Minimum Volatility Research Articles

A Tale of Two Low Volatility Indexes

Low volatility and minimum volatility indexes have been written about extensively in financial literature, and their index-linked investment vehicles have grown to track a significant amount of assets. While rankings-based and optimized low volatility indexes share a common objective—to deliver higher risk-adjusted returns than the broad market over a long-term investment horizon—their similarity ends there. Using the S&P 500 Low Volatility Index and S&P 500 Minimum Volatility Index, the authors show that there are meaningful differences regarding their risk/return profiles, sector composition, and factor exposures. The differences suggest that market participants should conduct thorough due diligence on sources of returns and evaluate whether active risks taken are compensated or not.

Managing Risks Beyond Volatility

Minimum volatility strategies enjoy broad support in the academic literature and have been applied extensively by institutional investors to reduce portfolio volatility. In this article, the authors discuss how such strategies can adapt to address risks beyond price volatility. Specifically, concentration, sustainability, and crowding risks could be mitigated using appropriate but simple optimization constraints. However, adding a diversification constraint increased exposure to residual volatility and had a negative impact on risk reduction and risk-adjusted performance. In contrast, to help manage environmental, social, and governance (ESG) risks, adding a significant sustainability constraint had only a small effect on the risk reduction properties. Finally, introducing constraints on the value exposure ensured the market-relative valuations of the strategy remained attractive for only a small increase in realized volatility. The authors show that simple constraints could be used effectively in minimum volatility strategies to manage risks beyond volatility.

Life Cycle Investing and Smart Beta Strategies

In traditional life cycle models, the equity-bond glide path shifts investment allocation from riskier assets to relatively safer assets as investors approach retirement. In this paper, we develop a smart beta glide path which seeks to take advantage of broad, persistent patterns within asset classes to identify securities with higher risk-adjusted returns than the market. Within equities, investors can shift from return-enhancing strategies — like value, momentum, size, and quality — to risk-reducing strategies like minimum volatility as they move through their life cycles. Adopting smart beta glide paths may improve Sharpe ratios by up to 20% over a standard equity-bond glide path.

Crowding, Capacity, and Valuation of Minimum Volatility Strategies

Minimum volatility (min vol) strategies are smart beta strategies that are designed to minimize risk. In the past 12 months, ending June 30, 2016, there were $7.8 billion flows into a total of 17 U.S.-equity exchange-traded fund min vol strategies. This represents just 0.04% of total equity market capitalization of the underlying securities. Capacity in these strategies is large because traditional active mutual funds tend to overweight high-volatility stocks. Were these funds to move to a neutral position in high-volatility securities, a shift of roughly $600 billion to min vol would take place. Current valuations of min vol strategies are not high relative to historical norms and are consistent with the observed outperformance of these strategies during periods of high uncertainty.

Capacity of Smart Beta Strategies: A Transaction Cost Perspective

Using a transaction cost model, and an assumption for the smart beta premium observed in data, we estimate the capacity of momentum, quality, value, size, minimum volatility, and a multi-factor combination of the first four strategies. Flows into these factor strategies incur transaction costs. For a given trading horizon, we can find the fund size where the associated transaction costs negate the smart beta premium, assuming current rebalancing trends and holding constant other market structure characteristics. With a trading horizon of one day, we find that momentum is the strategy with the smallest assets under management (AUM) capacity of $65 billion, and size is the largest with an AUM capacity of $5 trillion. Extending the trading horizon to five days increases capacity in momentum and size to $320 billion and over $10 trillion, respectively.

Monotonic Correlation Diagnostics of share price volatility for Shariah-compliant Islamic Bank: A New Insight of Islamic Financial Engineering

The objective of this paper is to analyze the relationship between volatility rates and return rates for a share price of Bank Islam Malaysia Berhad (BIMB) from the year 2010 until 2016. The maximum volatility rate is 3.96 in July 2011, while the minimum volatility rate is 0.46 in April 2014. Next, the nonparametric analysis calculated the monotonic relationship between volatility rates and return rate for a share price of BIMB. From the analysis, the significant value is 0.000. Hence, the result rejects the null hypothesis for a Spearman correlation analysis. The numerical result shows there is a monotonic association between volatility rate and return rate for a share price of BIMB. The Spearman correlation coefficient, rs in this analysis is 0.403 indicated that there is a moderate positive correlation between volatility rate and return rate for BIMB share price.

