Volatility - The Good, the Bad, and the Ugly
By Rob Brown, PhD, CFA
I. Introduction The 1966 Italian epic spaghetti western “The Good, the Bad and the Ugly,” starred Clint Eastwood as “Blondie” (The Good), Lee Van Cleef as “Angel Eyes” (The Bad), and Eli Wallach as “Tuco” (The Ugly)1. I draw the analogy between this piece of Americana and a discussion of volatility because in both cases there is a highly nuanced storyline and the characters play ambiguous, overlapping, but nevertheless distinct roles – for better, worse, or terrible.
Volatility has been one of the most prominent topics among institutional investors and their investment managers since the advent of The Great Dislocation2. This dialogue was recently reenergized by volatility’s several-fold increase resulting from the global contagion3 emanating out of Europe. As Greece found itself unable to refinance its government debt and the market vigilantes questioned the viability or relative attractiveness of the Euro currency, the VIX soared from 15.6 in April to 45.8 in May.
It is generally said that hedge funds, on average, are exposed to “short volatility.” The meaning of this statement is that if volatility were to spike upward by enough within a sufficiently short time period, hedge funds would deliver negative returns – potentially severely negative returns. How could hedge funds convey “short volatility?” In effect, this would mean that hedge funds were selling insurance against rare and isolated extreme negative events. Recall that sellers of insurance must pay out claims when catastrophe strikes, i.e., they experience losses. Now, I don’t mean that hedge funds are literally or directly selling insurance – only in the most indirect and fuzzy sense. But the analogy holds and it holds quite strongly.
1“The Good, the Bad and the Ugly” is a 1966 Italian epic spaghetti western film directed by Sergio Leone, starring Clint Eastwood, Lee Van Cleef, and Eli Wallach. The movie was first released in Italian (Il buono, il brutto, il cattivo) in Italy in 1966 and later in English in the U.S. in 1967. 2 “The Great Dislocation” refers to the global economic decline and associated financial markets upheaval that felt its first initial tremors in 2007, its major collapse in 2008, and continues through today. 3 The recent global contagion was first initiated on April 23, 2010. During the 14 day period spanning April 23, 2010 through May 7, 2010, inclusive, the Russell 2000 returned -18.835%, High Yield CDX returned -5.979%, and Investment Grade CDX earned -1.802%. The VIX closed at 15.58 on April 12, 2010 and at 45.79 on May 20, 2010.
II. You are exposed to volatility Let’s step back for a moment and remind ourselves of what hedge funds are. They are a direct alternative to traditional vanilla long-only managers. Hedge funds exist because they provide a more distilled, concentrated and more efficiently structured mechanism for obtaining exposure to active management bets (alpha, out-performance relative to some predetermined benchmark). But, unfortunately, they also carry, embedded within themselves, exposure to something else. Hedge funds also expose the investor to certain factor exposures (e.g., interest rates, credit spreads, commodities, or equity risk premia)4. One of the factors that almost all hedge funds are exposed to is volatility.
Some factor exposures are easier to understand and evaluate than others. Domestic interest rates are reasonably well defined by the U.S. Treasury bond term structure and by the parallel interest rate term structures within the derivatives markets. Unfortunately, volatility is one of the most difficult factors to identify, evaluate, or understand.
Perhaps an analogy will help. Consider the difference between a broken bone and cancer. A broken bone is simple, straightforward and is cured with well-defined and well-understood remedies. In contrast, cancer spans a vast array of only vaguely related maladies whose causality (much less treatment) is poorly understood. Interest rates are like the broken bone, volatility is like cancer. We have a tendency to speak of volatility as if it were one thing, behaving in a well- defined sense. But it is not one phenomenon, but many behaviors that are only loosely related, poorly understood, and only partially treatable – some of which, as seen below, may actually be beneficial in a perverse way (think of Clint Eastwood in The Good, the Bad and the Ugly).
