Introduction
Persistent economic uncertainty has led investors to seek safer harbors and increased the demand for
“low volatility” assets. Low volatility is shorthand for lower downside volatility, as no investor objects to
volatility when returns are high. In keeping with this shift in risk preferences, CBOE’s Low Volatility
IndexSM (LOVOLSM) pares downside volatility by combining two of its most popular benchmarks. The
LOVOL Index blends the CBOE Buywrite IndexSM (BXMSM) and the CBOE VIX Tail Hedge IndexSM VXTHSM 1
in a 40% /60% mix that seeks to achieve intermediate levels of protection against tail events while
preserving participation in normal to bullish markets. The LOVOL has a small probability of generating
monthly returns below -10%, a watermark for many investors, and tends to perform better than the
VXTH in less volatile market conditions. This leads to a more level path of returns and a correspondingly
more compact frequency distribution of returns.
1. Month-End Returns Sorted by Market Conditions
Chart 1 Monthly Rates of Return Sorted by S&P 500 Total Return Index, QII 2004 – QIII 2012
15%
Month-End Rates of Return April 2004 - October 2012
10%
5%
0%
-5%
-10%
8.92%
6.68%
4.87%
4.12%
3.61%
3.26%
2.58%
1.93%
1.51%
1.39%
1.06%
LOVOL
BX M
0.14%
-0.43%
-1.13%
-3.10%
-4.51%
-6.01%
-8.43%
-16.81%
-20%
-1.86%
SPTR
VXTH
10% Watermark
-15%
SPTR Rate of Return Ascending Order
15%
70
Month-End Rates of Return April 2004 - October 2012
10%
60
5%
50
0%
40
-5%
30
-10%
20
-15%
10
8.92%
6.68%
4.87%
4.12%
0
3.61%
3.26%
2.58%
VIX
1.93%
1.51%
1.39%
1.06%
0.14%
LOVOL
-0.43%
-1.13%
-3.10%
-4.51%
-6.01%
-8.43%
-16.81%
-20%
-1.86%
SPTR
SPTR Rate of Return Ascending Order
Source : CBOE
1
The BXM is a buy-write index; it overlays a one month at-the-money SPX call over an investment in the S&P 500.
The VXTH overlays one-month 30-delta calls on the CBOE Volatility Index® (VIX®) over an investment in the S&P
500. The weight of the VIX calls depends on the current value of nearby VIX futures.
Chart 1 is a graph of historical month-end index returns sorted by increasing values of S&P 500 returns,
serving as a proxy for market conditions. It illustrates the tradeoffs between downside volatility and
returns. The BXM cushions returns against severe downturns in exchange for lower returns in bullish
markets. The VXTH typically provides full protection against severe downturns in exchange for lower
returns in less volatile markets. By construction, the LOVOL index bridges the space between the BXM
and VXTH.
2. The View from Rolling Monthly Returns
Index percentile values for rolling monthly returns shown in Chart 2 provide a more representative
picture of what returns might prevail in an arbitrary one-month period. The lower panel is a statistical
summary of the distribution of rolling monthly returns. Based on the chart and these statistics, LOVOL
monthly returns are likely to be less volatile than returns of the S&P 500, BXM and VXTH. They tend to
have a lower standard deviation, a smaller negative semi-deviation, and smaller negative skew and
excess kurtosis. The LOVOL gives up relatively little in mean and median returns. The overall effect is to
compress the frequency distribution to a more compact mass around its median stripped of
exceptionally low lows and high highs, as illustrated in Chart 3.
Chart 2 Percentile Distribution of Rolling Monthly Rates of Return, QII 2004 – QIII 2012
30%
Percentile Values of Rolling Monthly Returns, 2006 - 2012
20%
10%
0%
-10%
-20%
SPTR
BXM
VXTH
LOVOL
-30%
Mean
Median
Std. Dev.
Neg. Semi. Deviation
SKEW
Excess Kurtosis
Source: CBOE
LOVOL
0.52%
1.29%
3.93%
3.00%
-0.39
2.89
SPTR
0.45%
1.48%
5.60%
3.76%
-0.98
3.56
VXTH
0.60%
1.25%
4.44%
3.55%
-0.19
2.29
100%
99%
95%
90%
80%
70%
60%
50%
40%
30%
20%
10%
5%
1%
0%
-40%
BXM
0.38%
1%
4.08%
2%
-1.61
6.86
Chart 3 Frequency Distribution of Rolling One-Month Returns
Frequency Distributions,
Rolling Monthly Returns
50%
45%
40%
35%
SPTR
BXM
VXTH
LOVOL
30%
25%
20%
15%
10%
5%
Source : CBOE
25.0%
22.5%
20.0%
17.5%
15.0%
12.5%
10.0%
7.5%
5.0%
2.5%
0.0%
-2.5%
-5.0%
-7.5%
-10.0%
-12.5%
-15.0%
-17.5%
-20.0%
-23%
-25%
-28%
-30%
0%
3. Chronological Returns
Chart 4 shows two graphs of the LOVOL and its components. The top one is a standard chart of
historical index values. Since performance in this type of chart is highly dependent on the starting
date, the second chart resets all index values to 100 at the beginning of each year. This provides yet
another view of the relative performance of the LOVOL and its component indexes under different
market conditions.