Designing Low-Volatility Strategies

Since the Global Financial Crisis hit in 2008, low volatility has garnered increased attention from institutional investors. In this article, the authors delve into the practicalities of low-volatility investing, including construction issues, their performance in different market regimes, and the effect of recent increased demand on the strategy’s behavior. They discuss that although heuristic approaches tend to be simpler, only optimization-based approaches can take full advantage of the correlation between stocks. Constraints are essential in creating a well-behaved and investable low-volatility index. The authors show how different constraints can improve a minimum volatility strategy without having a significant impact on its volatility. Via attribution analyses, they analyze the sources of long-term outperformance of a minimum volatility index and discuss the valuation of minimum volatility indexes after the recent increases in demand and outperformance.

Revisiting Inflation and Individual Equities

This paper reexamines the inflation-hedging properties of individual equities. When determining inflation betas for individual equities we use multivariate regressions, which utilize all available data and account for equity market factor and reporting lags in inflation indices. We show how such an approach can even be used to create inflation-sensitive strategies for customized inflation indices. The facet of customization is necessary since different kinds of inflation impact different investors. For example, in retirement an investor is more concerned about medical expenses. We illustrate strategies for the US headline CPI, Forbes Cost of Living Extremely Well Index (CLEWI), and the US Medical Care Price Index. When constructing inflation-sensitive portfolios, besides using equally weighting scheme, we show how alternative weighting schemes can be used alongside the choice of inflation sensitive equities to accentuate inflation sensitivity, by using maximum beta optimization or to manage equity risk exposure — low volatility and equity beta as result of using minimum volatility optimization.

Monotonic Correlation Diagnostics of share price volatility for Shariah-compliant Islamic Bank: A new insight of Islamic Financial Engineering

The objective of this paper is to analyze the relationship between volatility rates and return rates for a share price of Bank Islam Malaysia Berhad (BIMB) from the year 2010 until 2016. The maximum volatility rate is 3.96 in July 2011, while the minimum volatility rate is 0.46 in April 2014. Next, the nonparametric analysis calculated the monotonic relationship between volatility rates and return rate for a share price of BIMB. From the analysis, the significant value is 0.000. Hence, the result rejects the null hypothesis for a Spearman correlation analysis. The numerical result shows there is a monotonic association between volatility rate and return rate for a share price of BIMB. The Spearman correlation coefficient, rs in this analysis is 0.403 indicated that there is a moderate positive correlation between volatility rate and return rate for BIMB share price.

10.5937/ekonhor1403211d = Markowitz portfolio rebalancing with turnover monitoring

Active portfolio management implies periodic rebalancing, i.e. a change in the structure of the existing portfolio. Rebalancing is aimed at improving the performance of the managed portfolio by adjusting it with respect to the given objective. The main objective of this research is to test two portfolio rebalancing strategies, one based on market risk and another on optimal risk-return tradeoff. We use optimal volatility or Sharpe of portfolio as a criterion for the initial portfolio allocation and rebalancing over the observed period. In order to obtain solutions that can be applied in practice, we impose rebalance triggers designed to control the portfolio turnover and corresponding transaction costs. the results suggest that the minimum volatility strategy can be accepted as an eligible investment alternative for risk adverse investors since it provides superior risk performance compared to the reference S&P 100 index and 1/n portfolio, with a relatively low level of turnover and a low rebalance frequency.

Formation of uranium based nanoparticles via gamma-irradiation

The ability to fabricate nuclear fuels at low temperatures allows for the production of complex Uranium metal and alloys with minimum volatility of alloy components in the process. Gamma irradiation is a valuable method for the synthesis of a wide range of metal-based nanoparticles. We report on the synthesis via room temperature radiolysis and characterization of uranium (depleted, d-U) metal and uranium–lathanide (d-ULn, Ln=lanthanide surrogates) alloy nanoparticles from aqueous acidic salt solutions. The lanthanide surrogates chosen include La and Eu due to their similarity in ionic size and charge in solution. Detailed characterization results including UV–vis, TEM/HR-TEM, and single particle EDX (elemental analyses) are presented for the room temperature formed nanoparticle products.

