in-depth Invesco Actively Managed Low Volatility Strategies The Case for

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1 Invesco in-depth The Case for Actively Managed Low Volatility Strategies We believe that active LVPs offer the best opportunity to achieve a higher risk-adjusted return over the long term. Donna C. Wilson Director of Portfolio Management Invesco Global Quantitative Equity (GQE) With contributions from Anna Gulko, Edward Leung and Andrew Waisburd of the Invesco GQE Research Team Low volatility investing seeks to reduce total risk and has the potential to deliver comparable or better returns than a related cap-weighted index over a full-market cycle. The goal is to generate higher risk-adjusted returns than the related cap-weighted index. This investment style is supported by academic evidence 1 that dates back 40 years, but has recently gained popularity because investors have not been adequately compensated for the risk taken, especially within large-cap developed equity markets. In addition, there is considerable evidence over the last two decades across global and regional equity markets that investors could have earned higher returns by investing in lower risk stocks. 2 Invesco Global Quantitative Equity began exploring low volatility investing in 2004 and launched global and European strategies in 2005 and a US strategy in In this paper we investigate different implementations of low volatility portfolios (LVPs), discuss benchmarks, and then compare two simulated low volatility portfolios a passive LVP and an active LVP. 3 We show that both portfolios equally reduced total risk and added considerable value over the Standard & Poor s 500 Index during a 20 year time period ending December 2011, a period that included at least five different market cycles. However, the actively managed LVP delivered higher risk-adjusted returns by utilizing return (alpha) forecasts 4 and relaxing of traditional benchmark centric-constraints. Further, the actively managed LVP generated higher alpha with only a limited increase in risk over that of a passive LVP and that level of total risk was still much lower than the total risk of a capitalization weighted index.

2 Implementing low volatility portfolios As a result of academic evidence and historic performance, many different varieties of low volatility portfolios have been introduced to investors. Each version shares the goal of reducing total risk, however, portfolio construction techniques differ widely. Quantitative screening is a technique typically used by Index and ETF providers to construct a portfolio of low volatility stocks. For example, the S&P 500 Index is screened based on volatility, and the 100 least volatile stocks then become the constituents of the S&P 500 Low Volatility Index. Stock weights are based on the inverse of their corresponding volatility, thus the low-volatility stocks have a much higher weight than the more volatile ones. Another technique, and likely the most prevalent, is to construct a LVP using an optimizer and a risk model to determine optimal weights. With the use of an optimizer and a risk model, passive and actively managed LVPs can be Many different varieties of low volatility portfolios have been introduced to investors. Each version shares the goal of reducing total risk, however, portfolio construction techniques differ widely. produced, both of which have historically offered a better risk/return profile than a cap-weighted index. Passive LVPs, which serve as the basis for a minimum variance portfolio, have the single objective to reduce total risk. They are designed to capture the low volatility anomaly (premium received for investing in low volatility stocks). Portfolio construction requires a number of subjective assumptions and parameter choices with regard to the total risk target as well as sector/industry/style exposures and maximum and minimum weight on individual stocks. Expected returns are not included in the optimization process. The MSCI Global Minimum Volatility Index series is an example of a passive LVP. Active LVPs, also constructed with an optimizer, have the objective of maximizing total return while also reducing total risk. Similar to passive LVPs, portfolio construction decisions are made on the level of total risk, sector/industry/style exposures, and individual position size. In addition, alpha forecasts are included in the optimization, which allows for a better return/risk solution than a passive LVP. Regardless of the portfolio construction technique, LVPs have greater potential to reduce risk relative to a comparable cap-weighted index. They share common characteristics such as 1. Lower beta 2. Lower total risk as measured by standard deviation 3. Smaller average market capitalization 4. Larger absolute sector/industry/style factor exposures that vary over time based