Nevertheless, we can appreciate some of volatility’s most obvious characteristics. Recall my earlier reference to how exhibiting short volatility is potentially analogous to selling insurance. Carry this analogy a bit further. The insurance industry has always experienced three distinctly different levels of profitability:
1. They experience quite attractive profitability during normal periods (the vast majority of the time). The Good. 2. They experience unappealing, disappointing profitability during extended periods of quiescence (something that happens only occasionally) as a result of increased, and sometimes unbridled competition. The Bad.
3. And, they experience terrible losses when disaster strikes on a major scale (this is a rare event). The Ugly.
4 Hedge funds are not a separate or distinct asset class. They do not bring a unique or differentiated factor exposure to the investor. Nothing about them in anyway suggests that they have any basis for being identified as a separate asset class. Historically, hedge funds have exhibited three identical phases – the good, the bad, and the ugly. The following exhibit identifies the three faces of volatility.5
The three faces of volatility
GOOD BAD UGLY
82.2% of the time 9.0% of the time 8.8% of the time
Normal times of not too much and not too Long quiescent periods of exceptional Extreme and exceptional idiosyncratic little volatility quiet and serenity volatility
Highly attractive hedge fund returns Poor unattractive hedge fund returns Painful hedge fund returns
Statistics based on hedge fund returns spanning the time period 02.01.1977 through 04.30.2010
III. Volatility’s impact on hedge fund returns To make this discussion a bit more specific, we need to examine the data. This will require adopting a specific definition of volatility. Again, let me remind the reader of the dangers inherent in such a definition: it approximates the gross oversimplification entailed when one intends to discuss the overarching behaviors of and treatments for cancer, but focuses on only a single type, e.g., melanoma.
Nevertheless, for this discussion, I restrict myself to the volatility of S&P 500 daily returns.6 The following graphic shows how S&P 500 volatility has changed over the last 33+ years.
5 Hedge fund returns are based on the HFRI Fund Weighted Composite Index provided by Hedge Fund Research Inc. This is an equal-weighted index of individual hedge funds and is the most comprehensive index that HFRI provides. It was last updated on May 17, 2010, and covers the time period from 01.01.1990 through 04.30.2010. For the time period spanning 02.01.1977 through 12.31.1989, hedge fund returns were provided by the HFN Hedge Fund Aggregate Index provided by HFN HedgeFund.net. This is an equal-weighted index of individual hedge funds and is the most comprehensive index that HFN provides. It was last updated on May 22, 2010, and as of that date reflected the returns of 4,889 individual hedge funds. 6 Characteristically, alpha (out-performance) is not so much affected by the absolute level of volatility, but instead tends to be more powerfully driven by changes in the level of volatility. For this reason we use the proportionate percentage change in daily volatility for the current month relative to its average level over the two prior months. In all cases the daily returns of the S&P 500 Index were used to make these calculations. As a result, the measure of volatility that was used throughout this article was more specifically defined by: “The percentage change in the annualized standard deviation of daily returns over the current month relative (in a proportionate percentage) to the average of the annualized standard deviation of daily returns over the two prior months.” Measure of monthly volatility over the last 33+ years
Oct ‘87 Black Monday. Financial panic of 1987 413 Oct ‘00 USS Cole Yemen bombing. Argentine economic crisis. Energy price crisis Jan ‘00 335 Oct ‘89 Y2K crisis. Dot‐com mania accelerates. n) Non‐proliferation treaty crisis o
i Savings and loan t a i crisis. Keating five v de
d r 257 Aug ‘98 Sep & Oct ‘08 US embassy bombings
nda Lehman Brothers collapses. a
t Aug ‘82 Africa. Russian financial The “Great Dislocation” s Latin American debt crisis. Russia defaults in
e crisis. Mexico’s ng 178 liquidity crisis ha c (
Aug ‘90
y Iraqi invasion of ilit
t Kuwait. Persian a l
o Gulf crisis v 100 of
e ur s a Me 22
‐57 Feb Apr 1977 2010 When this measure of domestic stock market volatility is compared to the performance of the hedge fund universe7 since February 1977, volatility explains 11% of hedge fund returns – that’s a pretty big portion8, providing us with a strong indication as to volatility’s critical importance.
