2016 low volatility or minimum variance

The low volatility factor is one of the most interesting smart beta factors. First of all, through its low exposure to volatility it provides less risk, and secondly it has offered significant outperformance during the long term. This outcome is the opposite of what standard financial theory would predict, which is that higher return implies higher risk.

IntroductionThe low volatility factor is one of the most interesting smart beta factors. First of all, through its low exposure to volatility it provides less risk, and secondly it has offered significant outperformance during the long term. This outcome is the opposite of what standard financial theory would predict, which is that higher return implies higher risk.

There are several potential explanations for this outperformance, split between the behavioural approach and the rational approach. These explanations are reviewed in the first section of this paper.

Once the investor is convinced on the long-term performance of the low volatility factor, she has to build a portfolio to capture this factor. Basically, two methods are possible. The low volatility methods consist of selecting low volatility stocks and constructing a portfolio. These methods are reviewed in the second section.

The minimum variance methods consist of creating a minimum variance portfolio by combining all stocks through an optimisation process. These methods are reviewed in the third section.

Reasons for OutperformanceThe potential reasons for outperformance are split between the behavioural approach, where investors are not rational and are subject to behavioral bias, and the rational approach, where the outperformance is compensation for a risk or a constraint.

The main arguments reviewed in the academic literature are:

1. The behavioural preference for lottery ticket-like stocks leads to high beta stocks. A stock can be considered similar to a lottery ticket: an investor cannot lose more than the value of the stock but the potential upside is theoretically infinite; this is contrary to a bond, for instance, where upside is constrained. The stock is thus globally positively skewed. This effect is amplified by the value of the beta; therefore, higher beta stocks have a higher lottery ticket feature.

2. The behavioural representativeness bias pushes investors to invest in high beta and high volatility stocks. High beta and high volatility stocks are generally associated with stories and anecdotes. Those stories are not necessarily associated with additional effective information, but they give investors the feeling of more knowledge and this incentivises the investors to overweight those high beta and high volatility stocks.

3. The behavioural overconfidence pushes investors to high beta stocks. Human beings tend to be overconfident of their abilities. More than half of investors believe that they are better than average. As such, it makes sense for those overconfident investors to invest in high beta stocks — in order to maximize the profit they will raise from their hypothetical ability.

Low Volatility or Minimum Variance?May 2016 | by Frederic Jamet, Credential, Head of Investments SSGA France, 2016

State Street Global Advisors 2

Low Volatility or Minimum Variance?

Figure 2: Low Volatility Methods

DimensionMSCI EMU Risk Weighted Index

Euro Stoxx Low Risk Weighted 100 Index

S&P 500 Low Volatility Index

SSGA Volatility Tilted Strategy

Underlying Universe

MSCI EMU Euro Stoxx S&P 500 MSCI World

Holdings Full universe 100 100 Full universe

Methodology Weight by volatility

Weight by volatility

Weight by volatility

Tilt market cap weights by volatility

Time Series Standard Deviation of Returns

Weekly price returns over prior 3 years

Monthly price returns over prior 12 months

Daily price returns over prior 252 trading days

Monthly total returns over prior 60 months

Rebalancing Frequency

Semi-Annually Quarterly Quarterly Annually

3rd-Party Index Yes Yes Yes No

Comments Less concentrated than S&P Low Vol

Most responsive and highest conviction.

Most responsive and highest conviction.

Tilt off cap-weight — lower expected tracking error.

Source: State Street Global Advisors (SSGA), MSCI, STOXX, S&P. As of May 2016.

Figure 1: Variance of a Portfolio4. The rational leverage constraint leads investors to look for high beta stocks to use their implicit leverage. High beta stocks offer additional leverage compared to low beta stocks. Any investors who wish to have or need additional leverage will overweight high beta stocks over low beta stocks in order to use their implicit leverage.

