Realized Volatility Indices: Measuring Market Risk

Transcription

1 December 2015 CONTRIBUTORS Tim Edwards, PhD Senior Director, Index Investment Strategy Craig J. Lazzara, CFA Managing Director, Index Investment Strategy Realized Volatility Indices: Measuring Market Risk Risk is like fire: If controlled it will help you; if uncontrolled it will rise up and destroy you. Theodore Roosevelt The measurement and monitoring of risk is a paramount concern of investment management. In order to provide benchmark references for risk, in December 2015, S&P Dow Jones Indices launched a series of indices measuring the current levels of volatility for a range of global equity and commodity markets. The focus of this paper is the S&P Realized Volatility Index Series, which measure the volatility over various time periods of selected major benchmarks and market segments. The S&P Realized Volatility Indices can be used to analyze broad or specific market risk environments, and they provide a perspective on how the market has reacted to historical events. As an introductory example, Exhibit 1 shows the long-term behavior of the S&P Month Realized Volatility Index, annotated with the events coincident to periods of market turbulence. Exhibit 1: S&P Month Realized Volatility Index Lehman Bankruptcy Cuban Missile Crisis Collapse of Bretton Woods, 1973 Oil Crisis October 19, 1987 Black Monday Early 80s Recession Internet Bubble Debt Bursts, September Ceiling 11 Attacks Crisis Source: S&P Dow Jones Indices LLC. Data from January 1960 to December The S&P Month Realized Volatility Index was launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance.

2 OUTLINE This paper is structured as follows. In Section 1, we describe the basics of volatility and its interpretation as a measure of market confidence, or fear, and we introduce the S&P Realized Volatility Indices. In Section 2, we demonstrate some of the typical properties of realized volatility indices, with a particular focus on simple extrapolations. Sections 3 and 4 discuss the relationship between volatility and returns, while Section 5 outlines some of the potential applications of volatility to investment and risk management. Section 6 contains brief conclusions, while a full list of the realized volatility indices, and some detail on their particular calculation, is provided in the Appendices. 1. VOLATILITY: THE BASICS Among the various measures of risk used to describe and evaluate investments or portfolios, volatility is frequently considered paramount. Indeed, volatility is often used interchangeably with risk, particularly in the context of evaluating risk/return ratios. This widespread use arose, in part, due to the mathematical convenience of volatility; among other applications, it is a key ingredient of modern portfolio theory. However, volatility is more than just a statistical feature; it can be highly meaningful in itself. The fundamental role of volatility is found dually as the measure of movement and the measure of uncertainty in markets and prices. If the level of a benchmark such as the S&P 500 is interpreted as the price of the market, then the volatility of the S&P 500 can be interpreted as the confidence that market participants have in that price. If market participants are uncertain about the future, or if they are prone to alter their view rapidly and comprehensively (in light of emerging earnings reports or central bank announcements, for example), then one might expect large price swings to be commonplace. If, on the other hand, market participants are confident that current prices lie close to their putative fair value, and if those same participants are unlikely to change their views in the short term, then one might expect only small price fluctuations from day to day, absent a material change in circumstances. Thus, the degree to which prices are stable or fluctuating is indicative of the level of confidence shared by market participants. Of note is the transition from backward- to forward-looking measures: volatility is defined by the magnitude of recent moves, which at the time of calculation is derived from historical fact, but it is taken to provide information about the current state of the market s participants, and, by implication, to provide a modicum of insight into their future behavior. 1 This partly explains why volatility is frequently incorporated as the principal measure of risk. Historical Example: Volatility in U.S. Equities During the Debt Ceiling Crisis In August 2011, a debate erupted in the U.S. Congress over a normally esoteric legislative procedure known as raising the debt ceiling. 2 Normally a procedural affair, the process had become increasingly politicized in light of a highly controversial stimulus program, the so-called QE2 program of bond purchases by the U.S. Federal Reserve. As the deadline approached and with differences seeming insurmountable a political dispute escalated into the threat of a default on U.S. Treasury bonds. The potential consequences cast great uncertainty over the financial markets, and the S&P 500 swung wildly over the period. The crisis was resolved, in part, by the Aug. 2, 2011, increase of the debt ceiling. However, the damage to confidence was longer lasting, and on Aug. 5, 2011, 1 2 See Is Volatility Predictive? which follows. The debt ceiling is a legal limit on the gross amount of debt that can be issued by the U.S. Treasury. As expenditures of the U.S. government are authorized by separate legislation, the practical effect of the debt ceiling is to give the U.S. Congress the ability to halt previously approved or promised payments. 2

