Annual Progress Report on Post Doctoral Fellowship

Annual Progress Report on Post Doctoral FellowshipAbhijeet Chandra (MS12IPF01)Mentor (& Co-author): Prof. M. ThenmozhiDoMS, IIT Madras(July 2012June 2013)

IntroductionResearch-in-progress:Investor sentiment index and stock market returnsIndia VIX and risk managementLiquidity in currency options market in IndiaVisible Output:Investor sentiment index: 5th Meeting of AoBF&EIndia VIX: Communicated as NSE Working PaperLiquidity in currency options: IICM Working PaperFuture plan:RevisionsInvestor Sentiment Index and Stock Market ReturnsAccepted for presentation at the 5th Annual Meeting of the Academy of Behavioral Finance & EconomicsDePaul University, Chicago, IL, USASeptember 17-20, 2013MotivationTheorists challenging the underlying assumptions of CAPM, EMH and other finance theories (Slovic et al., 1977; Kahneman & Tversky, 1979; Thaler et al., 1985):Rational expectations, of economic agents,Ability to quickly processing of information,Every market participant is correct on the average.Investor sentiment affects aggregate financing patterns of investors (Shiller, 2000; Henderson et al., 2006; Kim & Weisbach, 2008).Sentiment of market participants drives prices to abnormal levels (Baker and Wurgler, 2007; Baker, Wurgler & Yuan, 2012).Slovic et al, 1977: Behavioral Decision TheoryKahneman & Tversky,1979: The Prospect Theory: Decision Making under Risk and UncertaintyThaler et al., 1985: De Bondt, Werner F.M. and Richard H. Thaler. "Does the Stock Market Overreact?" Journal of Finance 40.

Shiller, 2000:

4Research ObjectivesRelationship between aggregate investor sentiment and stock market returns:Create a quantitative measure of aggregate investor sentiment for Indian market;Correlation between aggregate investor sentiment measure and stock market in the form of return predictability;Effect of total investor sentiment on Indian stock market; andCausality between sentiment measure and market returns.Data and VariablesMarket-related implicit proxies for investor sentiment:Turnover-volatility multiple (TVM),Ratio of imbalances between total buy volume to total sale volume (IBS),Ratio of trading volume of put options to that of call options (PCR),No. of IPOs (NIPO), andDividend premium (DP)Stock market returns: NSE Nifty index logarithmic returnsData frequency: Monthly (156 obs.)Period: Jan-2000 to Dec.2012Sentiment Index: ConstructionAggregate sentiment index:First principal component of orthogonalized five MRIPs; explains 48% of the sample variance.TotSenttt = 0.301*TVRt + 0.045*IBSt 0.209*PCRt + 0.345*NIPOt 0.0688*DPt To filter out the idiosyncratic noise, aggregate sentiment index is decomposed into:Rational component using five macro series (Industrial Production Growth, Inflation, Term Premium, Short-term Interest Rate, & Exchange Rate), andIrrational component (Senttt): residuals of first-step regression of the above fundamental factors and aggregate sentiment measure.Sentiment Index: PropertiesDescriptive StatisticsCorrelation(p-value)MeanSDMinMaxTVMIBSPCRNIPODPSenttNiftyTVM0.0720.0310.0110.2031.00(.)IBS0.0060.057-0.3200.2410.231(0.094)1.00(.)PCR0.2960.1370.0980.589-0.098(0.271)-0.072(0.125)1.00(.)NIPO3.9851.6240.00018.00-0.395(0.000)-0.108(0.118)-0.286(0.032)1.00(.)DP-0.0670.342-3.0912.0140.268(0.072)0.628(0.032)-0.019(0.231)-0.197(0.103)1.00(.)Sentt0.0846.328-13.2434.680.682(0.000)0.142(0.327)0.126(0.301)0.037(0.128)0.197(0.098)1.00(.)RetNifty8.0410.01216.8318.9760.451(0.082)0.104(0.429)0.331(0.004)0.521(0.003)0.329(0.042)0.634(0.008)1.00(.)Sentiment Index and Market Returns