on the risk environment. Even with these commonalities, differences in portfolio construction may result in shorter-term return divergences, even though the longer-term volatility reduction goal is achieved. Introducing alpha forecasts into the portfolio construction process not only adds to the expected return, but also to the expected risk of an active LVP relative to an otherwise comparable passive LVP. However, we demonstrate the possibility of adding significant alpha with only a limited increase in risk over that of a passive LVP, which is still much lower than the risk of a capitalization weighted index. Benchmarking low volatility strategies Both MSCI and S&P have developed indices to serve as benchmarks for low volatility strategies. S&P launched the S&P 500 Low Volatility Index in April The Global Minimum Volatility Index series was launched by MSCI in Despite the existence of these indices, there appears to be no standard benchmark for active low volatility portfolios. Most agree that a benchmark for LVPs should be investable, transparent and passive. However, as noted in a 2011 paper by Blitz and Van Vilet, 5 investable minimum variance portfolios resemble active LVPs rather than being a natural benchmark for such strategies. They argue that current low-volatility benchmarks, as well as the investable LVPs, are equally effective at minimizing volatility, so it is not obvious why any one particular approach should be elevated to the official benchmark status. As such, they recommended benchmarking low volatility portfolios to a capitalization weighted market index using a risk-adjusted performance metric such as Sharpe ratio. They concluded that this approach recognizes that low volatility investing is not primarily aimed at beating a certain low volatility index, but at establishing a risk/return profile favorable to a passive investment in the capitalization-weighted index. The Case for Actively Managed Low Volatility Strategies 2

3 Figure 1 - Cumulative Returns for Simulated Active and Passive LVPs and the S&P 500 Index S&P 500 Index Passive LVP Active LVP Cumulative Log Returns (Simulated) Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Source: Invesco and Standard and Poor s. See disclosures at the end for important information regarding simulated returns. There is no guarantee that the simulated returns shown can be realized in the future. We concur, and used the S&P 500 Index as the benchmark for the LVPs for both return and risk comparisons. Comparing performance results: Passive and active low volatility simulated portfolios After considerable research we determined that while a passive LVP accomplished the goal of reducing risk and delivering comparable or better-than-index returns, it was not the best low volatility portfolio we could produce. The active LVP, which includes alpha forecasts, delivered a higher risk-adjusted return, with total risk comparable to the passive LVP. Effectively, the passive LVP also serves as a proxy benchmark for the active LVP. The passive LVP has low enough turnover to be considered a buy and hold portfolio and it meets the other standard requirements for a benchmark because it is also transparent and investable. Further, comparing performance between a market index and a passive and active LVP allows disentangling of return due to alpha and return due to low volatility portfolio construction. We demonstrate this for a US investment universe by comparing two simulated low volatility portfolios a passive LVP and an active LVP. Each portfolio uses the same large-cap universe of over 700 stocks as the investable universe. Portfolio settings such as the maximum weight on individual stocks, sector/industry/style exposures, transaction cost estimates, and other parameters used to construct the portfolios were also the same. The total risk target for both portfolios was set as the midpoint between the S&P 500 Index and the predicted risk of the minimum variance portfolio. 6 In both cases, the portfolios were rebalanced monthly relative to cash benchmark, which eliminated any capweighted index comparisons. Neither of these portfolios utilized derivatives, allowed shorting, or permitted the use of leverage. Including the alpha forecasts in the active LVP was essentially the only construction difference between the two LVPs. Figure 1 demonstrates the cumulative log returns (net of transactions costs, gross of fees) for the LVPs for the 20 year period ending December 31, Table 1 demonstrates a summary of our findings and is consistent with the academic research in several ways. First, both the passive and active LVPs reduced total risk about 20% relative to the S&P 500 Index, providing effective downside protection. Second, both the passive and active LVPs delivered higher risk adjusted returns than the S&P 500 Index. A key contributor to this outcome was the unconstrained portfolio parameters (relaxing the typical benchmark-relative constraints). However, the active LVP generated higher, more consistent, and statistically significant excess returns than the passive LVP. The additional freedom from the unconstrained portfolio construction process allowed greater utilization of alpha forecasts at lower levels of total risk. In addition, the active LVP participated more fully in up markets than the passive LVP, which is one of the notable challenges of lowvolatility investing. The Case for Actively Managed Low Volatility Strategies 3