Chart 4. Time series of CBOE LOVOL Index and Time Series with Yearly Resets at 100
180
160
140
120
100
80
60
Source: CBOE
3/22/11
3/22/10
3/22/11
11/22/10
100
7/22/10
7/22/09
3/22/09
3/22/12
BXM
100
100
3/22/08
11/22/07
100
BXM
SPTR
VXTH
7/22/07
3/22/07
11/22/06
7/22/06
3/22/06
100
SPTR
3/22/10
LOVOL
3/22/09
11/22/09
3/22/08
11/22/08
130
120
110
100
90
80
70
60
50
3/22/07
7/22/08
3/22/06
VXTH
100
3/22/12
0
LOVOL
11/22/11
20
7/22/11
40
4. Construction of CBOE LOVOL Index
The CBOE LOVOL Index combines an investment in the BXM with a specified number of VXTH units.
Specifically, LOVOL holds a portfolio of S&P 500 stocks and simultaneously sells at-the money or near
out-the-money SPX calls and buys 30-delta VIX calls on a monthly basis. At VIX option expirations, the
VIX calls in the VXTH are settled, and a new number of VXTH units is selected such that the weight of the
VXTH in the LOVOL Index equal to 60%. The weight of the BXM at VIX option expirations is thus 40%. At
SPX expirations, the ATM SPX call in the BXM index is settled and a new call is sold. The value of the
LOVOL Index at each close is chained from its previous closing value according to the standard formula:
LOVOLt = LOVOLt −1 * (1 + Rt )
where Rt is the daily rate of return of the index. The daily rate of return of the LOVOL index depends on
whether that date is a VIX roll date, an SPX roll date or a “regular date” :
 Regular Date:
(1 + M t ) * ( S t + Dt ) − C tS + 100 * M t * N t * C tV
Rt =
(1 + M t −1 ) * S t −1 − C tS−1 + 100 * M t −1 * N t −1 * C tV−1
Mt = Number of VXTH units in portfolio at close of date t
Nt = Number of VIX calls in VXTH at close of date t
St = Value of S&P 500 at close of date t
Dt= S&P 500 dividends on date t
Ct S = Midquote of S&P 500 call in BXM at close of date t
Ct V= Midquote of VXTH call at close of date t
 VIX Expiration/Roll Date:
Rt =
(1 + M t −1 ) * ( S10 + Dt ) − C10S + 100 * M t −1 * N t −1 * Max(0, SOQ VIX − K V )
*
(1 + M t −1 ) * S t −1 − C tS−1 + 100 * M t −1 * N t −1 * C tV−1
(1 + M t ) * St − C tS + 100 * M t * N t * C tV
(1 + M t ) * S10 − C10S + 100 * M t * N t * C10V
S10 = S&P 500 value at 10:00 a.m. Chicago time
C10S = Midquote of S&P 500 call in BXM at 10:00 a.m.
SOQVIX = Settlement value of VIX options
KV = Strike of 30 delta VIX call at settlement
C10V = Ask price of new 30 delta VIX call at 10:00 a.m.
The new numbers of VXTH calls and VXTH units are determined at 10:00 a.m. as:
Nt =
S 10
X
*
1− X 100 * C10V
where X is selected according to the following Table:
F = One Month Forward Value of VIX
X = Portfolio Weight of VIX Calls
F < = 15%
0%
15% < F <= 30%
1%
30% < F <= 50%
½%
F > 50%
0%
Mt =
.6 * ( S10 + Dt − C10S )
.4 * ( S10 + Dt + 100 * C10V )
 S&P 500 Expiration / Roll Dates
Rt =
V
(1 + M t ) * ( SOQ SPX + Dt ) − max(0, SOQ spx − K S ) + 100 * M t * N t * C10
*
((1 + M t ) * S t −1 − C tS−1 + 100 * M t −1 * N t −1 * C tV−1
V
(1 + M t ) * S vwap + 100 * M t * N t * C12
:30
V
(1 + M t ) * SOQ spx + 100 * M t * N t * C10
*
(1 + M t ) * S t − C tS + 100 * M t * N t * C tV
S
V
(1 + M t ) * S vwap − C vwap
+ 100 * M t * N t * C12
:30
SOQSPX = settlement value of SPX options
KS = strike of settling SPX options
SVWAP = S&P 500 at 12:30, end of BXM VWAP period
CvwapS = VWAP price of new BXM call
C12;30V = midquote of VIX call at end of BXM VWAP period
Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a
copy of Characteristics and Risks of Standardized Options (ODD). Copies are available from your broker, by calling
1-888-OPTIONS, or from The Options Clearing Corporation at www.theocc.com. Futures and options on CBOE’s
volatility indexes have several unique features that distinguish them from most equity and index options, and
investors are strongly encouraged to closely read and understand the ODD and the VIX options FAQ at
http://www.cboe.com/micro/vix/vixoptionfaq.aspx and other informational material before investing. No statement
within this paper should be construed as a recommendation to buy or sell a financial product or to provide investment
advice. Past performance is not indicative of future results. Supporting documentation for any claims, comparisons,
statistics or other technical data in this paper is available from CBOE upon request. CBOE®, Chicago Board Options
Exchange®, CBOE Volatility Index® and VIX® are registered trademarks and BuyWrite, BXM, CBOE Low Volatility
Index, CBOE VIX Tail Hedge Index, SPX and VXTH are service marks of Chicago Board Options Exchange,
Incorporated (CBOE). S&P® and S&P 500® are trademarks of Standard & Poor’s Financial Services, LLC and have
been licensed for use by CBOE.
Copyright © 2012 Chicago Board Options Exchange, Incorporated. All rights reserved.