Analysis of NIFTY Futures

8/8/2019 Analysis of NIFTY Futures

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Analysis of NIFTY Futures

Contents`Introduction ................................ ................................ ................................ ................................ ...... 3

Futures Pricing ................................ ................................ ................................ ................................ ... 3

Nifty Futures Explained ................................ ................................ ................................ ...................... 5

Analysis ................................ ................................ ................................ ................................ ............. 6

NIFTY INDEX Futures expiring in September2010 ................................ ................................ .............. 6

t-statistic (p-value) ................................ ................................ ................................ ......................... 6

Adjusted R-square 99.4% ................................ ................................ ................................ ............ 6

Time Series: Test for Stationary................................ ................................ ................................ ...... 6

Comparison of Actual, Theoretical and Regression Model Results ................................ ................ 11

NIFTY INDEX Futures expiring on 26th

August2010 ................................ ................................ .......... 13

t-statistic (p-value) ................................ ................................ ................................ ....................... 13

Adjusted R-square 99.4% ................................ ................................ ................................ .......... 13

Time Series: Test for stationary ................................ ................................ ................................ .... 13

Comparison of Actual, Theoretical and Regression Model Results ................................ ................ 17


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IntroductionFutures are standardized financial instruments in which two party form a contract to sell and

buy the specified asset in the specified standardized quantity and quality at a future date on a

price that is agreed upon today. This price is called the future price of the asset for the given

period.

These securities are exchange traded and the underlying asset for these securities may vary

from the traditional commodities to financial assets like the currency, securities etc. or it can

be even a reference like equity index or the interest rates. In futures contract both parties are

under the obligation to honor the contract. Since these are the exchange traded securities

these are safe form counter party risk as the exchange act as the counter party for both the

buyer and the seller and at the settlement date it can be settled eitherthrough the delivery of

the asset or through the cash settlement. These contracts are marked to margin to remove any

risk for default from the either party.

Futures PricingThe pricing of futures are determined by the equilibrium between the demand and supply

among the buyers and sellers at the time of trading the contract.

There are different arguments when it comes to the pricing of the futures contract. If thesupply of the underlying asset is in plentiful or can be created freely than the futuresare set to

be priced through the arbitrage argument.When the asset are limited then the demand and

supply is the only force that is setting the price of these contracts. So the forward price

represents the expected future value of the underlying discounted at the risk free rate. As any

deviation from the theory will lead to the arbitrage and create the opportunity to create a

riskless profit.

Se e s

B ye s


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Thus, for a simple, non-dividend paying asset, the value of the future/forward,F(t), will be

found by compounding the present value S(t) at time tto maturity Tby the rate of risk-free

return r.

Or, with continuous compounding

When the deliverable commodity is not in plentiful supply (or when it does not yet exist)

rational pricing cannot be applied, as the arbitrage mechanism is not applicable. Here the

price of the futures is determined by today's supply and demand for the underlying asset in

the futures.

In this Study we have tried to use this model to study and see how closely the actual pricing

of a nifty future index follows the Arbitrage argument of rational pricing.

We have taken ln(F(t)) as the dependent variable and the ln S(t) and ln(r(T-t)) as the

independent variable.

Where F (t) = Future price at the time t

S (t) = spot price at time t

T-t = Time to maturity


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Nifty Futures Explained


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Anal sis

NIFTYINDEX Futures expiring in September2010

As per Regression analysis, it can be seen that value of coefficients of ln_x (which is log of

Spot Price) and RT (product of interest rate and time left to maturity) is 0.999969 and

0.359943.

t-statistic (p-value)

The p-value of the coefficients is less than 0.05 which shows that they are significantly

different from zero.

Adjusted R-square 99.4%

This basically shows that 99.4% of the variation in the dependent variable (ln_f i.e. the log of

price of futures price of Nifty Index). 99.4% is a very significant value which means that

almost all variables responsible for change in value of futures price have been considered.

Time Series: Test for Stationar


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Above figure shows the ADF test conducted for checking the whether the Time -series data is

necessary that has been used. As we can see the p-value is less than 0.05 which shows that

the hypothesis that Time-series data is stationary has a unit root can be rejected and hence,

the time-series is stationary.

Assumption 1: Mean of error

Mean of residual was a compared to zero and p -value was calculated.

p-value = 0.9985

This shows that Null hypothesis cannot be rejected that mean of error term is zero, which

basically shows that error term is not significantly different from zero. So, th is assumption is

satisfied.


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Assumption 2: Normality

The p-value was calculated by conducting Histogram-Normality test on residuals, the p-

value was 0.531 which means that the null hypothesis of that error term is normality

distributed cannot be rejected.


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Assumption 3 Hetroscedasticity

Here, p-value > 0.05, so it cannot be said that the regression estimates are Homoscedastic in

nature. i.e. with change in observations, the variations in the error term should not change

and should remain constant and also does not have any tendency of any kind of trend.

