The document provides an analysis of the Philadelphia Semiconductor Sector (SOX) Index, detailing its history, performance relative to benchmarks, and momentum analysis for investment strategies. It discusses the cyclical nature of the index, its volatility compared to other major indices, and the impact of different trading strategies on returns. The findings suggest that a momentum-based trading approach can yield better results than a simple buy-and-hold strategy, particularly over specific lookback periods.

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Philadelphia Semiconductor
Sector (SOX) Index Analysis
A.R. Alvarez
November 2015

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SOX Index Outline
 SOX Index History
 SOX Index vs. Benchmarks
 SOX Index Momentum Analysis
 Appendix: SOX Background

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SOX Index History
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SOX Index Companies
 SOX Established Dec 1993; Options Trading
Started Sept 1994; Split 2:1 July 1995
 Top 30 Semiconductor Companies By
Market Cap
 Of 16 Companies on Index Sept 1994:
 Eight Still on Index (ADI, AMAT, CY, INTC, MU,
NVLS, TER, TXN)
 Four Were Bought (IRF, LSI, MOT, NSM);
Acquiring Company on Index
 Four Dropped Off (AMD, IDTI, LSCC, VLSI)
 Index Weight Limited to ~8%; Limits Impact
of Larger Market Cap Companies
 Market vs. Index Modified Market Cap
 Aggregate MC ~$800B vs. Index MMC~$450B
 Max Company MC: Intel $166B vs. ~$39B Index
MMC; Similar to TI Which Has MC of ~$60B)
 Median Company MC & Index MMC ~$14B
 Min Company Market Cap Infinera ~$2.4B
Ticker Name
Weight
(%)
Index
MMC
($B)
Market
Cap ($B)
ADI Analog Devices, Inc. 4.11 $18.4 $20.0
AMAT Applied Materials, Inc. 3.65 $16.3 $19.7
ARMH ARM Holdings plc 1.79 $8.0 $23.1
ASML ASML Holding NV 1.79 $8.0 $40.3
ATML Atmel Corporation 1.01 $4.5 $3.6
AVGO Avago Technologies 7.21 $32.3 $35.7
CAVM Cavium, Inc. 1.13 $5.0 $4.0
CY Cypress Semiconductor 0.92 $4.1 $3.4
INFN Infinera Corporation 0.74 $3.3 $2.4
INTC Intel Corporation 8.74 $39.1 $166.0
KLAC KLA-Tencor Corporation 2.89 $12.9 $10.2
LLTC Linear Technology Corp 3.11 $13.9 $11.3
LRCX Lam Research Corporation 3.25 $14.5 $11.8
MCHP Microchip Technology Inc. 2.92 $13.0 $10.4
MRVL Marvell Technology Group 1.34 $6.0 $5.0
MSCC Microsemi Corporation 0.97 $4.3 $3.5
MU Micron Technology, Inc. 3.69 $16.5 $18.6
MXIM Maxim Integrated Products 3.14 $14.1 $10.8
NVDA NVIDIA Corporation 4.33 $19.4 $15.4
NXPI NXP Semiconductors NV 4.20 $18.8 $22.3
ON ON Semiconductor 1.27 $5.7 $4.7
QCOM Qualcomm Incorporated 7.74 $34.7 $95.4
QRVO Qorvo, Inc. 2.09 $9.4 $7.7
SNDK SanDisk Corp. 4.45 $19.9 $16.0
SUNE SunEdison, Inc. 0.69 $3.1 $2.5
SWKS Skyworks Solutions Inc. 3.39 $15.2 $15.8
TER Teradyne Inc. 1.11 $5.0 $4.0
TSM Taiwan Semiconductor Mfg 5.97 $26.7 $116.5
TXN Texas Instruments Inc. 8.80 $39.4 $60.5
XLNX Xilinx Inc. 3.48 $15.6 $48.7
Market Close Oct'22 2015 100% $447 $809

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SOX Index Employs Algorithm to Limit Contribution of Largest Market
Cap Companies; Balances Bi-Modal Nature of Market Cap
SOX Company Market Caps
Market Cap of Companies in SOX ($B)

