THE LOW-VOLATILITY ANOMALY: Does It Work In Practice?

THE LOW-VOLATILITY ANOMALY: Does It Work In Practice?

Glenn Tanner

McCoy College of Business, Texas State University, San Marcos TX 78666 E-mail: [email protected]

ABSTRACT

This paper serves as both an empirical test of the low-volatility anomaly and an examination of the benefits of the anomaly in a portfolio sense. Since the introduction of the Standard & Poor’s Low Volatility exchange- traded fund in 2011, individual investors have been easily able to buy into this anomaly. We find that since the fund’s inception, the fund has delivered superior risk-adjusted returns relative to other common exchange- traded index funds. However, we find that the low-volatility fund’s impact is negligible when added to a portfolio of popular, diversified index funds.

Keywords: Volatility, Risk, Stock Returns, Portfolios

JEL Codes: G11, G17

1. INTRODUCTION

Though the low-volatility anomaly has received increased mainstream attention recently, it is not a new phenomenon. More than 40 years ago, Haugen (1975) first documented that low-volatility portfolios consistently produced higher risk-adjusted returns than high-volatility portfolios. While many academic studies confirmed and advanced Haugen’s work (see for example, Baker (2011 and 2012)), we suggest that the anomaly did not fully become recognized by the finance industry until 2011, when Standard and Poor’s introduced a family of low volatility stock indexes. Shortly after the index introduction, two exchange traded funds that tracked the S&P 500 Low Volatility Index were introduced, allowing investors to easily invest in the low- volatility anomaly.

We examine the performance of the largest of these funds, both on its own and in a typical diversified portfolio context for an individual investor. We find that the anomaly continues to thrive, as the fund has produced exceptional risk-adjusted returns compared to other common index funds. However, we find that as an addition to a well-diversified portfolio, the low-volatility fund has a miniscule impact on the risk-return efficiency of the portfolio. Using linear programming techniques to construct ex post minimum risk portfolios, we show that in spite of its excellent individual risk-return profile, the Low Volatility Index exchange traded fund only marginally moves the ex post efficient frontier of several common assets.

2. THE LOW VOLATILITY INDEX

Standard and Poor’s introduced the “S&P 500 Low Volatility Index” on April 4, 2011. The index contains the 100 least volatile stocks in the S&P 500 based on the daily return standard deviation over the prior 252 trading days. The index is rebalanced quarterly, with each stock’s weighting set inversely proportional to its volatility.

Standard and Poor’s back-tested the index to 1991 and found that the strategy not only produced better risk- adjusted returns than the S&P 500, but also dominated the index by generating higher average annual returns and lower standard deviations. These figures are reproduced in Table 1. Though one could easily argue that these back-tested results are inflated by selection bias, these numbers were likely extremely appealing to investors.

On May 5, 2011, investors were afforded the opportunity to take a position in this index, as PowerShares debuted an exchange-traded fund (ETF) designed to mimic the index. The PowerShares S&P 500 Low Volatility Portfolio is listed on the New York Stock Exchange Arca and trades with the ticker symbol SPLV.

Since its inception, the fund has experienced a 17% annual turnover rate and carries an expense ratio of 0.25%.

As of December 2013, the fund’s largest sector holdings were in Utilities (25%), Consumer Staples (20%), and

Industrials (17%). The fund had assets of $4.28 billion and experienced average daily volume of nearly 1.3 million shares over the previous three months.

3. DATA

We first examined how individual investors can benefit from ownership of SPLV by comparing the fund with other typical index investments. We obtained weekly return data beginning on SPLV’s inception date through year-end 2013 for SPLV and seven more exchange traded index funds covering broad asset classes:

 Corporate Bonds -- U.S. Credit Bond Index, which covers investment grade US corporate debt and dollar- denominated foreign debt

 Treasury Bonds -- Barclays 10-20 Year Treasury Bond Index

 Developed International -- MSCI EAFE Index, an international equity index representing developed markets outside of North America

 Global Stocks -- S&P Global 100, one hundred multinational blue chip companies

 Emerging Markets -- FTSE Emerging Index, over 800 large and midcap companies in 22 emerging markets

 Large Stocks (Domestic) – Standard & Poor’s 500

 Small Stocks (Domestic) -- CRSP US Small Cap Index, a broadly diversified index of over 1700 small US companies

We annualized the weekly returns and standard deviations and estimated the beta of each asset class relative to the S&P 500. We also calculated the Sharpe ratios, a measure of return to total risk taken, for the sample period.

