This article is a brief interlude to an introductory series on the statistical regularities of the stock market. The idea is to take what I discussed in the last article about beta, and apply it to a realworld long/short pairs trade.
The term "Betting against beta" was coined in a recent paper (Frazzini & Pedersen 2014) to refer to profitable strategies exploiting the fact that the returns of risky strategies are often meanvariance riskinefficient; the authors identify these risk inefficiencies in a number of assets, from stocks, to bonds and commodities. The findings are not new, portfolio managers have been aware of the riskinefficiency of the market since testing began on the CAPM model some 40 years ago; as early as Banz (1981), it was clear how to arbitrage a systematic risk factor. Frazzini & Pedersen's important contribution is to show how widespread meanvariance riskinefficiency is in the financial markets.
Betting against beta has received mostly peripheral attention in a few articles on this website, but I would like to explore the BAB strategy specifically in the equity space for the retail investor. The basic premise of this beta arbitrage strategy is that the market overpays for high beta stocks and underpays for low beta stocks. This means it opens up a longshort arbitrage opportunity along the theoretical riskreturn axis of the CAPM's security market line (SML). Figure 1 shows the basic concept of the strategy, which is to rotate the SML counterclockwise back to its "true" relation. This can be done by applying pressure in the form of a long position in low beta stocks, and relief through a short on highbeta stocks.
Figure 1: Author's strategy diagram based on Fama & French (2004: 33)
Theoretical Returns
Even though we know of the beta anomaly, before running out and putting our hardwon cash into the financial casino, it is worth taking a look at what returns we might expect from this particular portfolio strategy. While the stylized fact that highbeta stocks are not riskefficient holds, the exact measured return depends a lot on the period and country under examination.
Table 1 reports what a zerobeta portfolio might look like based on reported statistics from two different papers, which I picked more or less at random.
ZEROBETA PORTFOLIOS FORMED ON BETA COMPONENTS  
Portfolio 
S&P500 
Estimate 1 
Estimate 2 

low 
high 
low 
high 

Beta 
1 
0.64 
1.70 
0.51 
1.36 
Excess return 
0.062 
0.11 
0.12 
0.13 
0.19 
SD 
0.142 
0.16 
0.42 
0.11 
0.29 
Sharpe 
0.437 
0.73 
0.29 
1.15 
0.63 
Portfolio weight 
1.563 
0.588 
1.961 
0.735 

Net leverage  annual financing 
1.15 
0.003 
1.70 
0.014 

Return portfolio 
0.107 
0.111 

SD portfolio 
0.14 
0.12 

Sharpe portfolio 
0.76 
0.89 

Author's calculations based on: Table 3 Frazzini & Pedersen (2014); Tables 5&6: Pettengill et. al. (1995), and S&P500 data from irrationalexuberance.com 
Both papers written about 20 years apart, give comparable results for the BAB strategy. Based on Table 1, the strategy returns about 11% excess annual return above the riskfree rate, which I assumed to be 2%. Frazzini & Pedersen (2014) report about an 8.7% annual excess return beyond the riskfree rate for US markets. They note that the betas are measured with error (I used their average exante measure), and they state their portfolio is not entirely zerobeta, as my artificial one is. Moreover, they form and reform the portfolios each month. Based on their findings and these numbers the excess returns of the strategy are likely to fluctuate somewhere in that 911% range.
In other words, you are not going to trounce the historical market return of 810%. In fact, betting on beta would be a better strategy, if you care only about absolute returns, and not about their riskefficiency.
However, the betting against beta strategy is more riskefficient than a buyandhold strategy of the S&P500 as evidenced by the much higher Sharpe ratio. Note that as a riskefficient portfolio, the strategy can be scaled up through leverage to achieve higher total returns. It can also be scaled down to reduce risk and returns. In that latter scenario, the first estimate of the portfolio has a slight net cash balance from the shortsale proceeds, the second estimate of the strategy is a slightly levered portfolio wherein the proceeds from the short sales do not cover the ongoing financing needs of the long position.
This strategy sounds all well and good in theory where there are no trading costs, very long periods of time, all securities can be borrowed, and financing is always done at the riskfree rate. In the next section, I will try and translate the strategy into the retail investing environment using realworld variables.
Practical Considerations
There are a number of practical considerations to implementing an abstract strategy. Since you are trying to capture systematic effects, you need a fair number of securities in the portfolios at the extrema of the SML so as not to have your strategy diluted by idiosyncratic risk. An educated guess is that you would probably need at least about 30 in each component portfolio. You are also going to have to find these 60 securities by estimating betas, which unless you are setup with good data and processing capabilities, could prove challenging. Furthermore, you are looking at about 60+ commission charges oneway, unless you have extremely low trading costs or a highportfolio value, this could eat into returns quickly. For most retail investors a stockbased implementation would represent a both a computational challenge and large upfront cost.
An ETF Implementation of Betting against Beta
This essentially leaves most small investors with an ETFbased strategy. The obvious candidates are the paired Invesco highbeta and lowvolatility ETFs. Crossing provider lines are the high and lowvolatility emerging market ETFs, EEHB and EEMV, from Invesco and iShares. To spice things up I threw in two "mismatched" ETFs, the Brazilian largecap is reported as one of the highest beta ETFs by etfDB.com, along with KBWD, one of the lowest beta ETFs. Table 1 gives an overview of their basic attributes.
Table 1: Betting Against Beta ETFs  
IDHB 
EEHB 
EEMV 
KBWD 

