Low volatility or minimum variance ?

1. 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.
Introduction
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.
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 Outperformance
The 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

2. State Street Global Advisors 2
Low Volatility or Minimum Variance?
Figure 2: Low Volatility Methods
Dimension
MSCI 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 Method
The 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.

3. State Street Global Advisors 3
Low Volatility or Minimum Variance?
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 Method
The 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 Index
MSCI 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
–– Value
Industry 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
Feb
2010
2011 2013 2014 Feb
2016
0
250
— Eurostoxx Low Risk Weighted — MSCI EMU Risk Weighted — MSCI EMU

4. State Street Global Advisors 4
Low Volatility or Minimum Variance?
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.
Conclusion
Both 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
Half-lives: 125d
var; 250d cor
500–520d var
& cor
Half-lives: 125d
var; 250d 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 Europe
SSGA Europe
Managed Volatility
MSCI 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.
Feb
2010
2011 2013 2014 Feb
2014
250
200
150
100
50
0
300
— SSGA Europe Managed Volatility
— MSCI Europe
— MSCI Europe Minimum Volatility
Low Volatility

5. State Street Global Advisors 5
Low Volatility or Minimum Variance?
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Low Volatility or Minimum Variance?
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