Asian Journal of Management. 9(2): April- June, 2018
ISSN
0976-495X (Print)
2321-5763 (Online)
DOI: 10.5958/2321-5763.2018.00145.2
Vol. 09| Issue-02|
April-June 2018
Available online at
www.anvpublication.org
Asian Journal of Management
Home page www.ajmjournal.com
RESEARCH ARTICLE
Applying log Periodic Power Law to Currency Market Crashes–A Study in
Indian Context
Dr. Varun Sarda1, Dr. Yamini Karmarkar2, Dr. Neha Lakhotia Sarda3
1
Faculty, Prestige Institute of Management and Research, Indore
2
Reader, IIPS, DAVV, Indore
3
Freelancer and Entrepreneur, Indore
*Corresponding Author E-mail: inboxofvarun@gmail.com, ykarmarkar@gmail.com,
neha.pimd@gmail.com
ABSTRACT:
The term volatility has come to be used synonymously with the financial market nowadays. In these critical
times of turbulence it is becoming increasingly difficult for the investor to time the market. It is quite often seen
that large rise is followed by large falls and small rise by small fall. This is especially more significant in the
case of currency markets on which there is global impact of numerous economies and polities. It would be also
be of great help if some mechanism is generated to predict an upcoming crash, since it can guide the naïve
individual investors who are generally the most affected group in the financial markets. In this paper an attempt
has been made for the same using Log Periodic Power Law. Purpose: The study will help the investors to be
able to predict currency market movements and act accordingly so that their returns are maximized.
Design/Methodology:-Secondary data is used for analysis. Findings:-It appears that log periodicity may be
used to predict the movement of Rupee against US Dollar. Implication or Limitation: -Data for a longer period
may be taken for better results. Type of Research Paper:-Empirical Paper.
KEYWORDS: Log periodicity, currency market, currency.
Numerous instances have been observed when a sudden
movement in the exchange rate affects adversely the
earnings of corporate world.
INTRODUCTION:
The movement of exchange rate and the way it is
determined becomes an important factor in the process
of prediction of the rates. Even a small fluctuation in
the exchange rate can affect the business houses
manifolds. Today, the exchange rate system followed
by India is Liberalized Exchange Rate Management
System (LERMS). Since India is subject to nice volume
of trade even a minor change or fluctuation in the price
downwards can affect the various corporate houses
attached to it in a severe way.
Factors Influencing the Currency Market:
Numerous factors affect the movement of the currency
market. They are listed as follows:(a) Change of Interest Rate:
The fluctuation in the interest rate of a country
influences the fluctuation of the currency also. An
upward movement in the interest rate leads to an
appreciation of the currency. Even an expectation of a
change in the interest rates can also be a major
contributor in increasing the valuation of currencies for
a country. Though speculation is involved in the mere
expectation still markets are seen to react sharply to it.
Received on 07.04.2018
Modified on 20.04.2018
Accepted on 29.04.2018
©A&V Publications All right reserved
Asian Journal of Management. 2018; 9(2):920-924
DOI: 10.5958/2321-5763.2018.00145.2
920
Asian Journal of Management. 9(2): April- June, 2018
(b) Inflow of Foreign Funds:
Exchange rate of a country is determined by the
demand and supply of currency in that country. Due to
immense trade linkage of India with other developed
economies across the Globe, huge investments in the
form of FDI and FII are made in the country. When
huge quantity of foreign money is invested in India it
depreciates against the INR and similarly when lesser
amount is invested the foreign currency appreciates
against the Indian Rupee.
official exchange rates can be artificially manipulated
by the government.
Interest Rate Parity:
This is a non-arbitrage condition which says that, an
investor has two options either to save in the domestic
currency or invest in a foreign currency. Let the home
currency be Rupee and the foreign currency is US
Dollar. Then the investor can either save in Rupee
receiving an interest income in Rupee or convert his
home currency to US Dollars and invest in USA
receiving interest income in US Dollars and then
converting back to Rupees in the Forward market. The
theory says that both the above interest income should
be the same and if they are not then arbitrageurs can
earn a risk-less return.
(c) Oil Prices:
A major portion of the import payment of the country
comprises of payment for oil. A hike in oil prices
results into the Government buying more USD against
INR to meet the import liability. This results in heavy
demand for the USD, thereby depreciating the INR. The
nature and maturity of the markets enable the foreign
players to escape such fluctuations.