4 Table 1 - Summary Statistics for Simulated Active and Passive LVP versus the S&P 500 Index (January 1992 to December 2011) S&P 500 Index Passive LVP Active LVP Total Annualized Return 7.80% 10.00% 12.20% Total Annualized Risk 15.00% 12.00% 12.40% Sharpe Ratio Annualized Excess Return 2.20% 4.38% T-Statistic* * Up Market Capture % 92.60% Down Market Capture % 83.00% Annual Turnover 3.20% 60% Annual Estimated Transaction Costs 0.03% 0.52% Average # of Assets *Significant at the 5% level. Source: Invesco, StyleADVISOR, and Standard and Poor s. See disclosures at the end for important information. There is no guarantee that the simulated returns will be realized in the future. Table 2 observes different performance patterns of LVPs versus the S&P 500 over five market cycles. For simplicity, we used calendar years to analyze these cycles rather than specific monthly beginning or ending points. These market cycles demonstrate that investors must have a longer-term perspective to fully appreciate and understand the risk and return benefits of a low volatility investing. As observed over the entire 20 year simulation period, both the passive and active LVPs reduced total risk, as measured by standard deviation, relative to the S&P 500 regardless of the market cycle. More importantly, they both helped to preserve wealth by providing downside protection during the down market cycles of and Further, the LVPs outpaced the S&P 500 Index with the exception of the bull markets of and , when the portfolio s low beta exposure limited upside participation. Despite underperforming the S&P 500 during the tech bubble, the active LVP delivered meaningfully better performance than Table 2 - Return and Risk by Market Cycle: Summary Annualized Statistics for the Simulated Active and Passive LVP S&P 500 Return Bull Market - Tech Bubble Tech Bust Recession Easy Money Recovery Global Financial Crisis Recovery 28.6% -14.6% 14.7% -18.5% 14.1% Excess Return vs. S&P 500 Passive LVP -6.8% 8.5% 1.9% 10.5% 4.2% Active LVP -1.2% 12.8% 6.1% 4.5% -0.7% Standard Deviation Passive LVP 11.6% 13.8% 7.7% 14.4% 14.1% Active LVP 11.8% 14.7% 7.8% 16.5% 14.3% S&P % 18.8% 8.4% 17.6% 19.0% Source: Invesco, StyleADVISOR, and Standard and Poor s. See disclosures at the end for important information. There is no guarantee that the simulated returns will be realized in the future. The Case for Actively Managed Low Volatility Strategies 4

5 the passive LVP. This is due to the addition of the alpha forecast and the relaxed portfolio constraints, which partially offset the negative return attributable to a lower beta or market exposure in a strong market. During the recovery, the active LVPs alpha exposure helped the portfolio participate in the upside. However, in the recovery, the active LVPs alpha exposure disadvantaged the portfolio. Obviously, active alpha is not guaranteed to produce extra return at all times. Nevertheless, the longer term results clearly demonstrated the value added from the active LVP at lower levels of total risk. Investors have not been adequately compensated for the risk taken. Is the low volatility premium the source of the outperformance for the Passive and Active Low Volatility Portfolios? Next we investigate the source of excess returns for the LVPs or more specifically, how much of the low volatility anomaly (premium received for investing in low volatility stocks) contributed to returns. While there is evidence to support this anomaly, it was a fairly weak source of returns for the active LVP as well as the passive LVP. To attribute the performance of the passive and active LVPs, we used the Fama-French-Carhart (FF-C) Four Factor model. 