5. The rational regulatory constraint restricts increasing exposure to equity whatever the beta. Most regulatory constraint relates to accounting equity weights more than beta-adjusted equity weights: it is not possible to invest 100% in low beta stocks to claim 50% equity exposure.

6. The rational short-selling constraint limits the arbitrage of the low beta stocks. The rational investor who would like to profit from the low beta anomaly would need to short sell the overvalued high beta stocks and buy the undervalued low beta stocks. Many regulations, such as Solvency II, Basel III and the Dodd-Frank Act, prohibit most institutional investors from selling short or borrowing money — thus preventing the arbitrage of the low beta stocks.

7. The rational relative utility of investors vis à vis the benchmark pushes them to hold a neutral or high beta portfolio. Contrary to the capital asset pricing model (‘CAPM’), most investors are required to outperform the benchmark more than to create alpha. For example, it can be more rational to hold a high beta stock with no alpha than a low beta stock with a positive alpha in order to outperform a benchmark that has a positive expected performance. Investors with benchmarks are thus biased to neutral or high beta stocks. All the above reasons push investors to overweight high beta stocks and to underweight low beta stocks, thus creating low expected returns for high beta stocks compared to low beta stocks. They also prevent investors from making the profitable arbitrage that would cancel this inefficiency.

All these reasons support the belief that the low volatility and minimum variance premium will continue to hold.

Low Volatility or Heuristic MethodThe aim is to construct a portfolio of stocks that is fully invested and offers low risk, where risk is expressed by the annualised volatility of the portfolio return σ. According to standard hypothesis, the variance — which is the square of the volatility — is equal to the sum of all weighted equity variances, plus the sum of all weighted covariances (as shown in Figure 1). The covariance is the product of the variance of two stocks with their correlation.

From this equation, two main methods are possible: low volatility or heuristic methods, and minimum variance or optimisation methods.

The low volatility or heuristic approach consists of minimising the sum of all weighted equity variance by ranking stocks by volatility and selecting the lowest volatility stocks. The covariances are not taken into account. Once selected, the stocks are either equally weighted or weighted according to the inverse of volatility in order to overweight the lowest volatility stocks of the sample.

Essentially, three independent sets of parameters must be chosen.

First, the volatility of the stocks has to be estimated. Most providers use a systematic historical volatility from one year to five years.

Second, a selection of a subset of the universe is created. All components are ranked from lowest to highest volatility and depending on the target number of index constituents, the top ranked components are selected for the index. It is possible to keep the full universe but the impact in terms of decreasing the volatility will then be lower.

Third, the weighting of the selected subset is finalised. The usual method is to weight according to the inverse of the volatility, i.e. the stock has a larger weight if its volatility is lower.

A summary of the methods used by different providers is shown in Figure 2.



It is important to understand that while the simple application of the method will create a lower risk portfolio, the portfolio will still be exposed to other risks.

The main residual risk is active sector exposure. Low volatility methods overweight low volatility defensive sectors like Healthcare, Consumer Staples, Utilities and Telecom, and underweight high volatility cyclical sectors like Energy, Materials, Banks and Consumer Discretionary.

Another residual risk is over-exposure to smaller companies. Because the methods do not target size exposure, the portfolio will pick up more mid cap stocks than large cap stocks. Mid cap stocks are not necessarily more volatile, but they are more numerous, and it is easier to create a low risk portfolio by combining a large number of stocks.

Those residual risks may be significant, thus most methods set up additional controls in order to maintain a degree of diversification and to limit tracking error. However, these additional constraints make the methods less optimal in terms of risk reduction. It is important to understand the methods, but also to understand and to accept the embedded constraints.

The performance can be analysed through two representative indices in the eurozone: the Euro Stoxx Low Risk Weighted 100 Index and the MSCI EMU Risk Weighted index.

