented by business equipment, had a tremendous rise and fall. On the other hand consumer non-durables simply chugged along and actually outperformed during the bear market period.

Bull Market CAGR
(Jan ’95 – Feb ’00)
Bear Market CAGR
(Apr ’00 – Sep ’01)
S&P 500 25.8% -14.8%
Business Equip. 48.5% -52.0%
Consum. Non-Durables 12.5% 19.7%
Growth of $1 for High and Low Beta Equities
Source: Ken French Data Library

To summarize: the low beta sector (consumer non-durables) was rather boring during the strong bull market of the late 1990s, but when distress came along it was superior to the high beta sector (business equipment). Low beta assets, in theory, have less exposure to systematic volatility. Therefore, they may not decline as much as the overall market or high beta assets during market drawdowns.

Does this relationship between beta and annualized returns apply to the remaining nine sectors in the Ken French series (note: the sector labeled “other” was omitted)?

Return vs. Beta (Jan 1995 - Feb 2000)

Return vs. Beta (Apr 2000 - Sep 2001)
Source: Ken French Data Library

The relationship between return and beta appears pretty obvious. The initial conclusion here is that high beta sectors tend to outperform during bull markets while low beta sectors do so during bear markets.

Let’s extend this hypothesis further back in time. Rather than visually inspecting the relationship over multiple time periods I instead quantified the relationship using correlation coefficients. The chart below summarizes these coefficients between annualized returns and beta during various bull and bear markets. The t-stat is included in parentheses below each coefficient and I’ve highlighted those that are statistically significant in boldface

Bull Markets
Jul ’63 – Feb ’66 0.82
Jun ’70 – Dec ’72 -0.21
Jul ’82 – Dec ’84 0.18
Jan ’88 – Jun ’90 0.22
Jan ’95 – Feb ’00 0.60
Nov ’01 – Jul ’07 -0.38
Apr ’09 – Jun ’16 0.13
Bear Markets
Dec ’68 – May ’70 -0.40
Feb ’73 – Sep ’74 -0.73
Aug ’87 – Dec ’87 -0.79
Apr ’00 – Sep ’01 -0.91
Sep ’08 – Feb ’09 -0.71

The tendency for high beta sectors to outperform during bull markets is certainly possible. However, the correlations presented here show that it has not been tremendously persistent over the past few decades as only two of the six bull markets showed statistical significance. There is a strong case to be made that low beta sectors have performed better than their high beta counterparts during bear markets with four out of the five cases statistically significant. In other words the historical advantage enjoyed by low beta sectors may be partially explained by the fact that they simply didn’t lose as much when things got ugly.

So, a more refined conclusion is that low beta sectors have the potential to outperform during periods of duress. But I want to be careful. There are always exceptions and the table above provides a clue. Notice the correlations on beta were similar to the correlations on volatility–that beta and volatility were essentially synonymous in the situations examined. It follows that sector volatility was more than likely a major contributor to beta, and sector correlations to the overall market should be rather high


What about a low beta asset with very low correlation to the market, where the correlation coefficient is the main driver of beta rather than volatility?

Precious metal equities

The table below summarizes beta and its constituent components for PME over several of the periods previously mentioned. In all cases the relative volatility was exceptionally high, which is expected since precious metal equity is a particularly volatile asset. Also the corresponding values of beta were very low, and in some instances even negative! All of this because of the exceptionally low, and sometimes negative correlations that PME has with the broader market. Adding insult to injury the only time PME was highly correlated with the S&P 500 was during the depths of the great recession–precisely the wrong time for assets to be highly correlated!

Market Exposure of Precious Metal Equity
(July 1963 – Jun 2016)
Beta Correl. Vol. Ratio
Bull (Jan ’88 – Jun ’90) -0.27 -0.14 1.99
Bull (Jan ’95 – Feb ’00) 1.07 0.29 3.63
Bear (Apr ’00 – Sep ’01) -0.18 -0.09 2.09
Bull (Nov ’01 – Jul ’07) 0.22 0.08 2.67
Bear (Sep ’08 – Feb ’09) 2.60 0.67 3.90
Bull (Apr ’09 – Jun ’16) 0.26 0.08 3.09

Precious metal equity presents a great lesson when it comes to beta. Beta comes in different flavors, and its entirely possible for an asset to have very low beta but still be incredibly risky. As beta declines from a value of 1 the asset may exhibit less systematic volatility, but retain the unsystematic/idiosyncratic volatility specific to itself–whether good or bad.

Low beta isn’t a catch-all for “safe” assets. Any asset, regardless of how it compares to the broader market, requires diligence to understand the nature of its risk.

A few comments:
1. Only a few decades were examined and some of the time periods that were regressed were rather short–leading to small sample sizes.
2. There were certainly situations where high beta assets out-performed the S&P 500, despite the fact that the correlations did not show statistical significance. For instance, during the bull market from June 1970 through December of 1972 the wholesale and retail industries (the “Shops” sector) had a beta of 1.12 and produced an annualized return of 30.9% compared to 22.1% for the S&P 500. Other examples can be found as well.
3. The analysis above only accounts for market beta, and ignores exposure to other factors that have been demonstrated to impact returns (size, value, momentum, etc.). Momentum may be a particularly interesting factor to examine in the context of bull and bear markets.

What I’m Reading
Here’s Why Technical Analysis Gets a Bad Rap (Michael Batnick)
The Money Management Gospel of Yale’s Endowment Guru (Geraldine Fabrikant)
Turning Over Accepted Wisdom with Turnover (Cliff Asness)
Living in an Extreme Meritocracy Is Exhausting (Victor Tan Chen)
Evidence Based Investing for Dummies (Tony Isola)