FEBRUARY 2012
KEY TOOLS FOR HEDGING AND TAIL RISK MANAGEMENT
Tail Risk in the Past 25 Years: Since mid-1986 the worst monthly declines for select indexes include: down 28.2% for the S&P GSCI
Index, down 21.5% for S&P 500, down 20.2% for MSCI EAFE, and a decline of only 8.6% for the CLL Index (Exhibit B).
Tail Risk and Diversification in 2008: Changes for indexes in 2008 -
S&P 500 ® down 37.0%; two indexes with options and stocks - CLL down 23.6% and VXTH SM down 19.3%; three futures-based indexes
(with no stock positions) -- VXMT, DyVX and VTRsk, respectively increased 83.9%, 132.3% and 174.3% (Exhibit A).
SM
Lower Volatility: The CLL has incurred about 70% of the volatility of the S&P 500 over the last 26 years. Select portfolios with the VXTH and the future-based indexes have had less volatility than the S&P 500 over the last 70 months (Exhibits C, F, and O).
Enhanced Returns for Portfolios: Portfolios with small allocations to the futures-based indices and the VXTH had higher returns (and lower volatility) than the S&P 500. The annualized returns over the past 70 months were 2.4% for the S&P 500; 3.4% for a portfolio of 20% VXTH and 80% S&P 500; and 6.0% for a portfolio of 10% VTRsk (or 10%
DyVX) and 90% S&P 500 (Exhibits I and O).
Higher Risk-adjusted Returns: Certain portfolios with the VXTH and the future-based indexes have had a higher Sortino Ratio than key stock indices over the last 70 months (Exhibits F and L).
This article analyzes five benchmarks that are designed to provide protection during declining equity markets (visit www.cboe.com/benchmarks and www.spvixviews.com/indices for more details).
Exhibit A: Benchmark Indexes
Price History
Begins
2008
Annual % Return
2009 2010 2011 Index
CBOE S&P 500 95-110
Collar Index (CLL)
CBOE VIX Tail Hedge
Index (VXTH)
S&P 500 VIX Mid-term
Futures Index (VXMT)
S&P 500 Dynamic VIX
Futures Index (DyVX)
S&P 500 VIX Futures Tail
Risk Index - Short Term
(VTRsk)
S&P 500 Index
(Total Return)
Ticker
(Bloomberg)
CLL
<Index>
VXTH
<Index>
SPVIXMTR
<Index>
SPDVIXT
<Index>
Options or Futures Position(s)
Buys three-month out-of-the-money S&P 500 put options at 95% of the S&P 500 value. Sells one-month out-of-the-money S&P 500 call options at 110% of the S&P 500 value.
Buys one-month 30-delta VIX call options. The weight of the VIX calls in the portfolio varies at each roll depending on the perceived likelihood that a "black swan" event could occur in the near future.
Buys a combination of VIX futures positions in order to reflect the expectations of the VIX
Index level in 5 months. Some of the VIX futures are rolled daily in order to maintain a constant average weighted five-month term.
Buys a combination of VIX futures positions in order to reflect dynamic allocation between the S&P 500 Short-Term VIX Futures Index and S&P 500 Mid-Term VIX Futures Index. The rules-based allocation is done with the goal of aiming to lower the roll cost of investments linked to future implied volatility.
SPVXTRST
<Index>
Calculated using a weight of 45% of 2x the S&P VIX Short-Term Futures Index and 55% of the Inverse S&P 500 Short-Term Futures Index. The goal of the index is to provide a long volatility exposure whose cost is partially or completely mitigated (due to negative roll yield) via a rebalanced short exposure.
Hold stocks?
