Download A Rational Expectation Model

FINANCIAL GLOBALIZATION
AND
STOCK PRICE VOLATILITY:
A RATIONAL EXPECTATION MODEL
SAIKAT BHATTACHARYYA
Research Scholar, Department of Commerce, University of Calcutta
Assistant Teacher, Bangabasi College-School
8/1 Santosh Mitra Square
Kolkata-700012
Address for Communication
House No: 110, Duttapara, Baruipur
South 24 Parganas
Kolkata-700144
Email Address: [email protected]
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Abstract
Financial Globalization is the imperative of time. This paper seeks to find out, in light of
Rational Expectation Hypothesis, whether it has any impact on stock price volatility.
Rational expectation based dividend discount model of asset price determination is used
here and solved through recursive method to have multiple equilibria. One of the
solutions leads the stock price to present value of future flow of dividends, the true value
of the asset. All other solutions imply the existence of to rational bubble. Whatever may
be the case, we find if the dividend from a domestic stock follows a well defined path with
random fluctuation (which follows first order auto regression AR[1]) around it, any
process of liberalization, which also has its own path with white noise disturbances, is
not going to inject any additional volatility in stock prices, provided the agents behaves
rationally using all the information they have under a perfect information assumption.
Key words: Stock Price Volatility, Rational Expectation, Bubble, Globalization,
Economic policy, Dividend discount model.
JEL Classification no: G12, F32, F36, F49
Acknowledgement: Support and helpful comments on earlier drafts from Dr. Ratan
Kumar Ghosal, Professor in Economics, Department of Commerce, University of
Calcutta, is gratefully acknowledged.
-2-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
I. Introduction:
Since early 1990s, inflow of private capital into the emerging market economies
has increased significantly. This is mostly due to the fact that these emerging economies
have made their financial sector open for foreign capital. Henry (1997b) analyzes a
group of 11 countries and shows empirically that stock market liberalization has a
positive impact on the private investment. Assets of these countries have become more
attractive and inflow of foreign fund is raising the price of the equities. Henry (1997a)
shows how the equity prices have increased. Now the question is whether the
liberalization of financial market has increased the volatility of the stock (here we’ll use
the terms stock, share, equity synonymously) market compared to the pre-liberalization
era. In this epoch of globalization, capital is moving freely across the globe. All types
global portfolio fund is venturing around the world for speculative gain. Conventional
wisdom suggests that this will enhance the volatility of stock price. Hence, to resist this
instability some sort of restrictions are required to protect free flow of hot money. There
are theoretical literatures supporting this conventional wisdom. Erturk (2005) outlined a
‘non-imperfectionist’ account of why and how the capital account liberalization can
systematically lead to economic volatility even in the absence of market imperfection. He
has pointed out that opening up of the capital account opens the scope for currency
substitution and erratic capital movements across the border. These two factors are
intertwined with each other and make the asset price more volatile. Bacchetta and
Wincoop (1998) analyze the impact of financial liberalizations and reforms in emerging
markets on the dynamics of these markets. They show that liberalization leads to rich
dynamics of capital flows and often implies an overshooting as portfolios adjust. Asset
prices overshoot as well. Edwards, Biscarri and Gracia (2003) after studying six
emerging market economies (who have liberalized their financial account in early
nineties) have found that cycles in these countries tend to have shorter duration and larger
amplitude and volatility compared to developed countries. On the contrary, Jayasuriya
(2005) found that volatility may decrease, increase, or remain unchanged following
liberalization.
A liberalization measure cannot be once and for all. It is most unlikely that the
domestic authority all of a sudden opens all gates and channels of financial flow. Rather
-3-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
it is a process, where the government gradually withdraws the restrictions on the inflow
and outflow of foreign capital. Financial globalization, like many other socio-economic
and political policies will certainly invite controversy and hence instigate much desired
debate among the policy makers, parliamentarians, social thinkers, economists at all
levels of the society. So, prior to the commencement of the program people get adequate
information, if not all, regarding the course and duration of the program, even if the
government does not explicitly declare the same. Hence, it would not be very unrealistic
to assume that the agents rationally anticipate the policy change and its path. In this paper
we’ll develop an analytical framework to show whether opening up of capital account
introduces any additional volatility into the domestic stock market in light of the broad
periphery of rational expectation hypothesis. This is the primary quest of this paper. Here
we are to develop a rational expectation model to observe the effect of liberalization of
capital account on the volatility of stock market.
As far as the ‘tool’ is concerned, Rational Expectation based ‘Dividend Discount
Model’ is used and is solved through recursive method1. One of the solutions results the
stock price equal to the future flow of earning with a random component. The other
solutions in addition to the present value of the future flow of earning and the random
component give rise to speculative bubble, which create price risk. The speculative
bubble and the random component are the sources of volatility in the stock market. Now
the question is how the liberalization programme affects both of these two components.
As far as the empirical studies are concerned econometricians are not unanimous
in their opinion regarding the presence of ‘bubble’. Some economists argue that bubbles
are not only a theoretical possibility, rather they can be found in empirical estimation.