The Sharpe Ratio is the return on the asset less the risk-free interest rate, divided by the standard deviation of the asset returns. The results are presented in Table 2. It is rare for a financial anomaly to survive into commercialization, but the low volatility anomaly succeeded – the SPLV fund posted the highest Sharpe Ratio of all the assets by a fairly large amount, supporting Haugen’s 40-year-old results.

Modern investment theory, however, suggests that it is unwise to consider assets in isolation; rather, an asset should be evaluated on its impact in a diversified portfolio of other assets. This impact is highly influenced by the correlation of the assets. Table 3 presents the correlation table for these eight assets. The table shows that SPLV has an extremely high correlation to both Large and Small Domestic stocks, and thus has similar correlations to the other five assets.

4. PORTFOLIO OPTIMIZATION

To examine the impact of SPLV on portfolio returns, we took the returns on these assets since the introduction of SPLV and simple linear programming to determine optimal ex post portfolios at various levels of return, similar to Clarke (2006). First, we constructed the feasible set of portfolios using the seven traditional assets without SPLV; the upward-sloping portion of the line represents the ex post efficient frontier of the included assets – the portfolios that provided minimum risk for a given level of return.

The potential attractiveness of SPLV can already be seen in Figure 1, as the fund plotted above the efficient frontier constructed from the seven other index funds. This means that not only did SPLV produce better risk- adjusted returns than any of the other investments, but it also produced a more favorable risk-return profile than any portfolio that could be constructed out of the other seven assets.

To quantify the benefits of SPLV, we recalculated the efficient frontier with SPLV included, which is presented in Figure 2. For almost all levels of return, the new efficient frontier lies above the old, meaning that SPLV created lower risk portfolios for each level of return. Examining the portfolio weights for portfolios on the efficient frontier showed that SPLV would have been a significant contributor to the minimum risk portfolio for all but the lowest return portfolios. Table 4 presents SPLV’s weighting in each optimal portfolio, as well as the reduction in standard deviation from the portfolio achieved by adding SPLV. The results for the nine and ten percent return portfolios are particularly impressive – SPLV made up the overwhelming majority of the minimum risk portfolios, while reducing the standard deviation of both portfolios by about 25%.

5. IMPACT OF SHORT-SELLING AND LEVERAGE

The efficient frontier can be extended with short-selling and buying on margin. However, these two strategies

have not always been available or practical for individual investors. In fact, Asness (2012) hypothesizes that the

low volatility anomaly is caused by investors who demand high returns, but are leverage-constrained and thus

overbid for high risk stocks. However in 2006, Proshares introduced a family of “geared” exchange traded

funds that made both shorting and leveraging easy to accomplish. The Short S&P500 ETF (ticker = SH) seeks

to deliver a daily return that is the inverse of the S&P 500. With a historical correlation to the S&P 500 of -

0.996 and a beta of -1.00, SH effectively allows individual investors to easily short the market. The Ultra S&P500 ETF (SSO) seeks daily returns that are double that of the S&P 500 and the UltraPro S&P500 ETF (UPRO) attempts to deliver daily returns triple the S&P 500 return. With correlations to the index of 0.996 and above and betas of 2.01 and 3.02, these two funds effectively allow individual investors to leverage the market.

We add these funds’ risk and return measures to our investment universe and again use linear programming to calculate the new efficient frontier with all assets except SPLV. Figure 3 shows how the addition of these geared ETFs alters our efficient frontier. The results are dramatic, as the geared ETFs produced significant risk- return benefits at nearly all risk levels. Table 5 documents how much improvement the geared funds made relative to SPLV-included portfolios in Table 4, and presents the portfolio weightings of the geared funds in various minimum risk portfolios. Interestingly, all minimum risk portfolios included some positive weighting of the “high-risk” leverage portfolios in the optimal solution. Further, the risk reduction achieved from the geared portfolios was particularly substantial at both the lowest and highest levels of portfolio return.