Potassium Carbonate as a Salt for Deep Eutectic Solvents

 Abstract—Deep Eutectic Solvents (DES) are emerging as new class of green solvents with the favorable properties of low cost, minimum volatility, biodegradability and suitability for many industrial applications. In an attempt to synthesize a new class of DES, potassium carbonate was used as a salt with glycerol as a hydrogen bond donor (HDB). The basic physical properties of this DES were measured at different temperatures and salt:HBD molar ratios. The physical properties measured included density, viscosity, surface tension, refractive index and pH at a temperature range of 20 - 80 o C. The system didn't show a freezing points in DSC thermograms, however glass transition temperatures were observed. This system exhibits similar physico-chemical properties to other reported DES. The values of these properties indicated that the prepared DES may have great potential for industrial applications.

Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance

A number of quantitative or fundamental weighting schemes have been shown to produce robust outperformance with respect to standard cap-weighted equity indices over long time periods. Over periods ranging from a few months to a few years, however, such alternative weighting schemes can generate substantial downside risk relative to cap-weighted indices, which would be a source of concern for most investment managers or chief investment officers. In this article, the authors focus on two reasonable proxies for well-diversified, efficient frontier portfolios, namely, the maximum Sharpe ratio (MSR) portfolio and the global minimum volatility (GMV) portfolio. They address the question of how to use these building blocks to design an improved equity benchmark while satisfying target levels of average and extreme tracking error with respect to cap-weighted indices. The authors find that robust proxies for the GMV portfolio provide defensive exposure to equity that does well in adverse market conditions, while robust proxies for MSR portfolios provide greater access to the upside of equity markets. Because the relative performance of these two diversification approaches depends on market conditions, they expect a combination of both approaches to lead to a smoother conditional performance and higher probability of outperformance of the cap-weighted index, an intuition that is confirmed in empirical tests. Empirical analysis also suggests that “diversifying the diversifiers” still leads to high levels of relative downside risk, in particular when the performance of cap-weighted indices is unusually strong. In this context, the authors introduce an explicit relative risk control mechanism designed to reduce the consequences of severe short-term underperformance with respect to the cap-weighted index and confirm through out-of-sample empirical tests that “tracking the tracking error” would allow investors to achieve better access to outperformance per unit of extreme relative risk taken. Overall, the results reported in this article suggest that it is possible to achieve robust outperformance versus cap-weighted indices by diversifying model risk and by controlling relative risk compared to the cap-weighted indices. <bold>TOPICS:</bold> <ext-link>Portfolio construction</ext-link>, <ext-link>portfolio theory</ext-link>, <ext-link>factor-based models</ext-link>

Ten Things You Should Know About Low-VolatilityInvesting

Academic evidence shows that low-volatility stock portfolios earn high risk-adjusted returns. Several asset managers have created mutual funds that target this specific segment of the stock market. MSCI launched a minimum volatility index in April 2008, which, in hindsight, was good timing. This new low-volatility investment style is gaining momentum among institutional investors, especially since the experience of the financial crises. Based on experience with low (or minimum) volatility research and running low-volatile equity portfolios for our clients, the author summarizes 10 important things that potential investors should know about minimum volatility investing. <b>TOPICS:</b>Mutual funds/passive investing/indexing, volatility measures, style investing

Benchmarking Low-Volatility Strategies

In this article, Blitz and van Vliet discuss the benchmarking of low-volatility investment strategies, which are designed to benefit from the empirical result that low-risk stocks tend to earn high risk-adjusted returns. Although the minimum-variance portfolio of Markowitz is the ultimate low-volatility portfolio, the authors argue that it is not a suitable benchmark, as it can only be determined with hindsight. This problem is overcome by investable minimum- variance strategies, but because various approaches are equally effective at minimizing volatility, it is ambiguous to elevate the status of any one particular approach to benchmark. As an example, the authors discuss the recently introduced MSCI Minimum Volatility indices and conclude that these essentially resemble active low-volatility investment strategies themselves, rather than a natural benchmark for such strategies. In order to avoid these issues, they recommend to simply benchmark low-volatility managers against the capitalization-weighted market portfolio, using risk-adjusted performance metrics such as the Sharpe ratio or Jensen’s alpha. <b>TOPICS:</b>Portfolio construction, VAR and use of alternative risk measures of trading risk, manager selection