Sentiment Index and Market ReturnsModel 1Model 2Constant-0.1925(0.1301)[0.3185]-0.0132(0.0001)[0.0083]Sentt (t-1)-0.1987(0.0259)[0.0000]-0.3234(0.0188)[0.0000]RetNifty(t-1)--0.02485(0.0193)[0.0810]R20.35610.4124Adj. R20.35540.3087F-stat79.427883.9810Sentt is the total investor sentiment and RetNifty is the Nifty returns.Standard error and pvalue are reported in ( ) and [ ], respectively.Model 1: RetNifty = 0 + 1*Sentt(t-1) + Model 2: RetNifty = 0 + 1*Sentt(t-1) + RetNifty (t-1) + SummaryConstruction of composite investor sentiment measure from MRIPs and decompose it into rational and irrational sentiment components;Statistically significant negative relationship between past level of investor sentiment and present stock market returns;Our measure of investor sentiment serves as a strong contrarian predictor of future stock market returns;More significant predictor than past returns (Verma-Soydemir, 2009);Irrational and idiosyncratic sentiment of market participants causes and determines movements in stock prices (Baker and Wurgler, 2007; Baker, Wurgler & Yuan, 2012).India Volatility Index andRisk ManagementBased on the work carried out under National Stock Exchange Commissioned Research InitiativeCommunicated as NSE Working PaperForthcomingIndia Volatility Index (India VIX)Introduced by National Stock Exchange of India Ltd. in April 2008Measures market expectations of near-term volatilityIn terms of the rate and magnitude of changes in pricesA proxy for risk widely recognized in academia and industryDiagonally opposite movements of India VIX and Nifty Index

Research QuestionsIs India VIX a true indicator of market risk?Does it capture risk more accurately, compared to other traditional risk measures?Does India VIX indicate investor sentiment?How is India VIX related to market returns?How do we use India VIX for trading?Data Variables and MethodsData period: 1-Mar-2009 to 30-Nov-2012Daily closing prices of Nifty Index spot and futures, India VIX, and Low Volatility Index (LVX).Data source: National Stock Exchange of India Ltd. DatazoneMethodologyMultiple regression frameworkFinite sample performance criteria: Root mean square error (RMSE), Mean absolute error (MAE), Mean absolute percentage error (MAPE)Quantile regression approachComputed volatility estimates:Std. Dev., GARCH(1,1), EGARCH(1,), Realized Volatility, and Ex-post VolatilityIndia VIX as Risk Measure: Theoretical BackgroundImplied volatility index efficient in reflecting historical volatilityFlemming (1998), Jiang & Tian (2005), Dowling & Muthuswamy (2005)Limited efficiency of implied volatility index in estimating historical volatilityBecker et al. (2006), Frijns et al. (2008), Becker et al. (2009)Even if biased, implied volatility index does a better job than any historical volatility measuresEvidence from 12 volatility indices: Siriopoulos & Fassass (2009)Unbiased estimate of future realized volatility: Kumar (2012).India VIX as Risk Measure: PerformanceIndependent variable: India VIX (in percentage terms)Dependent variableConstantAdj. R-squareF-StatisticStd. dev. of Nifty returns(STDEV)-0.002241(0.000398)[-5.627820]0.059930(0.001534)[39.05863]***0.6251911525.576Daily variance estimator(RVOL1)-0.000360(2.11E-05)[-17.10039]0.002245(8.12E-05)[27.64348]***0.455032764.1617Realized volatility(RVOL2)-0.007205(0.000421)[-17.10039]0.044891(0.001624)[27.64348]***0.455032764.1617(B) Independent variable: Return on GARCH volatility estimatesStd. dev. of Nifty returns(STDEV)0.012610(0.000194)[64.98644]0.004906(0.002747)[1.786133]*0.0023913.190272Daily variance estimator(RVOL1)0.000196(8.51E-06)[23.02321]0.000230(0.000121)[1.904725]**0.0028673.627976Realized volatility(RVOL2)0.003920(0.000170)[23.02321]0.004591(0.002410)[1.904725]**0.0028673.627976Standard errors and t-statistics are reported in ( ) and [ ] respectively.*** Significant at 1% level; ** significant at 5% level; * significant at 10% .India VIX as Risk Measure: Performance(C) Independent variable: Return on EGARCH volatility estimatesDependent variableConstantAdj. R-squareF-StatisticStd. dev. of Nifty returns(STDEV)0.012606(0.000194)[64.86276]0.002424(0.002938)[0.825161]-0.0003490.680891Daily variance estimator(RVOL1)0.000196(8.53E-06)[22.93766]5.92E-05(0.000129)[0.459236]-0.0008640.210898Realized volatility(RVOL2)0.003914(0.000171)[22.93766]0.001184(0.002579)[0.459236]-0.0008640.210898(D) Independent variable: Ex post volatility estimatesStd. dev. of Nifty returns(STDEV)0.010466(0.000256)[40.96350]0.052056(0.004401)[11.82765]***0.131916139.8933Daily variance estimator(RVOL1)0.000113(1.14E-05)[9.916760]0.002012(0.000196)[10.23976]***0.102031104.8527Realized volatility(RVOL2)0.002262(0.000228)[9.916760]0.040232(0.003929)[10.23976]***0.102031104.8527Standard errors and t-statistics are reported in ( ) and [ ] respectively.