S&P 500
S&P 500
No stocks
No stocks
No stocks
SPTR
<Index>
None S&P 500
June 1986
March 2006
Dec. 2005
Dec. 2005
Dec. 2005
Jan. 1970
-23.6% 17.6% 4.1%
-19.3% 16.0% 21.1%
83.9% -23.6% -13.2% -7.6%
132.3% 0.7% 20.7%
174.3% -21.0% -3.0%
-37.0% 26.5% 15.1%
-8.8%
5.9%
8.8%
10.1%
2.1%
Exhibit B: Histogram with Frequency of Monthly Returns for
CLL and S&P 500 (July 1986 - January 2012)
Exhibit C: Returns and Volatility (July 1986 – January 2012)
140
S&P 500
CLL
137
124
10%
120
100
CLL had only 1 month with losses of 8% or below.
103
9%
20% BXM
10% BXM
S&P 500
10% CLL
20% CLL
80 73
8%
MSCI EAFE
60
59
40
40
26
24
S&P GSCI
20
1 0 1 0 1 0
10
1
11
2 1 0 0 0 0 0
7%
Russell 2000
0
6%
12% 14% 16% 18%
Standard Deviation
20% 22%
Exhibit B: Since mid-1986 the worst monthly declines for select indexes include: down
28.2% for the S&P GSCI Index, down 21.5% for S&P 500, down 20.2% for MSCI
EAFE, down 17.4% for BXM, and a decline of only 8.6% for CLL Index.
Exhibit C : The portfolio with an allocation of 20% BXM and 80% S&P 500 had a return of 9.2% and standard deviation of 14.8%. For more analysis, please see our January
2012 paper on index option writing at www.cboe.com/benchmarks
Sources for all Exhibits on this page: Bloomberg, Ibbotson, ACG.
Asset Consulting Group 231 South Bemiston Avenue, 14th Floor ♦ Saint Louis, Missouri 63105 ♦ 314 862 4848 1

FEBRUARY 2012
KEY TOOLS FOR HEDGING AND TAIL RISK MANAGEMENT
VXTH AND CLL (April 2006 - January 2012)
Exhibit D: Growth of $1 for VXTH, CLL and S&P 500 Indexes
(April 2006 - January 2012)
$1.60
$1.40
VXTH $1.46
$1.20
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
S&P 500 $1.15
CLL $0.96
Exhibit E: Histogram with Monthly Returns for VXTH and S&P
500 Indexes (April 2006 - January 2012)
40
35
S&P 500
VXTH
30
30
29
25
20
15
10
5
0
The worst monthly declines were down 15.1% for S&P 500 and down 10.7% for VXTH.
0 0
1
0 0 0
4
3
8
6
14
19
9 9
4 4
0 0 0 0 0 0
Exhibit D: The growth in the value of a dollar invested on March 31, 2006. The VXTH has outperformed the S&P 500 since inception.
Exhibit F: Metrics for Returns, Risk, and Risk-adjusted Returns
(April 2006 - January 2012)
April 2006 - January 2012
R
Standard Deviation
Beta vs. Market
S
K e k u t e u w o r s n n e s s tr i s
Sharpe Ratio
Semi-Standard Deviation
Sortino Ratio (MAR=Cash Eq.)
Jensen's Alpha vs. S&P 500
Correlation to S&P 500
S&P 500
2 .
3 7 % -
MSCI
EAFE
0 .
3 1 % 4
S&P
GSCI
.
5 1 % 0
CLL
.
7 3 %
VXTH
6 .
6 7 %
17.72% 21.41% 26.46% 11.45% 14.50%
-
1.00
0
0
.
.
6
9 6
0.12
3
1.11
0
-
.
0 .
9
6
7
0.01
-
0.83
.
7 4
1
0
.
8 6
-0.1
-
0.60
.
2 9
-
0
0 .
6
-0.16
0
0 .
0.59
.
4 1
2 9
0.4
13.5%
0.30
0.00%
1.00
16.1%
0.13
20.3%
-0.05
8.4%
-0.01
-2.15% -4.53% -3.12%
0.92
0.55
0.92
10.8%
0.78
4.49%
0.72
Exhibit E: Since April 2006 the VXTH had only 9 months with losses of 4% or below versus 13 months for the S&P 500. Conversely, the VXTH participated in 42 of the 43 positive months indicating upside participation as well as cushioning declines.
