*“More empirical effort may have been put into testing the CAPM equation than any other result in finance. The results are quite mixed and, in many ways, discouraging.”
*Mark Rubinstein

*“The CAPM is a theoretical ‘tour de force’ though ‘empirically vacuous’,”
*Fama and French

The Capital Asset Pricing Model (CAPM) suggests that the return for any given stock should be proportion to its beta or sensitivity to broad stock market returns. In other words, the CAPM implies that high beta stocks should outperform low beta stocks. However, the empirical data and research shows that low beta/low volatility tends to systematically outperform high beta/volatility. A good summary of this anomaly by Alpha Architect can be read here, by AQR here, and also by Robeco here. A more detailed article by one of the pioneers in low volatility investing- Eric Falkenstein– can be read here.

There are a variety of proposed explanations for low volatility effect, and readers are encouraged to do their own research. One plausible reason for why the anomaly likely exists is that asset managers and individuals are often restricted from using leverage. This drives asset managers to seek out stocks that have embedded leverage or higher beta thus increasing demand and reducing future returns. In contrast, lower volatility or lower beta stocks tend to have less embedded leverage, and greater tracking error to the market index and often underperform in bull markets. This helps to drive down demand and increase their returns over time.

To demonstrate this effect, we performed our own analysis using FTSE/Russell data. The chart below shows the results from investing in the top 50 or 100 stocks by low volatility, low beta and high beta from the largest 500 stocks in the US by market capitalization:

Consistent with the academic research, low volatility and low beta materially outperforms high beta stocks over the last 20 years. We can also clearly see that low volatility and low beta stocks are highly correlated in terms of their performance. Both low volatility and low beta stocks tend to have low firm-specific or idiosyncratic risk which implies an inherently high correlation to the market index. At the extreme where the correlation is near to one, the only factor that changes the relative ranking is the volatility component of the beta calculation so the fact that the two strategies have similar performance makes sense.

Some other observations emerge from this chart: low volatility tends to slightly outperform low beta, and a more concentrated portfolio for high beta leads to substantially worse performance than being more diversified. In contrast, concentration in low volatility is beneficial**. **We can more clearly see the relative performance in terms of total return of high and low risk stocks by bull and bear market regime in the table below (note HB= High Beta**, **LB = Low Beta, and LV= Low Volatility while the number relates to the number of stocks chosen):

The evidence shows that high risk stocks do outperform during bull markets and underperform in bear markets. In fact, if we look at the table below which sums the returns across regimes (rather than compounding them) we see that high beta stocks actually outperform low beta/volatility stocks on an arithmetic basis. Falkenstein also found a significant differential between geometric/compound returns versus arithmetic for high beta stocks which was not present for low vol/low beta stocks.

Given that bull markets tend to last much longer than bear markets it is reasonable to say that the CAPM is approximately true most of the time (high beta outperforms low beta) but because of the mathematics of compounding (losses hurt more than gains) it is not true across market cycles. The fact that high beta firms tend to have lower quality and higher financial leverage is perhaps one good reason why the outperformance in bull markets is more than erased during bear markets.

** ****The Case for a Dynamic Approach**

The opportunity for a dynamic approach is substantial- if you could switch between high and low beta/volatility it is possible to have a more asymmetric return profile that can outperform in bull markets and in bear markets. In contrast having exposure to low volatility/low beta is symmetric- while you outperform over a market cycle, you tend to underperform during bull markets. Let’s look at the magnitude of the opportunity by comparing the two best portfolios- the lowest 50 stocks by volatility and the highest 100 stocks by beta. We will subtract the low vol portfolio from the high beta portfolio to illustrate the magnitude of the difference between the two:

What we see is that high beta has predictably substantial outperformance in bull markets, and underperformance in bear markets. The opportunity in terms of total return difference is at times near or exceeding triple digit performance which means that even capturing a small fraction during each regime can substantially enhance overall returns.

So how would we capture this performance differential? The most likely candidate is to use the most pervasive and powerful anomaly in finance which is momentum. We can apply either the CAGR or rate of change (ROC) differential between high beta and low volatility or we can look at a basic trend-following proxy which is the price versus the simple moving average (SMA)**.** Both methods are well established in the empirical research and are directly related mathematically. To compare high and low risk we divide the cumulative total return value of the equity curve of each portfolio by the other starting from the same date. For example, if we use the total return of the high beta portfolio and divide it by the low volatility portfolio, if the CAGR or ROC of this return stream is positive we would trade high beta instead of low volatility and vice versa. The same applies to using the simple moving average rule.