*** Significant at 1% level; ** significant at 5% level; * significant at 10% .India VIX as Risk Measure: PerformanceRoot Mean Square Error (RMSE)India VIX (%)GARCH volatility estimatesEGARCH volatility estimatesEx post volatilityStd. dev. of Nifty returns (STDEV)0.0035920.0058610.0058690.005467Daily variance estimator(RVOL1)0.0001900.0002570.0002580.000244Realized volatility (RVOL2)0.0038020.0051430.0051520.004880(B) Mean Absolute Error (MAE)Std. dev. of Nifty returns (STDEV)0.0022940.0039010.0039030.003557Daily variance estimator(RVOL1)9.00E-050.0001310.0001310.000119Realized volatility (RVOL2)0.0018010.0026140.0026150.002378(C) Mean Absolute Percent Error (MAPE)Std. dev. of Nifty returns (STDEV)17.7246032.4866532.5171629.2306Daily variance estimator(RVOL1)52.5368099.93958100.304984.30777Realized volatility (RVOL2)52.5368099.9358100.304984.30777India VIX as Risk Measure: SummaryIVIX explains realized volatility in all three cases and results are statistically significant.GARCH volatility estimate also explains realized volatility but results are not as statistically significant as in case of IVIX; EGARCH volatility estimate yields statistically insignificant results, hence not capable to capture realized volatility.Ex-post volatility also captures realized volatility with statistically significant results, but the explanatory power of this measure vis--vis IVIX is very low (low R-square values).Using performance criteria such as RMSE, MAE, and MAPE supports the above findings:India VIX emerges as the best estimate of realized volatility compared to measures from ARCH/GARCH family and ex-post volatility measures;India VIX explains realized volatility irrespective of measures used to compute the same.India VIX and Stock Returns: BackgroundAs market volatility rises, investors demand higher expected returns and prices go up!Inverse relationship between volatility and returnsFlemming et al. (1995), Dash & Moran (2005), Kumar (2012), Sarwar (2012)Volatility index as a barometer of investors downside fear than that of their excitementWhaley (2009), Giot (2005a)Asymmetric nature of volatility index-return relationshipWhaley (2000), Simon (2003), Skiadopoulos (2004), Ting (2007), Kumar (2012)Counter evidence: Dowling & Muthuswamy (2005), Siriopoulos & Fassass (2009)India VIX and Stock Returns: ModelingOur model takes the form of multiple regression as follows:IVIXt = 0 + 1*IVIXt-1 + 2*NiftyRet+ + 3*NiftyRet- + 4*DevMA5+ + 5*DevMA5- + where,IVIXt is first difference of the IVIX at time t,IVIXt-1 is the lagged value of change in India VIX,NiftyRet+ and NiftyRet- are positive and negative Nifty returns for same day, andDevMA5+ and DevMA5- are positive and negative percentage deviations of the closing Nifty from its five-day moving average.India VIX and Stock Returns: ResultsVariableModel 1Model 2Model 3Model 4Model 5Model 6Constant0.421748(0.153655)[2.744781]***0.291226(0.146569)[1.986960]**0.300961(0.133550)[2.253540]**0.153416(0.141911)[1.081067]0.253676(0.133795)[1.895999]**0.085257(0.132001)[0.645881]India VIXt-1-0.018025(0.005845)[-3.084024]***-0.002456(0.005765)[-0.425984]-0.030570(0.005124)[-5.966468]***-0.010671(0.005657)[-1.886461]**-0.034244(0.005308)[-6.451712]***-0.024601(0.005305)[-4.637139]***Nifty Rett (+)-48.13079(4.782851)[-10.06320]***-32.81898(4.882665)[-6.721530]***-42.34883(5.479945)[-7.727966]***Nifty Rett(-)-95.61711(5.468687)[-17.48447]***-104.6000(5.983996)[-17.47995]***-84.47708(7.686176)[-10.99078]***DevMA5t (+)0.010245(0.001106)[9.261779]***0.003085(0.001398)[2.205922]**DevMA5t (-)-0.003135(0.000953)[-3.289066]***-0.008306(0.001137)[-7.306667]***Adj. R-square0.0090500.1053980.2534030.1803940.2634260.308731F-statistic9.51120755.90176159.165569.15717111.748083.98100India