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\title{Hedging Effectiveness Analysis of High Market Cap Indian Stocks Using OLS and GARCH Hedge Ratios}
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             \author[1]{Dr. P.A.Mary  Auxilia}

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\date{\small \em Received: 11 December 2016 Accepted: 31 December 2016 Published: 15 January 2017}

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\begin{abstract}
        


Managing portfolios is a daunting task in the current environment of complex integrated financial markets. Fund managers are always facing the question of whether to Hedge or not. Though hedging is done for minimizing the value erosion of the portfolio,  there have been times where hedging has proved to be a wrong decision. In this context, this research is done to find out the impact of dynamic hedging of a portfolio comprising of high market cap stocks using Nifty index futures during the period from Jan 2007 to Dec 2012. As the study focused on the practical aspects of trading, hedge ratio required to hedge the portfolio was determined with two important econometric methods OLS (Ordinary least squares) and GARCH (Generalized autoregressive conditional heteroscedasticity) using Eviews software. The research proves that the equity risk of a portfolio can be offset by hedging the portfolio with nifty index futures. The study concludes that during periods of uncertainty an investor holding a portfolio containing high market cap stocks can do hedging. The traditional simple OLS model is preferred to complex GARCH model in calculating hedge ratio.

\end{abstract}


\keywords{hedging, high market capitalization, index futures, OLS, GARC.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
conomic development of a country to a large extent is dependent on the smooth functioning of its financial markets. A financial market that is robust is expected to foster economic growth and social welfare  {\ref (Singh, 1991)}. Financial markets pose a great risk to the investor's in spite of its high returns. The market risk can be reduced by portfolio insurance (Wikipedia). Derivative markets help in increasing the trading volume in financial markets because the objective of trading is not only for investment purposes but also for risk management objectives of market participants (Madhumathi \& Ranganatham, 2012). \hyperref[b0]{Adams and Montesi, (1995)} found that corporate managers prefer futures to options by virtue of the large transaction costs in option trading. Investors recognize that there is a close relationship between changes in the index and changes in the values of their portfolios. This makes index futures contract is used as a tool to show how movements in the market affects the value of a portfolio \hyperref[b6]{(Grant, 1982)}. Forecasting hedge ratio is important for hedgers in derivative market, as forecasting is an important tool in decision making. \hyperref[b9]{(Koenker \& Bassett, 1978)}.\par
Hedge ratio can be determined with different models derived by econometrics -OLS, ARCH, GARCH and VECH models to name a few.  {\ref Ederington (1979)} and  {\ref Johnson (1960)} employed portfolio theory to derive the minimum variance hedge ratio (HR) as the "average relationship between the changes in the cash price and the changes in the futures price". \hyperref[b2]{Engle (1982)} suggested ARCH model. If an autoregressive moving average model (ARMA model) is assumed for the error variance, then the model is known as generalized autoregressive conditional heteroskedasticity GARCH model \hyperref[b1]{(Bollerslev 1986)}.\par
Individual and institutional investors are exposed to equity risk. Predicting the movement of market is not an easy task as rightly proved by the Nobel laureate (Eugene  {\ref Fama, 2013} {\ref Fama, \& 1966))}. Stock prices are extremely difficult to predict in the short run, and that new information is very quickly incorporated into prices. In order to minimize the risk due to the adverse movement in the market there is a need for the investors to protect their portfolio value. For investors in India it is even more challenging as the volatility in Indian market is not constant and it varies over time (Securities and Exchange Board of India, 1998). \hyperref[b8]{Mary \& Vishwanath, (2013)} proved that in high PE stock portfolios, capital can be protected by hedging. With this bckground, this research examines whether hedging the portfolio with Index futures gives economic benefit to the investors.\par
II. 
\section[{Research Methodology a) Data collection}]{Research Methodology a) Data collection}\par
The research is done with only secondary data obtained from periodicals, journals, website and magazines. Period of study is from January 2008 -December 2012 and daily stock and nifty index futures closing prices were taken. 2007 data is used for determining the hedge ratio. 