9,10 The FF-C Model is an extension of the Capital Asset Pricing Model (CAPM), which posits that returns are fully explained by a single market factor and an idiosyncratic component. The FF-C Model includes three additional factors that are well known sources of excess return size, value, and momentum. The CAPM or market factor represents beta or the excess returns of stocks with high minus low market sensitivity. The size factor represents the excess returns of small- minus big-cap stocks. The value factor, measured by book to price, represents the excess returns of high exposure to value minus low exposure to value (or growth stocks). The momentum factor represents the excess returns of upward momentum minus downward momentum stocks. To estimate the portfolio s exposure to each of the four factors we used a regression analysis. The monthly excess returns of the passive and active LVPs from January 1992 to December 2011 were the dependent variables while the monthly factor returns to the FF-C factors were the independent variables 11. Table 3 presents our findings for a Passive LVP. The regression analysis shows the excess returns of the passive LVP are positively related to the market, value and momentum factors, and negatively related to size, with an adjusted R-squared of 72%. The portfolio on average had a market or beta exposure of 0.63, which is expected from a LVP. We can also see that relatively small amount of monthly alpha (13 basis points) remained after accounting for these four factors but it was not statistically significant. Given that there was no return forecast inputs into the optimization, this alpha is likely sourced from explanatory factors not utilized in this analysis. Table 4 presents our findings for the Active LVP. Table 3 - Simulated Passive LVP, January 1992 December 2011 Monthly Alpha Market/Beta Value Size Momentum Coefficient T-statistic * 7.46* -5.32* 2.73* Adjusted R-Squared 0.72 *Significance at the 5% percent level Table 4 - Simulated Active LVP, January 1992 December 2011 Monthly Alpha Market/Beta Value Size Momentum Coefficient T-statistic 3.77* 34.53* 6.22* -3.63* 4.05* Adjusted R-Squared 0.84 *Significance at the 5% percent level The Case for Actively Managed Low Volatility Strategies 5

6 The regression analysis shows the excess returns of the active LVP are positively related to the market, value, and momentum factors, and negatively related to size, with an adjusted R-squared of 84%. The portfolio on average had a market or beta exposure of 0.77, which is higher than the LVP, but still lower than the market. There were however, some other distinct differences. First, the average monthly alpha for the active LVP increased to 35 basis points from 13 basis points for the passive LVP. This alpha remained after accounting for the additional four factors. Second, unlike the passive LVP, the alpha generated from the active LVP is statistically significant, which indicates that the alpha explained performance in excess of the standard four factors. Third, the adjusted R-squared of 84% for the active LVP is a meaningful increase over the passive LVPs adjusted R-squared of 72%. This demonstrates that including alpha forecasts explained more of the variation in return than was accounted for by the more traditional factors. Next, we investigated the extent to which the performance of the excess returns of the active and a passive LVP is a function of the low volatility anomaly. In Tables 5 and 6, we show the results from decomposing the historical excess return for each of these LVPs by a fifth factor, Low Volatility. We constructed a monthly Low Volatility factor by 1) sorting the investable universe by volatility (as defined by MSCI Barra s Total Risk) then dividing that list into five equal groups of stocks ranging from the highest to the lowest volatility, 2) calculating the one month forward return to the highest volatility group and the lowest volatility group, and lastly, 3) calculating the Low Volatility independent variable as the return spread of the high volatility group minus low volatility group. This factor calculation closely resembles the methodology used to calculate the returns for the four FF-C factors. Tables 5 and 6 present our findings for the passive and the active LVP, respectively, with the inclusion of the low volatility factor. Several observations are worth noting. First, the introduction of the low volatility factor does not meaningfully change our previous findings. In particular, the adjusted R-squared was unchanged for the passive LVP at 72% and the active LVP at 84%, when a Low Volatility factor was introduced. This indicates that the low volatility anomaly does not explain substantially more variation in return than is explained by the more traditional factors. Second, the coefficient on the Low Volatility factor was negative and not statistically significant for the passive LVP demonstrating that investing in lower volatility stocks did not explain any portion of the passive LVPs returns through time. Third, for the active LVP, the coefficient on the Low Volatility factor was negative and statistically significant at the 10% level, which indicates that investing in lower volatility stocks did explain some portion of the active LVPs returns through time. The impact, however, was fairly weak relative to the other factors in the FF-C model. Table 5 - Simulated Passive LVP, January 1992 December 2011 Monthly Alpha Market/Beta Value Size Momentum Low Volatility Coefficient T-statistic * 7.36* -5.41* 2.74* Adjusted R-Squared 0.72 *Significance at the 5% percent level Table 6 - Simulated Active LVP, January 1992 December 2011 Monthly Alpha Market/Beta Value Size Momentum Low Volatility Coefficient T-statistic 3.81* 34.53* 6.11* -3.74* 4.09* -1.82** Adjusted R-Squared 0.84 *Significance at the 5% percent level ** Significant at the 10% level The Case for Actively Managed Low Volatility Strategies 6