Beta v. SPY (provider) 
0.95 
1.59 
0.85 
1.4 
0.82 
1.53 
1 (.87) 
3.58 (1.9) 
0.6 

Correlation 
 
0.92 
0.92 
0.60 
0.58 

Market Cap 
all 
all 
large 
large + mid 
large 
small + mid 

Expense ratio 
0.18 
0.25 
0.25 
0.25 
0.25 
0.29 
0.25 
0.77 
1.55 

Geography 
world 
developed exUS 
US 
emerging markets 
Brazil 
US 

Definition 
proxy market portfolio 
200 highest beta stocks 
200 lowest volatility stocks 
100 highest beta stocks 
100 lowest beta stocks 
200 highest beta stocks 
ca. 230 low volatility stocks 
29 financials 
ca. 32 financials 

Provider 
Vanguard 
Invesco 
iShares 
globalX 
Invesco 

Source: product websites + etfDB.com 
Aside from the exotic mismatched ETFs, BRAF and KBWD, most of them have reasonable expense ratios for the service of finding the highbeta and lowvolatility stocks on a regular basis. KBWD's expense ratio is really high by industry standards, but also provides some access to a riskier niche space (small+midcap finance), while transforming those into monthly payments. As a side note, if you have more than USD 15,000 to devote to this strategy, buying KBWD's stocks individually might be a wiser choice than holding an expensive ETF for a long period.
Table 2 reports the value of our first bettingagainstbeta pair for international developed equity markets, and requires a bit of explanation. One thing that might catch the reader's attention is the fact that the lowvolatility group has a higher beta when measured against the proxy for the worldportfolio, VT. These VT portfolio betas (Beta_VT) are substantially lower than betas of the stocks relative to the S&P500 (Beta_SPY), which may have to do with the liquidity of the ETF or a measurement issue.
Table 2: BAB ETF Portfolio for Developed International Equity  
VT 
IDHB 
IDLV 

Beta 
 
1.59 
0.85 
Beta (ETF v. VT) 
0.99 
0.43 
0.69 
Beta_portVT 
1 
0.89 

ETF correlation 
 
0.92 

Distributions (%) 
2.4 
2.7 
3.26 
Borrow  lend (%) 
3 
3** 
6.5 
Financing gains 
5.4% 
4.3% 

Capital gains 
6.6% 
15% 

Excess returns 
9.4% 
16% 

SD excess returns 
26% 
26% 

Sharpe 
0.36 
0.64 

Weights 
1 
0.35 
0.65 
Riskfree rate  scale 
0.026 
0.55 

Author's calculations based on yahoo & IB securities lending tool; *portfolio weights using beta vs. SPY; **assumed Period: ETF inception until 20141010 
The financing gains are the weighted dividends and borrow/lend fees netted against one another. The capital gains issue from the weighted position values. The entire portfolio has a similar standard deviation to that of the market, but its Sharpe ratio is about 70% higher, indicating greater riskefficiency. The portfolio can be scaled up to achiever higher returns with more absolute risk. The returns for this combination are considerably higher than the 911% predicted by theory.
The next BAB pair, presented in Table 3, is based on the S&P500 stocks.
Table 3: BAB ETF Portfolio for S&P500  
SPHB 
SPLV 