3 Standard & Poor s Ratings Services 3 downgraded its credit rating on the U.S. Shortly thereafter, on Aug. 9, 2011, the U.S. Federal Reserve announced it would keep interest rates at exceptionally low levels for at least two more years. The market was rocked by the news flow throughout the period, down 7% one day and up 5% the next (see Exhibit 2). Exhibit 2: S&P 500 Performance During the Debt Ceiling Crisis Source: S&P Dow Jones Indices LLC. Data as of November Past performance is no guarantee of future results. Charts are provided for illustrative purposes. Between Aug. 4, 2011, and Aug. 15, 2011, the overall level of the S&P 500 was more or less unchanged; on balance, the events of the period did not change market participants overall outlook. The large price swings evidence the uncertainty of the period. S&P Realized Volatility Indices The levels of the S&P Realized Volatility Indices seek to provide a statistical measure of the magnitude of recent daily moves in a reference index, such as the S&P 500. The indices are updated daily based on the most recently available information, but they are based on more than one day s return for example, the most recent 21 trading days in the case of the indices that measure one-month volatility. S&P Dow Jones Indices calculates its realized volatility indices as the annualized, root-mean-square of daily growth rates for a reference index over a predetermined period, expressed as a number of percentage points. 4 The levels of the realized volatility indices can be interpreted in terms of annual changes: a level of 20 for a realized volatility index, for example, indicates a degree of movement on a daily basis that corresponds, annually, to a volatility of approximately 20%. 5 In calculating volatility, a choice must be made in how far back in history it is to be measured. Obviously, more than one day s changes are required if we are to get a sense of the underlying S&P Dow Jones Indices, a subsidiary of McGraw-Hill Financial, Inc., is a separate entity and operates independently of its affiliate, Standard & Poor s Ratings Services. Readers unfamiliar with the calculation of volatility can find further details in the section Calculating S&P Realized Volatility Indices in Appendix B. Note that volatility is a measure of differences across a sample; it is not the expected change in the level of the index. 3

4 distribution. But there is a range of possible and valid dates, each covering more and older historical price changes. There is no right answer. Shorter-term volatility measures react faster to changes in the environment; longer term measures tend to display the broader trend more clearly and are less susceptible to random biases. Exhibit 3 provides two comparable examples: the S&P Global Month Realized Volatility Index and the S&P Global Month Realized Volatility Index, each reflecting realized volatility on a different timescale for the blue-chip S&P Global Exhibit 3: Two Measures of Volatility in the S&P Global 1200 Source: S&P Dow Jones Indices LLC. Data from January 1991 to December The S&P Global 1200 Realized Volatility Indices were launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. 2. PROPERTIES OF REALIZED VOLATILITY Exhibit 3 demonstrates several common properties of the S&P Realized Volatility Indices, which include the following. They are typically range-bound and mean-reverting indices. Many indices, particularly those tracking investable securities, tend to increase over the long term; in contrast, there is no longterm growth trend associated with volatility. Instead, volatility takes a range of values sometimes elevated, sometimes depressed, and frequently returning to the long-term average. Volatility is subject to occasional precipitous spikes, with a propensity to rise rapidly but to decline much more gradually. More generally, volatility itself is volatile, with shorter-term measures frequently displaying large changes on a day-to-day basis. These properties are not limited to equity volatility; Exhibit 4 demonstrates that many of the same properties can also be found in the commodity markets. 4