The results for the eurozone are shown on Figure 3 and in the accompanying graph. Both low volatility portfolios have a lower risk and lower beta than MSCI EMU and both have a higher return. However, it appears that the Euro Stoxx Low Risk Weighted is more efficient (higher return, lower risk and lower beta) than the MSCI EMU Risk Weighted.

Minimum Variance or Optimisation MethodThe minimum variance or optimisation approach consists of directly minimising the total variance of the portfolio, thus taking into account the variance of each stock and the correlation of each stock with all other stocks. The process is more complex as it involves the estimation of all variances and correlations, and it involves the use of a quadratric optimisation to solve the equation shown in Figure 1.

The estimation of variance and correlation is based on forecasted variance and correlation more than simple historical variance and correlation.

The quadratic optimisation is decomposing each stock into portfolio of factor exposures, and thus decomposing the portfolio of stocks into a portfolio of factor exposures. A typical list of factors used for decomposition is shown in Figure 4.

Figure 3: Low Volatility in EMU Euro Stoxx Low Risk

Weighted IndexMSCI EMU Risk Weighted Index MSCI EMU Index

Return (%) 11.0 7.6 6.1

Volatility (%) 11.3 3.5 15.8

Return/Volatility 1.0 0.6 0.4

Beta 0.7 0.8 1.0

Source: STOXX, MSCI. February 2010 to February 2016 in Euro terms.

Figure 4: List of Factors Style Factors

– Exchange Rate Sensitivity

– Short-Term Momentum

– Growth

– Liquidity

– Size

– Leverage

– Medium-Term Momentum

– Volatility

– ValueIndustry and Country Factors

– Account for a company’s particular business and country of domicile.

Currency Factors

– Accounts for interaction of currency of stock returns.

– Provides framework to view risk from the perspective of any base currency.

Source: Axioma, 2011.

Low Volatility

50

100

200

150

Feb2010

2011 2013 2014 Feb2016

0

250

— Eurostoxx Low Risk Weighted — MSCI EMU Risk Weighted — MSCI EMU



A summary of the methods used by different providers is shown on Figure 5

The performances can be analysed through two representative indices in Europe: the SSGA Europe Managed Volatility Strategy and the MSCI Europe Minimum Volatility Index.

The results for Europe are shown in Figure 6 and the accompanying chart. Both low volatility portfolios have a lower risk and lower beta than MSCI Europe and both have a higher return. However, it appears that the SSGA Europe Managed Volatility is more efficient (higher return, lower risk and lower beta) than the MSCI Europe Minimum Volatility.

ConclusionBoth methods have their advantages.

The low volatility methods have the benefit of being straightforward, robust and transparent. It is easy to verify that each stock is a low volatility stock, and thus easy to deduce that the whole portfolio is a low volatility portfolio. However, these methods are not absolutely optimal as they do not take into account the correlation of the stocks between them.

The minimum variance methods have the benefit of offering the state of the art in terms of the effective minimum variance portfolios. However, they are more sophisticated and complex.

At the end of the day, the choice between a low volatility or minimum variance method may be less important than the choice amongst low volatility methods or amongst minimum variance methods and their associated set of parameters.

Figure 5: Minimum Variance (Optimization) Methods

Dimension

MSCI Europe Minimum Volatility Index

STOXX Global Minimum Variance Index

FTSE Global Minimum Variance Index

SSGA Europe Managed Volatility Strategy

Risk Model BARRA GEM Axioma Fundamental

FTSE Statistical model

Axioma Fundamental

Underlying universe

MSCI Europe STOXX Global 1800

FTSE Developed

MSCI Europe

Rebalancing Frequency

Semi-Annually (turnover cap 20% ann.)

Quarterly (turnover cap 30% ann.)

Semi-Annually (avg. 30% ann.)

Quarterly (avg. 25% ann.)

