IFM Project Submission

Forward Rate/Spot Rate analysis

Analysis on whether forward rate is an unbiased estimator of future spot rates

Submitted By: Saurabh Sharma (267), Hiren Madan (223), Vishal Sharma (160), Abhinav Jangra (103), Anik Bhushan (208)

Group No. 14

Abstract:In the previous decades, there have been numerous exact studies both in backing of or restricting the Forward Rate Unbiasedness Hypothesis. This speculation contends that the forward rate completely mirrors the data with respect to swapping scale desires thus forward premiums anticipate the bearing change in future spot rates. In this paper, we look at month to month information on the spot and one month forward costs for the yen, the euro and the sterling pound, all in respect to the INR. Our motivation is to concentrate on the relationship between forward rates and future spot rates prior and then afterward the start of the Global Financial Crisis of September 2008, by testing if the forward rate is a fair-minded estimator without bounds spot rate. To test this theory, the routine technique is taken after, by utilizing an OLS relapse with the adjustment in spot conversion standard as the indigent variable, while the forward premium as the free variable. To bolster this theory, the steady term would not vary from zero, the forward's coefficient premium would not altogether contrast from one and the slip term would not display any serial connection. At last, we reason that forward trade rates have little impact as estimates of future spot trade rates subsequent to the Forward Rate Unbiasedness Hypothesis is rejected.

Literature Review:On making the financial arrangement of India RBI needs to consider the relationship between Interest rates, Spot Rates & Forward rates. As indicated by Cornell (1987), there is frequently the conviction that the forward rate must be an unprejudiced indicator of the spot rate, generally theorists could benefit from the inclination by taking one position in the spot market and the inverse position in the forward business sector. One well known speculation is the desires hypothesis of a forward rate model. In the "straightforward productivity" determination of forward trade markets, it is frequently contended that the forward rate "completely reflects" accessible data about the conversion scale desires; subsequently the forward rate is normally seen as a fair-minded indicator without bounds spot rate. The desires hypothesis places that the monetary specialists have the capacity to process data quickly. Through the arbitrage exercises of the monetary operators and business sector modification, the forward rates mirror the data that is required to focus future trade rates. Another theory is the irregular walk model. This model underlines the arbitrary normal for swapping scale conduct. This speculation expresses that, since current 1 Valuable help with the article's readiness was given by Dr D. Gross from the International Monetary Fund (IMF) in Washington. Help with the type of supportive remarks and recommendations by different staff individuals in the Research

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Department of the South African Reserve Bank (SARB) is likewise thankfully recognized. On the other hand, the perspectives communicated in this paper are those of the creator and don't essentially speak to those of the SARB. Periodic PAPER NO 13 1 SA RESERVE BANK spot rates synopses all the pertinent data that decides future trade rates, current spot rates are the best indicators of future spot rates. Observational work by Edwards (1983) and Cornell (1987) underpins the impartial forward-rate speculation (UFH). By difference, Meese and Rogoff (1983) and Longworth (1981) have found that present spot rates anticipate future trade rates fundamentally superior to anything the relating forward rates. Past tests led by Hakkio (1985) and others demonstrate that the proof supporting this UFH is very feeble. They find that a non-consistent danger premium is available in a few noteworthy remote trade markets. The ramifications of these discoveries is that one can't utilize the forward rate specifically as a future's measure spot rate. Rather, forecast of the conversion scale ought to be founded on the assessed coefficients from an appropriated swapping scale determination.

1.1 Selection of Currency Pairs

We have selected INR vs USD, EURO, German Marks, SWIS FRANKS, for our analysis. We gathered monthly data from 2009 to 2012 for the monthly Spot as well as 30, 60, 90 days forward rates of USD/INR. The below table shows descriptive statistics for the data.

INR/EUR INR/USD INR/GBPMean 65.56 48.65 76.98Standard Error 0.96 0.85 1.38Median 70.42 54.95 87.72Standard Deviation 7.35 6.50 10.58Sample Variance 53.98 42.30 111.91Kurtosis -0.93 -1.27 -1.38Skewness 0.41 -0.34 -0.14Range 25.23 19.46 32.17Minimum 60.24 44.64 70.92Maximum 85.47 64.10 103.09Count 40 40 40

Only Forward data of USD/INR is available on free sources hence we have done co relation testing on USD/INR. However Eur, USD , GBP have a very strong correlation hence if we can prove our hypothesis for the USD/INR pair it is fair to assume it should be applicable for other pairs as well.