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SOX Index Cycles

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SOX Index Cycle Min-Max
The Median “Up” Cycle was 123% vs. a Median “Down” Cycle of -
57%, But The Distribution Was Bi-Modal to an Extreme
Median Min Max
Up 123% 50% 496%
Down -57% -69% -22%
Neutral 3% -4% 9%

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SOX Index Cycle Lengths
The Median “Up” Cycle Length was 19 Mths vs. a Median “Down”
Cycle Length of 10 Mths
Median Min Max
Up 19 6 30
Down 10 7 17
Neutral 14 11 17

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SOX Index vs. Semi Revenue

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SOX Index / Semi Sales Ratio
Avg Std Dev
1995 - 1999 26 9
2000 - 2004 39 16
2001 - 2009 20 4
2010 - 2014 18 3
1995 - 2004 25 12

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SOX Index Summary
 Eight “Up-Down” and 2 “Neutral” Cycles; Currently in The Early Phase of
“Down” (Or “Sideways”) Portion of It’s 8th Cycle
 Peaked During “Internet” Bubble of 1999 & 2000; Still Trades at ~50% of
2000 Peak, Even Though Has Had a Steady Rise From 2008 Financial Crises
 Fairly Extreme Movements Either Up (>100%) or Down (> -75%) Over
Relatively Short Periods
 Median Up-Cycle Gain (123%) Was ~2X The Median Down-Cycle
 Median Up-Cycle Length (~20 Mths) Was ~2X Median Down- Cycle, So
Relative Slope (~6.5% Per Month) Was Same For Both Portions
 Setting Aside Two Neutral Cycles, Only One Cycle Was Less Than ±30%;
The Down-Cycle From June to Dec 2011 Which Only Dropped ~22%
 SOX Index Tends to Lead Semi Revenue By a Few Months on Down-Cycles
and Aligns Closely on Up-Cycles
 The Most Recent Cycle is an Exception Where Semi Revenue Starting
Declining Well Before Index Started to Drop (Due to Heavy 2015 M&A ?)

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SOX Index
Benchmarks
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SOX Index vs. S&P500 & NASDAQ

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$1,000 Becomes:
Benchmark Performance: B&H
S&P $4,250
Russell $4,571
DJI $4,611
NASDAQ $6,241
SOX $5,066

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SOX Index Relative Performance
vs. NASDAQ: SOX Performance Generally Worse in any Given 5
Year Period; Slightly Worse Overall
vs. S&P500: SOX Performance Better in “Good” 5 Year Periods
& Worse in “Bad” 5 Year; Slightly Better Overall
Similar Performance For All 5 Indices in Last 5 Year Period
CAGR
CAGR S&P500 Dow R2000 NASDAQ SOX
1995 - 1999 25% 26% 14% 38% 36%
2000 - 2004 -3.5% 1% 5% -12% -11%
2005 - 2009 -1.2% 2.4% -0.2% 1.4% -3.0%
2010 - 2014 13% 14% 13% 16% 14%
1995 - 2004 7.7% 7.9% 8.1% 9.6% 8.2%

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SOX Index Relative Performance
vs. NASDAQ: SOX Relative Volatility ~50% Higher, Decreasing
Modestly Over Time
vs. S&P500: SOX Relative Volatility ~2x Higher, Decreasing
Significantly Over Time
SOX Has Much Greater Volatility For Similar/Lower Returns
Volatility
Volatility S&P500 Dow R2000 NASDAQ SOX
1995 - 1999 16% 16% 14% 21% 40%
2000 - 2004 20% 20% 23% 35% 57%
2005 - 2009 24% 22% 30% 25% 32%
2010 - 2014 16% 15% 22% 18% 25%
1995 - 2004 19% 18% 22% 25% 39%