Constraints Active Country: +/-5% or 3x

Active Country: +/5%

Active Country: 0.9x-5% to 1.1x+5%

Active Country: +/-3%

Active Sector: +/-5%

Active Industry: +/-5%

Sector: <20% Sector: <25% Industry: <10%

Max Security: <1.5% & <20x

Security: 4.5%/8%/35%

Max Security: <1% & <20x

Max Security: <2%

Min Security: 5bps

Min Security: 1bps

Min Security: 5bps

Risk Factors: +/-0.25 (ex. beta)

Risk factors: +/-0.25 (ex. Size and Volatility)

Eff. Holdings: 1,000

Size: Controlled

Variable base currency

Yes Yes Yes Yes

Estimation period

Half-lives: 250d var; 750d cor


500–520d var & cor


Third-Party Index

Yes Yes Yes No

Comments More cap-weight-relative constraints — better for managing tracking

Less concentrated — less prone to idiosyncratic risks

Less cap-weight-relative constraints — higher expected efficiency

Higher conviction min-vol strategy

Source : MSCI, STOXX, FTSE, SSGA, 2016.

Figure 6: Minimum Variance in EuropeSSGA Europe

Managed VolatilityMSCI Europe

Minimum Volatility MSCI Europe

Return (%) 11.8 11.1 7.8

Volatility (%) 9.6 10.1 13.2

Return/Volatility 1.2 1.1 0.6

Beta 0.6 0.7 1.0

Source: SSGA, MSCI. February 2010 to February 2016 in Euro terms.

Feb2010

2011 2013 2014 Feb2014

250

200

150

100

50

0

300

— SSGA Europe Managed Volatility

— MSCI Europe

— MSCI Europe Minimum Volatility

Low Volatility



ssga.com | spdrs.com

For investment professional use only. Not for public use .

For Investors in Finland The offering of funds by the Companies has been notified to the Financial Supervision Authority in accordance with Section 127 of the Act on Common Funds (29.1.1999/48) and by virtue of confirmation from the Financial Supervision Authority the Companies may publicly distribute its Shares in Finland. Certain information and documents that the Companies must publish in Ireland pursuant to applicable Irish law are translated into Finnish and are available for Finnish investors by contacting State Street Custodial Services (Ireland) Limited, 78 Sir John Rogerson’s Quay, Dublin 2, Ireland.

For Investors in France This document does not constitute an offer or request to purchase shares in the Companies. Any subscription for shares shall be made in accordance with the terms and conditions specified in the complete Prospectuses, the KIID, the addenda as well as the Companies’ Supplements. These documents are available from the Company centralizing correspondent: State Street Banque S.A., 23–25 rue Delariviere-Lefoullon, 92064 Paris La Defense Cedex or on the French part of the site spdrseurope.com. The Companies re undertakings for collective investment in transferable securities (UCITS) governed by Irish law and accredited by the Central Bank of Ireland as a UCITS in accordance with European Regulations. European Directive no. 2009/65/CE dated 13 July 2009 on UCITS, as amended, established common rules pursuant to the cross-border marketing of UCITS with which they duly comply. This common base does not exclude differentiated implementation. This is why a European UCITS can be sold in France even though its activity does not comply with rules identical to those governing the approval of this type of product in France. The offering of these compartments has been notified to the Autorité des Marchés Financiers (AMF) in accordance with article L214-2-2 of the French Monetary and Financial Code.

For Investors in Germany The offering of SPDR ETFs by the Companies has been notified to the Bundesanstalt für Finanzdienstleistungsaufsicht (BaFin) in accordance with section 312 of the German Investment Act. Prospective investors may obtain the current sales Prospectuses, the articles of incorporation, the KIIDs as well as the latest annual and semi-annual report free of charge from State Street Global Advisors GmbH, Brienner Strasse 59, D-80333 Munich. Telephone +49 (0)89-55878- 400. Facsimile +49 (0)89-55878-440.

For Investors in Luxembourg The Companies have been notified to the Commission de Surveillance du Secteur Financier in Luxembourg in order to market their shares for sale to the public in Luxembourg and the Companies are notified Undertakings in Collective Investment for Transferable Securities (UCITS).