5 Exhibit 4: Volatility in the Commodity Markets Source: S&P Dow Jones Indices LLC. Data from March 1971 to December The S&P GSCI 1-Month Realized Volatility Index was launched on Dec. 14, All data prior to those dates are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. Although the levels of the indices in Exhibits 3 and 4 are clearly prone to rapid changes, they also display a degree of persistence, or stability, in overall level. This suggests that current volatility levels may provide a fair estimate of future levels, a phenomenon that is worthy of greater attention and provides the subject for our next section. Is Volatility Predictive? As we stated previously, a critical aspect of realized volatility lies in its description as a historical measure of market sentiment that can be extrapolated into the near future. If we restrict ourselves to the simplest predictive applications, we are asking if the current level of volatility that day s closing level in a realized volatility index is a decent estimate for the future index level. There is a trivial persistence in volatility that should not be confused with its predictive aspects: longerterm measures of volatility do not usually change by much on a day-to-day basis, in part because only a small proportion of their historical inputs change from one day to the next. 6 The key test is a comparison between old and new levels once the new data come to dominate, whether that is the next day, the next month, or the next year. Indeed, the stability in index levels demonstrated in Exhibits 1, 3, and 4 reflects more than just a trivial effect. Market confidence, which ultimately relies on human behavior, typically demonstrates a degree of persistence. More broadly, history shows us that most of the time, the general risk environment one day will be similar to the previous day s. However, from time to time, the risk environment changes dramatically; it is these exceptions that are notable. 6 For example, in a 21-day volatility index, 20/21 of one day s inputs are the same as the previous day s. 5

6 In fact, Exhibits 3 and 4 demonstrate both stability and exceptions: the S&P Global 1200 Realized Volatility Indices and the S&P GSCI Realized Volatility Indices show changes that are rapid and significant such as those that occurred in 2008 without any clear warning. Outside of such spikes, broad periods of persistent trends may be seen. To examine the predictive aspects of volatility in a specific example, Exhibit 5 compares the S&P Month Realized Volatility Index to its level 21 trading days later (the closest possible comparison that avoids any overlap among inputs). Exhibit 5: S&P Month Realized Volatility Index, Non-Overlapping 21-Day Periods Source: S&P Dow Jones Indices LLC. Data from December 1960 to December The S&P Month Realized Volatility Index was launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. Exhibit 5 shows that, in the short term, volatility levels for the S&P 500 were reasonably persistent; in particular, there was a strong historical correlation between the levels of the S&P Month Realized Volatility Index at points in time 21 days apart. Exhibit 6, which provides the correlations of the S&P Month Realized Volatility Index to its subsequent levels over various time intervals, shows that the predictive accuracy decays significantly over time. 6

7 Exhibit 6: S&P Month Realized Volatility Index Serial Correlation Source: S&P Dow Jones Indices LLC. Data from December 1960 to December The S&P Month Realized Volatility Index was launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. As Exhibit 6 demonstrates, at one, two, or five days apart, there was a nearly perfect historical correlation between current and subsequent volatility levels. The first comparison based on distinct data at 21 days apart results in a still-meaningful correlation of 0.67 (as was shown in Exhibit 5). However, by the time 252 trading days had passed approximately one year only a slight correlation remained between current and subsequent levels of volatility. In conclusion, past volatility has provided a meaningful short-term prediction of future volatility for the S&P 500 albeit not perfectly, even in the short term, and with decreasing success in the longer term. A similar conclusion holds for many other markets and indices. The predictive aspects of volatility can be improved upon and indeed industries of academics and practitioners have augmented the field of risk prediction with more sophisticated measures. However, as a first approximation, predicting future volatility with recent historical volatility is a highly tractable and remarkably successful model of market behavior. It is certainly a success by the standards of the general field of market divination. 3. THE RELATIONSHIP OF VOLATILITY CHANGES TO RETURN Although a negative relationship between volatility and return is familiar in practice, 7 there are two aspects that deserve particular emphasis. First, market volatility tends to rise as the market falls a pattern that has led many market participants to consider volatility-linked investments as hedging strategies (see Section 5). Second, relatively high levels of volatility tend to be associated with lower market returns. Note that these two observations are not equivalent: historically, volatility tends to rise precipitously and fall more gradually. Thus, for a considerable proportion of the time that volatility was above average, it was falling. The perspective of volatility as measuring market confidence gives a natural interpretation of the first relationship (between changes in volatility and market returns). As market confidence decreases, the expectation of future volatility increases and, consequently, market participants would theoretically demand a higher return in compensation for their increased risks (if they are acting rationally ). One way to attempt to receive a higher return is to purchase securities at lower prices, and, hence, as volatility increases, one could expect selling pressures and market declines. 7 Edwards, Tim, and Craig J. Lazzara, The Landscape of Risk, December