\section[{Year ( )}]{Year ( )} 
\section[{C c) Sampling Framework}]{C c) Sampling Framework}\par
Based on prefixed parameter ten High Market cap stocks are drawn from the population using a non probability sampling technique, judgement sampling method. The sample consists of 10 stocks constituting a portfolio worth 1 crore (10 million) rupees. Each stock is given an equal weightage of rupees 10 lakhs (1 million) worth.\par
Hedging Effectiveness Analysis of High Market Cap Indian Stocks Using OLS and GARCH Hedge Ratios As on 1/1/2008 the portfolio was constructed for 1 crore rupees by giving equal weightage of 10 lakhs (1 million) rupees to each stock. Number of shares bought for a value of 10 lakhs for each stock is as follows:\par
ii. Hedged Portfolio return\par
The number of nifty futures contract required to hedge the portfolio worth Rupees 1 crore is determined by calculating the hedge ratio. In this study hedge ratio is obtained using two different econometric methods i) Ordinary Least squares -OLS ii) GARCH , and the results are compared to find out the method which gives better returns.\par
The hedge ratio for 2/1/2008 is calculated using previous one year data i.e daily closing price of stock and closing price of nifty index futures from 1/1/2007 to 31/12/2007. Hedge ratio is calculated for every 3 months. So, for each stock every year hedge ratio is determined 4 times and for the total period of study it was determined 20 times for rebalancing of the portfolio. Likewise, hedge ratios were calculated for all the stocks in each sample set based on two methods OLS and GARCH with the help of Eviews software.\par
Hedge ratio calculation:? = ? (?S/ ?F)\par
where ?S is the standard deviation of ?S, the change in the spot price during the hedging period, standard deviation of ?F, the change in the futures price during the hedging period, ? is the coefficient of correlation between ?S and ?F.\par
Rebalancing is done every three months to adjust the number of contracts to be hedged and the trading profit is calculated. Number of contracts to be hedged: Vp x h* / Vi Vp -Value of the portfolio. h* -Hedge ratio. Vi -Value of one index future.\par
The portfolio value without hedging and the hedged portfolio value is compared to prove the hedging effectiveness. For proving this statistical tests are done with the help of SPSS software.  
\section[{?F is the}]{?F is the} 
\section[{T-Test -Mcap OLS hedged return and Mcap GARCH hedged return}]{T-Test -Mcap OLS hedged return and Mcap GARCH hedged return}\par
Ho : There is no significant difference between the Mcap OLS hedged portfolio returns and GARCH hedged portfolio returns. H1: There is a significant difference between the Mcap OLS hedged portfolio returns and GARCH hedged portfolio returns.  
\section[{Findings and Discussion}]{Findings and Discussion}\par
Indian equity investors can hedge their portfolio with nifty index futures as hedging reduces loss to a great extent based on this study. Even during the worst of times hedged portfolio value remains unscathed compared to the unhedged open portfolio. Use of complex heteroscedastic models are discouraged as simple OLS model is giving better results than complex heteroscedasticity GARCH models as observed. Even when there are differences in performance, they are very minimal which can be ignored. It can be noticed that when a portfolio is hedged it can withstand harsh bearish conditions like that of 2008 crash.\par
Though we have ignored the transaction cost it can affect the portfolio performance if more churning is done or if the transaction costs are prohibitive. However in the current low cost (brokerage) scenario the impact of transaction cost will be minimal in the Indian context. Fund managers can use either fundamental factors or technical tools to decide when to hedge the portfolio. This study is useful for Investors in selecting the right kind of stocks for the portfolio. In this study it is proved that high Mcap stocks can be hedged effectively using index hedging. Investors can invest in high Mcap stocks as they provide the best appreciation even during uncertain periods and hedging is very effective. 