For Investors in the Netherlands This communication is directed at qualified investors within the meaning of Section 2:72 of the Dutch Financial Markets Supervision Act (Wet op het financieel toezicht) as amended. The products and services to which this communication relates are only available to such persons and persons of any other description should not rely on this communication. Distribution of this document does not trigger a licence requirement for the Companies or SSGA in the Netherlands and consequently no prudential and conduct of business supervision will be exercised over the Companies or SSGA by the Dutch Central Bank (De Nederlandsche Bank N.V.) and the Dutch Authority for the Financial Markets (Stichting Autoriteit Financiële Markten). The Companies have completed their notification to the Authority Financial Markets in the Netherlands in order to market their shares for sale to the public in the Netherlands and the Companies are, accordingly, investment institutions (beleggingsinstellingen) according to Section 2:72 Dutch Financial Markets Supervision Act of Investment Institutions. For Investors in Norway: The offering of SPDR ETFs by the Companies has been notified to the Financial Supervisory Authority of Norway (Kredittilsynet) in accordance with applicable Norwegian Securities Funds legislation. By virtue of a confirmation letter from the Financial Supervisory Authority dated 28 March 2013 (16 October 2013 for umbrella II) the Companies may market and sell their shares in Norway.

For Investors in Spain SSGA SPDR ETFs Europe I plc and SSGA SPDR ETFs Europe II plc have been authorised for public distribution in Spain and are registered with the Spanish Securities Market Commission (Comisión Nacional del Mercado de Valores) under no.1244 and no.1242. A copy of the Prospectuses and Key Investor Information Documents, the Marketing Memoranda, the fund rules or instruments of incorporation as well as the annual and semi-annual reports of SSGA SPDR ETFs Europe I plc and SSGA SPDR ETFs Europe II plc may be obtained from the Spanish distributors. The complete lists of the authorised Spanish distributors of SSGA SPDR ETFs Europe I plc and SSGA SPDR ETFs Europe II plc is available on the website of the Securities Market Commission (Comisión Nacional del Mercado de Valores).

For Investors in Switzerland The information provided does not constitute advice or an offer or solicitation to purchase shares. This document is directed at qualified investors only, as defined by Article 10(3) of the Swiss Act on Collective Investment Schemes (CISA) and Article 6 of the Swiss Ordinance on Collective Investment Schemes (CISO). Certain of the funds are not registered with the Swiss Financial Market Supervisory Authority (FINMA) which acts as supervisory authority in investment fund matters. Certain of the funds referenced herein have not been authorised by the FINMA as a foreign Collective Investment Scheme under Article 120 of the Collective Investment Schemes Act of June 23, 2006. Accordingly, the shares of these funds may not be offered to the public in or from Switzerland unless they are placed without public solicitation as such term is defined by FINMA from time to time. In relation to those funds which are registered with FINMA, prospective investors may obtain the current sales Prospectuses, the articles of incorporation, the KIIDs as well as the latest annual and semi-annual reports free of charge from the Swiss representative, State Street Fund Management Ltd., Beethovenstrasse 19, 8027 Zurich, from the Swiss paying agent, State Street Bank GmbH Munich, Zurich Branch, Beethovenstrasse 19, 8027 Zurich as well as from the main distributor in Switzerland, State Street Global Advisors AG , Beethovenstrasse 19, 8027 Zurich. Before investing please read the Prospectuses and KIIDs, copies of which can be obtained from the Swiss representative, or at spdrseurope.com.

For Investors in the UK The Companies are recognised schemes under Section 264 of the Financial Services and Markets Act 2000 (“the Act”) and are directed at ‘professional clients’ in the UK (within the meaning of the rules of the Act) who are deemed both knowledgeable and experienced in matters relating to investments. The products and services to which this communication relates are only available to such persons and persons of any other description should not rely on this communication. Many of the protections provided by the UK regulatory system do not apply to the operation of the Companies, and compensation will not be available under the UK Financial Services Compensation Scheme.