Fisher effect:
Fisher (1930) studied the relationship between interest
rates and inflation. It was postulated in the study that
the nominal interest rate is equal to the sum of the real
interest rate and the expected rate of inflation. He
hypothesized that the nominal interest rate can be
decomposed into two components, namely–real interest
rate and an expected rate of inflation. He claimed a oneto-one relationship between inflation and interest rates
with real interest rates being unrelated to the expected
rate of inflation and determined by the real factors in
the economy, such as productivity of capital and
investor time preference.
(d) Political Factors:
Political factors also influence the fluctuations in
currency market. Statements by politicians are always
seen to create waves in the entire country since public’s
response is reflected in the economic and financial
parameters of the country. Also, political unrest and
uncertainty results into a loss in the confidence.
(e) Natural Calamities:
Natural calamities happening across a Nation also
affects the economy adversely. The effect of the same
can thus be observed in the valuation of currency also.
Asset market model:
In this model exchange rates are thought of as being the
outcome of the conditions for international asset market
equilibrium. Monetary asset model assumes that
international investors are risk-neutral. This means that
the domestic and foreign assets which are identical in
all respects (other than their currencies) are perfect
substitutes for investors. Thus they should pay the same
expected returns.
Some relevant important concepts
Purchasing Power Parity (PPP):
It refers to the theory of long-term exchange rates based
on relative price levels of two countries. The reason
behind the fluctuations related to PPP is because of the
inflation between two countries. In other words it is the
quantity of goods which can be bought in a given
country with a certain amount of money. The concept is
based on the law of one price which states that if there
are no transaction costs, same goods will have the same
price in all the markets. The estimation of purchasing
power parity is complicated because of the fact that
countries differ in price levels across various
commodities. The commodities used by different
people in different countries are different. Thus, to
study and analyze the purchasing pattern amongst
consumers it is necessary to compare the costs bringing
them down at the same uniform price level using price
index. Some statistical difficulties can also come up in
the process of multilateral comparisons between two
countries. At the time of estimating the PPP
comparisons inflationary effects are to be taken into
account. The process of determination of exchange rate
through PPP assumes all the more significance because
Section-2
Literature Review:
Investors must be compensated by higher returns to
induce them to hold an asset that might crash
(Blanchard, 1979). Blanchard and Watson (1982)
introduced the concept of Rational Expectation bubbles
which allow for arbitrary deviations from fundamental
prices while keeping the fundamental anchor point of
economic modeling.
A major problem relates with detecting the bubbles
since they are helpful in predicting the financial
impacts. Research related to testing the explosive trends
in time series of asset prices and foreign exchange rate
has also been carried out by Evans (1991)
921
Asian Journal of Management. 9(2): April- June, 2018
The set of assumptions on which the study done by
Johansen and Sornette (1999a) is based are as follows
(a) The key assumption used here is that a crash may
be caused because of the local reinforcing imitation
between traders. This can be defined as a tendency
of traders to imitate their friends thus increasing up
to a certain point called the “critical point”. This
results into formation of a bubble. Since many
investors place sell orders at this point it results
into a crash.
(b) Investors adopt a rational outlook since they
remain invested with a possibility of being
compensated by a higher rate of growth of bubble
for taking the risk of crash.
reconcile with the economic intuition or facts (Lux and
Sornette, 2001). Raul Matsushita et. al (2005), found
that crashes result from a build-up of correlations.
Imitation between traders in a bull market leads to a
bubble. Stress pushes the market into a state of critical
time interval. This critical point is the threshold point
where many traders place orders at the same time
thereby provoking a crash. Crashes thus are outliers
with characteristics distinct from population.
Section-3
OBJECTIVES:
The objective of the study is to find out whether the
crashes in the Indian Currency market follow the log
periodic power law. The study should enable the
prediction of financial crashes in the currency markets.
If prediction of crashes becomes possible then measures
may be taken by the regulatory bodies and authorities to
prevent a great impending loss of money and mental
peace of many investors and lives of some of them.
The above study was based on the fact that prices
increase with the increase in the probability of a crash.
They have based the focus of the study on the following
parameters like system of traders who are influenced by
their neighbors, local imitation turning into global
cooperation, global cooperation causing crash.