Emerging Asia: Essays on Crises‚ Capital Flows‚ FDI and Exchange Rates

DOI: 10.1355/ae28-3h Emerging Asia: Essays on Crises, Capital Flows, FDI and Exchange Rates. By Ramkishen S. Rajan. London: Palgrave Macmillan, 2011. Pp. xiii, 175. Rajan's book is true to its title: his primary foci are on FDI and exchange rates within the framework of financial and economic crises and the role played by capital flows in them. He sets the tone and direction of his volume by arguing that Much of the prevailing discussion of the contemporary phenomena impacting the global economy is largely journalistic in nature, lacking any solid analysis or debate (p. xii). He goes on: Many scientific works are either narrow in their perspective or not easily comprehensible. This book therefore aims to discuss international economic in a straightforward manner that makes it intelligible to students of applied economics, public policy and international issues (p. xii). Rajan generally achieves his aims within the pages of five parts of his book that deal with (i) crisis, capital flows and exchange rates; (ii) exchange rate volatility, crisis and controls; (iii) global financial architecture; (iv) monetary and financial issues; and (v) foreign direct investment. While his focus is broadly on Asia, the book also contains a useful chapter on India that will particularly interest readers whose attention centres on that national economy. The book begins by reminding readers that financial crises hit Asian economies hard during 1997-99 and then again in 2008-09 when they experienced severe capital shocks. The boom and bust cycles that Asian economies experienced were reflected in balance of payments capital account data that evidenced the persistent crises and recoveries. His balance of payments perspective set the stage for the author's focus on the roles that foreign direct investment (FDI) and exchange rate regimes played in the episodes of crises and recoveries. The author's foci on foreign exchange markets, FDI and other balance of payments capital account financial flows provides readers with a fundamental linkage to the money and the real economies at national levels. This feature is one of the book's strengths. In addition, when he discusses foreign exchange markets two factors stand outothe maintenance of convertibility and the optimum mix of stability and flexibility (e.g., minimum volatility) and coordinating exchange rate and overall monetary policies within an economy. Rajan is quick to point out that coordination does not imply straight-jacketing all Asian economies in a common exchange rate regime due to differences in monetary policy approaches and their connection to real economic activity; that is, the generation of income, output, employment and price levels. For example, Rather than adopting a single immediately, East Asian economies might consider gradually moving towards pegging to a basket, starting with individual weights and varying of extents of flexibility around the pets, with a graduate convergence of time. (p. 25). The author pegs his discussion of exchange rate regimes to their potential impact on highly open real economies by noting that given the heavy reliance of Asia on external trade, FDI and capital flows, the obvious desire by many Asian policy-makers is to minimize volatility in understandable (p. 35). He further states that the link between currency volatility, trade, investment and growth is not unambiguous (p. …

TESTS FOR NONLINEAR COINTEGRATION

This paper develops tests for the null hypothesis of cointegration in the nonlinear regression model with I(1) variables. The test statistics we use in this paper are Kwiatkowski, Phillips, Schmidt, and Shin’s (1992; KPSS hereafter) tests for the null of stationarity, though using other kinds of tests is also possible. The tests are shown to depend on the limiting distributions of the estimators and parameters of the nonlinear model when they use full-sample residuals from the nonlinear least squares and nonlinear leads-and-lags regressions. This feature makes it difficult to use them in practice. As a remedy, this paper develops tests using subsamples of the regression residuals. For these tests, first, the nonlinear least squares and nonlinear leads-and-lags regressions are run and residuals are calculated. Second, the KPSS tests are applied using subresiduals of size b. As long as b/T → 0 as T → ∞, where T is the sample size, the tests using the subresiduals have limiting distributions that are not affected by the limiting distributions of the full-sample estimators and the parameters of the model. Third, the Bonferroni procedure is used for a selected number of the subresidual-based tests. Monte Carlo simulation shows that the tests work reasonably well in finite samples for polynomial and smooth transition regression models when the block size is chosen by the minimum volatility rule. In particular, the subresidual-based tests using the leads-and-lags regression residuals appear to be promising for empirical work. An empirical example studying the U.S. money demand equation illustrates the use of the tests.