\section[{IV.}]{IV.} 
\section[{Conclusion}]{Conclusion}\par
The research proves that the equity risk of a portfolio can be offset by hedging the portfolio with nifty index futures. The hedged value determined based on OLS (Ordinary least squares) method is high for Market Cap stock portfolios than GARCH (Generalized autoregressive conditional heteroscedasticity) model. So, the traditional simple OLS model is preferable to complex GARCH model in calculating hedge ratio/beta. During periods of financial crisis like 2008-2009 maximum loss covered by hedging the portfolio is up to 68\%. The protection of a portfolio through hedging should not encourage investors to use it indiscriminately for unwarranted situations. Only Unhedged portfolio can fulfill the objective of the portfolio by giving good returns. Hedging should be used as an anchor in a sailing ship charting risky waters. Hence use of hedging should be restricted to special situations where there is an inherent risk of market crash and the portfolio should be unhedged under normal circumstances. This spring's another question; when to hedge or whether to hedge or not?. This situation is a tricky one as further research is needed to find out the suitability of stop loss or other models to initiate hedging. Both fundamental and technical analysis tools may be employed to arrive at the decision. 
\section[{Mean}]{Mean}\begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.13737373737373737\textwidth}P{0.7126262626262626\textwidth}}
1\tabcellsep Reliance\\
2\tabcellsep Infosys\\
3\tabcellsep HUL -Hindustan Unilever Ltd\\
4\tabcellsep HDFC\\
5\tabcellsep HDFC Bank\\
6\tabcellsep ONGC-Oil and Natural Gas Corporation\\
7\tabcellsep NTPC\\
8\tabcellsep Tata Consultancy Services\\
9\tabcellsep ITC\\
10\tabcellsep SBI -State Bank of India\\
\tabcellsep Source: www.nse.com\\
d) Financial Analysis\tabcellsep \end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.85\textwidth}}
Source: Authors compilation.\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.85\textwidth}}
Source: Authors research output using data from www.nse.com\end{longtable} \par
 
\caption{\label{tab_2}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.3957427536231884\textwidth}P{0.10086050724637681\textwidth}P{0.14089673913043477\textwidth}P{0.13858695652173914\textwidth}P{0.07391304347826086\textwidth}}
\multicolumn{2}{l}{In similar way unhedged portfolio return is}\tabcellsep \tabcellsep \tabcellsep \\
calculated every month for 5 years\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep 2017\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep Year\\
Date Portfolio Value in Rs. Hedge ratio Nifty Value of nifties to be hedged in Rs. Profit/ Loss in Rs. Date Portfolio Value in Rs. Hedge ratio Nifty Value of nifties to be hedged in Profit/ Loss in Rs. Value of extra nifties hedged in Rs. tot hedge in Rs. Un hedged value in Rs. Trading profit in Rs. Hedged value in Rs. Rs.\tabcellsep 1-Jan-08 9998896.1 0.6802 6144.35 6801249 0 1-Jan-08 9998896.1 0.7015 6144.35 0 0 9998896.1 9998896.05 7014226\tabcellsep 1-Feb-08 8778964.8 0.6802 5317.25 5885506 429521 1-Feb-08 8778964.8 0.7015 5317.25 429521 88637.4 6158444 8778964.8 944178.89 9723143.69 6069806\tabcellsep 3-Mar-08 7977702.3 0.6802 4953 5562387 409065.1 3-Mar-08 7977702.3 0.7015 4953 421874.68 -140211 5596358 7977702.3 1366053.6 9343755.82 5736569\tabcellsep Volume XVII Issue III Version I Global Journal of Management and Business Research ( ) C\\
Value of extra nifties hedged in Rs.\tabcellsep 0\tabcellsep 85946.06\tabcellsep -135954\tabcellsep \\