VIX and Stock Returns: SummaryWe examine the impact of Nifty on implied volatility w.r.t. its sign-based historical returns and deviations from central tendency:Change in India VIX is regressed upon its own lagged value, +ve and -ve returns on Nifty, and +ve and -ve % deviation of Nifty from its 5DMA.Nifty returns exhibit significant directional impact on India VIX:Higher +ve returns Greater declines in India VIX, andHigher ve retunrs Greater increases in India VIX.Any positive returns by themselves reduces fear in market and changes investor sentiment to positive node.Downward trend of stock prices reinforces the effect of negative returns and IVIX rises even more.Results obtained by using quantile regression approach and by replacing India VIX with LVX provide similar results and support our findings thus far.India VIX and Market Timing: BackgroundCapital market equilibrium and investors risk-aversion allows MRP to be positively related to market portfolio variance (Merton, 1987) and also to expected volatility (French et al., 1987)Any unexpected +ve change in volatility leads to unexpected ve stock returns.This argument used to design trading strategies based on volatility index movements.Copeland & Copeland (1999)Market timing strategies based on portfolio size (small-cap vs. large-cap) and portfolio style (value and growth)Bagchi (2012)Positive and significant relationship between India VIX and value-weighted portfolios based on beta, market-to-book value, and m-capIndia VIX and Market Timing: MethodsPortfolio proxies:CNX Nifty index futures as a proxy for large-cap portfolio, andNifty Midcap 50 index as a proxy for mid-cap portfolio.Difference in returns on Nifty futures index and the Nifty midcap futures index on the percentage change in India VIX:(RNifty, t RMidcap, t )= + *IVIXt + twhere,RNifty, t is returns on the Nifty futures index at time t,RMidcap, t is returns on the Nifty Midcap futures index at time t, andIVIX is the change in India VIX.Market Timing with India VIX: ResultsHolding period(in days)%-age change in IVIXNumber of days*Cumulative returnsDaily average returns111111020304050702716141-0.145560.095030.054740.026360.01595-0.002110.003360.005260.005640.0048511-10-20158770.126510.063970.001540.003782222210203040508333221820.118560.102710.048230.027050.018310.001480.002940.003310.004420.0045222-10-20186990.074910.047110.000790.002193333310203040509338272220.095030.109760.064350.017390.011530.001080.002710.003550.002370.0024533-10-202051170.087830.054160.000830.00212101010101010203040501376154383-0.02198-0.018940.032970.021180.02172-0.00017-0.000310.000930.001640.002241010-10-202881970.049300.080010.000340.00189* indicates the number of days the portfolio remains in a given position.Positive percentage change in the India VIX implies long large-cap portfolio, and negative percentage change in the India VIX indicates long mid-cap portfolio.Market Timing with India VIX: ResultsWe switch from mid-cap to large-cap portfolio when India VIX increases, and vice versa.Tested for different holding periods, i.e. 1, 2, 3, and 10 days;Also, different percentage changes in India VIX levels taken as signal to switch portfolios.Switching to large-cap portfolio based on India VIX changes results in +ve cumulative returns in 17/20 cases.Switching portfolios based on lower (10%) change in India VIX gives negative returns in two cases.Using higher percentage change in India VIX as signal to switch portfolio appears a useful strategy to maintain +ve portfolio returns.SummaryIVIX a better predictor of realized volatility than traditional conditional models.Significant negative relation between IVIX and Nifty returns.Two indices move independently in case of higher upward movements;Not so significant relationship for higher quantiles in case of negative movementsStrong candidate for risk management and portfolio insuranceHigher percentage change in IVIX acts as a signal to switch between large- and mid-cap portfolios - This portfolio size-based strategy ensures