Finally, we determine the overall value of SPLV in a full portfolio context by constructing an efficient frontier with all of the assets available, including the geared ETFs. We do not present the graph because the two efficient frontiers, with and without SPLV, are visually indistinguishable. Table 6 summarizes that SPLV had a very minimal impact on the risk/risk return profile of optimal portfolios. SPLV’s weightings in the minimum risk portfolios peak at about 11% and the risk reduction the fund provided was miniscule. These results indicate that while SPLV’s risk-adjusted returns have proven to be exceptional since its introduction, SPLV did very little as an addition to broad portfolio. In other words, the low-volatility anomaly continued to persist, yet was not very useful in a portfolio context with geared ETFs.

6. THE CASE FOR GEARED ETFs

We find one additional surprising result that is relevant for individual investors seeking to maximize their risk- adjusted portfolio returns. Table 7 presents the non-zero portfolio weights for the minimum risk portfolios for each level of return. Interestingly, the optimal weighting for the S&P 500 (and the Small Cap Index) was 0%

for all portfolio returns. For all portfolios, optimal risk/return balance was achieved primarily using Treasury Bonds and combinations of the geared S&P 500 ETFs. Optimal low-risk portfolios used low amounts of Treasuries and a combination of the Ultra S&P500 and the Short S&P500 ETFs. Optimal high-risk portfolios were achieved by higher weightings in Treasuries, but increasing leverage in the S&P 500 using the Ultras and the UltraPros.

Table 8 documents the size and activity of these ETFs relative to SPLV. Not only are the geared portfolios much smaller in size than even SPLV, but their high trading volume relative to size suggests that more investors may simply be holding them short-term, attempting to time the market. Regardless, it seems likely that many individual investors are not capitalizing on a simple way to improve the risk-return characteristics of their portfolios.

7. CONCLUSION

The PowerShares’ S&P500 Low Volatility Portfolio exchange traded fund (SPLV) has been a successful attempt to capitalize on the low-volatility anomaly. Consistent with prior research, SPLV has produced superior risk-adjusted returns since its introduction in May 2011. However, we also find that the fund’s usefulness is minimal in a portfolio context with other index funds and ETFs, particularly with geared S&P 500 ETFs which simulate short-selling and buying on margin. We document that these geared funds are likely underused by individual investors seeking to maximize the risk-return relationship in their overall portfolios.

REFERENCES

Asness, C., Frazzini, A., & Pedersen, L.H. (2012). Leverage Aversion and Risk Parity. Financial Analysts Journal, 68(1), 47-59.

Baker, M., Bradley B., & Wurgler J. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low- Volatility Anomaly. Financial Analyst Journal, 67(1), 40–54.

Baker, N. L., & Haugen, R. (2012). Low Risk Stocks Outperform within All Observable Markets of the World.

SSRN Working Paper, no. 2055431.

Clarke, R., de Silva, H. & Thorley, S. (2006). Minimum-variance portfolios in the US equity market. Journal of Portfolio Management, 33(1), 10–24.

Haugen, R., & Heins, A. J. (1975). Risk and the Rate of Return on Financial Assets: Some Old Wine in New

Bottles. Journal of Financial and Quantitative Analysis, 10(5), 775–784.