tot hedge in Rs.\tabcellsep \tabcellsep 5971452\tabcellsep 5426433\tabcellsep \\
Unhedged value in Rs.\tabcellsep 9998896.1\tabcellsep 8778964.8\tabcellsep 7977702.3\tabcellsep \\
Trading profit in Rs.\tabcellsep 0\tabcellsep 915510.3\tabcellsep 1324575\tabcellsep \\
Hedged value in Rs.\tabcellsep 9998896.05\tabcellsep 9694475\tabcellsep 9302278\tabcellsep \end{longtable} \par
  {\small\itshape [Note: Source: Authors research output using data from www.nse.com]} 
\caption{\label{tab_3}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.05642135642135642\textwidth}P{0.20360750360750363\textwidth}P{0.19256854256854258\textwidth}P{0.19992784992784993\textwidth}P{0.19747474747474747\textwidth}}
\tabcellsep Date\tabcellsep Unhedged portfolio value\tabcellsep OLS Hedged value in Rs.\tabcellsep GARCH Hedged value in Rs.\\
\tabcellsep 1-Jan-08\tabcellsep 9998896\tabcellsep 9998896\tabcellsep 9998896\\
\tabcellsep 1-Feb-08\tabcellsep 8778965\tabcellsep 9723144\tabcellsep 9694475\\
\tabcellsep 3-Mar-08\tabcellsep 7977702\tabcellsep 9343756\tabcellsep 9302278\\
\tabcellsep 1-Apr-08\tabcellsep 7555383\tabcellsep 9162612\tabcellsep 9113811\\
\tabcellsep 2-May-08\tabcellsep 8424073\tabcellsep 9480263\tabcellsep 9419544\\
\tabcellsep 2-Jun-08\tabcellsep 7651525\tabcellsep 9264630\tabcellsep 9215956\\
\tabcellsep 1-Jul-08\tabcellsep 6433563\tabcellsep 9009214\tabcellsep 8981359\\
Year\tabcellsep 1-Aug-08\tabcellsep 7296548\tabcellsep 9167081\tabcellsep 9227024\\
16\tabcellsep 1-Sep-08 1-Oct-08\tabcellsep 7178987 6620391\tabcellsep 9138187 9122432\tabcellsep 9187090 9103742\\
Volume XVII Issue III Version I\tabcellsep 3-Nov-08 1-Dec-08 1-Jan-09 2-Feb-09 2-Mar-09 1-Apr-09 4-May-09 1-Jun-09\tabcellsep 5387486 4918888 5374288 4993423 4824524 5377937 6449779 7717239\tabcellsep 9218522 9308613 9201967 9170367 9124227 9163493 9534188 9762530\tabcellsep 9101810 9150694 9085503 9027243 8971733 9050244 9398719 9594129\\
( ) C\tabcellsep 1-Jul-09\tabcellsep 7550233\tabcellsep 9811931\tabcellsep 9650388\\
Global Journal of Management and Business Research\tabcellsep 3-Aug-09 1-Sep-09 1-Oct-09 3-Nov-09 1-Dec-09 4-Jan-10 1-Feb-10 2-Mar-10 1-Apr-10 3-May-10 1-Jun-10 1-Jul-10 2-Aug-10 1-Sep-10\tabcellsep 8241071 8105053 8979411 7907787 8633103 9051016 8590524 8642354 8948289 8866261 8520929 8926718 9392359 9543286\tabcellsep 10034082 10007535 10298128 9932823 9913832 10188779 10134538 10041111 10014283 10002144 9918298 10030060 10358432 10478217\tabcellsep 9895867 9863872 10183521 9787841 9800858 10081953 10060727 9955496 9901625 9887423 9795859 9916299 10193533 10301716\\
\tabcellsep 1-Oct-10\tabcellsep 10563767\tabcellsep 10974948\tabcellsep 10603327\\
\tabcellsep 1/11/2010\tabcellsep 10524647\tabcellsep 10964823\tabcellsep 10564207\\
\tabcellsep 1/12/2010\tabcellsep 10258371\tabcellsep 10874342\tabcellsep 10329223\\
\tabcellsep 14-Jan-11\tabcellsep 9945800\tabcellsep 10905671\tabcellsep 10202263\\
\tabcellsep 1-Feb-11\tabcellsep 9802455\tabcellsep 11055185\tabcellsep 10642861\end{longtable} \par
  {\small\itshape [Note: Source: Authors research output using data from www.nse.co e) Statistical Analysis]} 
\caption{\label{tab_4}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.28694267515923566\textwidth}P{0.04331210191082803\textwidth}P{0.04331210191082803\textwidth}P{0.04331210191082803\textwidth}P{0.4331210191082802\textwidth}}
12000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
10000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
8000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