Covariance Estimation in Dynamic Portfolio Optimization: A Realized Single Factor Model

Realized covariance estimation for large dimension problems is little explored and poses challenges in terms of computational burden and estimation error. In a global minimum volatility setting, we investigate the performance of covariance conditioning techniques applied to the realized covariance matrices of the 30 DJIA stocks. We find that not only is matrix conditioning necessary to deliver the benefits of high frequency data, but a single factor model, with a smoothed covariance estimate, outperforms the fully estimated realized covariance in one-step ahead forecasts. Furthermore, a mixed-frequency single-factor model - with factor coefficients estimated using low-frequency data and variances estimated using high-frequency data performs better than the realized single-factor estimator. The mixed-frequency model is not only parsimonious but it also avoids estimation of high-frequency covariances, an attractive feature for less frequently traded assets. Volatility dimension curves reveal that it is difficult to distinguish among estimators at low portfolio dimensions, but for well-conditioned estimators the performance gain relative to the benchmark 1/N portfolio increases with N.

Subsampling vector autoregressive tests of linear constraints

This paper studies subsampling VAR tests of linear constraints as a way of finding approximations of their finite sample distributions that are valid regardless of the stochastic nature of the data generating processes for the tests. In computing the VAR tests with subsamples (i.e., blocks of consecutive time series), both the tests of the original form and the tests with the subsample OLS coefficient estimates centered at the full-sample estimates are used. Subsampling using the latter is called centered subsampling in this paper. It is shown that the subsamplings provide asymptotic distributions that are equivalent to the asymptotic distributions of the VAR tests. In addition, the tests using critical values from the subsamplings are shown to be consistent. The subsampling methods are applied to testing for causality. To choose the block sizes for subsample causality tests, the minimum volatility method, a new simulation-based calibration rule and a bootstrap-based calibration rule are used. Simulation results in this paper indicate that the centered subsampling using the simulation-based calibration rule for the block size is quite promising. It delivers stable empirical size and reasonably high-powered causality tests. Moreover, when the causality test has a chi-square distribution in the limit, the test using critical values from the centered subsampling has better size properties than the one using chi-square critical values. The centered subsampling using the bootstrap-based calibration rule for the block size also works well, but it is slightly inferior to that using the simulation-based calibration rule.

Dedicated stock portfolios

T he Markowitz portfolio model introduced in 1952 expressed the optimal relationship between portfolio volatility and expected return. While tlie procedure was quite capable of providing perfectly accurate answers to questions such as, “Given a population of securities, what single combination would have had the lowest volatility in monthly return over the preceding period?”, the computing power of the times limited its application. A decade later, Sharpe introduced the singleindex model [1963]. In essence, Sharpe’s model replaced the exact, but cumbersome, Markowitz formula for portfolio volatility with a simplified approximation that assumed all the interrelationships among security returns could be attributed to the fact that they all respond differentially to the pull of the single index. Sharpe represented his single index by the returns to the market itself, but others (King [1966], for example) soon provided evidence that other common forces were pulling security returns as well. King at the time noted industry-related factors, but since then attention has shifted from aggregate stock marketor industry-related portfolios to more generalized economic factors. In some models the factors are real (economic variables such as unexpected changes in inflation, industrial production, and term and default premiums in bond yields see Chen, Roll, and Ross [1986]), while in others they are portfolios, derived from factor analysis (Chen [1983]). The factor analytic portfolios allegedly mimic the behavior of the underlying economic variables actually responsible for the correlations between security returns. Index models that initially were regarded as routes to a simplified expression for portfolio volatility eventually became widely accepted as ways to track targets such as the S&P 500. But times have changed since 1952. There have been significant advances in computing hardware and in the algorithms to compute portfolio volatility (Von Holhenbalken (19751). Analysts are now fully capable of obtaining Markowitz solutions for several hundred securities at a time, which makes the relative computational simplicity of index models less valuable. The latest advances in hardware and software now make it possible to construct dedicated stock portfolios based on all the information in the full covariance matrix of security returns. These portfolios are dedicated to a mission of risk management such as hedging against inflation or against unexpected changes in interest rates that may dramatically increase the present value of the liabilities of pension funds. Just as the Markowitz model provides the reactively accurate answer to the minimum volatility question posed above, it also provides the more accurate answer to the question, “Which combination of securities would have achieved the greatest degree of tracking power in the past?” While the relative predictive power of the Markowitz and index models remains an open question (and one that obviously