Active Versus Passive Low-Volatility Investing

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1 Active Versus Passive Low-Volatility Investing Introduction ISSUE 3 October 013 Danny Meidan, Ph.D. (561) Low-volatility equity investing has gained quite a lot of interest and assets over the past few years. The primary objective of low-volatility investing is to reduce the volatility of equity portfolios without sacrificing long-term returns relative to capitalization-weighted indices. In theory, this should be possible to do if capitalization-weighted indices are not on the meanvariance efficient frontier. Investors currently have a multitude of low-volatility investment offerings from which to choose. These offerings include passive low-volatility portfolios from traditional index providers, such as S&P or MSCI, and active investment offerings from investment management firms that are primarily quantitative in nature. In addition, some fundamental managers also offer solutions that attempt to reduce the overall volatility of equity portfolios. This article attempts to highlight the limitations of so-called passive low-volatility indices relative to some of the more active offerings that are available from various quantitative managers. Important Things to Look For in Low-Volatility Equity Strategies To facilitate a more effective discussion, we first introduce some key concepts concerning risk and returns that are highly important when considering low-volatility portfolios. The first point we would like to raise is that as the number of stocks in a portfolio increases, the correlations between the stocks play an increasingly important role in determining the overall portfolio risk. To understand this argument, recall that the total risk of a portfolio of stocks can be written as follows: i, j Variance of Portfolio Returns = N N i 1 j 1 w i w j i where is the covariance between stock i and stock j, i, i i is the variance of stock i, and N is the number of stocks. This expression has N elements contributing to the total risk of the portfolio, each element involving either the variance of a particular stock (and its squared weight in the portfolio) or the covariance between two specific stocks (and the product of their weights in the portfolio). If we were to place each one of these N components in a matrix, such as the one depicted in Figure 1, then the sum of all the elements in the matrix is the total risk of the portfolio. 1 Moreover, of the N elements contributing to the total risk of the portfolio, the N elements in the diagonal of the matrix involve the N variance terms, while the remaining N -N terms in the off-diagonal of the matrix involve the covariances among the stocks. Consequently, for a portfolio consisting of 1000 stocks, the total risk is determined by the 1000 variance terms and the 999,000 covariance terms. In other words, as the number of stocks increases, it is primarily the covariance terms that determine the total risk of the portfolio rather than the variance terms. Moreover, the covariance terms depend on the volatilities of the individual stocks, but their sign and magnitude are also influenced by the correlation of the relevant stocks returns. As a result, all else equal, if the correlation between two stocks is negative or extremely low, the total contribution to the portfolio risk from the interaction between those two stocks will also be negative or very low. Stock 1 Stock Stock 3 Stock N-1 Stock N, j Stock 1 Stock Stock 3 Stock N-1 Stock N Figure 1: Elements Contributing to Total Portfolio Risk 1 Using this type of decomposition, the contribution to total risk from each individual stock can be viewed as the sum of all the elements in its corresponding row (or column). The covariance between two stocks is computed as the product of the estimated standard deviations of the two stocks multiplied by the correlation coefficient of the two stocks. Mathematically this is: C , 1 1, FOR INSTITUTIONAL INVESTOR USE

2 This implies that low-volatility portfolios need not be comprised solely of low-volatility stocks; volatile stocks with low correlations to other stocks can also help reduce portfolio risk. Hence, it is paramount to take correlations into consideration when constructing low-volatility equity portfolios. 3 In regards to the total return of low-volatility portfolios we have found that, although these portfolios should be considered absolute-return products, both investors and investment managers will inevitably compare their performance to capitalization-weighted indices over time. Reducing an equity portfolio s volatility is actually not that difficult per se, since one can always do that with a combination of stock and cash. However, if the goal is to also keep up with a rising market over time, then a low-volatility portfolio needs to be able to reduce volatility and, at the same time, tap into an alpha source that will allow it to compensate for transaction costs incurred from trading the portfolio and any loss of return associated with the reduction in risk. This is illustrated in Figure where we show a hypothetical chart of the efficient frontier, which represents the lowest possible level of portfolio risk for a given level of expected return in a portfolio of risky securities. In this illustration, the capitalization-weighted index (the market ) is plotted away from the efficient frontier, since it is unlikely that a portfolio weighted solely based on the size of its constituents attains the best risk/reward tradeoff. If one were to use cash or Treasury bills to reduce the market-portfolio s risk