8 Exhibit 1 may be taken to provide one example of this pattern. Exhibit 7 expands on Exhibit 1 by providing a direct comparison of the data in Exhibit 1 and the level of the S&P 500 during the period. Exhibit 7: S&P 500 and S&P Month Realized Volatility Index Source: S&P Dow Jones Indices LLC. Data from December 1960 to December The S&P Month Realized Volatility Index was launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Charts are provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. The inverse relationship between changes in volatility and index performance is not limited to U.S. equities. Exhibit 8 provides an international example, demonstrating that an inverse relationship frequently occurred between changes in the S&P Japan 500 and the S&P Japan Month Volatility Index. 8

9 Exhibit 8: S&P Japan 500 and S&P Japan Month Realized Volatility Index Source: S&P Dow Jones Indices LLC. Data from December 2003 to December The S&P Japan 500 Index was launched on Dec. 14, The S&P Japan Month Realized Volatility Index was launched on Dec. 14, All data prior to those dates are based on back-tested performance data. Past performance is no guarantee of future results. Charts are provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. Generally, the strength of the negative relationship between equity markets and their volatility varies from market to market and from period to period. Exhibit 8 demonstrates a less obvious connection than Exhibit 7; our choice of the Japanese equity markets for Exhibit 8 was deliberate. Japan has, for the past few decades, been notable for demonstrating one of the weakest such relationships among single-country markets. Nonetheless, even in Japan there remains a negative relationship, particularly at the extremes of the distribution. Another notable exception to the typically negative relationship between return and volatility is found in commodities, in which extremes of volatility can be associated with supply shocks sudden disruptions to supply caused by weather or geopolitical events. Supply shocks tend to be associated with significant price increases, which can lead to a positive relationship between increasing volatility and increasing prices. Exhibit 9 compares the S&P GSCI 3-Month Realized Volatility Index to the S&P GSCI (Excess Return). Occasionally, a positive relationship is discernible; e.g., in the period. 9

10 Exhibit 9: S&P GSCI (Excess Return) and the S&P GSCI 3-Month Realized Volatility Index Source: S&P Dow Jones Indices LLC. Data from December 1981 to December The S&P GSCI Excess Return Index was launched on Dec. 14, The S&P GSCI 3-Month Realized Volatility Index was launched on Dec. 14, All data prior to those dates are based on back-tested performance data. Past performance is no guarantee of future results. Charts are provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. The measured correlation between changes in volatility and returns will depend on the time period as well as on the particular market. Exhibit 10 provides a set of comparisons, displaying the negative correlation between (non-overlapping) 21-day changes in various indices and their realized volatility over a decade ending in Exhibit 10: Correlations Between Indices and Realized Volatility Market or Segment Reference Index Correlation to Respective 1-Month Realized Volatility Index Global Large-Cap Equity S&P Global Emerging Market Equity S&P Emerging BMI U.S. Large-Cap Equity S&P U.S. Small-Cap Equity S&P SmallCap European Equity S&P Europe U.K. Equity S&P United Kingdom Japanese Equity S&P Japan Australian Equity S&P/ASX Indian Equity S&P BSE SENSEX Broad Commodity S&P GSCI Gold S&P GSCI Gold Crude Oil S&P GSCI Crude Oil Source: S&P Dow Jones Indices LLC. Data from December 2005 to December Past performance is no guarantee of future results. Table is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with back-tested performance. 10