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Indices Comparison Summary
 The SOX, S&P500, DJI, Russell 2000, and NASDAQ Indices Move in Unison
(Relatively High Correlation), But With Different Volatilities
 For 20 Year Period 1995 – 2004, The NASDAQ, SOX, and S&P500 CAGR was
9.6%, 8.2%, & 7.7% With a Volatility of 25%, 39%, & 19% Respectively
 SOX Relative Risk (CAGR/Volatility) Was Worse Than NASDAQ or S&P500
 Individual 5 Year Periods For Most Part Exhibit Similar Relative Results
 $1,000 Invested in Each of the 5 Indices in May 1994 Had Value of ~$6,000,
~$5,000, ~$4,600 & ~$4,000 (Excluding Dividends) Sept 2014 For NASDAQ,
SOX, DJI / Russell 2000, and S&P500 Respectively
 Whereas The Four Benchmark Indices are Currently Above or Close to
Their All Time High, The SOX is at ~50% of It’s 2000 Peak
 If One Were Unlucky Enough to Have Invested at or Near The SOX Peak in
2000, They Would Still Have Lost ~50% of The Investment as of Oct 2015
 The SOX Has Exceeded Its Pre-2008 Financial Crises ‘Peak’, But It Took 6
Years to Recover


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SOX Index
Momentum Analysis
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SOX Index Momentum
 Objective:
 Determine if a Simple Momentum Rule Can Be Utilized on the SOX Index to Obtain a
Better Return Than a “Buy & Hold” Strategy
 Calculations:
 Daily and End of Month Market Close Calculations Utilized
 Lookback Periods:
 Absolute Performance: 3, 6, and 12 Month
 Absolute Performance With Non-Zero (2.5%) Cutoff: 6 Months
 Moving Average: 200 Day Simple Moving Average and Various Exponentially
Weighted Moving Averages
 Buy-Sell Decisions Made Once Per Month; Last Trading Day of the Month
 Tax Scenarios (Deferred vs. Instant):
1) Taxed Only at End of Holding Period (IRA Type Account); Also True for B&H
2) Taxed at 33% on a Trade Gain, No Tax Benefit on Trade Loss
 Fees/Spread: Low Cost ($10) Trades, Spread Not Taken Into Account
 Invested Return and Maximum Draw-Down Calculated
 Momentum Rule Criteria:
 Buy on Positive Momentum: “Current” Price Greater Than Lookback Period Price
 Sell on Negative Momentum: “Current” Price Lower Than Lookback Period Price)

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B&H vs. 3 Mth Lookback B&S
B&H Taxed No Tax
$1,000 Becomes $3,726 $5,509 $10,928
$ Trades (B&S) n/a 58 58
Avg Trades/Year n/a 2.9 2.9
Max Draw Down 70% 50% 42%
Median Draw Down 49% 32% 23%
3 Mth Lookback

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B&H vs. 6 Mth Lookback B&S
B&H Taxed No Tax
$1,000 Becomes $3,726 $2,502 $3,969
$ Trades (B&S) n/a 44 44
Avg Trades/Year n/a 2.2 2.2
Max Draw Down 70% 52% 38%
Median Draw Down 49% 37% 29%
6 Mth Lookback

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B&H vs. 12 Mth Lookback
B&H Taxed No Tax
$1,000 Becomes $3,726 $1,833 $2,243
$ Trades (B&S) n/a 26 26
Avg Trades/Year n/a 1.3 1.3
Max Draw Down 70% 61% 55%
Median Draw Down 49% 34% 33%
12 Mth Lookback

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SOX Index & 200 Day SMA

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B&H vs. 200 Day SMA B&S
B&H Taxed No Tax
$1,000 Becomes $3,726 $4,364 $7,012
$ Trades (B&S) n/a 38 38
Avg Trades/Year n/a 1.9 1.9
Max Draw Down 70% 43% 28%
Median Draw Down 49% 31% 21%
200 Day SMA

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Impact of Non-Zero Threshold
Criteria: 6 Mth Look Price ≥ 2.5% Higher
Than Current Price to “Buy”
B&H Taxed No Tax
$1,000 Becomes $3,726 $3,700 $5,632
$ Trades (B&S) n/a 42 42
Avg Trades/Year n/a 2.1 2.1
Max Draw Down 70% 51% 36%
Median Draw Down 49% 32% 26%
6 Mth LB / 2.5% Criteria