by investing, for example, 0% in cash and 80% in the market, this would have the effect of not only reducing the risk of the portfolio but also lowering the expected return of the portfolio. A low-volatility equity strategy can potentially achieve the same level of risk reduction but, at the same time, also possibly attain a higher level of expected return by utilizing a systematic investment process that can achieve excess returns over time. In sum, for a lowvolatility strategy to generate market-like or above-market long-term returns, the investment approach should (i) target return as well as volatility reduction, and (ii) employ a systematic and repeatable method of beating the market over time. What are Passive Approaches to Low-Volatility Investing? Illustrative example, not to scale. Figure : Low Volatility and the Efficient Frontier Traditional index providers such as S&P, MSCI, and Russell Investments now offer low-volatility indices. These indices are typically presented as passive, (relatively) low-cost, approaches to low-volatility investing and may be accessible via exchange traded funds, mutual funds, or other investment vehicles. The construction methodologies of these low-volatility indices are available directly from the index providers. Following is a brief description of these methodologies: 4 S&P Low Volatility Indices These indices are designed to measure the performance of the least volatile stocks within their respective benchmark indices. Constituents are weighted inversely proportional to their corresponding volatility of daily returns over the past year, so that the least volatile stocks receive the highest weights. According to S&P, 5 these indices are designed to serve as benchmarks for low-volatility or low-variance strategies in their respective regional stock markets. The S&P Low Volatility indices are rebalanced quarterly. MSCI Minimum Volatility Indices These indices are calculated by optimizing a parent MSCI Equity Index (such as the MSCI USA Index, the MSCI World Index, or the MSCI EAFE Index, among others) using an estimated covariance matrix to produce a portfolio that has the lowest expected absolute volatility for a given set of constraints. The estimated security covariance matrix is based on the relevant Barra multi-factor equity model. The constraints used in the optimization process may vary 3 This is analogous to the asset allocation world. The addition of investment styles with low correlation to other asset classes in the portfolio can reduce overall portfolio volatility. While individual asset classes can be volatile, in a well-constructed portfolio there will be other investments that partially offset that volatility, resulting in a more stable return pattern. 4 For brevity, our descriptions of the index construction methodologies are incomplete; they are only intended to provide a general overview of what these strategies attempt to do. For a more complete description, we refer the readers to the index providers websites. 5 S&P Indices: S&P Low Volatility Index Methodology (May 01).

3 based on the parent index used. These constraints include minimum and maximum position holdings, country weight constraints, sector weight constraints, risk factor exposure constraints, and turnover constraints. 6 The MSCI Minimum Volatility Indices are rebalanced semiannually. Russell Defensive Indices The Russell Stability Indices attempt to define a third dimension of style investing (in addition to small/large and growth/value): defensive versus dynamic stocks. There are four major steps in the construction of the Russell Defensive Indices: identifying the stability descriptive variables (debt-to-equity ratios, earnings variability, return on assets, 1- month stock price volatility and 60-month stock price volatility); combining these variables into quality and volatility components; computing the quality and volatility scores for each stock; and performing the final construction of the Dynamic and Defensive Indices. 7 The Russell Defensive Indices are reconstituted annually. Some Drawbacks of Passive Approaches to Low-Volatility Investing While the backtested low-volatility investing approaches described herein have generally kept up with or outperformed the respective capitalization-weighted indices they are typically compared to over the past 15 years or so, there are important shortcomings to these so-called passive approaches. We discuss some of these drawbacks below. Passive low-volatility investing is not really passive The low-volatility indices previously described are often presented as passive-like strategies that can be used as benchmarks for other low-volatility strategies. However, low-volatility strategies, like those from MSCI or Russell Investments, employ quite a few assumptions and investment decisions, such as limits on individual stock positions, constraints on risk factors, weights on various input variables, and constraints on turnover and rebalancing frequencies. These, in many ways, resemble assumptions and choices made by active managers. One would expect truly passive indices to be much simpler and less subjective. In addition, low-volatility indices lack some of the characteristics that are typical of truly passive capitalization-weighted indices, such as simplicity, breadth, transparency, and low turnover. For example, the S&P 500 Low Volatility Index includes only 100 out of the 500 stocks in the S&P 500 Index. It is debatable if this portfolio is sufficiently diversified and, more importantly, there is probably ample opportunity to use many other stocks from the S&P 500 investment