Section-4
1. When does a crash occur?
Crashes happen when large groups of agents place sell
orders all at once. A peculiarity regarding this group of
agents is that they don’t know each other and crash are
not plotted by them. They create a lot of imbalance in
the system leading the market makers unable to absorb
this imbalance and thereby lowering the price. In fact at
times these traders do not agree with each other and
make a rough submission of almost equal number of
buy and sell orders thereby not making a crash happen.
Another relevant question answered in the study is that
by what mechanism do the traders organize a
coordinated sell-off? The answer to the same is that
since the World is being organized into a close network
of traders in the form of family, friend etc. they
influence each other locally.
METHODOLOGY:
When the range of downward fluctuations of the
currency market is less (that is between 1% and 2%)
various technical analysis tools can be used to predict
them but for a range above this log periodicity may be
used to give better result. We have analyzed the falls in
the Indian currency market which occurred on 19 th
March 1996, 6th February 1996, 7th October 2008, 12th
October 2008, and 13th November 2008. The period of
study is from 1993 to 2010 for both consideration of
falls and log periodicity. The time series data for the
variable of study consisting of Indian Rupee and US
Dollar exchange rate is collected from various
publically accessible websites. According to various
researches done by Didier Sornette and Anders
Johansen and equation provided by David S. Bree and
Nathan Joseph in November 2007 in “Log Periodic
Power Law fits to financial crashes: a preliminary
replication”–
2. Fight between Order and Disorder:
In the case of asset prices the main story revolves
around order and disorder. Here, order refers to a state
when everybody is of the same opinion and as against
that the state of disorder is the one in which buyers and
sellers disagree with each other. This state is referred to
as the normal time and the former represents a state of
crash.
Yt=A+B (tc–t) {1+C cos ( log (tc–t)+)
(1)
Where:
Yt >0 is the price;
A>0 the value of Yt at the critical time;
B< 0 the increase in Yt over the time unit before the
crash;
|C|<1 is the proportional magnitude of the fluctuations
around the exponential growth;
tc >0 is the critical time;
t <tc is any time into the bubble, preceding tc ;
=0.33±0.18
=6.36±1.56 is the frequency of the fluctuations during
the bubble;
Ilinski (1999) points out in a study conducted that
traders expect the price to rise and the same is reflected
in the prediction model. Traders support the bubble and
the bubble supports them. Market level does not stay
constant in a bubble, it rises. Therefore, the market
must rise and compensate the buyers for taking risk.
Market price is a reflection of the greed of the buyers
and the fear of the sellers. Many Rational Expectation
bubbles are seen to exhibit shapes which are difficult to
922
Asian Journal of Management. 9(2): April- June, 2018
0≤ ≤2 is a shift parameter.
Table 3 showing Date of Crash and percentage fall
Date of crash
Percentage fall
6-Feb-96
-2.180339985
19-Mar-96
-2.630668051
7-Oct-08
-2.06185567
12-Oct-08
-2.051783097
13-Nov-08
-2.446043165
Section-5
findings and discussions:
Study of the falls in Rupee and log periodicity:
Figure 1 below shows the number of falls in Rupee
from 23rd October 1993 to 21st April 2010. Here we
have considered the falls from<(0) % to>(-0.40) %,≤
(0.40) % to> (0.80) %, ≤ (-0.80) % to> (-1.20) % and so
on till < (-2.4) %. As a result of analysis it was found
out that total number of working days was 6025, on
2262 days the percentage change in the value of Rupee
was zero, for 1858 days Rupee has risen that is closed
in green, and on 1904 days it has gone down that is
closed in red.
Log periodicity has been observed to fit well in the
stock market where the percentage fall in a particular
day is more (i.e. to the extent of 10% or even more) but
in case of currency market this is limited (not more than
3 % for the period of study, in India).
Two years data prior to the date of crash is used to fit in
equation (1). A few of the Graphs for the above fits are
presented below.
Table 1-The fall of Rupee-Column 1 shows the values on the XAxis and Column 2 shows the values on the Y-Axis which are
plotted in the following graph
X(%Percentage Fall)
Y=Number of Times
< (0) and > (-0.40)
1564
≤ (0.40) and > (0.80)
234
≤ (-0.80) and > (-1.20)
72
≤ (-1.20) and > (-1.60)
23
≤ (-1.60) and > (-2.00)
6
≤ (-2.00) and > (-2.40)
3
<(-2.4)
2
Graph 1:-for fall in Rupee value on 6th February 1996.
