semiconductor index (sox) analysis

ARA Research

ARA (Nov’15)- © 2015 -

ARA Research

Philadelphia Semiconductor Sector (SOX) Index AnalysisA.R. AlvarezNovember 2015

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

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ARA Research

SOX Index History

ARA ResearchARA Research

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ARA Research 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 $20.0AMAT Applied Materials, Inc. 3.65 $16.3 $19.7ARMH ARM Holdings plc 1.79 $8.0 $23.1ASML ASML Holding NV 1.79 $8.0 $40.3ATML Atmel Corporation 1.01 $4.5 $3.6AVGO Avago Technologies 7.21 $32.3 $35.7CAVM Cavium, Inc. 1.13 $5.0 $4.0

CY Cypress Semiconductor 0.92 $4.1 $3.4INFN Infinera Corporation 0.74 $3.3 $2.4INTC Intel Corporation 8.74 $39.1 $166.0KLAC KLA-Tencor Corporation 2.89 $12.9 $10.2LLTC Linear Technology Corp 3.11 $13.9 $11.3LRCX Lam Research Corporation 3.25 $14.5 $11.8MCHP Microchip Technology Inc. 2.92 $13.0 $10.4MRVL Marvell Technology Group 1.34 $6.0 $5.0MSCC Microsemi Corporation 0.97 $4.3 $3.5

MU Micron Technology, Inc. 3.69 $16.5 $18.6MXIM Maxim Integrated Products 3.14 $14.1 $10.8NVDA NVIDIA Corporation 4.33 $19.4 $15.4NXPI NXP Semiconductors NV 4.20 $18.8 $22.3ON ON Semiconductor 1.27 $5.7 $4.7

QCOM Qualcomm Incorporated 7.74 $34.7 $95.4QRVO Qorvo, Inc. 2.09 $9.4 $7.7SNDK SanDisk Corp. 4.45 $19.9 $16.0SUNE SunEdison, Inc. 0.69 $3.1 $2.5SWKS Skyworks Solutions Inc. 3.39 $15.2 $15.8TER Teradyne Inc. 1.11 $5.0 $4.0TSM Taiwan Semiconductor Mfg 5.97 $26.7 $116.5TXN Texas Instruments Inc. 8.80 $39.4 $60.5XLNX Xilinx Inc. 3.48 $15.6 $48.7

Market Close Oct'22 2015 100% $447 $809

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ARA Research

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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ARA Research SOX Index Cycles

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ARA Research 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 MaxUp 123% 50% 496%

Down -57% -69% -22%Neutral 3% -4% 9%

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ARA Research SOX Index Cycle Lengths

The Median “Up” Cycle Length was 19 Mths vs. a Median “Down” Cycle Length of 10 Mths

Median Min MaxUp 19 6 30

Down 10 7 17Neutral 14 11 17

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ARA ResearchSOX Index vs. Semi Revenue

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ARA ResearchSOX Index / Semi Sales RatioAvg Std Dev

1995 - 1999 26 92000 - 2004 39 162001 - 2009 20 42010 - 2014 18 31995 - 2004 25 12

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ARA Research 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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ARA Research

SOX Index Benchmarks


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ARA ResearchSOX Index vs. S&P500 & NASDAQ

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ARA Research

$1,000 Becomes:Benchmark Performance: B&H

S&P $4,250Russell $4,571

DJI $4,611NASDAQ $6,241

SOX $5,066

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ARA ResearchSOX 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 SOX1995 - 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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ARA ResearchSOX 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 SOX1995 - 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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ARA ResearchIndices 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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ARA Research

SOX Index Momentum AnalysisARA ResearchARA Research

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ARA Research 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&H2) 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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ARA ResearchB&H vs. 3 Mth Lookback B&SB&H Taxed No Tax

$1,000 Becomes $3,726 $5,509 $10,928$ Trades (B&S) n/a 58 58Avg Trades/Year n/a 2.9 2.9Max Draw Down 70% 50% 42%Median Draw Down 49% 32% 23%

3 Mth Lookback

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ARA ResearchB&H vs. 6 Mth Lookback B&SB&H Taxed No Tax


6 Mth Lookback

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ARA ResearchB&H vs. 12 Mth LookbackB&H Taxed No Tax


12 Mth Lookback

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ARA ResearchSOX Index & 200 Day SMA

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ARA ResearchImpact 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 42Avg Trades/Year n/a 2.1 2.1Max Draw Down 70% 51% 36%Median Draw Down 49% 32% 26%

6 Mth LB / 2.5% Criteria

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ARA ResearchSOX 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 42Avg Trades/Year n/a 2.9 2.9 2.2 2.2 1.3 1.3 1.9 1.9 2.1 2Max 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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ARA ResearchWW Semiconductor Sales

Growth Rate Drop From Historical 15% CAGR to 6% Since 2000Given 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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ARA Research 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 IndexSecurities (Initiated Dec 1st 1993 at Base Value = $100)

Total Return Index (XSOX): Reinvests Cash Dividends on Ex-Date.; Synchronized toValue 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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ARA Research 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 = TheLast Sale Price Multiplied By Number of Shares Outstanding

Step 2) Calculate Weight of Each Index Component = Its Market Value Divided By Total Market Valueof Index

Step 3) Employ Capitalization Weighting Adjustment/Modification Algorithm to Limit Contribution ofLargest Market Cap Companies to 8% or Less (See Rebalancing Section)

Step 4) Calculate Aggregate “Modified” Capitalization Weighted Market Value = Sum of Each IndexComponent's Weight and Last-sale Price