universe to further reduce the risk of the portfolio through diversification. Furthermore, the turnover of a portfolio like the S&P 500 Low Volatility Index is not inconsequential. In fact, these indices appear to be stuck between a rock and a hard place. On one hand, they would like to behave as bona fide low-volatility strategies this requires subjective assumptions and substantial trading. On the other hand, they would like to appear passive-like, so they attempt to simplify the investment process or limit trading by introducing turnover constraints. For example, the MSCI Minimum Volatility Indices have a strict turnover constraint regardless of whether a temporarily higher turnover could be more advantageous in reducing volatility further. As a result, it is debatable as to whether the MSCI Minimum Volatility Index is truly a (long-only) minimum variance portfolio, or rather a crude approximation of one, even if the risk estimates used in the portfolio optimization process are accurate. In fact, it is likely that the volatility of the portfolio can be further reduced by weakening or eliminating some of the constraints placed on the strategy due to its attempts to appear passive-like. In sum, the quandaries faced by providers of such strategies create a situation where these indices are neither truly active strategies, nor are they truly passive strategies. Overemphasis of volatilities versus correlations Earlier, we explained that in a portfolio of many stocks it is the correlation terms that determine most of the portfolio risk. However, some of the aforementioned low-volatility indices do not even take the correlations between the stocks into consideration during the index construction process. In particular, both the S&P and Russell approaches consider the individual stock price volatilities but, to the best of our knowledge, do not examine or utilize the correlations between the stocks directly. This does not mean that those investment offerings are not low-volatility portfolios: empirical evidence actually shows that both the S&P and Russell strategies have volatility levels that are lower than capitalization-weighted indices. However, it does suggest that those portfolios are missing out on opportunities to reduce portfolio risk further. Moreover, since correlations between stocks tend to change over time, a 6 See MSCI: MSCI Global Minimum Volatility Indices Methodology (January 01). 7 See Russell Investments: The Third Dimension of Style: Introducing the Russell Stability Indices (December 010). 3

4 regime in which correlations between low-volatility stocks are high can severely hamper the ability of such strategies to provide downside protection during such a regime. Active strategies using a reasonable risk model should, in many cases, be able to reduce risk more effectively than these low-volatility indices and better adapt their holdings to changing market environments. Passive low-volatility investing does not control for or maximize return Another point made earlier in this article was that investors are likely to compare the performance of their low-volatility portfolios to capitalization-weighted indices over time despite the lower risk of the low-volatility portfolios. One way low-volatility portfolios can keep up with a rising market over the long term is to tap into a valid and sustainable alpha source that will compensate for transaction costs and any reduced risk premium associated with the reduced risk. The backtests of the low-volatility indices discussed herein have been successful at beating capitalization-weighted indices over the past 15 years or so, but these indices do not directly attempt to target or control returns. In fact, even the MSCI Minimum Volatility Index approach, which uses a complete risk model in the portfolio construction process, 8 does not attempt to control or target returns; it simply aims to minimize portfolio risk subject to multiple constraints. As a result, it appears that these portfolios either (i) have benefited from a period that has been extremely favorable toward low-volatility portfolios over their respective backtest periods, or (ii) have tapped into some risk premium inadvertently and/or in a suboptimal fashion, and have been compensated for bearing that risk. Neither is necessarily sustainable over the longer term. Conversely, quantitative active low-volatility managers use various approaches to generate alpha; these approaches typically involve substantial research and effort to implement. 9 Moreover, active low-volatility managers typically attempt to either (i) maximize returns for a target level of risk, or (ii) minimize risk for a target level of return, or excess return. There can be substantial differences over the long term between approaches that either combine low-risk stocks in a portfolio or simply attempt to reduce portfolio risk, versus more sophisticated approaches typically used by active lowvolatility managers that aim to operate along both the risk and the expected return dimensions of the efficient frontier. Infrequent rebalancing and updates of risk estimates As mentioned above, the low-volatility indices discussed herein reconstitute and rebalance periodically, ranging from quarterly (S&P) to semiannually (MSCI) to annually (Russell). The goals of the rebalancing process are to reevaluate which stocks should belong in these indices, and readjust their weights based on the prevailing stock characteristics at the time of rebalancing. Rebalancing so infrequently may be suboptimal and can result in missed opportunities to adjust the portfolios to changing