11 4. THE RELATIONSHIP OF VOLATILITY LEVELS AND RETURN The interaction between volatility levels and market returns is also important, and it is integral to the importance of volatility in risk management. While the previous exhibits demonstrate an inverse relationship between market performance and volatility trends, it is not easy to tell from those exhibits whether the market is more likely to be rising or falling during periods of elevated volatility levels; both crisis and recovery are associated with longer periods of high volatility. Returning to the U.S. large-cap market for our example, Exhibit 11 plots the negative relationship between the S&P Month Realized Volatility Index and the coincident return of the S&P 500 during the 63-day period over which volatility was measured. Exhibit 11: Negative Correlation Between Volatility Levels and Return in the S&P 500 Source: S&P Dow Jones Indices LLC. Data as of December The S&P Month Realized Volatility Index was launched on Dec. 14, All data prior to that date are based on back-tested performance data. Past performance is no guarantee of future results. Chart is provided for illustrative purposes and reflects hypothetical historical performance. Please see the Performance Disclosures at the end of this document for more information regarding the inherent limitations associated with backtested performance. A trend going from the upper left to the lower right is clearly visible in Exhibit 11, in particular toward the higher end of the volatility range. Otherwise stated, Exhibit 11 demonstrates that the higher the volatility during the period, the more likely the performance of the index was negative, and the greater the losses. As with volatility changes, the strength of the relationship between the level of volatility and the performance of the index varies from market to market and period to period and there are notable exceptions to the rule. However, broadly speaking, both increases in volatility and high levels of volatility are associated with disappointing returns. According to theory, elevated risk levels are supposed to occur in tandem with elevated returns; however, history suggests the opposite. For these reasons alone, monitoring volatility can provide important information to an investment analysis. 11

12 5. FURTHER APPLICATIONS OF VOLATILITY The practical uses of volatility are highly diverse, even at a basic level any brief enumeration cannot hope to be comprehensive. Some important and common uses of volatility include the following. Market timing: Trends and levels in volatility can identify potentially attractive entry or exit points, or otherwise generate trading signals. For a simplified example, the most volatile periods in equities have, in hindsight, frequently identified favorable purchase points for long-term investors 8 a pattern that relates to the mean-reverting nature of volatility and its negative correlation with returns. Asset allocation: The short-term persistence of volatility supports risk-targeting asset allocation strategies. Examples include risk parity, which aims to allocate across assets inversely in proportion to their volatility, and risk control, which aims to deliver a constant level of overall portfolio risk by reducing exposure to assets as their volatility increases. Impact estimation and historical studies: Important events and news tend to generate higher volatility and a greater persistence of those higher levels. As shown in Exhibit 2, volatility may indicate the degree of uncertainty during the period. Understanding the performance of derivatives and hedging strategies: For a range of trading strategies, including options replication and traditional portfolio insurance, realized volatility is a primary driver of realized performance. More broadly, volatility expectations drive valuations of a wide range of derivatives, including options. Direct investment: Increasingly, investors are using ETFs, futures, and other instruments to gain direct exposure to increases or decreases in volatility, particularly in relation to the CBOE Volatility Index (VIX ). The S&P Realized Volatility Indices seek to measure realized volatility, which is different, though closely related. Direct comparisons between investments: All else being equal, particularly if the expected returns are the same, a less volatile asset is typically preferred to a more volatile asset. More generally, a higher ratio of expected return to volatility is usually preferred. 8 Note the difference compared to the previous section: high or increasing volatility levels tend to be associated with falling markets, which in themselves may present an attractive entry point for investors willing to ride out the presiding turbulence. For a further examination of this phenomena, see The Landscape of Risk, Edwards & Lazzara op cit. 12