We can obtain a better understanding of the negative contribution resulting from volatility if we strip out its effect from historic hedge fund returns. The following exhibit9 shows the probability
7 The hedge fund returns are based on the HFRI Fund Weighted Composite Index provided by Hedge Fund Research Inc. This is an equal-weighted index of individual hedge funds and is the most comprehensive index that HFRI provides. It was last updated on May 17, 2010, and covers the time period from 01.01.1990 through 04.30.2010. For the time period spanning 02.01.1977 through 12.31.1989, hedge fund returns were provided by the HFN Hedge Fund Aggregate Index provided by HFN HedgeFund.net. This is an equal-weighted index of individual hedge funds and is the most comprehensive index that HFN provides. It was last updated on May 22, 2010, and as of that date reflected the returns of 4,889 individual hedge funds. 8 When one completes a simple ordinary least square regression of monthly hedge fund returns on the measure of volatility described in Footnote 6, it is found that the R-Squared statistic is approximately 0.11 (I am them imposing the interpretation that this implies that approximately 11% of the variation of returns is being explained by the volatility measure used.) It is also noteworthy that the t-Statistic for volatility is 6.99 and the P-Value for volatility is 0.000000. 9 This table shows what the probability was of earning a hedge fund return equal to or worse than the percentage return indicated during any randomly selected window consisting of 12 consecutive months. These results were calculated by bootstrapping the existing data set to create a time series consisting of 12,000 months, which preserved all of the multi-dimensional time series attributes of the original time series. A similar procedure was followed for the hedge fund returns but with the impact of volatility stripped out. The removal of the impact of volatility was based on the factor loading given to the volatility measure from the regression described in Footnote 8. of earning less than a certain return, “X%,” during a randomly selected 12-month window. Note how the removal of the S&P 500 volatility factor exposure from hedge fund returns significantly reduces their probability of experiencing an extreme negative outcome.
Frequency (probability) with which losses GREATER THAN "X%" occurred during any 12‐month window
Losses greater than . . . ‐11% ‐10% ‐9.5% ‐6% ‐5.5% ‐4% ‐3.5% ‐3% ‐2.5% ‐2% ‐1% ‐0.5% 0%
Hedge fund composite 2.0 2.3 2.5 2.8 3.0 3.3 3.8 4.5 5.3 5.8 6.8 7.5 8.0 index
Hedge fund composite index with "Volatility" 1.0 1.3 1.5 1.8 2.3 2.5 2.5 2.8 3.0 3.3 4.3 4.5 5.0 stripped out
Statistics based on hedge fund returns spanning the time period 02.01.1977 through 04.30.2010
But as with the insurance industry analogy, volatility is a multi-faceted creature. It is not all bad. Although Blondie, Angel Eyes, and Tuco were all gunslingers seeking confederate gold, one of them was “The Good.”
During long, extended periods of exceptional quiescence, hedge fund returns do disappear. Recall that hedge funds deliver attractive returns because they are successful with the harvesting of mispricings and dislocations within the marketplace (no matter the nature of their source or causality). But just as the most talented, best equipped fisherman, even if he’s fishing in the best spot within the ocean, will return home unrewarded with a poor catch – if there are no fish in the ocean to harvest.
Thus, even the most talented, best equipped hedge fund manager, even if he’s investing within the best possible market niche, will return home unrewarded and with little or no returns – if there are no mispricings or dislocations to exploit. Those somewhat rare, long, extended periods of quiet, limited volatility are directly associated with the evaporation of marketplace mispricings – the food that hedge funds feed off of. We need disruptions to
restock markets with new mispricings. The following table10 shows how hedge funds have performed, on average, during:
