does market volatility affects hedge effectiveness

8/8/2019 Does Market Volatility Affects Hedge Effectiveness

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Title of the Paper: Does Market Volatility Affects Hedge Effectiveness? An Empirical

Investigation of Time-Invariant and Time-Varying Hedges During Period of Financial

Crisis in Indian Futures Market.

Authors Detail

1. Sanjay Kumar Thakur, PhD Student in Finance, SJMSOM,IIT Bombay. India.

2. SVD Nageswara Rao, Associate Professor, SJMSOM, IIT Bombay, India.

Author for Correspondence

Sanjay Kumar Thakur , PhD Student, Shailesh J. Mehta School Of Management, Indian

Institute of Technology Bombay, Powai, Mumbai. PIN-400076. India.

Phone No.: +91-22-25764785

Email Id: [email protected]


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DOES MARKET VOLATILITY AFFECTS HEDGE EFFECTIVENESS?AN EMPIRICAL

INVESTIGATION OF TIME-INVARIANT AND TIME-VARYING HEDGES DURING PERIOD OF

FINANCIAL CRISIS IN INDIAN FUTURES MARKET.

Sanjay Kumar Thakur and SVD Nageswara Rao

ABSTRACT

Financial derivatives are extensively used as hedging instruments worldwide, including

emerging markets like Malaysian, Italian, and Portuguese equity markets. However,

hedging ones stock position through futures is still the road less traveled in India.

This study is, therefore, an attempt to explore Indian futures market for hedging by equity

holders in general as well as in period of financial crisis. We have estimated effectiveness

of the optimal hedge ratio based on HKM [Herbst, Kare and Marshall (1993)] methodology

with benchmark model JSE [Johnson (1960), Stein (1961) and Ederington (1979)]

methodology for futures. Hedge ratio based on HKM methodology is a time-variant

whereas hedge ratio based on JSE methodology is a constant and time-invariant. To bring

the comparison of hedge effectiveness on equal level (from transaction cost point of view),

time-varying hedge ratio estimated based on HKM methodology time-invariant and then

Bases using the hedge ratios are estimated.

For empirical validation of the Effectiveness of the optimal hedge ratios and their stability

in normal as well in the period of financial crisis, the study of S&P Nifty Index {National

Stock Exchange of India (NSE) 50 Index and its futures is conducted using daily data for

the year 2005 (representing normal period) and January,2007 to June,2009 (representing

turbulent time period) based on the value of volatility index.

Result suggest that hedge using HKM model is more effective than that of hedge based on

JSE model. The results are statistically significant at 95% confidence level. An additionalcontribution of this study is to help the hedger to decide when to re-balance the hedge.

KEYWORDS : Hedging, Market Risk, Capital Market, Futures Market, Regression, Time-

Varying Hedging Models.


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DOES MARKET VOLATILITY AFFECTS HEDGE EFFECTIVENESS? AN EMPIRICAL

INVESTIGATION OF TIME-INVARIANT AND TIME-VARYING HEDGES DURING PERIOD OF

FINANCIAL CRISIS IN INDIAN FUTURES MARKET.

1.INTRODUCTION

Risks are omnipresent and exist from time immemorial. In financial parlance, risk is any

variation from an expected outcome. So, for an investor, risk includes an outcome when one

may not receive expected return (Stein, 1961). Traditionally, hedging has been motivated by

the desire to reduce riskby taking a position opposite to the exposure. The quest for better

hedge has been the motive for sophisticated risk management and hedging techniques.

Derivatives are used as tool to transfer risk i.e for hedgers (Bodla and Jindal,2006) and,

therefore, they are extensively used as hedging instruments worldwide, including emerging

markets like Malaysian, Italian, and Portuguese equity markets.

However, hedging ones stock position through futures and options is still the road less

traveled in India. Even when it is done, the techniques used have been too nave and

primitive. Lack of suitable hedging models for Indian market is a challenge to the risk

management system of participants and regulators. It is also a deterrent for attaining greater

market depth, and may severely affect the stability of Indian markets. Further, availability

of high frequency data in the recent past will help validate such models empirically.