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SOX Index Momentum Summary
 A Momentum-Based Trading Rule Can Yield Better Results Than B&H
 Lookback Period Matters: Only 200 Day SMA and 3 Mth Lookbacks
Provided Greater Returns Than B&H in a Taxed Account
 Taxes Matter: In a Deferred Tax Account Momentum-Based Trading Yields
Much Better Results Than B&H in All Cases Except for 12 Mth Lookback
 No Momentum Rule Will Outperform B&H All of The Time; There Can be
Significant Periods (Years) of Underperformance
 3 Month Lookback Period Gave Best Overall Performance Over 20 Yr
Period, But in a Taxed Account Underperformed B&H for First 14 Years
 200 Day Simple Moving Average Gave Acceptable Performance and Even in
a Taxed Account Out-Performed B&H For Most of the 20 Yr Period
B&H Taxed No Tax Taxed No Tax Taxed No Tax Taxed No Tax Taxed No Tax
$1,000 Becomes $3,726 $5,509 $10,928 $2,502 $3,969 $1,833 $2,243 $4,364 $7,012 $3,700 $5,632
$ Trades (B&S) n/a 58 58 44 44 26 26 38 38 42 42
Avg Trades/Year n/a 2.9 2.9 2.2 2.2 1.3 1.3 1.9 1.9 2.1 2
Max Draw Down 70% 50% 42% 52% 38% 61% 55% 43% 28% 51% 36%
Median Draw Down 49% 32% 23% 37% 29% 34% 33% 31% 21% 32% 26%
3 Mth Lookback 6 Mth Lookback 12 Mth Lookback 200 Day SMA 6M LB / 2.5% Crit

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Appendix:
SOX Index
Background Information
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WW Semiconductor Sales
Growth Rate Drop From Historical 15% CAGR to 6% Since 2000
Given Industry Size & Penetration Don’t Expect Return to 15% CAGR Unless
Global GDP Exceeds 4 – 4.5% Consistently
“Semiconductor Industry Primer 2014”
D. Wong (Wells Fargo) Nov’15
15% CAGR
6% CAGR

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SOX Index Summary
 PHLX Semiconductor Sector Index is a Modified Capitalization Weighted
Index Made Up of the Major Companies in the Semiconductor Sector
 Two Versions
 Price Return Index (SOX): Calculated Without Regard To Cash Dividends on Index
Securities (Initiated Dec 1st 1993 at Base Value = $100)
 Total Return Index (XSOX): Reinvests Cash Dividends on Ex-Date.; Synchronized to
Value of The Price Return Index at The Close on Dec 22, 2009
 Both Indexes Reflect Extraordinary Cash Distributions
 Index Eligibility (Main Points)
 Be Listed on NASDAQ Stock Market or New York Stock Exchange
 Have Minimum Market Capitalization of $100 Million
 Have Traded at Least 1.5 Million Shares in Each of Previous Six Months
 Index Evaluation
 Index Securities Evaluated Every Sept; Additions/Deletions Effective 3rd Friday of Sept
 Securities Meeting Eligibility Criteria as of End of July Ranked By Market Capitalization
 Top 30 Securities By Market Capitalization Included in Index

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SOX Index Calculation
 Value of Index Equals Aggregate Value of Index Share Weights
Step 1) Calculate Total Market Value of Index = Sum of Market Value of Each Index Component = The
Last Sale Price Multiplied By Number of Shares Outstanding
Step 2) Calculate Weight of Each Index Component = Its Market Value Divided By Total Market Value
of Index
Step 3) Employ Capitalization Weighting Adjustment/Modification Algorithm to Limit Contribution of
Largest Market Cap Companies to 8% or Less (See Rebalancing Section)
Step 4) Calculate Aggregate “Modified” Capitalization Weighted Market Value = Sum of Each Index
Component's Weight and Last-sale Price
Step 5) Divide Aggregate Weighted Market Value By Divisor, Which Scales Aggregate Value to Lower
Value More Suitable For Reporting
 Index Balancing
 Index Employs a Modified Market Capitalization Weighting Methodology
 Each Qtr, Index Rebalanced Such That Max Weight of Any Security Does Not Exceed 8% and No
More Than 5 Securities Are at That Cap
 Excess Weight of Any Capped Security is Distributed Proportionally Across Remaining Index
Securities
 If After Redistribution, Any of The 5 Highest Ranked Index Securities are Below 8%, These
Securities are Not Capped
 Next, Any Remaining Index Securities in Excess of 4% are Capped at 4% and The Excess Weight
is Redistributed Proportionally Across Remaining Index Securities
 Process is Repeated, As Necessary, To Derive The Final Weights