Figure 1-The fall of Rupee in percentage is taken on the X-Axis and
the frequency (number of days it has fallen) is taken on Y-Axis.
We have tried to fit in equation (1) to Indian Rupee and
US Dollar exchange rate data with various values of
Beta, Omega and Phi as suggested by David Bree,
Didier Sornette, Anders Johansen and others.
Table 2 Combinations of different values of Beta, Omega and Phi
for Indian Rupee and US Dollar exchange rate
(Beta)
(Omega)
(Phi)
0.33
11
0
0.5
11
0
0.51
7.92
0
0.51
4.8
2
0.51
4.8
6.2831
0.55
7.92
0
0.55
7.92
6
0.15
7.92
6
Graph 2:-for fall in Rupee value on 19th March 1996
The table below shows the dates of crashes and the
percentage fall (more that 2%) in Rupee value during
the study period.
923
Asian Journal of Management. 9(2): April- June, 2018
against US Dollar using log periodicity. Out of the five
crashes none was found to fit the equation. It appears
that log periodicity cannot be applied to the Indian
currency further market; this may be due to the fact that
in India though we have full Current Account
Convertibility but we still have restrictions on Capital
Account Convertibility further there are evidences that
the Indian Central Bank intervenes in the currency
market to affect the exchange rate of Rupee. Therefore
the currency market is yet to be fully floating so the log
periodicity will be more applicable in a situation where
there will be no restriction and control on exchange rate
determination.
Section-7
Scope for further study:
The study can be applied more effectively to those
currencies which are fully market driven. Also the
study would probably fit much better to currency
derivatives.
Graph 3:-for fall in Rupee value on 7th October 2008.
Section-8
REFERENCES:
1
2
3
4
Graph 4:-for fall in Rupee value on 12th October 2008
5
6
7
8
9
10
11
12
Graph 5:-for fall in Rupee value on 13th November 2008.
13
The above graphs 1 to 5 clearly shows that the curve
fitted on the data and the actual data are far off which
tells that log periodicity cannot be applied to the
currency market in India.
14
15
Section-6
CONCLUSION:
We have tried to study five crashes in Indian currency
market from 1993 to 2010 in the value of Indian Rupee
924
Anders Johansen, Didier Sornette and Olivier Ledoit (2009)
Predicting Financial Crashes using Discrete Scale Invariances,
http://lanl.arxiv.org/abs/cond-mat/9903321v3.pdf.
Cooray, A (2000): “The Fisher Effect: a review of the
Literature,” Macquaire University, Department of Economics.
Blanchard O.J. (1979), Speculative Bubbles, Crashes and
Rational Expectations, Economics Letters, 3, 387-89.
Blanchard Oliver J. and Watson, Mark W., Bubbles, Rational
Expectations and Financial Markets (July 1982), NBER
Working Paper No. W0945. Available at SSRN:
http://ssrn.com/abstract=226909.
Evans G.W. (1991), Pitfalls in Testing for Explosive Bubbles in
Asset Prices, American Economic Review 81, 922-930.
Fisher, I. (1930), The Theory of Interest, Macmillan, New York.
Gustav Cassel, “Abnormal Deviations in International
Exchanges”, in Economic Journal, (December, 1918), 413-415.
Ilinski, K. (1999), Critical Crashes? International Journal of
Mod. Phys. C. In press, preprint available on condmat/9903142.
Johansen Anders and Sornette Didier, (1999a), Critical Crashes,
RISK, 12, 91-94.
Johansen A, Ledoit O and Sornette D. (2000), Crashes as
Critical Points, to appear in International Journal Theory and
Applied Finance, 3 No 1 (January 2000); Preprint available on
http://www.nbi.dk/˜johansen/pub.html.
Lux T and Sornette D (2001), On Rational Bubbles and Fat
Tails, in press in the Journal of Money, Credit and Banking (eprint at http://xxx.lanl.gov/abs/cond-mat/9910141).
Matsushita Raul, Gleria Iram, Figueiredo Annibal and Silva Da
Sergio (2005), Log Periodic Crashes Revisited, Physica A
World Economy–Interest Rate Parity 1 (entry written for the
Princeton Encyclopedia of the World Economy) by Menzie D.
Chinn (1/2/07), Professor of Public Affairs and Economics,
University of Wisconsin
www.wikipedia.com.
www.oanda.com.