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1.1MOTIVATION

Johnson (1960) has pointed out that hedgers prefer to hedge through futures market as it is

easier to square off and opt for cash settlement than taking actual delivery as is the case

with forward market, since the objective is to take advantage of relative price movements.

Hartzmark (1987) showed that hedging with futures is profitable. Evidence suggests that

futures are the most preferred choice for hedging in India. Therefore, this study focuses on

hedging price risk of equity through individual futures contracts. However, the models

used have been too nave and primitive and based on the assumption that the price

movements are negatively correlated, and hence gains from one market offset the losses in

the other. Even National Stock Exchange of (NSE) India Ltd., whose NCFM (NSE's

Certification in Financial Markets) certification is mandatory for market participants,

discusses nave hedging only. This study is, therefore, an attempt to explore Indian futures

market for hedging by equity holders. We reviewed the advances in HKM [Herbst, Kare

and Marshall (1993)] methodology, and compared it with JSE [Johnson (1960), Stein

(1961) and Ederington (1979)] methodology. We present a comparative study of HKM and

JSE methodology for estimating optimal hedge ratio and hedge Effectiveness for futures.

Finally, we propose to test JSE and HKM methodologies for estimating hedge

Effectiveness using daily data from Indian financial futures market.

The paper is organized as follows:


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Section 2 covers a brief review of hedging and its evolution in chronological order followed

by statement of hypotheses in Section 3. Results are discussed in Section 4 and conclusions

are included in Section 5.

2.REVIEW OF LITERATURE

There are two main hypotheses to explain hedging. They are: (i) Destabilizing force

hypothesis; and (ii) Market completion force / Non-destabilization hypothesis.

Destabilizing force hypothesis propounds that derivatives market attracts highly levered

and speculative participants due to lower trading costs, which creates artificial price

bubbles and increases volatility in spot market. Market completion force / non-

destabilization hypothesis states that introduction of derivatives complements the spot

market and improves information flow resulting in better investment choices for investors.

It may bring more private information to the market and disseminate the same faster. Some

studies suggest a possibility of speculators moving to derivatives market from spot market

due to lower transaction costs and other benefits like cash settlement. This may lead to

reduction in volatility.

Available evidence on financial futures can be divided into five areas:

(i) impact of (launch of) futures on spot market volatility {Shenbagaraman (2002),

Hetamsaria and Swain (2003), Nagraj and Kotha (2004), Thenmozhi and Thomas (2004),

Hetamsaria and Deb (2004), Josi and Mukhopadhyay (2004), Bodla and Jindal (2006),

Bagchi (2006), Rao (2007)}; (ii) Lead-lag relationship (reflected in price and non-price

variables) between futures and spot market { Srivastava (2003), Sah and Omkarnath


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(2005), Praveen and Sudhakar (2006), Mukherjee and Mishra (2006), Gupta and Singh

(2006)}; (iii) role of futures in price discovery {Sah and Kumar (2006), Gupta and Singh

(2006), Kakati and Kakati (2006)}; (iv) Impact of information and expiration effect on spot

prices {Thenmozhi and Thomas (2004), Barik and Supria (2005), Mishra, Kanan, and

Mishra (2006), Mukherjee and Mishra (2007)}, and (v) Better forecasting methods for

greater accuracy of derivatives prices { Ramasastri and Gangadaran (2005), Shrinivas,

Dulluri and Raghvan (2006), Mitra (2006)}.

There is very little evidence of hedging in the Indian context. Lack of evidence on such a

contemporary issue is surprising. There is evidence of hedging in different international

markets though {Johnson (1960) and Stein (1961) in commodity market, Dale (1981), and

Herbst, Kare, and Marshall (1993) in foreign exchange market, Ederington (1979), and

Franckle (1980) in fixed income securities market.} The evidence on use of equity and

equity futures as hedges is missing. Therefore, we have presented below a review of

literature from commodity, foreign exchange, and fixed income securities market.