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SOX Index Companies 2013 - 15
Ticker Name
Weight
(%)
Index
MMC
($B)
Market
Cap
($B)
Ticker Name
Weight
(%)
Index
MMC
($B)
Ticker Name
Weight
(%)
Index
MMC
($B)
ADI Analog Devices, Inc. 4.1 $18.4 $20.0 ADI Analog Devices, Inc. 3.9 $19.8 ADI Analog Devices, Inc. 3.8 $9
AMAT Applied Materials, Inc. 3.7 $16.3 $19.7 ALTR Altera (Intel) 2.7 $13.5 ALTR Altera (Intel) 3.3 $7
ARMH ARM Holdings plc 1.8 $8.0 $23.1 AMAT Applied Materials, Inc. 6.2 $31.4 AMAT Applied Materials, Inc. 6.3 $14
ASML ASML Holding NV 1.8 $8.0 $40.3 ARMH ARM Holdings plc 1.4 $6.9 AMD Advanced Micro Devices 0.7 $2
ATML Atmel Corporation 1.0 $4.5 $3.6 ASML ASML Holding NV 2.0 $10.3 ARMH ARM Holdings plc 1.8 $4
AVGO Avago Technologies 7.2 $32.3 $35.7 ATML Atmel Corporation 0.8 $4.0 ASML ASML Holding NV 3.0 $7
CAVM Cavium, Inc. 1.1 $5.0 $4.0 AVGO Avago Technologies 4.2 $21.6 ATML Atmel Corporation 1.0 $2
CY Cypress Semiconductor 0.9 $4.1 $3.4 BRCM Broadcom (Avago) 4.3 $21.8 AVGO Avago Technologies 3.4 $8
INFN Infinera Corporation 0.7 $3.3 $2.4 CREE Cree 0.9 $4.8 BRCM Broadcom (Avago) 3.8 $9
INTC Intel Corporation 8.7 $39.1 $166.0 FSL Freescale (NXP) 1.5 $7.7 CREE Cree 2.2 $5
KLAC KLA-Tencor Corporation 2.9 $12.9 $10.2 INTC Intel Corporation 7.8 $40.0 FSL Freescale (NXP) 1.2 $3
LLTC Linear Technology Corp 3.1 $13.9 $11.3 KLAC KLA-Tencor Corporation 3.3 $16.7 INTC Intel Corporation 8.0 $18
LRCX Lam Research Corporation 3.2 $14.5 $11.8 LLTC Linear Technology Corp 2.6 $13.0 KLAC KLA-Tencor Corporation 3.3 $8
MCHP Microchip Technology Inc. 2.9 $13.0 $10.4 LRCX Lam Research Corporation 3.1 $16.1 LLTC Linear Technology Corp 2.9 $7
MRVL Marvell Technology Group 1.3 $6.0 $5.0 MCHP Microchip Technology Inc. 2.2 $11.0 LRCX Lam Research Corporation 2.7 $6
MSCC Microsemi Corporation 1.0 $4.3 $3.5 MRVL Marvell Technology Group 1.7 $8.7 LSI LSI CORP 1.4 $3
MU Micron Technology, Inc. 3.7 $16.5 $18.6 MU Micron Technology, Inc. 8.1 $41.4 MCHP Microchip Technology Inc. 2.6 $6
MXIM Maxim Integrated Products 3.1 $14.1 $10.8 MXIM Maxim Integrated Products 2.1 $10.6 MRVL Marvell Technology Group 1.8 $4
NVDA NVIDIA Corporation 4.3 $19.4 $15.4 NVDA NVIDIA Corporation 2.6 $13.5 MU Micron Technology, Inc. 4.7 $11
NXPI NXP Semiconductors NV 4.2 $18.8 $22.3 NXPI NXP Semiconductors NV 4.0 $20.6 MXIM Maxim Integrated Products 2.6 $6
ON ON Semiconductor 1.3 $5.7 $4.7 ON ON Semiconductor 0.9 $4.7 NVDA NVIDIA Corporation 2.7 $6
QCOM Qualcomm Incorporated 7.7 $34.7 $95.4 QCOM Qualcomm Incorporated 8.3 $42.3 NXPI NXP Semiconductors NV 3.2 $7
QRVO Qorvo, Inc. 2.1 $9.4 $7.7 RFMD RF Micro Devices (Quorvo) 0.9 $4.8 ON ON Semiconductor 1.0 $2
SNDK SanDisk Corp. 4.5 $19.9 $16.0 SNDK SanDisk Corp. 3.9 $19.7 QCOM Qualcomm Incorporated 7.6 $17
SUNE SunEdison, Inc. 0.7 $3.1 $2.5 SUNE SunEdison, Inc. 1.3 $6.7 SNDK SanDisk Corp. 4.6 $10
SWKS Skyworks Solutions Inc. 3.4 $15.2 $15.8 SWKS Skyworks Solutions Inc. 2.8 $14.0 SWKS Skyworks Solutions Inc. 1.5 $3
TER Teradyne Inc. 1.1 $5.0 $4.0 TER Teradyne Inc. 0.9 $4.8 TER Teradyne Inc. 1.0 $2
TSM Taiwan Semiconductor Mfg 6.0 $26.7 $116.5 TSM Taiwan Semiconductor Mfg 4.2 $21.6 TSM Taiwan Semiconductor Mfg 5.9 $13
TXN Texas Instruments Inc. 8.8 $39.4 $60.5 TXN Texas Instruments Inc. 8.3 $42.3 TXN Texas Instruments Inc. 8.0 $18
XLNX Xilinx Inc. 3.5 $15.6 $48.7 XLNX Xilinx Inc. 3.0 $15.2 XLNX Xilinx Inc. 3.7 $8
Market Close Oct'22 2015 1.0 $447 $809 1.0 $509 1.0 $227
October 2015 October 2014 October 2013