Table 1: Risk and Return, 1991-2011

Annual Return Standard Deviation

S&P 500 8.53% 15.16%

S&P 500 Low-Volatility 10.19% 11.16%

Table 2: Risk/Return Characteristics, 2011-2013

Index Return Standard Deviation Beta Sharpe Ratio

Treasury Bonds 3.82% 9.82% -0.39 0.39

Corporate Bonds 0.28% 4.88% -0.06 0.05

International 6.12% 15.84% 0.05 0.38

Global 100 3.29% 18.22% 1.03 0.18

Emerging -7.86% 20.75% 1.01 -0.38

Large Stocks 9.88% 16.54% 1.00 0.60

Small Stocks 11.53% 21.53% 1.24 0.53

SPLV 9.80% 11.56% 0.60 0.85

Table 3: Correlation Matrix

Tbond Corp EAFE Global

Emergin

g Large Small SPLV

Tbond 1.00

Corp 0.71 1.00

International -0.11 0.12 1.00

Global -0.66 -0.20 0.10 1.00

Emerging -0.49 0.05 0.08 0.82 1.00

Large -0.65 -0.19 0.06 0.94 0.80 1.00

Small -0.61 -0.17 0.05 0.88 0.79 0.95 1.00

SPLV -0.41 0.03 0.03 0.79 0.63 0.86 0.80 1.00

Table 4: Impact of SPLV -- Minimum Risk Portfolios

Portfolio Return

Minimum Std Deviation without

SPLV

Minimum Std Deviation with

SPLV

Risk Reduction

from SPLV Weight of SPLV

5.00% 4.50% 4.50% 0% 0%

6.00% 4.72% 4.72% 0% 2%

7.00% 6.35% 5.51% 0.84% 38%

8.00% 9.25% 7.15% 2.10% 65%

9.00% 12.53% 9.42% 3.11% 84%

10.00% 15.97% 12.24% 3.73% 89%

11.00% 19.49% 17.82% 2.67% 31%

Table 5: Impact of Geared ETFs -- Minimum Risk Portfolios

Portfolio Return

Minimum Std Deviation with

SPLV

Minimum Std Deviation with Shorts and Ultras

(no SPLV)

Risk Reduction from Shorts and

Ultras

Weight of Shorts, Ultras

2.00% 4.28% 2.23% 2.05% 41%, 24%

3.00% 4.28% 2.81% 1.47% 34%, 26%

4.00% 4.36% 3.41% 0.95% 26%, 25%

5.00% 4.50% 4.02% 0.42% 19%, 23%

6.00% 4.72% 4.63% 0.09% 12%, 22%

7.00% 5.51% 5.24% 0.27% 5%, 21%

8.00% 7.15% 5.86% 1.31% 0%, 19%*

9.00% 9.42% 6.63% 2.79% 0%, 17%*

10.00% 12.24% 7.76% 4.48% 0%, 20%*

11.00% 17.82% 9.14% 8.68% 0%, 24%*

* = weighting of UltraPro

Table 6: All Assets -- Minimum Risk Portfolios

Portfolio Return

Minimum Std Deviation with Shorts and Ultras

Minimum Std Deviation with Shorts, Ultras, and

SPLV

Risk Reduction from

SPLV Weight of SPLV

2.00% 2.23% 2.21% 0.02% 5%

3.00% 2.81% 2.79% 0.02% 6%

4.00% 3.41% 3.39% 0.02% 8%

5.00% 4.02% 3.99% 0.03% 9%

6.00% 4.63% 4.60% 0.03% 10%

7.00% 5.24% 5.21% 0.03% 11%

8.00% 5.86% 5.85% 0.01% 9%

9.00% 6.63% 6.63% 0.00% 0%

10.00% 7.76% 7.76% 0.00% 0%

11.00% 9.14% 9.14% 0.00% 0%

Table 7: Minimum Risk Portfolios Weights

Portfolio Return SPLV Tbond EAFE Ultra UPro Short

2.00% 5% 24% 5% 26% 0% 40%

3.00% 6% 31% 6% 24% 0% 33%

4.00% 8% 37% 8% 22% 0% 26%

5.00% 9% 44% 9% 20% 0% 18%

6.00% 10% 51% 10% 18% 0% 11%

7.00% 11% 57% 12% 16% 0% 4%

8.00% 9% 65% 13% 5% 8% 0%

9.00% 0% 71% 12% 0% 17% 0%

10.00% 0% 70% 10% 0% 20% 0%

11.00% 0% 69% 7% 0% 24% 0%

Table 8: ETF Activity

Fund SPLV – Low

Volatility SH – Short SSO – Ultra UPRO – UltraPro

Net Assets $4.28B $2.03B $1.39B $437M

Avg Daily

Volume $28.52M $88.17M $592.06M $190.16M

Turnover 150.1 days 23.0 days 2.3 days 2.3 days

SPLV

TBond Corp Bond

Int'l

Global

Emerging S&P500

Small Stocks

-10.000 -5.000 0.000 5.000 10.000 15.000

0.000 5.000 10.000 15.000 20.000 25.000

Ret urn

Standard Deviation Figure 1

Feasible Set without SPLV

SPLV

TBond Corp Bond

EAFE

Global

Emerging S&P500

Small Stocks

-10.000 -5.000 0.000 5.000 10.000 15.000 20.000

0.000 5.000 10.000 15.000 20.000 25.000

Ret urn

Standard Deviation Figure 2

Feasible Set with SPLV

SPLV

TBond Corp Bond

EAFE

Global

Emerging S&P500

Small Stocks

-10.00 -5.00 0.00 5.00 10.00 15.00 20.00

0.00 5.00 10.00 15.00 20.00 25.00

Ret urn

Standard Deviation Figure 3

Efficient Set with Shorts, Ultras