1. The most quiescent 2-year period, 2. The most quiescent 3-year window, 3. Extreme peaks in volatility, and
4. Normal times.
Volatility has three faces The Good, the Bad, and the Ugly
Return (average annual Duration (how long did Coverage (time geometric mean) this last) period covered)
2‐year period when markets were the Bad most quiet and serene (from a volatility 11.0% 24 consecutive months Aug '02 ‐ Jul '04 standpoint) 3‐year period when markets were the Bad most quiet and serene (from a volatility 11.3% 36 consecutive months Aug '02 ‐ Jul '05 standpoint) Extreme and exceptional volatility (35 Ugly specific months of most extreme ‐83.3% 35 idiosyncratic months Feb '77 ‐ Apr '10 volatility) All of the rest of the time (not quiet and Good serene, but also not extremely 23.2% 328 months Feb '77 ‐ Apr '11 exceptional)
Statistics based on hedge fund returns spanning the time period 02.01.1977 through 04.30.2010
We must be careful while interpreting the average annual returns appearing in the table above. This return data suffers from a significant level of selection and survivorship bias, which causes the hedge fund returns to look better than they really were. There is no way of knowing what the extent of this bias was, but one might make a crude adjustment downward, by subtracting perhaps 10% from each number. With this adjustment, the returns to hedge funds during the two- or three-year window of serene quiescence come out “Bad.”
10 This table shows the annualized returns (average annual geometric mean return) for the four different time periods indicated. It is important to note that only the first two rows are for contiguous time periods. The last two rows report statistical results for non- contiguous time periods. It is critical to appreciate that the returns for hedge funds reported in this table suffer from extreme selection and survivorship bias and therefore appear to be far higher than would realistically be the case. However, the objective of this table and article was to draw relative comparisons and there exists no reason to believe that these relative comparisons have been biased by the selection and survivorship biases.
Corrected for selection and survivorship bias, Volatility has three faces The Good, the Bad, and the Ugly
Return (average annual Duration (how long did Coverage (time geometric mean) this last) period covered)
2‐year period when markets were the Bad most quiet and serene (from a volatility 1.0% 24 consecutive months Aug '02 ‐ Jul '04 standpoint) 3‐year period when markets were the Bad most quiet and serene (from a volatility 1.3% 36 consecutive months Aug '02 ‐ Jul '05 standpoint) Extreme and exceptional volatility (35 Ugly specific months of most extreme ‐93.3% 35 idiosyncratic months Feb '77 ‐ Apr '10 volatility) All of the rest of the time (not quiet and Good serene, but also not extremely 13.2% 328 months Feb '77 ‐ Apr '11 exceptional)
Statistics based on hedge fund returns spanning the time period 02.01.1977 through 04.30.2010
Thankfully, “The Good” times have historically occurred 82.2% of the time. During such periods, markets provide not too much and not too little volatility – allowing hedge funds to avoid paying off on the insurance that they are short (sold) while still operating within a market environment that continually restocks mispricings and dislocations.
IV. How should one deal with volatility? We have no control over the environment. Therefore, we will inevitably enter a long period of extended quiescence during which hedge fund returns are poor and unappealing as mispricings become scarce. This occurred once before during the last 33+ years, and will happen again. There is nothing to be done other than to question whether one should attempt to adjust one’s allocation to active management bets (both in terms of percentage and potency) in line with their estimates as to the size and number of mispricings or dislocations within markets (number of fish in the sea). The greater the preponderance of marketplace mispricings, the larger one’s allocation to hedge funds should be.
As regards those rare extremes in volatility – as the Athenian general and statesman, Pericles, commented: “The key is not to predict the future, but to be prepared for it.” 11 The likelihood of one being able to predict, before the fact, the occurrence of extreme and exceptional volatility is probably akin to an expert’s ability to forecast earthquakes before the fact. We know they’re
11 The quotation “The key is not to predict the future, but to be prepared for it” is attributed to a noted general and statesman of Athens, Pericles who is believed to have lived from 495 to 429 BC. coming, we just don’t know when or how bad they’ll be. As complex and confusing as volatility is, we can prepare for the incidence of Tuco (The Ugly).