Step 5) Divide Aggregate Weighted Market Value By Divisor, Which Scales Aggregate Value to LowerValue 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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ARA ResearchSOX Index Companies 2013 - 15Ticker Name Weight

(%)Index MMC ($B)

Market Cap ($B)


Index MMC ($B)


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 $9AMAT Applied Materials, Inc. 3.7 $16.3 $19.7 ALTR Altera (Intel) 2.7 $13.5 ALTR Altera (Intel) 3.3 $7ARMH ARM Holdings plc 1.8 $8.0 $23.1 AMAT Applied Materials, Inc. 6.2 $31.4 AMAT Applied Materials, Inc. 6.3 $14ASML ASML Holding NV 1.8 $8.0 $40.3 ARMH ARM Holdings plc 1.4 $6.9 AMD Advanced Micro Devices 0.7 $2ATML Atmel Corporation 1.0 $4.5 $3.6 ASML ASML Holding NV 2.0 $10.3 ARMH ARM Holdings plc 1.8 $4AVGO Avago Technologies 7.2 $32.3 $35.7 ATML Atmel Corporation 0.8 $4.0 ASML ASML Holding NV 3.0 $7CAVM 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 $8INFN Infinera Corporation 0.7 $3.3 $2.4 CREE Cree 0.9 $4.8 BRCM Broadcom (Avago) 3.8 $9INTC Intel Corporation 8.7 $39.1 $166.0 FSL Freescale (NXP) 1.5 $7.7 CREE Cree 2.2 $5KLAC KLA-Tencor Corporation 2.9 $12.9 $10.2 INTC Intel Corporation 7.8 $40.0 FSL Freescale (NXP) 1.2 $3LLTC Linear Technology Corp 3.1 $13.9 $11.3 KLAC KLA-Tencor Corporation 3.3 $16.7 INTC Intel Corporation 8.0 $18LRCX Lam Research Corporation 3.2 $14.5 $11.8 LLTC Linear Technology Corp 2.6 $13.0 KLAC KLA-Tencor Corporation 3.3 $8MCHP Microchip Technology Inc. 2.9 $13.0 $10.4 LRCX Lam Research Corporation 3.1 $16.1 LLTC Linear Technology Corp 2.9 $7MRVL Marvell Technology Group 1.3 $6.0 $5.0 MCHP Microchip Technology Inc. 2.2 $11.0 LRCX Lam Research Corporation 2.7 $6MSCC 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 $6MXIM Maxim Integrated Products 3.1 $14.1 $10.8 MXIM Maxim Integrated Products 2.1 $10.6 MRVL Marvell Technology Group 1.8 $4NVDA NVIDIA Corporation 4.3 $19.4 $15.4 NVDA NVIDIA Corporation 2.6 $13.5 MU Micron Technology, Inc. 4.7 $11NXPI NXP Semiconductors NV 4.2 $18.8 $22.3 NXPI NXP Semiconductors NV 4.0 $20.6 MXIM Maxim Integrated Products 2.6 $6ON 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 $7QRVO Qorvo, Inc. 2.1 $9.4 $7.7 RFMD RF Micro Devices (Quorvo) 0.9 $4.8 ON ON Semiconductor 1.0 $2SNDK SanDisk Corp. 4.5 $19.9 $16.0 SNDK SanDisk Corp. 3.9 $19.7 QCOM Qualcomm Incorporated 7.6 $17SUNE SunEdison, Inc. 0.7 $3.1 $2.5 SUNE SunEdison, Inc. 1.3 $6.7 SNDK SanDisk Corp. 4.6 $10SWKS Skyworks Solutions Inc. 3.4 $15.2 $15.8 SWKS Skyworks Solutions Inc. 2.8 $14.0 SWKS Skyworks Solutions Inc. 1.5 $3TER Teradyne Inc. 1.1 $5.0 $4.0 TER Teradyne Inc. 0.9 $4.8 TER Teradyne Inc. 1.0 $2TSM Taiwan Semiconductor Mfg 6.0 $26.7 $116.5 TSM Taiwan Semiconductor Mfg 4.2 $21.6 TSM Taiwan Semiconductor Mfg 5.9 $13TXN Texas Instruments Inc. 8.8 $39.4 $60.5 TXN Texas Instruments Inc. 8.3 $42.3 TXN Texas Instruments Inc. 8.0 $18XLNX 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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ARA ResearchSOX 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


Index MMC ($B)

Ticker NameALTR 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 DevicesATHR 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 CreeCREE Cree 3.16 $5.6 HITT Hittite Microwave (ADI)CRUS Cirrus Logic 0.57 $1.0 INTC Intel CorpHITT Hittite Microwave (ADI) 1.04 $1.8 KLAC KLA-Tencor CorpINTC Intel Corp 7.48 $13.2 LLTC Linear Technology CorpKLAC KLA-Tencor Corp 3.94 $7.0 LRCX Lam Research CorpLLTC Linear Technology Corp 3.72 $6.6 MU Micron TechnologyLRCX 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 MicroelectronicsNETL Netlogic Micro (BCOM) 1.26 $2.2 TER TeradyneNSM 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 ElectronicsPOWI 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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ARA Research SOX Index Cycles TableCycle 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 MaxUp 123% 50% 496%

Down -57% -69% -22%Neutral 3% -17% -4%

Median Min MaxUp 19 6 30

Down 10 7 17Neutral 14 11 17

Cycle Change Summary Cycle Length Summary

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ARA Research 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 StudyStep 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 StudyStep 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 PerformedStep 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