Some others change some of the assumptions and found no bubble. Shiller (1981),
LeRoy and Porter (1981), West (1987, 1988) have pioneering works in this area. Very
recent studies suggest irrational bubble rather than a rational one [Vissing-Jorgensen
(2004) presented a good survey]. This happens to be a burning area of debate and is a
good research question in its own merit. Here we will not go into into that controversy.
We’ll rather discuss the problem of volatility with respect to liberalization,
notwithstanding the existence of bubble.
-4-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
At first in this paper we’ll develop a rational expectation based dividend discount
model of stock price determination, taking the process of liberalization in consideration
and some conclusive proposition will be drawn in section II regarding the relationship
between liberalization of capital account and sock price volatility. Here we find two
alternative set of solutions, one accepting the bubble and the other by not accepting it.
Lastly before making some concluding remarks in section IV we’ll discuss the policy
matters in section III.
II. The Model:
In this section we shall frame a model based on expectational difference equation
to see the impact of liberalization of capital account on the volatility of asset price. The
model is kept as simple as possible to avoid computational difficulties without deviating
from the primary focus.
Let dt, be the rate of return (dividend) resulting from each unit of the stock at
period t. Now let dt fluctuates around a steady-state growth trend given as,
d t  a (1   ) t  u t
(1)
Where, ut is the cyclical factor and it is supposed to follow a first order autoregressive
process AR[1].
u t  u t 1  et1
(2)
Here, e1t is a random element, which follows a white noise process i.e.
E (et1 )  0 .
Var (et1 )   2  A Constant; and
Cov(et1 s , et1 )  0 if s  0 .
Let,   1 . By the virtue of this restriction, we are actually assuming the shock to be
stationary i.e. it eventually dies down. Hence it is stationary. Following the basic
properties of AR[1] process and due to the assumption   1 we can say that,
Var(ut )  
2
1 2
and Corr (u t , u t  s )   s . So, both the variance and autocorrelation are
increasing in θ.
-5-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Again, τ be the ‘tax’ imposed per unit of inflow and outflow of stock. This ‘tax’
includes all impediments and barriers that have to be faced by the overseas investors. By
liberalization of capital account means gradual reduction of restrictions on the flow of
capital across the border. Here in our model by liberalization we mean gradual reduction
of τ. The liberalization program cannot be once and for all. The gradualist approach thus
seems quite reasonable. Let the time path for τ be:
 t   t 0  et2
(3)
Now, if the government strictly follows the liberalization program irrespective of sociopolitical situation, the random component e t2 can be dropped. But that would hardly be a
realistic assumption. It would be fair to assume E (et2 )  0 .
Let us suppose that the process of liberalization starts and terminates at period 0
& T respectively.
Further, Let Pt be the price of a stock that an overseas investor is ready to pay for
each unit of domestic stock.
Pt  R[ E t Pt 1  (d t   t )]
(4)
This is an expectational difference equation and it owes some explanation. Et ( Pt 1 )
stands for expectation of Pt+1 held at time t. That is, the expectation is formed based on a
set of information from all public and private sources at time-t. This information set
contains along with many other things all past values of P. dt and τt are exogenous
variables. R, the expected return from the stock market is assumed to be constant and
considered as a parameter, whose value lies between 0 and unity, in this model. The
rationale behind equation (4) is given in appendix: I.
Finally, Let us assume that the exchange rate remains fixed at unity. Though
international capital movement and thus the volatility are related with the intertwined
effect of asset price fluctuation and floating exchange rate. As we are only interested to
find the relationship between volatility and financial globalization, we are ignoring
floating exchange rate.
-6-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
The Solution:
The foundation of the model is now complete and now we will move forward
towards the solution of the system. Solving the problem recursively we have the time
path for Pt (the solution is given in appendix: II).
Pt  Lim R Et Pt 1i
i
i 
Ra (1   ) t
[1  ( R ) T ]
1
t

 R  0
 Ru t
1  R(1   )
1  R
1  R
(5)
The second term in the above equation is the present value of the future flow of
dividend, if it grows along its steady state growth trend. The last component depicts the
effect of random fluctuation of the dividend on the price of the stock. Whenever the
economy is in depression we can expect a negative ut and vice versa. It would not be very
illogical to expect this random component fluctuates with the ups and downs of the
business cycle. The third term shows the present value of the stream of successive ‘tax’
relives that one overseas investor expects, thanks to the liberalization programme. As we
have assumed that the liberalization programme starts and terminates at period-0 and
period-T respectively, total expected reduction of the value of the share would be
[1  ( R ) T ]
. Surely, this would be lower than the one with a constant high level of
R  0
1  R
t
‘tax’ (i.e. in a closed economy where  0   1  .....) .Symbolically,
R t 0
[1  ( R ) T ]
1  ( R) T
 R 0
1  R
1 R
Thus liberalization raises the net present value of the future flow of earning of the asset.