positive returns.India VIX can be useful for traders and investors to mitigate risk.Regulators can introduce Volatility-based derivative products whose payouts are explicitly linked to volatilityLiquidity in Currency Options Market in IndiaPresented at the XIth Capital Markets Conference 2012Indian Institute of Capital Markets, Navi MumbaiDecember 2012IICM-SSRN Working Paper: http://ssrn.com/abstract=2255475 LiquiditySignals the feasibility for a trader to buy or sell a security for a fair price;Provides opportunity to move in and out of positions without any noticeable premiums or discounts on fair market prices.irrespective of trade sizeTrading of options on USD-INR currency pair introduced by NSE in Oct. 2010.Currency options trading at NSE generates highest trading volume in the world (WFE, 2011).139,296 contracts worth Rs.636.78 cr. as on Dec. 2010;11,103,261 contracts worth Rs 6,057.03 cr. as on Sep. 2012.31Theoretical backgroundLiquidity-as-sentiment theory (Baker & Stein, 2004):Rational investors under-react to the info contained in trade order flows, thereby boosting liquidity;Market is dominated by irrational investors, and hence overvalued;High liquidity signals a positive sentiment of irrational investors, leading to low expected returns.32Theoretical background contLiquidity and VolatilityInventory models of liquidity:Negative relationship between liquidity and volatility (Stoll, 1978; Amihud & Mendelson, 1980; Copeland and Galai, 1983)Information-based models of liquidity (mixed relationship):Informed trading amidst a larger group of uninformed traders leads to a positive relationship between volatility and liquidity (Admati & Pfleiderer, 1988; Barclay & Warner, 1993)Specialist knowledge of the presence of informed traders results in a negative relationship between volatility and liquidity (Foster & Vishwanathan, 1990; Pastor & Stambaugh, 2003)33Theoretical background contAmbiguous information gives rise to illiquidity in the market where risk-neutral arbitrageurs chose not to trade in a rational equilibrium (Ozsoylev & Werner, 2011).Virtually, no study on liquidity in currency options market;We attempt to study the issue of liquidity and its relationship with other factors in the currency market in India.34ContributionsValidates the behavioral finance-based theories of liquidity:Liquidity-as-sentiment theory (Baker & Stein, 2004),Liquidity under rational equilibrium theory (Ozsoylev & Werner, 2011)Adopts a contemporary approach to examine the issue of liquidity in currency options market:Liquidity measurement in a time-series framework, Fresh evidences from an emerging market,Examines the dynamic relationship of liquidity with returns, volatility, and speculation.35Research ObjectivesHow is liquidity (or lack of it) in the Indian currency options market related to exchange rate returns?Whether it influences (or gets influenced by) exchange rate volatility?Whether speculators capital drive the liquidity in currency options market?36Measures of (il-)liquiditySome proxy measures of liquidity:Bid-ask spread (Amihud & Mendelson, 1986; Eleswarapu, 1997; Brennan & Subrahmanyam, 1996);Trading volume (in the sense of Black, 1971);Open interest (Pan & Poteshman, 2006)Our study uses Amihud (2002) measure of illiquidity as follows:The daily ratio of absolute price change per Rupee of daily trading volume:

37Data and Measurement VariablesData variables:Illiquid: Market-level illiquidity in USD-INR currency options market, following Amihud (2002),ExReturn: Spot USD-INR exchange rate return,ExVol: Exchange rate volatility [following conditional volatility measure GARCH(1,1)],OptSpec: Speculation in currency options market, adapted from Campbell et al. (1993).Sample period: Nov. 2010 Oct. 2012First 5 months data exhibit abnormal trend; hence removed.Data used for further analysis: April 2011-Oct. 2012.Data source: NSE and RBI websites38MethodologyPreliminary analysis: Co-integration test:There exists co-integration between variables;implying long-term equilibrium relationship.