market conditions. Active low-volatility strategies tend to adjust their risk models more often and rebalance more frequently and, consequently, are nimbler in nature. This can result in superior downside protection at times of crisis, when it is most needed. Passive low-volatility investing can be too predictable Transparency is touted as a major advantage of the low-volatility index approaches, but some of the more passive-like approaches to low-volatility investing that are offered by index providers are probably overly transparent. For example, the S&P 500 Low Volatility Index is particularly easy to replicate. This index, which rebalances quarterly, screens stocks based on their volatility of daily returns over the past year, keeps the 100 least volatile stocks, and weights them in the index inversely proportional to their one-year volatilities measured using daily stock returns. While investors can take some comfort in knowing exactly how these indices are constructed, this transparency is a two-edged sword. As more money flows into instruments that follow these indices, their market impact at the rebalancing dates becomes more substantial, and algorithmic traders can profit from the predictability of the trading patterns at each index reconstitution, to the detriment of the indices themselves. For example, in the case of the S&P 500 Low Volatility Index, due to the length of time over which volatility is measured (one year), one could conceivably predict the composition of the rebalanced index with a relatively high degree of precision a week or two in advance of a rebalancing date. While funds following such an index will make the required trades on or very close to the reconstitution date to avoid the potential for high tracking error (driving prices up or down in the process), sophisticated algorithmic traders can benefit by moving in ahead of the index funds and closing their positions shortly after the reconstitution date. In this scenario, the traders have profited, and the index fund has met its 8 The S&P and Russell strategies do not take stock correlations into account in the portfolio construction process. 9 Debating the validity of the various approaches used by active managers is beyond the scope of this article. 4

5 objectives by tracking the index; the losers are the investors in the index fund, who have effectively paid much higher transaction costs (embedded in the index returns themselves) than any index backtest would indicate. It is worth noting that the more popular an index becomes, the bigger the opportunity for traders to take advantage of such rebalancing events since the rebalancing trades at the index reconstitution are more likely to move markets, and trading in advance of the reconstitution is more likely to be profitable. 10 Conclusion The limitations of passive low-volatility portfolios discussed herein may have the unintended consequence of controlling and reducing portfolio risk in an ineffective manner. Moreover, some of the potential drawbacks listed above may be most damaging at times of crisis, or when low-volatility indices grow substantially larger as they increase in popularity. Active lowvolatility portfolios can mitigate some of the disadvantages of low-volatility indices, and can potentially offer greater meanvariance efficiency and the ability to meet investors long-term goals more consistently. In particular, active low-volatility strategies utilize estimates of both stock volatilities and correlations, and are typically less constrained than low-volatility indices, allowing them to potentially provide superior risk reduction and greater downside protection. Moreover, unlike lowvolatility indices, active low-volatility strategies directly strive for both risk reduction and excess returns while operating along both the risk and the expected return dimensions of the efficient frontier. Lastly, active low-volatility strategies are more flexible and nimbler, allowing them to adapt to changing market environments more rapidly. These strategies, however, tend to be somewhat more complex, can have higher turnover, and are not necessarily suitable for every investor. Low-volatility equity investors should carefully consider if their long-term investment goals are likely to be met by passive low-volatility investing, or if they are more likely to be met by a potentially more-optimal, active approach. Reference Lynch, Anthony and Mendenhall, Richard R., New Evidence on Stock Price Effects Associated with Changes in the S&P 500 Index, Journal of Business, This material is for general informational purposes only. It is not intended as investment advice, as an offer or solicitation of an offer to sell or buy, or as an endorsement, recommendation, or sponsorship of any company, security, advisory service, or product. This information should not be used as the sole basis for investment decisions. Past performance does not guarantee future results. Investing involves risk, including the loss of principal and fluctuation of value. 10 There is some academic evidence consistent with these types of trading patterns around index reconstitution dates. For example, Lynch and Mendenhall (1997) find that for S&P 500 additions during the period in their study there is a significant positive cumulative average abnormal return of approximately 3.8% over the period starting the day after the announcement of the index addition and ending the day before the effective date of the change. They find a similar but inverted price movement pattern for S&P 500 deletions. 5

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