Important Information This document has been issued by State Street Global Advisors Limited (“SSGA”). Authorised and regulated by the Financial Conduct Authority. Registered No. 2509928. VAT No. 5776591 81. Registered office: 20 Churchill Place, Canary Wharf, London, E14 5HJ. Telephone: 020 3395 6000. Facsimile: 020 3395 6350 Web: ssga.com.

SPDR ETFs is the exchange traded funds (“ETF”) platform of State Street Global Advisors and is comprised of funds that have been authorised by European regulatory authorities as open-ended UCITS investment companies (“Companies”).

SSGA SPDR ETFs Europe II plc issue SPDR ETFs, and is an open-ended investment company with variable capital having segregated liability between its sub-funds. The Company is organised as an Undertaking for Collective Investments in Transferable Securities (UCITS) under the laws of Ireland and authorised as a UCITS by the Central Bank of Ireland.

This document is not, and under no circumstances is to be construed as, an offer or any other step in furtherance of a public offering in the United States, Canada or any province or territory thereof, where the Companies are not authorised or registered for distribution and where the Companies prospectuses have not been filed with any securities commission or regulatory authority. Neither this document nor any copy hereof should be taken, transmitted or distributed (directly or indirectly) into the United States. The Companies have not and will not be registered under the Investment Company Act of 1940 or qualified under any applicable state securities statutes.

State Street Global Advisors 6State Street Global Advisors


© 2016 State Street Corporation. All Rights Reserved. ID6822-IBGE-2521 0616 Exp. Date: 30/06/2017

The views expressed in this material are the views of Frederic Jamet for the period ended 30 June 2016 and are subject to change based on market and other conditions. The information provided does not constitute investment advice and it should not be relied on as such. All material has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. This document contains certain statements that may be deemed forward-looking statements. Please note that any such statements are not guarantees of any future performance and actual results or developments may differ materially from those projected. Past performance is not a guarantee of future results.

The information provided does not constitute investment advice as such term is defined under the Markets in Financial Instruments Directive (2004/39/EC) and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell any investment. It does not take into account any investor’s or potential investor’s particular investment objectives, strategies, tax status, risk appetite or investment horizon. If you require investment advice you should consult your tax and financial or other professional advisor. All material has been obtained from sources believed to be reliable. There is no representation or warranty as to the accuracy of the information and State Street shall have no liability for decisions based on such information.

Exchange traded-funds (ETFs) trade like stocks, are subject to investment risk and will fluctuate in market value. The value of the investment can go down as well as up and the return upon the investment will therefore be variable. Changes in exchange rates may have an adverse effect on the value, price or income of an investment. Further, there is no guarantee an ETF will achieve its investment objective.

Investing involves risk including the risk of loss of principal.

Diversification does not ensure a profit or guarantee against loss.

Performance quoted represents past performance, which is no guarantee of future results. Investment return and principal value will fluctuate, so you may have a gain or loss when shares are sold. Current performance may be higher or lower than that quoted. Visit spdrseurope.com for most recent month-end performance.

Equity securities may fluctuate in value in response to the activities of individual companies and general market and economic conditions.

Investing in foreign domiciled securities may involve risk of capital loss from unfavourable fluctuation in currency values, withholding taxes, from differences in generally accepted accounting principles or from economic or political instability in other nations.

The whole or any part of this work may not be reproduced, copied or transmitted or any of its contents disclosed to third parties without SSGA’s express written consent.

You should obtain and read the Companies’ Prospectuses prior to investing. Prospective investors may obtain the current Prospectuses, the articles of incorporation, the Key Investor Information Documents (KIIDs) as well as the latest annual and semi-annual reports free of charge from State Street Global Advisors, or from spdrseurope.com

2016 low volatility or minimum variance

Economy & Finance