13 6. CONCLUSIONS With the introduction and publication of realized volatility indices for a wide range of market benchmarks and time periods, S&P Dow Jones Indices aims to provide market participants with transparent measures for the fundamental risks that drive markets. The indices may also provide independent benchmarks for the measurement of market confidence and movement. The indices have wide applications for investors and can contribute to better-informed investment decisions and outcomes. The interplay, evolution, and relative levels of the S&P Realized Volatility Indices could help characterize the balance between confidence and fears within and across markets, providing a more comprehensive viewpoint of the risk and opportunity set at any point in time. APPENDIX A: THE INDICES A full and updated list of indices is available at At time of writing, they include 1-, 3-, 6- and 12-month volatility indices for each (see Exhibit 12). Exhibit 12: Realized Volatility Indices U.S. Equity and Sector Indices Global Indices Commodity Indices S&P 500 S&P BSE SENSEX S&P GSCI S&P MidCap 400 S&P China 500 S&P GSCI Brent Crude S&P SmallCap 600 S&P Emerging BMI S&P GSCI Crude Oil S&P Composite 1500 S&P Europe 350 S&P GSCI Gold S&P 500 Consumer Discretionary S&P GCC Composite Shariah Dow Jones Commodity Index (DJCI) S&P 500 Consumer Staples S&P Global 1200 DJCI Brent Crude S&P 500 Energy S&P Japan 500 DJCI Crude Oil S&P 500 Financials S&P MILA Pacific Alliance Select DJCI Gold S&P 500 Health Care S&P Pan Asia BMI - S&P 500 Industrials S&P South Africa 50 - S&P 500 Information Technology S&P United Kingdom - S&P 500 Materials Dow Jones Global Select RESI Equity - S&P 500 Telecommunication Services - - S&P 500 Utilities - - Dow Jones U.S. Select REIT - - Source: S&P Dow Jones Indices LLC. Table is provided for illustrative purposes. 13

14 APPENDIX B: CALCULATING THE S&P REALIZED VOLATILITY INDICES S&P Dow Jones Indices calculates realized volatility indices as the annualized root-mean-square of daily growth rates for a reference index over a predetermined period, expressed as a number of percent. This section is designed to explain just what is meant by the preceding sentence. 9 A few items of terminology are required before we can get into the details. First, as a practical matter, calculating realized volatility requires a reference the object whose volatility is being measured. This is typically obvious in context: in the case of the S&P Month Realized Volatility Index, the reference index is the S&P 500. Note that we have not specified the total return version; the S&P Realized Volatility Indices use price indices as their underlying reference. Realized volatility requires further specifications: the interval over which price changes are measured, the number of intervals in the period, and the end point of the period. For example, one might specify the daily volatility of the S&P 500 over 63 trading days ending on Oct. 15, For the S&P Realized Volatility Indices, the interval is always a trading day in the reference index. Finally, one month is not a fixed length of time a longer period is captured by January than February. In order to compare like with like, S&P Dow Jones Indices uses 21 trading days to represent one month, and a corresponding multiple of 21 trading days to represent two months, three months, and so on, up to 252 trading days for a year. The next step is to determine how the change in the level of the index from one day to another is measured. There are two natural options: the percentage change and the continuous growth rate that results in that percentage change. The former is more familiar and easy to calculate, but the latter interacts more sensibly when comparing time periods of differing magnitudes. In the S&P Realized Volatility Indices, the daily index price change is measured as a growth rate, specifically the natural logarithm of price changes. Once the series of daily price changes in the reference index is aggregated, one must convert this series into a single number representing volatility. One option is to calculate the standard deviation of daily changes, which is one common measure of variation. However, standard deviation does not quite capture the sentiment we are looking for. If, for example, the market rises by close to 5% every day for a week, the standard deviation of daily moves during the week will be low, as each day s return was close to the average. Yet, the degree of movement in the market was unusually high, which would correspond to our comprehension of high volatility. The root-mean-square calculation is the alternative, which is equivalent to calculating standard deviation assuming a mean of zero. This alternative counts large price changes as such, even if they are close to the average for the period in question. For the S&P Realized Volatility Indices, the root-mean-square of daily changes is applied to calculate volatility. The next step in the calculation is to annualize the figure; in principle, converting daily movements into annual equivalents. The root-mean-square of daily returns is converted to an annual volatility by multiplying by the square root of 252, approximately the number of trading days in a normal year. The method used to annualize volatility is an approximation; many securities show a greater volatility in the long term than might be deduced from their short-term behavior, and vice-versa. Nonetheless, annualizing data in this way allows us to compare the risk of one asset to the risk of another over potentially different time periods. Finally, the resulting number is multiplied by 100, converting a percentage figure into a value, never less than zero and typically less than Further details are provided in the index methodology: 14