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SOX Index Sept vs. Oct 2010
 SOX Index Transitioned to
Modified Market Cap Algorithm
and 30 Companies Oct 2010
 Prior to That SOX Index Carrier
16 – 21 Companies, While the
iShares ETF (SOXX) Carried 52
Companies
 Since Oct 2010 Both The SOX
and SOXX Carried the Identical
30 Companies
 Blue = Companies Added
Oct’2010
 Weightings Shown are for SOXX
Ticker Name
Weight
(%)
Index
MMC
($B)
Ticker Name
ALTR Altera (Intel) 4.18 $7.4 ALTR Altera (Intel)
AMAT Applied Materials, Inc. 7.86 $13.9 AMAT Applied Materials, Inc.
AMD Advanced Micro Devices 3.25 $5.8 AMD Advanced Micro Devices
ATHR Atheros (Qcom) 1.45 $2.6 ATHR Atheros (Qcom)
AVGO Avago Technologies 3.88 $6.9 BRCM Broadcom (Avago)
BRCM Broadcom (Avago) 8.98 $15.9 CREE Cree
CREE Cree 3.16 $5.6 HITT Hittite Microwave (ADI)
CRUS Cirrus Logic 0.57 $1.0 INTC Intel Corp
HITT Hittite Microwave (ADI) 1.04 $1.8 KLAC KLA-Tencor Corp
INTC Intel Corp 7.48 $13.2 LLTC Linear Technology Corp
KLAC KLA-Tencor Corp 3.94 $7.0 LRCX Lam Research Corp
LLTC Linear Technology Corp 3.72 $6.6 MU Micron Technology
LRCX Lam Research Corp 3.74 $6.6 NSM National Semi (TI)
MKSI MKS Instruments 0.68 $1.2 NVLS Novellus Systems (Lam)
MRVL Marvell Technology Group 6.85 $12.1 SNDK SanDisk Corp.
MU Micron Technology, Inc. 4.22 $7.5 STM ST Microelectronics
NETL Netlogic Micro (BCOM) 1.26 $2.2 TER Teradyne
NSM National Semi (TI) 2.16 $3.8 TSM Taiwan Semiconductor Mfg
NVDA NVIDIA Corporation 4.26 $7.5 TXN Texas Instruments Inc.
NVLS Novellus Systems (Lam) 1.77 $3.1 WFR MEMC Electronics
POWI Power Integrations 0.63 $1.1 XLNX Xilinx Inc.
RBCN Rubicon Technology 0.35 $0.6
SNDK SanDisk Corp. 3.73 $6.6
STM ST Microelectronics 0.46 $0.8
TER Teradyne Inc. 1.34 $2.4
TSM Taiwan Semiconductor Mfg 3.83 $6.8
TXN Texas Instruments Inc. 8.48 $15.0
VECO Veeco Instruments 1.13 $2.0
WFR MEMC Electronics 1.92 $3.4
XLNX Xilinx Inc. 3.67 $6.5
100% $177
September 2010October 2010