Hedge is used to reduce the risk associated with a cash position or an anticipated cash

position. Keynes in his Treatise on Money (1930) envisioned futures market as an

insurance scheme for hedgers, who pay premium to speculators for taking their risk. The

basic assumption here is that hedgers are generally long in cash marketand therefore, they

need to hedge their position by taking short position in forward market or future market.

In general, for a position consisting of a number, Xi of physical units held in market i,

hedge may be defined as a position in market j of size Xj*units such that the price risk


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of holding Xi and Xj* from time t1 to t2 is minimized(Johnson,1960). Therefore,

Hedge ratio could be defined as the number of Xj*units (of hedging instrument) in market

j required to hedge one unit held in market i (cash position). So, a hedger would

protect his position in physical/cash marketby simultaneously selling sufficient number of

futures contracts. Once the underlying asset is sold, futures position may be squared off by

taking equal and opposite position (long position, in this case) in futures contract. Let S1,

and S2 denote the spot prices, and F1 and F2 the prices of futures at t1 and t2

respectively. Then, hedge ratio (h) is defined as:

(S2 - S1) = (F2 F1) . h

h = (S2 - S1) / (F2 F1) ..(1)

If the change in spot price is equal to that of futures, i.e, if the price movements are parallel,

the gain from one market offsets the loss in the other. Otherwise, he would be left with a

residual capital gain or loss.

The hedger will take a total gain (loss) arising from price movements from t1 to t2, equal

to the positive (negative) value of x[(S2, - S1) - (F2 F1)] for x unit of inventory.

The hedge is perfectly effective if [(S2- S1) - (F2 F1)] is equal to 0.

(S2- S1) = (F2 F1)

h = 1

This indicates parallel shift in prices in cash and futures markets. This is one of the

underlying assumptions of Keynes theory. This is a nave approach to hedging.


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However, Working (1960) has negated this assumption of parallel movement in prices of

spot and futures. He argued that this assumption is false, and an improper standard to test

the effectiveness of hedging. The effectiveness of hedging used with commodity storage

depends on inequalities in the movements of spot and futures prices, and on reasonable

predictability of such inequalities. This implies Hedge effectiveness may be measured

through Variation from Bases.

Bt = St h * Ft .. (2)

Therefore, Basis (B) is used as a measure of Hedge Effectiveness.

In the Johnson (1960), Stein (1961), and Ederington (1979) (henceforth referred to as JSE)

methodology, spot prices are regressed on futures prices using ordinary least squares (OLS)

method.

S = a + b. F + u .(3)

where a is the intercept term (expected to be zero), and b, is the estimate of h*.

There are limitations of this model as mentioned by Herbst, Kare, and Marshall (1993). For

example, residuals from JSE estimation of optimal hedge ratio are serially correlated and

therefore, a Box-Jenkins autoregressive integrated moving average (ARIMA) technique

should be used to estimate the minimum risk hedge to account for the observed serial

correlation (Herbst, Kare and Caples,1989). A commonly used alternative is first

differences. The merits of levels versus differences are discussed, in the context of foreign

currency hedging, by Hill and Schneeweis (1982). Another alternative is to specify the

problem as minimizing the variance of returns on wealth. This leads to a regression of

percent price changes, which is fairly clean.


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Hedge ratio is estimated as first difference of prices. So, changes in spot price are regressed

on changes in futures price.

.S a b F u = + + .... (4)

Where, terms a and b are constants, S = S(t) - S(t-1) and F = F(t,T) - F(t-1, T) and

u represents the error term. The term b (slope of the line) is optimal hedge ratio (with

minimum variance).