7 Moreover, with regard to the active LVP, this evidence validates that the primary source of excess returns in the active LVP is the result of the inclusion of alpha forecasts and not low volatility itself. The combination of alpha forecasts along with the unconstrained nature of the portfolio construction process introduces the potential for higher levels of alpha at lower levels of risk. In this analysis, we demonstrated that as constraints were relaxed, simultaneously risk was reduced and more alpha was added. These findings should provide greater confidence in the active LVP. Summary and conclusions Low volatility investing has recently gained popularity because investors have not been adequately compensated for the risk taken, especially within large-cap developed equity markets. In addition, there is considerable evidence for at least the last two decades, across global and regional equity markets, that investors could have earned higher returns by investing in lower risk stocks. 2 As a result of academic evidence and historic performance, many different varieties of Low Volatility portfolios have been introduced to investors. Regardless of variations in portfolio construction techniques, LVPs share common characteristics relative to a comparable cap-weighted index. These include: 1. Lower beta 2. Lower total risk as measured by standard deviation 3. Smaller average market capitalization, and 4. Larger time-varying absolute sector/industry/ style factor exposures Using a performance attribution model, we also demonstrated that the historical alpha generated for the active LVP was higher than the passive LVP and also in excess of the standard return factors market, value, size, and momentum. In addition, a Low Volatility factor was created to determine if the exposure to lower volatility stocks explained some portion of the active LVPs returns. The result was immaterial. We concluded, therefore, that the active LVPs outperformance was a result of the inclusion of alpha forecasts and the relaxation of traditional benchmark centric-constraints and not the premium earned from investing in lower volatility stocks. These findings are particularly relevant to investors who are seeking higher risk-adjusted returns within their equity allocation while focusing on minimizing loss of principal. The goal of low volatility investing is to reduce risk, provide downside protection and allow for participation in the market without sacrificing returns over the long term. By incorporating alpha forecasts and portfolio construction techniques, we believe these same benefits are available, but with the added potential for higher than market returns. Low volatility investing also provides greater flexibility for investors when managing their risk budget. With this increased flexibility, investors could maintain or even increase their allocation to equities, if so desired. Despite the concerns about the associated risk with investing in equities, this highly liquid asset class has been able to provide long-term performance to help investors achieve their return targets and funding obligations. This alternative solution, which allows investors the potential to maintain or increase equity exposure without incrementally increasing risk, provides a compelling opportunity, especially in this low return environment. However, we believe that active LVPs offer the best opportunity to achieve a higher risk-adjusted return over the long term. To demonstrate this, we compared a passive LVP to the active LVP, using simulated returns. Both the passive and active LVP equally reduced total risk irrespective of market cycles and added considerable value over the S&P 500 Index during most cycles. However, over the 20 year simulation period, the actively managed LVP generated higher alpha with only a limited increase in risk over that of a passive LVP, and that level of total risk was still much lower than the total risk of a capitalization weighted index. The Case for Actively Managed Low Volatility Strategies 7