15 ABOUT S&P DOW JONES INDICES S&P Dow Jones Indices LLC, a part of McGraw Hill Financial, Inc., is the world s largest, global resource for index-based concepts, data and research. Home to iconic financial market indicators, such as the S&P 500 and the Dow Jones Industrial Average TM, S&P Dow Jones Indices LLC has over 115 years of experience constructing innovative and transparent solutions that fulfill the needs of institutional and retail investors. More assets are invested in products based upon our indices than any other provider in the world. With over 1,000,000 indices covering a wide range of assets classes across the globe, S&P Dow Jones Indices LLC defines the way investors measure and trade the markets. To learn more about our company, please visit LIKE WHAT YOU READ? Sign up to receive updates on a broad range of index-related topics and complimentary events. 15

16 PERFORMANCE DISCLOSURES The S&P Japan 500 was launched on Dec. 19, The S&P Global Month Realized Volatility Index, the S&P Global Month Realized Volatility Index, the S&P GSCI 1-Month Realized Volatility Index, the S&P GSCI 3-Month Realized Volatility Index, the S&P GSCI 12-Month Realized Volatility Index, the S&P Month Realized Volatility Index, the S&P Month Realized Volatility Index, the S&P Month Realized Volatility Index, and the S&P Japan Month Realized Volatility Index were launched on Dec. 14, However, it should be noted that the historic calculations of an Economic Index may change from month to month based on revisions to the underlying economic data used in the calculation of the index. Complete index methodology details are available at It is not possible to invest directly in an index. S&P Dow Jones Indices defines various dates to assist our clients in providing transparency on their products. The First Value Date is the first day for which there is a calculated value (either live or back-tested) for a given index. The Base Date is the date at which the Index is set at a fixed value for calculation purposes. The Launch Date designates the date upon which the values of an index are first considered live: index values provided for any date or time period prior to the index s Launch Date are considered back-tested. S&P Dow Jones Indices defines the Launch Date as the date by which the values of an index are known to have been released to the public, for example via the company s public website or its datafeed to external parties. For Dow Jones-branded indicates introduced prior to May 31, 2013, the Launch Date (which prior to May 31, 2013, was termed Date of introduction ) is set at a date upon which no further changes were permitted to be made to the index methodology, but that may have been prior to the Index s public release date. Past performance of the Index is not an indication of future results. Prospective application of the methodology used to construct the Index may not result in performance commensurate with the back-test returns shown. The back-test period does not necessarily correspond to the entire available history of the Index. Please refer to the methodology paper for the Index, available at for more details about the index, including the manner in which it is rebalanced, the timing of such rebalancing, criteria for additions and deletions, as well as all index calculations. Another limitation of using back-tested information is that the back-tested calculation is prepared with the benefit of hindsight. Back-tested information reflects the application of the index methodology and selection of index constituents in hindsight. No hypothetical record can completely account for the impact of financial risk in actual trading. For example, there are numerous factors related to the equities, fixed income, or commodities markets in general which cannot be, and have not been accounted for in the preparation of the index information set forth, all of which can affect actual performance. The Index returns shown do not represent the results of actual trading of investable assets/securities. S&P Dow Jones Indices LLC maintains the Index and calculates the Index levels and performance shown or discussed, but does not manage actual assets. Index returns do not reflect payment of any sales charges or fees an investor may pay to purchase the securities underlying the Index or investment funds that are intended to track the performance of the Index. The imposition of these fees and charges would cause actual and back-tested performance of the securities/fund to be lower than the Index performance shown. As a simple example, if an index returned 10% on a US $100,000 investment for a 12-month period (or US $10,000) and an actual assetbased fee of 1.5% was imposed at the end of the period on the investment plus accrued interest (or US $1,650), the net return would be 8.35% (or US $8,350) for the year. Over a three year period, an annual 1.5% fee taken at year end with an assumed 10% return per year would result in a cumulative gross return of 33.10%, a total fee of US $5,375, and a cumulative net return of 27.2% (or US $27,200). 16

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