This was an improvement, though it retained some serious flaws. One of the limitations

emerged from the assumptions of regression. Regression can be used when relationship

between Explained Variable (St) and Explanatory Variable (Ft) is stable. This implies

constant basis irrespective of time of observation. In reality, in a direct hedge, the basis

must decline over the life of the futures contract and become zero at maturity. Franckle

(1980), in his reply to Enderington (1979), drew attention to this point and suggested a

modified hedge ratio that incorporates the declining basis. Castelino (1990) argued that

regression based hedge ratios must be time dependent. However, he argued that time

dependent hedge ratios can not be of minimum variance. In tests with financial futures on

short term interest rates, he claimed superior results vis-a-vis JSE by accounting for time in

the hedge ratio estimation. But his results had two limitations: (a) it is based on an arbitrage

model for treasury bonds that is of limited applicability to hedges with other futures

contracts, and (b) it implicitly relies on the stability of spot-futures relationship from the

prior year into the year of the hedge. The problem of instability of hedge ratio was also

addressed by others, such as Grammatikos and Saunders (1983), and Malliaris and Urrutia


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(1991a, 1991b). However, they did not address the problems arising from the exclusion of

time.

Equation (4) suggests that the relationship is not stable but time-varying.

F(t) = S(t) erT

S(t) = F(t) e-rT

Taking natural logarithm on both sides,

In[S(t)/F(t,T)] = -rT ..(5)

Equation (12) can be estimated as

ln[S(t)/F(t,T)] = a +dT + i (6)

Where a is the intercept term (expected to be zero), and d (the slope), is the estimate of

r. Once the coefficient of T in Equation (6) is estimated by regression, the optimal hedge

ratio can be estimated as:

h* = edT ..(7)

An important difference between the JSE hedge ratio and that defined by Equation (7) is

that the later can be revised daily once the estimate of full cost of carry is available (from a

few trading days of a futures contract). The estimated hedge ratio h*will change daily


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depending on the term to expiration of the futures contract. The JSE hedge ratio b, on the

other hand, is a constant estimated solely from the past data. Historical data may provide

poor estimate of the minimum variance hedge ratio, especially when the spot-to-futures

relationship is not stable.

Researchers attempted to offer measures of futures hedge effectiveness which improve on

the coefficient of determination offered by Johnson and popularized by Ederington. (1979).

However, there is confusion due to synonymous use of the terms "effectiveness" and

"efficiency''. Some of the examples include Howard and Antonio (1984), Chang and

Shanker (1987), Chang and Fang (1989).

It is, therefore, pertinent to clarify the concepts here.

Hedge's effectiveness may be defined as the degree to which it reduces the risk associated

with a cash position. This definition deliberately ignores the cost of hedging. A hedge is

effective if it reduces risk relative to no hedge. A hedge is efficient if there does not exist

another hedge offering greater expected profit with the same or less risk (Herbst and

Marshall, 1990). Equivalently, a hedge is efficient if there does not exist another hedge

carrying less risk with the same or greater expected profit. A hedge can be said to be

effective if the variance of returns on the hedged portfolio is the lowest.

2.1ADJUSTMENTS FOR COMPARISON OF HEDGE EFFECTIVENESS


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The hedge ratio based on HKM model is time varying where as JSE model provides a

constant hedge ratio. Obviously hedge employed based on HKM Model may need more

frequent re-balancing which may increase transaction costs like commissions and cost of

personnel and technological resources. Transaction cost is not considered in our study.

However, HKM model based Hedge Ratio should be more efficient even if the hedge-

rebalancing is done less frequently as be the case with the hedge ratio based on JSE Model.

Therefore, we have estimated h* based on JSE method and HKM method on the previous

month data and hedge was employed for the next month keeping the hedge ratio constant

throughout during the period (without re-balancing the ratio).

As Hedge effectiveness may be measured through Variation from Bases. Therefore, Bases

(actual and absolute) based on JSE and HKM model is estimated for every month and of

the selected sample of data. Bases are calculated as follows:

BJSE = |S(t) hJSE*

F(t)|

BHKM = |S(t) hHKM*F(t)|

The lower the mean absolute basis (B), the better the hedge. Lower variance of basis means

more effectiveness.