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SOX Index Cycles Table
Cycle
Start
Cycle
End
Months
in Cycle
Cycle
Change
Cycle
Start
Cycle
End
Months
in Cycle
Cycle
Change
May-94 Sep-95 17 153% Feb-04 Aug-04 7 -65%
Oct-95 Jul-96 10 -52% Sep-05 Apr-06 20 50%
Aug-96 Sep-97 14 171% May-06 Sep-07 17 -4%
Oct-97 Aug-98 11 -50% Oct-07 Feb-09 17 -63%
Sep-98 Aug-00 24 496% Mar-09 May-11 27 133%
Sep-00 Sep-01 13 -69% Jun-11 Dec-11 7 -22%
Oct-01 Mar-02 6 72% Jan-12 Nov-12 11 9%
Apr-02 Jan-03 10 -57% Dec-12 May-15 30 93%
Feb-03 Jan-04 12 113% Jun-15 Oct-15 5 -17%
Median Min Max
Up 123% 50% 496%
Down -57% -69% -22%
Neutral 3% -17% -4%
Median Min Max
Up 19 6 30
Down 10 7 17
Neutral 14 11 17
Cycle Change Summary Cycle Length Summary

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Index Volatility
 Basic Definition:
 Standard Deviation of Historical Returns
 Basically a “Dispersion” Measure; Greater Dispersion (Volatility) Implies Greater Risk
 Upside & Downside Price Movements Are Equally Considered in the Volatility
Calculation; The Sortino Ratio Attempts to Capture Just Downside Volatility
 Calculation
Step 1) Calculate Daily Periodic Stock Return (Ri) = (Pi – Pi-1)/Pi ; Where Pi is Current
Day’s Closing Price and Pi-1 is Closing Price on Previous Day
 More Often Ri = Ln(Pi/Pi-1) is Used as it Better Represents a Continuously
Compounded Return; Approximately The Same For Most Short Intervals
 This was the Method Employed in This Study
Step 2) Decide on Time Period; Volatility for Both the Full 20 Year (1994 – 2014) as Well
as 5 Year Intervals Was Calculated for The 3 Indices Examined in This Study
Step 3) Calculate Daily Sample Variance = [ Sum(Pi-1 – Avg P)2 ] / (m-1); Where ‘m’ =
Number of Sample Data Points Over Which The Sum is Performed
Step 4) Calculate Annualized Sample Volatility = Sqrt (Sample Variance) x Sqrt (250);
250 Being The Number of Trading Days in a Typical Year
 Note: To Calculate Annualized Weekly or Monthly Volatility Multiply The
Corresponding Weekly or Monthly Volatility By Sqrt(52) or Sqrt(12) Respectively;
The Calculated Volatility Will Be Slightly Different in Each Case