Beta (stocks v. SPY) 
1.4 
0.82 
Beta (ETF v. VT) 
1.32 
0.58 
Beta_portVT 
0.02 

ETF correlation 
0.92 

Distributions (%) 
0.96 
2.41 
Borrow  lend (%) 
3.42 
1.62 
Financing gains 
0.9% 

Capital gains 
19% 

Excess returns 
18% 

SD excess returns 
14% 

Sharpe 
1.26 

Weights 
0.36 
0.62 
Riskfree rate  scale 
0.026 
0.51 
Here too, betting against beta seems to be a profitable strategy, but here more of the gains are coming from capital appreciation than financing (net dividends + securities lending). The Sharpe ratio is about 3.5 times that of the historical S&P; it beats the S&P500 by about 9.3% over the same period.
We now turn to the emerging markets with the same strategy. These ETFs come from two different companies, but still trade in the US market.
Table 4: BAB ETF Portfolio for Emerging Markets  
EEHB 
EEMV 

Beta (stocks v. SPY) 
1.59 
0.87 
Beta (ETF v. VT) 
0.68 
0.89 
Beta_portVT 
1.06 

ETF correlation 
0.60 

Distributions (%) 
2.13 
2.58 
Borrow  lend (%) 
1.17 
4.44 
Financing gains 
3.2% 

Capital gains 
14% 

Excess returns 
15% 

SD excess returns 
25% 

Sharpe 
0.59 

Weights 
0.34 
0.61 
Net Leverage  risk free 
0.0 
0.00 
Riskfree  scale 
0.026 
0.54 
The volatility of this pair is much higher than the S&P500 pair, leading to a lower Sharpe ratio; nevertheless, the strategy is more riskefficient than VT.
Table 5: "Mismatched" BAB ETF Portfolio  
BRAF 
KBWD 

Beta (stocks v. SPY) 
1.9 
0.6 
Beta_VT 
0.73 
0.78 
Beta_portVT 
0.73 

ETF correlation 
0.58 

Distributions (%) 
0.96 
8.08 
Borrow  lend (%) 
1.88 
2.81 
Financing gains 
15% 

Capital gains 
11% 

Excess returns 
25% 

SD excess returns 
16% 

Sharpe 
1.62 

Weights 
0.47 
1.5 
Net Leverage  risk free 
1.0 
0.0 
Riskfree  scale 
0.026 
0.90 
This oddball portfolio does the best in terms of the Sharpe ratio. Much of the profit comes in the form of distributions from the KBWD position, which also has a relatively low volatility compared to the developed and emerging market equity portfolios.
Practical Caveats and Risks
Even though all the distinct BAB portfolios seem to outperform the market, this period in the stock market has been unusually light on volatility, low on dispersion (which increases the efficiency of the trade due to the correlation between the ETFs controlling the variance of the portfolio), and had a strong uptrend. The profitability of the trade may decrease with a drastic shift in market conditions. That said the shallow SML slope has been observed for some 30+ years, and is likely to persist.
As a note, I could not get the borrow for any of the highbeta ETFs in their paper trading account at TD Ameritrade. Similarly, Interactive Brokers' public borrow tool did not have shares available for IDHB as of this writing; BRAF is also in short supply as of this writing.
A portion of the returns shown above are conditional on the net financing contribution. This contribution may not be realistic for retailer investors who may not get the security lending income from their brokers who do not pass this on to clients. Retail investors also face higher and variable securities borrowing costs, which can further erode the trade. Furthermore scaling the portfolio may not be efficient given the very high margin rates retail clients face.
I have done my best to present accurate information, and had other people look at my work for at least obvious mistakes, but this is not a substitute for doing your own financial homework. I encourage you to compute these trades or similar ones yourself, if not only to learn about the mechanics of a zerobeta portfolio.
I'm pretty busy with my PhD, so my promised article on value may be bit slower on coming. Until then, stay riskefficient.
Disclosure: The author is long SPLV, KBWD, IDLV.
The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.
Additional disclosure: I have a couple of small experimental BAB positions open using some of the ETFs named in this article.