Exhibit G: Changes for 5 Indexes in Months in Which S&P 500 had Big Moves (More than 8.8%)
Sep 2010
Apr 2009
Oct 2011
S&P
500
MSCI
EAFE
(April 2006 - January 2012)
S&P
GSCI CLL VXTH
Oct 2008 -16.8% -20.2% -28.2% -3.8% 6.1%
Feb 2009 -10.6% -10.3% -6.1% -5.4% -10.7%
Sep 2008 -8.9% -14.5% -12.4% -6.8% -2.3%
8.9% 9.8% 8.5%
9.6% 12.8% -0.9%
10.9% 9.6% 9.7%
5.4%
5.6%
4.9%
8.1%
8.6%
9.1%
Exhibit F: The VXTH index had risk-adjusted performance that was superior to that of the S&P 500 per metrics such as the Sortino Ratio, Sharpe Ratio and Jensen’s Alpha.
Please note that the above indices had negative skewness, and the measures of risk-adjusted returns are imperfect when measuring non-normal distributions.
Exhibit H: “Over - Under” Chart with Returns Relative to S&P
500 (April 2006 - January 2012)
20
15
10
5
In the 4th quarter, 2008, the
VXTH increased 0.16% versus a decline of 22% for the S&P 500.
Exhibit G: The CLL and the VXTH provided a cushion during the worst three months for the S&P 500 and MSCI EAFE since April, 2006. The trade-off is reduced upside participation in the three best months.
Exhibit I: Return and Volatility (April 2006 - January 2012)
4%
3%
20% VXTH
10% VXTH
2%
20% CLL
S&P 500
10% CLL
Russell 2000
0
-5
1%
-10 0%
-15
CLL
VXTH
-20
-25 -20 -15 -10 -5 0
S&P 500
5 10 15 20 25
Exhibit H: The CLL cushion during declines is clear and compelling while the upside participation is somewhat moderated based on the underlying option exposures.
MSCI EAFE
-1%
14% 16% 18% 20%
Standard Deviation
22% 24%
Exhibit I : The portfolio with an allocation of 20% VXTH and 80% S&P 500 had a return of 3.4% and standard deviation of 16.4%.
Sources for all Exhibits on this page: Bloomberg, Ibbotson, ACG.
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FEBRUARY 2012
KEY TOOLS FOR HEDGING AND TAIL RISK MANAGEMENT
VXMT, DyVX, AND VTRsk (April 2006 - January 2012)
Exhibit J: Growth of $1 for VXMT, DyVX, VTRsk and S&P 500
Indexes (March 31, 2006 – January 31, 2012)
$6.00
Exhibit K: Correlations of Weekly Changes for Select Indexes
(April 7, 2006 - February 3, 2012)
$5.00
DyVX $4.78
S&P
500
VIX
(Spot) VXMT DyVX VTRsk CLL VXTH
MSCI
EAFE
S&P
GSCI
$4.00
$3.00
$2.00
$1.00
$0.00
VTRsk $2.49
VXMT $1.53
S&P 500 $1.15
S&P 500 1.00
VIX (Spot) -0.72
1.00
VXMT
DyVX
VTRsk
CLL
VXTH
-0.70
0.73 1.00
-0.63
0.53 0.83 1.00
-0.60
0.56 0.64 0.82
1.00
0.89
-0.70 -0.68 -0.48 -0.42
1.00
0.87
-0.49 -0.53 -0.39 -0.33
0.83 1.00
MSCI EAFE 0.84
-0.64 -0.64 -0.59 -0.61
0.77 0.69 1.00
S&P GSCI 0.46
-0.30 -0.37 -0.36 -0.41
0.41 0.36 0.55 1.00
Exhibit J: The three futures-based indices added value due to the fact that they all rose more than 80% in 2008 (see also the annual returns table Exhibit A).