Assumption 4: Autocorrelation

Durbin-Watson stat

For 43 observations

In this case, d = 1.95

This means that we cannot reject the null hypothesis that there is No positive/negative

autocorrelation.

This shows that autocorrelation does not exist in this case.


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Removing Hetroscedasticity

Solving the regression equation using White test so as to remove hetrscedasticity, we get

There is a no change in values of coefficients. Only change that is there is in value of

individual standard errors.

Equation after satisfying all assumptions:

Which basically shows that the value of futures is dependent on both the Spot Price as well

as product of interest rate, but in actual scenario the model that is followed by NIFTY index

future depends on various market forces like trends (bullish/bearish) as well as costs like

brokerage cost.


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Comparison ofActual,Theoretical and Regression Model Results

As we can see the values obtained as per theoretical model are higher when compared to

those with regression model. The reason for this can be explained by saying that theoreticalmodel doesnt take care of various market trends and other costs like brokerage costs

involved while entering into the transaction

5200

5250

5300

5350

5400

5450

5500

5550

5600

Futures Price

egressed Value

Theoretical Value


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Analysis

Dependent Variable: LN_F

Method: Least Squares

Date: 08/25/10 Time: 15:30

Sample: 5/28/2010 8/24/2010

Included observations: 63

Variable Coefficient Std. Error t-Statistic Prob.

LN_S 1.000216 7.10E-05 14081.81 0.0000

RT -0.353349 0.119256 -2.962948 0.0043

R-squared 0.993965 Mean dependent var 8.578898

Adjusted R-squared 0.993867 S.D. dependent var 0.029564

S.E. of regression 0.002315 Akaike info criterion -9.267311

Sum squared resid 0.000327 Schwarz criterion -9.199275

Log likelihood 293.9203 Durbin-Watson stat 0.622251


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NIFTYINDEX Futures expiring on 26thAugust2010

As per Regression analysis, it can be seen that value of coefficients of ln_x (which is log of

Spot Price) and RT (product of interest rate and time left to maturity) is 0 1.000216 and -

0.353349.

t-statistic (p-value)

The p-value of the coefficients is less than 0.05 which shows that they are significantly

different from zero.

Adjusted R-square 99.4%

This basically shows that 99.4% of the variation in the dependent variable (ln_f i.e. the log ofprice of futures price of Nifty Index). 99.4% is a very significant value which means that

almost all variables responsible for change in value of futures price have been considered.

Time Series: Test for stationar


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The p-value was calculated by conducting Histogram-Normality test on residuals, the p-

value was 0.294 which means that the null hypothesis of that error term is normality

distributed cannot be rejected.

Assumption 3 Hetroscedasticity

Here, p-value < 0.05, so it can be said that the regression estimates are Homoscedastic in

nature. i.e. with change in observations, the variations in the error term will not change and

remain constant and also does not have any tenden cy of any kind of trend.

Assumption 4: Autocorrelation

Durbin-Watson stat

For 63 observations

In this case, d = 1.507


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This means that we can reject the null hypothesis that there is No positive/negative

autocorrelation. SO, there is some correlation which has to be removed.

Removing Autocorrelation

Solving the regression equation using Newey West test so as to remove auto-correlation, we

get

Dependent Variable: LN_F

Method: Least Squares

Date: 08/25/10 Time: 15:46

Sample: 5/28/2010 8/24/2010

Included observations: 63

Variable Coefficient Std. Error t-Statistic Prob.

LN_S 1.000216 7.10E-05 14081.81 0.0000

RT -0.353349 0.119256 -2.962948 0.0043

R-squared 0.993965 Mean dependent var 8.578898

Adjusted R-squared 0.993867 S.D. dependent var 0.029564

S.E. of regression 0.002315 Akaike info criterion -9.267311

Sum squared resid 0.000327 Schwarz criterion -9.199275

Log likelihood 293.9203 Durbin-Watson stat 0.622251

There is a no change in values of coefficients. Only change that is there is in value of

indivisual standard errors.

Equation after satisfying all assumptions:

Which basically shows that the value of futures is dependent on both the Spot Price as well

as product of interest rate, but in actual scenario the model that is followed by NIFTY index

future depends on various market forces like trends (bullish/ bearish) as well as costs like

brokerage cost.


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Comparison ofActual,Theoretical and Regression Model Results

As we can see the values obtained as per theoretical model are higher when compared to

those with regression model. The reason for this can be explained by saying that theoretical

model doesnt take care of various market trends and other costs like brokerage costs

involved while entering into the transaction.

4900

5000

5100

5200

5300

5400

5500

5600

Calculated

Theoretical

Actual

Documents

Analysis of NIFTY Futures