Final analysis: dynamic relationship between variables examined using:Vector error correction model (VECM) estimates, Impulse Response Functions, andVariance decomposition analysis.39Data AnalysisData grouped into two sets, to see if relationships between the variables change during the recent period:Entire data: April 2011 Oct. 2012, andRecent period: Nov. 2011 Oct. 2012.

Data series tested for:Stationarity using ADF and PP tests,ACF and PCFAppropriate lag length: 640Exchange rate, return and volatility

41Illiquidity and trading volume

42Descriptive StatisticsSpot USDOptTVolExReturnExVolIlliquidityOptSpecMean49.28346917139.70.0004003.37E-050.0003101.085039Median49.17750828563.00.0004522.83E-050.0004491.008025Maximum57.216503792800.0.0192440.0001670.0909143.076671Minimum43.9485022661.00-0.0265594.55E-06-0.1051200.032209Std. Dev.4.210975589338.30.0056662.34E-050.0123760.497921Skewness0.2733871.150509-0.0076901.5181310.0852050.963986Kurtosis1.5610995.5063064.5806406.54526823.895644.185466ADF test statistic-20.6989***#-5.454908**-20.66095***-3.97877**-10.64435***-9.568614***PP test stat.-20.7004***#-9.085177**-20.66237***-4.007201**-24.48080***-13.50272***Observations487487487487487459***Significant at 1% level; **Significant at 5% level; *Significant at 10% level.#The data series is stationary at 1st difference.Pair-wise CorrelationIlliquidityExReturnExVolOptSpecIlliquidity1.000000ExReturn0.630442***1.000000ExVol0.006241-0.0106131.000000OptSpec0.056967*0.013168-0.21044***1.000000***Significant at 1% level; **Significant at 5% level; *Significant at 10% level.Illiquidity is a proxy of illiquidity in currency options market computed as a daily ratio of absolute price change in spot exchange rate market and trading volume in derivative market; ExReturn is measured as the log return on daily changes in spot exchange rate of the USD-INR currency pair; ExVol refers to the daily exchange rate volatility measured by the GARCH(1,1) approach; and OptSpec measures the speculation in currency pair market following Campbell et al. (1993) methodology.Results and Findings (Entire data)Illiquidity ExReturn relationship:VECM (with 6 lags) shows negative relation,Evidence of turn-of-month effect,No day-of-week effect found.Illiquidity ExVol relationship:Illiquidity does not influence volatility, neither does volatility to illqidity,Global volatility, proxied by CBOE VIX, has no effect on illiquidity in currency options market.Illiquidity OptSpec relationship:Speculating activities drive illiquidity in currency options market (sig. at all 6 lags).45Results and Findings (Recent period)Negative bi-directional causality between Illiquidity and ExReturn;Significant at all lags.No significant causality from ExVol to Illiquidity; weak reverse causality.OptSpec tends to influence positively both Illiquidity (lag=1) and ExVol (all lags).Bi-directional causality between ExReturn and ExVol, former causing later positively, and vice versa.46Results and Findings cont47

ConclusionOur study theoretically supports Baker & Steins (2004) liquidity-as-sentiment theory whereby liquidity and returns are negatively related.Turn-of-month effect prevails (hypothetically) implying high illiquidity at turn-of-month when traders are busy looking at other things.No significant relationship between liquidity and exchange rate volatility (may be because other macro and global factors affects volatility more than market factors).Speculating activities in currency options market tend to drive liquidity in recent period.This liquidity pressure from speculators resulting in high illiquidity may further drive prices and volatility (Ozsoylev & Werner, 2011).48Limitations & Future ScopeOur measure of illiquidity follows time-series approach using market-level daily data;Cross-sectional framework using intraday data on various strike prices for currency options may yield better results.