Exhibit L: Metrics for Returns, Risk, and Risk-adjusted Returns
(April 2006 – January 2012)
R e t u r n
Standard Deviation
Beta vs. Market
S k e w n e s s
K u tr o s i s
Sharpe Ratio
Semi-Standard Deviation
Sortino Ratio (MAR=Cash Eq.)
Jensen's Alpha vs. S&P 500
Correlation to S&P 500
2
S&P
500
.
3 7 %
Bonds
6 .
5 9 %
17.72% 3.45%
1.00
0.02
0 .
6 3
0 .
9 6
0 .
1 3
1 .
6 8
0.12
13.5%
0.30
0.00%
1.00
1.34
2.4%
1.24
4.68%
0.12
10%VXMT
/90% S&P
4 .
0 5 %
13.51%
0.75
0 .
4 2
0 .
5 4
0.23
10.1%
0.52
1.51%
0.98
10%DyVX
/90% S&P
6 .
0 2 %
14.06%
0.77
0 .
2 6
0 .
0 9
0.36
10.3%
0.74
3.41%
0.97
10%VTRsk
/90%S&P
5 .
9 7 %
13.36%
0.67
0 .
3 4
0 .
1 4
0.37
9.8%
0.76
3.50%
0.88
Exhibit L: A 10% allocation to the futures-based indices had risk-adjusted performance that was superior to that of the S&P 500 per metrics such as the Sortino Ratio, Sharpe
Ratio and Jensen’s Alpha. Please note that the measures of risk-adjusted returns are imperfect when measuring non-normal distributions with negative skewness.
Exhibit K: The CLL and VXTH have a high correlation to the S&P 500 due to their stock exposure. All of the futures-based indices are negatively correlated to the stock indexes.
Exhibit M: Changes for 5 Indexes in Months in Which S&P 500 had Big Moves (More Than 8.8%) (April 2006 – January 2012)
Oct. 2008
Feb. 2009
Sep. 2008
Sep. 2010
Apr. 2009
Oct. 2011
S&P 500
-16.8% -2.4%
-10.6%
-8.9%
8.9%
9.6%
10.9%
BarC
Agg
-0.4%
-1.3%
0.1%
0.5%
0.1%
VXMT DyVX VTRsk
44.0% 77.6% 162.5%
6.6% 3.2% -1.0%
13.3% 14.5% 12.1%
-5.8%
-7.2%
1.7% 1.5%
-2.5% -7.0%
-16.0% -12.0% -28.9%
Exhibit M: The futures-based indices realized significant increases during September and October 2008. Conversely, they experienced double-digit declines during
October 2011, a month when the S&P 500 rose 10.9%.
Exhibit N: “Over – Under” Chart with Returns Relative to S&P
500 (April 2006 – January 2012)
20
Exhibit O: Returns and Volatility
7%
(April 2006 – January 2012)
15
6% 10% VTRsk 10% DyVX
10
5
In the 4th quarter of 2008, 10%
VTRsk 90% S&P 500 declined
3.3% versus a decline of 22% for the S&P 500.
5%
5% VTRsk
0
4%
10% VXMT
5% DyVX
-5
-10
3%
5% VXMT
-15
-20
-25
10% DyVX / 90% S&P 500
10% VTRsk / 90% S&P 500
2%
10%
S&P 500
13% 16%
Standard Deviation
19%
-20 -15 -10 -5 0
S&P 500
5 10 15 20 25
Exhibit N: Allocating 10% to the VTRsk and DyVX provided cushion during declines while also participating in rising markets.
Exhibit O : The portfolio with an allocation of 10% VTRsk and 90% S&P 500 had a return of 6.0% and standard deviation of 13.4%.
Sources for all Exhibits on this page: Bloomberg, Ibbotson, ACG.
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FEBRUARY 2012
KEY TOOLS FOR HEDGING AND TAIL RISK MANAGEMENT
Exhibit P: Pricing of VIX Spot Index and VIX Futures
Exhibit P: The VIX Spot Index is not an investable index. The VIX future returns will differ over time depending upon market expectations. Note the difference in the VIX
Spot Index versus two futures expirations during the very volatile August to December,
2008 period. “Contango” occurs when the futures are trading higher than the spot index. “Backwardation” occurs when the futures trade lower than the spot index.