Sufficiently effective volatility mitigating derivative instruments exist today with more than adequate pricing efficiency, market liquidity, and counterparty coverage. But we have to be careful. If one attempts to totally strip out any and all exposure to losses greater than “X%,” no matter their cause, i.e., perfectly eliminating the left-hand tail – then the cost of such a risk- eliminating strategy will be tragically prohibitive. The practical, prudent approach is to protect against some but not all tail risks. Specifically, one should only mitigate those left-hand tail risks that are not expected to come back (be reversed) with an extremely high degree of certainty. In estimating such “high degrees of certainty,” end-of-the-world type scenarios have to be left out of the analysis. Examples of left-hand tail events one shouldn’t mitigate against could include transitory and temporary demands for liquidity, forced selling, or forced deleveraging, which inevitably will be fully reversed. A perfectly hedged convertible bond position that had stripped out all exposure to interest rates, credit spreads, equities, and realized volatility provides an example. A bond basis trade consisting of a long bond and a long perfectly matched CDS position provides a second example. Both of these trades can and do fall victim to transitory and temporary demands for liquidity, forced selling, or forced deleveraging. But, so long as the trades can be maintained in their original form, such risks will inevitably be reversed. Tail risk exposures of this type should not be mitigated.
Finally, the effective protection against rare extremes in volatility must fully reflect its cancer- like attribute for taking on a multitude of different expressions – each requiring a different remediation effort. The following graphic12 shows how different asset categories experienced volatility extremes are highly differentiated points in time.
12 For this table, the seven asset categories were defined by daily returns for the: S&P 500, Russell 2000, Barclays U.S. Treasury Bond Composite, Barclays Capital U.S. Corporate Credit Baa-rated Index, JP Morgan Commodity Curve Index Energy Light Aggregate Index, JP Morgan Global Aggregate Bond Index, and the JP Morgan Diversified Emerging Country Debt Index. In each case, the volatilities used to construct this exhibit reflect the change in the absolute level of volatility using the exact same methodology as described in Footnote 6.
Volatility strikes different markets at different times
Aug S&P 500 Oct & Sep '08 Oct '00 Jan '00 '98
US SmallCap ‐ Aug Oct '08 Jan '00 Oct '97 Russell 2000 '98
Oct & US Treasury Bond Sep Sep Sep Jun '95 Composite '08 '01 '98
US Corporate Aug Oct '08 Jun '07 Jan '01 Jun '95 Credit Baa‐Rated '98
Commodities ‐ Sep May Apr '96 Jan '96 Energy Light '01 '94
Oct & Global Aggregate Jun '07 Jan '01 Sep Jun '95 Bond '98
Emerging Country Aug Oct & Sep '08 Oct '97 Debt '98
Based on daily returns spanning the time period 02.28.1994 through 05.20.2010
June 1995 was associated with the Oklahoma City Bombing and critical developments of the Mexican Peso Crisis. These events resulted in a rare, extreme spike upward in the volatility of the U.S. Treasury, corporate credit, and global bond markets. If one had used S&P 500 volatility tools to mitigate this risk, he would have been partially disappointed as to the effectiveness of his hedge.
V. Conclusion Volatility is a critical issue. Historically it has explained approximately 11% of hedge fund returns (on a proportionate basis). But more importantly, during periods of the most extreme and exceptional volatility, hedge fund returns have absolutely cratered. Thankfully, effective volatility hedging instruments exist that can be cost effectively applied to mitigate part of these left-hand tail events. Nevertheless, their application must be handled with care, lest long-term returns be unduly undermined. It is probably sufficient to restrict one’s risk mitigation to a sub- set of the potential volatility-induced risks. Ideally, one offsets only those tail events that are not expected to recover (be reversed) with an extremely high degree of certainty. Such events would typically be the result of temporary structural market dislocations. Overly simplified views of volatility characterize high volatility as bad and low volatility as good. This one-dimensional view is incorrect. It far more closely follows the three dominant personalities who define The Good, the Bad and the Ugly.
Rob Brown, PhD, CFA Managing Director of Investment Strategy and Research Benchmark Plus Management, LLC Tacoma, WA 98402 Office 253.573.0657 Ext 125 Cell 818.879.3956 [email protected]