Also, Basis (B) expressed as percentage of the average spot price will provide more clarity

about the deviation and stability of the basis.

3.HYPOTHESES

This study is an attempt to estimate hedge ratio and hedge Effectiveness. We have

compared JSE and HKM methodologies for estimating hedge Effectiveness using daily

nifty index data from Indian financial futures market for the period of January 01, 2005 to


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July 31, 2005 and November 01, 2007 to June 30, 2009. The model with the lower estimate

of B (in equation 2) was considered better.

The hypotheses are:

(1) H0: There is no difference between the mean Bases based on JSE and HKM

methodology.

H1: Bases based on JSE methodology is greater than that based on HKM methodology .

(2) H0: There is no difference between mean of bases (as % of the spot price) based on JSE and

HKM methodology.

H1 : Mean bases (as % of the spot price) based on JSE methodology is more than that based on

HKM methodology.

4.RESULTS AND DISCUSSION

0 JSE HKM

1 JSE HKM

H : B = B

H : B > B

0 JSE HKM

1 JSE HKM

H : % B = % B

H : %B > %B


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The daily closing prices are used for nifty index and its futures. The estimates of optimal

hedge ratio using the two methods (JSE and HKM) h*, and the Hedge Replication (Vt)

which is estimated as ( h* x Ft) are included in table 1 and table 2 for the normal period

(year 2005) and period of turbulence(November,2007- June,2009).

Table 1: Estimates of h* and Vt* during normal period (Year 2005)

Table 2: Estimates of h* and Vt* during Period of Turbulence)

h*JSE h*hkm Vt_JSE Vt_HKMNifty Index Mean Variance Mean Variance Mean Variance Mean Variance

Nifty_Feb050.9755 0.000 0.9980 0.000 2010.6333 911.8232 2056.8869 954.2578

Nifty_Mar050.9529 0.000 1.0002 0.000 1987.1538 3347.1158 2085.6335 3687.0902

Nifty_Apr051.0599 0.000 1.0020 0.000 2093.7578 3361.3119 1979.3583 3004.0335

Nifty_May050.9795 0.000 1.0039 0.000 1930.8780 2051.1708 1978.9011 2154.4693

Nifty_Jun050.9033 0.000 1.0085 0.000 1913.0179 2024.7796 2135.6964 2523.5895

Nifty_Jul050.9053 0.000 1.0069 0.000 2018.0976 1652.9175 2244.5625 2044.7032

h*JSE h*hkm Vt_JSE Vt_HKMNifty Index Mean Variance Mean Variance Mean Variance Mean Variance

Nifty_Jan081.0260 0.000 0.9974

0.000 5937.82 261143.15 5772.39 246794.86

Nifty_Oct080.9776 0.000 1.0007

0.000 3256.71 203214.25 3333.81 212950.47

Nifty_Jul081.0066 0.000 1.0017

0.000 4129.07 39062.46 4109.31 38689.42

Nifty_Apr090.9468 0.000 0.9997

0.000 3147.31 20680.14 3323.37 23058.46

Nifty_Sep080.9608 0.000 0.9972

0.000 4105.26 25067.26 4261.05 27005.91

Nifty_Jun080.9504 0.000 0.9962

0.000 4282.97 27847.30 4489.33 30595.43


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4.1VISUAL EVIDENCES

To visually see the performance of the hedge through these two models, we have plotted

the Actual Spot price and the Hedge Replication(Vt) based on both methodology. The

better hedge is one which can replicate the actual spot price more accurately. It is clearly

visible that Vt estimated based on HKM methodology replicate then actual index value

showing that hedge ratio estimated on HKM methodology is more effective than that of

hedge ratio estimated based on JSE methodology.

Secondly, the difference between the models, even though visibly may be small but will

have huge impact considering the size of the hedged instrument.