Liquidity-as-sentiment theory may further be tested under rational expectations of traders;This supposedly contributes to the liquidity-price-return relationship literature in the context of currency options market.49Future workInvestor Sentiment Index:Test the empirical as well as statistical validity of the Investor Sentiment Index with various proxies and other indicators of investor sentiment such as consumer confidence index.Use this Investor Sentiment Index to derive market price of risk/any other pricing kernel to be used in the behavioral asset pricing model.India VIX:Use the change in India VIX as a signal to switch between portfolios, we propose to test this approach with style-based portfolio such as growth versus value portfolios.Liquidity in Currency Options:Examine whether illiquidity in the market could be resulting from ambiguous information and how this gets influenced by risk-neutral arbitrageurs decision of not to trade in a rational equilibrium.Thanks!51India VIXDescriptive Statistics: Raw VariablesNiftyLVXIVIXCBOE VIXMean5146.3403683.98525.0536123.18010Median5232.0503883.89522.9600021.28000Maximum6312.4504520.70056.0700052.65000Minimum2573.1501661.87013.0400013.45000Std. Dev.624.3712610.95297.9405827.208186Skewness-1.534916-1.3884391.3769481.253091Kurtosis6.7235144.45354394.8597004.294683Jarque-Bera906.3077392.8145429.7343309.6657Probability0.0000000.0000000.0000000.000000Top Decile5825.1054294.91837.19433.514Bottom Decile4512.3752774.08416.97915.99Observations934934934934India VIX Descriptive Statistics: Return SeriesNifty ReturnIVIX ReturnLVX ReturnMean0.000808-0.0011210.001041Median0.000720-0.0020670.001070Maximum0.1633430.2081960.104831Minimum-0.060216-0.243570-0.031225Std. Dev.0.0140370.0519970.009539Skewness1.6588200.2222261.241408Kurtosis22.382634.47366017.71371Jarque-Bera15048.8092.201818665.095Probability0.0000000.0000000.000000Observations934934934India VIX Correlation: Raw VariablesIVIXNiftyCBOE VIXLVXIVIX1.000000Nifty-0.811718***1.000000CBOE VIX0.677311***-0.697315***1.000000LVX-0.866983***0.930436***-0.619206***1.000000*** significant at 1% level; * significant at 10% levelIVIX ReturnNifty ReturnLVX ReturnIVIX Return1.00000Nifty Return-0.494539***1.00000LVX Return-0.488565***0.919125***1.00000*** significant at 1% levelCorrelation: Return SeriesIndia VIX Descriptive Statistics: Volatility MeasuresStandard DeviationDaily Variance Estimator (RVOL1)Realized Volatility(RVOL2)Ex-post Volatility MeasureMean0.0126000.0001960.0039110.155179Median0.0110640.0001260.0025200.119212Maximum0.0427600.0018460.0369212.592992Minimum0.0050342.47E-050.0004940.0001481Std. Dev.0.0058740.0002580.0051560.154338Skewness2.6574134.7153004.7153005.213915Kurtosis12.7769527.8101327.8101368.73642Jarque-Bera4721.25326858.2526858.25165523.9Probability0.0000000.0000000.0000000.000000Observations915915915915India VIX Descriptive Statistics: Conditional Volatility EstimatesGARCH(1,1) VolatilityEGARCH(1,1) VolatilityMean0.0438450.045705Median0.0599650.058477Maximum7.5577537.663823Minimum-3.109903-2.964650Std. Dev.1.0030921.004331Skewness0.4464170.478095Kurtosis6.3743736.511658Jarque-Bera474.1430515.4981Probability0.0000000.000000Observations934934India