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31-12-2012

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Spot Rates USD, EUR, GBP

Spot Rates EUR/INRSpot Rates USD/INRSpot Rates GBP/INR

Models for predicting future spot ratesWe used the following Empirical model for testing the predictability of future spot rates-

Where Spot is the current spot rate at t + mForward is the Forward at time t

1.2 Creating the Null HypothesisIf the forward rates are an unbiased predictor of the future spot rates. We have assumed the following model. Where m stands for 1, 2, 3 based on the 30,60 & 90 forward rate.

We would proceed with a hypothesis testing of A = 0, Error = 0, and B= 1. Failure of being able to reject the hypothesis would imply Forward rate is unbiased predictor however if the hypothesis is rejected we can conclude that either forward rate can’t be used to estimate the spot rate or that the model that we have chosen is incorrect.

Tests1.3 Examining the data through Preliminary Testing Before we begin our hypothesis testing we will have to do some preliminary tests

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i. Unit TestsNon stationarity of time series is regarded as a problem in econometric analysis.

It has been shown in a number of theoretical works (see Phillips, 1986) that, in general, the statistical properties of regression analysis using nonstationary or trending time series are dubious. In Figure 1 below, the USD/INR spot rate and forward rate are clearly nonstationary as they are both subject to positive trends. However, they seem to be floating in time together in the long run. In such a case they are presumably integrated of the same order, and the fact that the differences.

30-06-2009

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Spot and Forward Rates

INR/USD30 day60 day90 day

Two methods would be used Augmented Dickey Fuller & Philips Peron test both with stationary and trend stationary. With the null hypothesis being the time series is a unit process.

Augmented Dickey Fuller test for INR/USD

t-Statistic Probability

Augmented Dickey-Fuller test statistic-

0.848666 0.7973

Test critical values: 1% level-

3.548208

5% level-

2.912631

10% level-

2.594027

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Conclusion: It is not a stationary series

Augmented Dickey Fuller test for INR/EUR

t-Statistic ProbabilityAugmented Dickey-Fuller test statistic

-1.648573 0.4517


3.548208

5% level-

2.912631

10% level-

2.594027


Augmented Dickey Fuller test for INR/GBP

t-Statistic ProbabilityAugmented Dickey-Fuller test statistic

-1.193199 0.6717


3.548208

5% level-

2.912631

10% level-

2.594027


ii. Co integration TestThe method used is Johansens Test. With the null hypothesis being the time series has a Co integration relationship.

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INR/USD Spot and Forward data Co integration Test

Hypothesized No of CE's Eigen Value Trace Statistic Critical Value ProbabilityNone * 0.272 13.2 18.4 0.23070At most 1 0.029 1.1 3.8 0.28810

Conclusion: Data is Not Co integrated hence further analysis is not possible



Conclusion: Data is Not Co integrated hence Further analysis is possible



Conclusion: Data is Not Co integrated hence Further analysis is possible

1.4 Hypothesis testing using T testsPost the Above tests, we would conduct T tests on the Constant, Coefficient and error term to find whether our Null Hypothesis can be accepted.

Spot rate and 60 day Forward rate

Variable Coefficient Std. Error t-Statistic Prob.

Constant 0.293401 0.334089 0.878212 0.38532 month Forward 0.923796 0.08599 10.74307 0.00

R-squared 0.752304 Mean dependent var 3.881916Adjusted R-squared 0.745785 S.D. dependent var 0.078487S.E. of regression 0.039573 Akaike info criterion -3.57264Sum squared resid 0.059508 Schwarz criterion -3.488196

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Log likelihood 73.4528 Hannan-Quinn criter. -3.542108F-statistic 115.4136 Durbin-Watson stat 0.975546

Spot rate and 90 day Forward rate

Variable Coefficient Std. Error t-Statistic Prob

C 0.438294 0.408622 1.072614 0.29023 month forward 0.886382 0.105161 8.428783 0

R-squared 0.651518 Mean dependent var 3.881916Adjusted R-squared 0.642347 S.D. dependent var 0.078487S.E. of regression 0.046938 Akaike info criterion -3.231257Sum squared resid 0.083722 Schwarz criterion -3.146813Log likelihood 66.62515 Hannan-Quinn criter. -3.200725F-statistic 71.04438 Durbin-Watson stat 0.608432

Conclusion as the P values are less than 0.05 the hypothesis that the co efficient of 2 & 3 month forward is zero has been rejected. Hence there is a co relation between Forward and Spot Rates.

SummaryAs we can see from conclusion, there exists co-relation between Forward rate and Spot rate as hypothesis : That the coefficient of the Forward rate in the correlation equation is zero ,is rejected with the help of T test.

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