6000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep Unhedged portfolio value\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep OLS Hedged value in Rs.\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep GARCH Hedged value in Rs.\\
4000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
2000000\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1-Jan-08\tabcellsep 1-Jan-09\tabcellsep 1-Jan-10\tabcellsep 1-Jan-11\tabcellsep 1-Jan-12\end{longtable} \par
 
\caption{\label{tab_5}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.24132492113564669\textwidth}P{0.2225552050473186\textwidth}P{0.18769716088328073\textwidth}P{0.018769716088328076\textwidth}P{0.018769716088328076\textwidth}P{0.010725552050473186\textwidth}P{0.1501577287066246\textwidth}}
Year\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
18\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Volume XVII Issue III Version I\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
( )\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Global Journal of Management and Business Research\tabcellsep \multicolumn{2}{l}{Differences Std. Deviation Mean MCAPOLS Mean 1.01E7 MCAPGARCH 9.847235E6}\tabcellsep t\tabcellsep N 63 63\tabcellsep df\tabcellsep (2-tailed) Sig Std. Deviation 642885.676 5.0545330E5\\
\tabcellsep 2.8910411E5\tabcellsep 2.2931995E5\tabcellsep \multicolumn{2}{l}{10.007}\tabcellsep 62\tabcellsep .000\\
\tabcellsep \tabcellsep \multicolumn{5}{l}{Source: Authors research output using data from www.nse.com}\end{longtable} \par
  {\small\itshape [Note: C 2017 © 2017 Global Journals Inc. (US) 1Figure 1: Comparison chart of unhedged portfolio value with OLS/GARCH hedged portfolio values.]} 
\caption{\label{tab_6}Table 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.7607431340872374\textwidth}P{0.03570274636510501\textwidth}P{0.01235864297253635\textwidth}P{0.01098546042003231\textwidth}P{0.005492730210016155\textwidth}P{0.0247172859450727\textwidth}}
Mean\tabcellsep \multicolumn{2}{l}{Differences Std. Deviation}\tabcellsep t\tabcellsep df\tabcellsep Sig (2-tailed)\\
\multicolumn{2}{l}{-1.64282E6}\tabcellsep 9.76155E5\tabcellsep -13.358\tabcellsep 62\tabcellsep .000\\
\multicolumn{3}{l}{Result: The table 8 \& 9 shows that Market Cap un}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{hedged portfolio value is Rs.84,93,523 while that of}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{Market Cap hedged portfolio(OLS) value is}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{Rs.1,01,00,000. The null hypothesis H 0 is rejected and}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{alternate hypothesis H 1 is accepted as sigma value is 0.}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{Inference: The objective of hedging the portfolio and}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{effectiveness is achieved as the Market Cap hedged}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{portfolio (OLS) return is around the expected value}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{which is proved by the rejection of null hypothesis. There}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{is 16\% gain over the unhedged value which is}\tabcellsep \tabcellsep \\
contributed by the hedge.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
III.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_7}Table 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9} \par 
\begin{longtable}{P{0.056666666666666664\textwidth}P{0.7933333333333333\textwidth}}
N\tabcellsep Std. Deviation\end{longtable} \par
 
\caption{\label{tab_8}Table 9 :}\end{figure}
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