(A)VISUAL EVIDENCES (DURING JANUARY,2005-JULY,2005)


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(B)

Nifty_Feb05

Comparative Hedge Performance

1900

1950

2000

2050

2100

2150

28 24 22 20 16 14 10 8 6 2 0

Time to Expiry

Index

Value

Actual Nifty IndexVt_JSE

Vt_HKM

Nifty_Mar05


1900

1950

2000

2050

2100

2150

2200

30 28 24 22 20 16 14 10 8 3 30 29

Time to Expiry

Index

Value

Actual Nifty Index

Vt_JSE

Vt_HKM

Nifty_Apr05


1850

1950

2050

2150

2250

27 23 21 17 15 10 8 6 2 1 0

Time to Expiry

Index

Value

Actual Nifty Index

Vt_JSE

Vt_HKM


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Nifty_May05


1850

1900

1950

2000

2050

2100

28 24 22 20 16 14 10 8 6 2 0

Time to Expiry

Index

Valu

e

Actual Nifty Index

Vt_JSE

Vt_HKM

Nifty_Jun05


1850

1950

2050

2150

2250

2350

30 28 26 23 21 17 15 13 9 7 3 30 29

Time to Expiry

Index

Value Actual Nifty Index

Vt_JSE

Vt_HKM

Nifty_Jul05


1850

2050

2250

2450

28 22 16 10 6 0

Time to Expiry

IndexValue

Actual Nifty

Index

Vt_JSE

Vt_HKM


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(B)VISUAL EVIDENCES DURING PERIOD OF TURBULENCE (NOVEMBER,2007-JUNE,2009)

Following are the graphs of six selected months during the period financial crisis.

Nifty_Jan2008: Comparative Hedge Performance

4700480049005000510052005300540055005600570058005900600061006200630064006500

34 30 28 24 22 20 16 14 10 8 6 2 0

Time to Expiry

Index

Value

Actual Index Value

Vt_JSE

Vt_HKM

Nifty_Oct2008: Comparative Hedge Performance

2400250026002700

2800290030003100320033003400350036003700380039004000

33 29 26 22 19 15 13 9 7 5 1

Time to Expiry

Index

Value

Actual Index Value

Vt_JSE

Vt_HKM

Nifty_Jul2008: Comparative Hedge Performance

3800385039003950400040504100415042004250

43004350440044504500

34 30 28 24 22 20 16 14 10 8 6 2 0

Time to Expiry

Index

Value

Actual Index ValueVt_JSE

Vt_HKM


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Nifty_Apr2009: Comparative Hedge Performance

2900

2950

3000

3050

3100

3150

3200

3250

3300

3350

3400

3450

3500

31 30 29 28 24 22 21 17 15 14 13 10 9 8 7 6 3 2 1

Time to Expiry

IndexValue

Actual Index Value

Vt_JSE

Vt_HKM

Nifty_Sep2008: Comparative Hedge Performance

380038503900395040004050410041504200425043004350440044504500

27 24 23 21 20 17 16 15 14 13 10 9 8 7 6 3 2 1 0

Time to Expiry

Index

Value

Actual Index Value

Vt_JSE

Vt_HKM

Nifty_Jun2008: Comparative Hedge Performance

3900

4000

4100

4200

4300

4400

45004600

4700

4800

4900

5000

27 24 23 22 21 20 17 16 15 14 13 10 9 8 7 6 3 2 1 0

Time to Expiry

Index

Valu

e

Actual Index Value

Vt_JSE

Vt_HKM


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4.2BASES AS MEASURE OF HEDGE PERFORMANCE :ACOMPARISON

The estimates of the absolute Bases and Bases as % of spot price using the two methods (JSE and HKM ar

the normal period (year 2005) and period of turbulence (November,2007- June,2009).