VIX as Risk Measure:Correlation between volatility measuresStd. Dev.RVOL1RVOL2Ex post Volatility MeasureGARCH Volatility EstimateEGARCH Volatility EstimateStd. Dev.1.00000RVOL10.948971***1.00000RVOL20.926482***0.984672***1.00000Ex post Volatility0.363974**0.319085**0.301089**1.00000GARCH Volatility 0.922315***0.923289***0.956223***0.236389**1.00000EGARCH Volatility 0.893097***0.779721***0.792348***0.308795**0.893625***1.00000*** significant at 1% level; ** significant at 5% levelIndia VIX and Returns:Quantile Regression ResultsConstantNifty Ret (+)Nifty Ret ()QuantileCoefficientStd. Errort-StatisticCoefficientStd. Errort-StatisticCoefficientStd. Errort-Statistic0.100-0.0407890.004830-8.445208***-2.8853200.622635-4.634048***-1.8713600.589094-3.176677***0.200-0.0290410.002741-10.59554***-2.3065640.347787-6.632114***-2.3126530.250906-9.217224***0.300-0.0208700.002360-8.842491***-2.1140440.247809-8.530949***-2.5270820.304024-8.312119***0.400-0.0134670.002359-5.709776***-2.0009820.279463-7.160094***-2.8758010.347046-8.286503***0.500-0.0085620.002322-3.687392***-1.6826960.295368-5.696958***-3.4795950.322039-10.80488***0.600-0.0026790.002287-1.171526-1.4349950.306797-4.677347***-3.6117490.274700-13.14797***0.7000.0034560.0025931.332803-0.7255210.484944-1.496091-3.8202240.281722-13.56028***0.8000.0123040.0022485.474460***-0.0753280.083317-0.904114-3.8900670.290346-13.39802***0.9000.0311280.0031869.771529***-0.0414100.315799-0.131128-4.3001890.453381-9.484719****** Significant at 1% level.Method: Quantile regression (Median); Sparsity method: Kernel (Epanechnikov) using residuals.India VIX and Returns:Quantile Regression SummaryQuantile regression estimates used to capture conditional quantile functions instead of conditional mean functions (as in OLS).Provides more robust results in support of earlier findings.Negative relationship b/w India VIX and Nifty index returns in either direction, particularly around the center of distribution (Q0.5)Relationship holds more for market declines than for advances; Effect is sharper for higher quantiles.A portfolio with some component of IVIX would not get adversely affected in sharp upward movements in the market.India VIX: Market TimingHolding period (in days)R-squareF-statistics1-0.161193(0.004484)[-35.95108]0.134635(0.028021)[4.804764]***0.03219423.085762-0.161603(0.004490)[-35.98797]0.127837(0.028044)[4.558404]***0.02911120.779053-0.162012(0.004496)[-36.03410]0.121602(0.028070)[4.332072]***0.02640418.766854-0.162373(0.004506)[-36.03569]0.114246(0.028115)[4.063491]***0.02333816.511965-0.162741(0.004512)[-36.06922]0.108393(0.028137)[3.852310]***0.02105514.8402910-0.164102(0.004535)[-36.18846]0.093022(0.028182)[3.300736]***0.01565610.8948415-0.165538(0.004548)[-36.39563]0.080082(0.028190)[2.840760]**0.0117288.06991520-0.166754(0.004561)[-36.55864]0.072786(0.028218)[2.579402]*0.0097616.653317***significant at 1% level, ** significant at 5% level, and *significant at 10% level.