8 1. Black, F., MC Jensen and M. Scholes The Capital Asset Pricing Model: Some Empirical Test Studies in the Theory of Capital Markets (1972) Clark, desilva, Thorley. Minimum-Variance Portfolios in the U.S. Equity Market, The Journal of Portfolio Management, Fall 2006; Haugen, Robert A. and Nardin L. Baker, The Efficient Market Inefficiency of Capitalization-weighted stock portfolios, The Journal of Portfolio Management, Spring 1991; Baker. M, Bradley. B, and Wurgler. J. Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly, Financial Analyst Journal, Volume 67, 2011 CFA Institute. 2. Ang, A., Hodrick, R., Xing, Y., Zhang, X. The Cross Section of Volatility and Expected Returns, Journal of Finance, Ang, A., Hodrick, R., Xing, Y., Zhang, X. High Idiosyncratic Volatility and Low Returns: International and Further US Evidence, Journal of Financial Economics, Simulated Performance Disclosure The simulations presented in this paper were created to consider possible results of a Low Volatility strategy. The performance results are simulated (not real) and were achieved by using Invesco s proprietary Stock Selection Model and a third party risk provider. It may not be possible to replicate these results. The simulated results were derived by back-testing and as a result there can be no assurance that these results can be achieved in the future. While the Model was used to reflect the investment process for a Low Volatility strategy, this Model does not factor in all the economic and market conditions that can impact results. The simulated performance returns shown are from 12/31/92 12/31/11. Invesco cannot assure that the simulated performance results shown for the low volatility strategy would be similar to the firm s experience had it actually been managing portfolios using this strategy. In addition, the results actual investors might have achieved would vary from those shown because of differences in the timing and amounts of their investments. The simulated performance is in U.S. dollars and the results do not reflect the deduction of investment advisory fees. Returns shown for this simulation would be lower when reduced by the advisory fees and any other expenses incurred in the management of an investment advisory account. For example, an account with an assumed growth rate of 10% would realize a net of fees annualized return of 8.91% after three years, assuming a 1% management fee. The simulation results include estimates of trading costs; however because these trades have not been executed, results may have under- or over-compensated for these costs. This transaction cost estimate is conservative given expectations and is used to produce more realistic simulation results. 4. The alpha forecasts utilized in the simulated active low volatility portfolio are sourced from Invesco Global Quantitative Equity s proprietary Stock Selection Model. There is no guarantee that simulated results can be realized in the future. 5. David Blitz and Pim Van Vilet, Benchmarking Low-Volatility Strategies, Journal of Index Investing, Vol 2, No. 1, Minimum variance (MV) portfolios were generated monthly from a large-cap universe, with zero alpha and transaction costs. The only constraint was asset bounds of 3%. The MV portfolio was generated each month from cash, with no benchmark, no industry, sector, beta, or style factor constraints, and a risk aversion parameter of The t-statistic is related to the information ratio and tells how significant the information ratio is. It takes into account the time over which the information ratio was achieved. Specifically, the t-statistic of a manager series vs. a benchmark series is the information ratio multiplied by the square root of the number of periods in a year. 8. To calculate the up capture, form a new series from the manager and benchmark series by dropping all time periods where the benchmark return is zero or negative. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The down capture is calculated analogously. 9. Fama, French. The Cross Section of Expected Stock Returns. The Journal of Finance (1992); 10. Carhart, M. On Persistence in Mutual Fund Performance Journal of Finance, Kenneth R. French Website. Monthly factor returns for FF-C four factor market, size, value and momentum - Data Library, U.S. Research Returns, Fama/ French Factors were found in the Data Library For One-On-One US Institutional Investor Use Only All material presented is compiled from sources believed to be reliable and current, but accuracy cannot be guaranteed. This is not to be construed as an offer to buy or sell any financial instruments and should not be relied upon as the sole factor in an investment making decision. As with all investments there are associated inherent risks. Please obtain and review all financial material carefully before investing. This does not constitute a recommendation of the suitability of any investment strategy for a particular investor. The opinions expressed are those of the author, are based on current market conditions and are subject to change without notice. These opinions may differ from those of other Invesco investment professionals. Invesco Advisers, Inc. 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