To test performance across a broad range of parameters/time frames we use the SMA strategy using 25,50,75,100,150 and 200 days traded daily and to test the CAGR/ROC strategy we use 20,60,90,120,180 and 252 days. Each day you would switch between the high beta and low volatility portfolio as the strategy dictates. The results are presented below:

What we notice is that the SMA strategies tend to perform better on average than the ROC strategies, and this is likely because of the positive autocorrelation of the high beta divided by low volatility time series (.039). Performance is relatively stable across both the SMA and ROC strategies which is also a good sign. To create a robust and continuous Dynamic Beta Strategy, we take all twelve signals (6 SMA strategies and 6 ROC) and use the following equation to allocate proportionally allocate between the high beta and low volatility portfolios:

*Allocation to High Beta= Sum of High Beta Signals (squared)/Total Number of Signals (Squared)*

*Allocation to Low Beta= 1- Allocation to High Beta*

The goal here is to tilt to high beta when there is a strong consensus to enhance accuracy. The results of this strategy can be seen below:

As you can see, the return of the Dynamic Beta Strategy is substantially higher than either the low volatility or the high beta strategy which indicates some positive timing ability across regimes. The Dynamic Beta Strategy has a higher Sharpe ratio (return/risk) and MAR (return/max drawdown) than any of its constituent parameters which indicates a synergy and variance reduction to the composite approach. Most importantly, the Dynamic Beta Strategy has a higher return and lower risk and drawdown than the S&P500 (SPY) which makes it an attractive strategy for investors who are looking to manage risk without potentially sacrificing returns. In contrast, traditional risk managed or tactical strategies that can allocate to cash or fixed income when market conditions warrant tend to have the downside of lower expected returns over time, higher tracking error, and greater timing risk: low volatility equities still have a positive beta to the broad market while cash has a zero beta so when you make a timing error the cost is lower. To visualize how the beta changes over time we plot the rolling 120-day Beta of the Dynamic Beta Strategy to the S&P500 (SPY) over time.

Clearly you can see a lot of shifts over time, and notably lower beta during bear markets and higher beta during bull markets. The average beta was .86 or lower than the index average over time due to the conservative “squaring” approach to signals allocated to high beta. This is prudent primarily because the high beta portfolio does poorly over time and the margin for error is therefore smaller. A good way to reduce timing risk and increase the margin for error is to use some type of factor screen to find higher returning high beta stocks. We will look at what causes high beta stocks to underperform and how to improve stock selection in the next post.

**Conclusion**

The CAPM predicts that higher risk stocks will outperform lower risk stocks, but the empirical research shows that the opposite is true. A closer analysis shows that the relative performance between high and low risk stocks is in fact regime-dependent. A Dynamic Beta Strategy can potentially shift the opportunity set offered by the CAPM or Security Market Line by switching between high and low risk stocks as their relative strength warrants. Since the performance of high and low risk stocks have substantially different relative return profiles in bull and bear markets, it is possible to capture large improvements in overall performance with reasonable timing skill. The fact that the relative return stream of high risk versus low risk shows a positive autocorrelation makes traditional and well-established momentum/trend-following strategies good candidates for generating timing signals between the two portfolios. The results show good parameter stability and a composite approach that combines a wide range of parameters demonstrates solid performance and risk-adjusted performance that is both superior to its component portfolios and to the broader index. A Dynamic Beta Strategy may also be more appealing to investors versus traditional tactical strategies because of lower tracking error- since it is always fully invested- and the potential for higher returns over time due to the ability to shift portfolio implied leverage or beta greater than the index when conditions warrant.

Definitions and Disclosures

There is risk of loss with any investment and past performance is not a guarantee of future results. Any graphs or charts contained herein cannot by themselves guide you in making any investment decision. We encourage all investors to use this report along with all other data sources and information to assess all relevant factors one needs to then draw conclusions, such as risk, volatility and diversification. “Risk” is generally discussed in terms of volatility. This presentation contains forward-looking statements. All strategies have risk such strategy fails to perform as expected. BSAM makes no assurance that any investment portfolio or products based on any strategy will accurately track expected performance, provide positive performance returns or perform consistently with forward-looking assumptions. Because no investor may invest directly in an index, data for all QuantX Index Strategies represented in this material does not reflect the deduction of any BSAM management fees, advisory fees or expenses, nor trading costs, all of which will decrease the return experienced by a client and this report should not be presented alone to advisory clients in order to market any related investable portfolio strategies. Value Added Index: The value-added index charts the total return gained by an investor from reinvestment of any dividends and additional interest gained through compounding.

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