Exhibit R: Average Daily Volume for SPX Options, VIX Futures, and VIX Options (2004 – 2011)
Exhibit Q: % Changes in October 2008
VTRsk
DyVX
VIX Index (spot)
VIX Feb '09 Futures
VXMT
VXTH
CLL
S&P 500
MSCI EAFE
S&P GSCI
-50% 0%
6.1%
-3.8%
-16.8%
-20.2%
-28.2%
77.6%
52.0%
47.9%
44.0%
50% 100%
162.5%
150% 200%
Exhibit Q: In October 2008 the VIX-based indexes rose, and the S&P 500 declined by
16.8%. The VIX-based indices can provide protective benefits during large drawdown periods. Note the difference in returns for the VIX spot index and VIX February 2009 futures. The VIX spot index often has bigger moves than the VIX futures, which reflect the future expected value of VIX.
Exhibit S: VIX Index and the PUT and Call Volume for SPX and
VIX Options (January 2007 - January 2012)
90
80.86
60
30
0
3-Jan-2007 3-Jan-2008 2-Jan-2009 4-Jan-2010 3-Jan-2011 3-Jan-2012
1,000,000
800,000
SPX Puts
600,000
SPX Calls
400,000
200,000
0
Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12
VIX Calls
VIX Puts
Exhibit R: Our rough estimates for average daily notional dollar value of trading in
2011 (with a delta-adjustment of 0.5 for options, and a beta adjustment of 3.0 for VIX products) are more than $48 billion for SPX options, $3 billion for VIX futures, and $1 billion for VIX options. Assets in VIX-related exchange-traded products (ETPs) reached
$5 billion in February 2012.
Exhibit S: As noted in Exhibit A on the first page, the CLL Index buys SPX puts and sells SPX calls, and the VXTH Index buys VIX calls. The index option volume often has spiked when the VIX Index rose sharply. The put-call ratios during the time period above were 1.68 for SPX options and 0.54 for VIX options.
Sources for all Exhibits on this page: Bloomberg, CBOE.
Asset Consulting Group is an investment consulting firm which provides a full scope of investment advisory services to a select group of clients. The Chicago Board Options
Exchange ® (CBOE ® ) provided financial support for this paper. The CBOE S&P 500 indices are designed to represent proposed hypothetical strategies. The actual performance of investment vehicles such as mutual funds can have significant differences from the performance of the hypothetical indices. Like many passive indices, the indices do not take into account significant factors such as transaction costs and taxes. Investors attempting to replicate the indices should discuss with their advisors possible timing and liquidity issues.
Past performance does not guarantee future results. Standard & Poor’s ® , S&P ® , and S&P 500 ® are registered trademarks of Standard & Poor’s Financial Services LLC and are licensed for use by the CBOE. CBOE and Chicago Board Options Exchange are registered trademarks of the CBOE, and the CBOE indices are servicemarks of the CBOE. CBOE calculates and disseminates the indices. The methodology of the indices are owned by CBOE and may be covered by one or more patents or pending patent applications. The information contained in this report is based on information obtained by ACG from sources that are believed to be reliable. Opinions and estimates offered constitute our judgment and are subject to change without notice, as are statements of financial market trends, which are based on current market conditions. We believe the information provided here is reliable, but do not warrant its accuracy or completeness. This material is not intended as an offer or solicitation for the purchase or sale of any financial instrument. The views and strategies described may not be suitable for all investors. This material has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for accounting, legal or tax advice. References to future returns are not promises or even estimates of actual returns a client portfolio may achieve. Any forecasts contained herein are for illustrative purposes only and are not to be relied upon as advice or interpreted as a recommendation. The views expressed are those of Asset Consulting Group.
They are subject to change at any time. These views do not necessarily reflect the opinions of any other firm. Copyright© 2012 Asset Consulting Group, LLC. All Rights Reserved.
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