Table 3

Table 4

|BJSE| |BHKM| |BJSE| as %of Spot

Nifty Index Sum Mean Variance Sum Mean Variance Mean Max. M

Nifty_Feb05 902.591 6.686 11.411 722.662 5.353 11.377 1.76% 3.80%Nifty_Mar05 7818.448 57.914 203.029 2372.458 17.574 144.979 4.91% 7.25%

Nifty_Apr05 3161.494 23.418 22.514 605.326 4.484 9.669 2.81% 4.03%Nifty_May05 427.087 3.164 3.299 330.772 2.450 5.971 0.83% 1.96%

Nifty_Jun05 1445.548 10.708 1.796 278.761 2.065 1.139 3.80% 5.07%

Nifty_Jul05 2374.071 17.586 18.434 498.655 3.694 13.527 2.42% 4.90%

|BJSE| |BHKM| |BJSE| as %of Spo

Nifty Index Sum Mean Variance Sum Mean Variance Mean Max. Nifty_Jan08 6980.881 51.710 25.303 841.621 6.234 20.018 7.74% 11.09%Nifty_Oct08 1752.901 12.984 6.320 523.691 3.879 6.068 3.44% 5.61%Nifty_Jul08 3145.064 23.297 13.940 461.875 3.421 16.052 5.25% 7.98%Nifty_Apr09 546.973 3.890 14.426 526.651 1.841 0.623 0.81% 11.45%Nifty_Sep08 4795.362 35.521 43.458 659.941 4.888 20.191 6.30% 8.60%Nifty_Jun08 4994.616 36.997 56.032 183.084 1.356 1.385 11.31% 12.14%


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Table 5 (a) : t-test Statistics

Nifty_Jan2008t-Test: Two-Sample Assuming UnequalVariances

Basis_JSE Basis_HKM

Mean 46.7238 3.456006

Variance 17.3216 6.46616

Observations 21.0000 21

Hypothesized Mean Difference 0.0000

df 33.0000

t Stat 40.6534

P(T


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Table 5 (b) : t-test Statistics

Nifty_Jan2008

t-Test: Two-Sample Assuming EqualVariances

%_Basis_JSE %_Basis_HKM

Mean 0.0227 0.0017

Variance 0.0000 0.0000

Observations 21.0000 21.0000

Pooled Variance 0.0000

Hypothesized Mean Difference 0.0000

df 40.0000

t Stat 40.0689

P(T


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5.CONCLUSIONS

We have estimated hedge ratios (h*) using one month January 2005 future data and kept both

hedge ratios constant for 1 month (from January, 2005 to July, 2005) implying that hedge is

employed without re-balancing. Then we estimated bases based on these two methodology.

For the period of financial crisis (November 2007 to June 2009), we selected six most

volatile months for Nifty Index during the global financial crisis (January 2008, October

2008, July 2008, April 2009, September 2008 and June 2008) based on Volatility Index

(VIX) of National Stock Exchange of India and repeated the same exercise to estimate hedge

ratios based on both methodology and their bases to estimate the hedge effectiveness keeping

hedge ratio time-invariant throughout these months. Effectiveness of optimal hedge ratios

using HKM model are found to be significantly better for index futures at 95% confidence

level. In all cases, hedge based on HKM methodology has been found more effective than

that of based on JSE methodology .

Key findings are as follows.

(1) Hedge Performance based on OHR estimated on theoretically superior method (like

HKM in case of Futures) has given superior results.

(2) Even after making h*HKM time-invariant, Hedge Performance based on hedge ratio

estimated on theoretically superior method (like HKM) has given superior results.

(3) Implication for Hedger : h*HKM and Basis estimated based on HKM methodology

allows a hedger to decide when to re-balance and re-balancing strategy based on Bases as 5

of the spot price.

These models with suitable modification(s) may be used for hedging in Indian stock,

commodity, and foreign exchange markets.


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6.REFERENCES

Abe De, J.; Frans De, R. & Veld, C. (1997), 'Out -Of-Sample Hedging Effectiveness Of

Currency Futures For Alternative Models and Hedging Strategy', Journal of Futures Markets

(1986-1998)17(7), 817-837.

Aggrwal, R. & Ldemaskey, A. (1997), 'Using Derivatives in Major Currencies For Cross-

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does market volatility affects hedge effectiveness

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