Hence, the domestic stock becomes more attractive to a foreign investor. These three
components together constitute the net (net of tax) true present value of the share in
addition
Pt* 
to
the
random
component.
That
is,
Ra (1   ) t
[1  ( R ) T ]
1
. The price of the share is supposed to
 R t 0
 Ru t
1  R(1   )
1  R
1  R
be equal to this true present value plus the random component.
Case:I (Solution without bubble)
Now
imposing
the
transversality
condition,
i.e. Lim R i Et Pt 1i  0 ,
i 
we
have Pt  P * . The presence of transversality condition rules out the possibility of a
-7-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
bubble. The restriction that is imposed on R (i.e. 0<R<1) is due to the presence of the
arbitrage opportunity (see: appendix: I) which ensures the equality between expected rate
of return from (risky) stock market and the sum of risk free interest rate and the risk
premium (risk premium is 0 for a neutral agent).
In absence of the bubble component what determines the variability of stock
prices? When the dividend, the ‘tax’ component follows a known path with a predetermined present value, the only variability determining factor happens to be the
random term ut. Surely, Var ( P * ) 
R
R
2
[Substituting the
Var (u t ) 
1  R
(1  R ) (1   2 )
value of Var(ut)]. The variability of the stock price depends on the variability of the
random term. No ‘tax’ component is there. Hence, there is no impact of liberalization on
the stock price volatility under perfect information and rational expectation.
Case:II (Solution with bibble)
But this is one of the solutions. With the presence of the bubble, which is a nonstationary (i.e. relaxing the assumption of presence of arbitrage opportunity) we can
expect multiple equilibria.
Let Pt  Pt*  Bt
(6)
Where Bt is the bubble. The first term in equation 5, being the unexplained component
with no base, is said to be the bubble.
Equation (6) to be a solution to the following condition has to be held (see appendix:III)
Bt  RE t Bt 1
or, Et Bt 1  R 1 Bt  Et Bt i  R i Bt
(7)
Let the probability of a bubble to burst in each period is π (assumed to be exogenous).
So, from equation 7 the value of the bubble at period (t+i) becomes
Bt i  [ R(1   )] i Bt  et3i
[probability (1-π)]
(8)
Bt i  et3i
[probability (π)]
-8-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Now incorporating the above relationships and [assuming E (et3i )  0 ] in equation 6 we
have two alternative solutions for Pt, depending on whether the bubble bursts or not.
Ra (1   ) t
[1  ( R ) T ]
1
t
Pt  Lim[ R(1   )] B0 
 R  0
 Ru t
i 
1  R(1   )
1  R
1  R
i
(9)
Pt 
Ra (1   ) t
[1  ( R ) T ]
1
 R t 0
 Ru t
1  R(1   )
1  R
1  R
Whenever the bubbles are created and when it rises it continues to rise monotonically
until it bursts and when it falls, it falls monotonically, and even it may be negative. A
negative bubble may be ruled out, as it is unrealistic, but we can sensibly assume a
secular downturn and let its lower limit be 0. This implies, whenever a bubble bursts the
stock price takes its second alternative in equation 9 and if it grows it can grow
limitlessly, as shown in the first alternative in equation 9. Whenever the bubble bursts the
asset price becomes equal to P*. If the bubble bursts when Ru t
1
 0 , that is, when
1  R
the economy is in upswing, Pt will continue to grow after a sudden fall and another
bubble will be created. On the contrary if it bursts when Ru t
1
 0 , it will take the
1  R
path of P* and move accordingly, as we have ruled out the possibility of a negative
bubble. Thus if we accept the presence of a speculative bubble, erratic fluctuation in asset
price is primarily determined by the bubble component and the probability of bursting
becomes very important, as far as the volatility of the market is concerned. The bubble
part does not include any tax component. Secondly, the random term ut in p* is another
volatility determining factor like case: I. This random component, as shown before (in
case: I) is independent of the policy of globalization. So, the proposition, which follows
from our model can be stated as: if the dividend from a domestic stock follows a well
defined path with random fluctuation (which follows first order auto regression AR[1])
around it, any process of liberalization, which also has its own path with white noise
disturbances, is not going to inject any additional volatility in stock prices, provided the
-9-
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
agents behaves rationally using all the information they have under a perfect
information assumption, irrespective of existence of any speculative bubble.
If the agents have all necessary information which plays any role in the
determination of stock price, they can calculate the present value of the future flow of
earning and can rationally anticipate the stock price. That is they have the idea of
equation 5. So, whatever variability is there is due to the random component in the
dividend path. If the policy change and its course are correctly anticipated by the agents
there would not be any additional volatility. But if the policy makers keep the agents in
dark, though there is no plausible reason for doing it when the government has incentive
to remain transparent, there might be some impact on volatility.
III. Policy Matters:
What we find in the earlier section that if the agents behave rationally, using all
the available information the liberalization is not going to affect the variability of the
asset price. Two components that we find in the earlier section, determine the volatility
are the random term associated with the dividend path and the second one, perhaps the
most important one, if it exists, is the bubble. These two components remain unaltered
with any change in the policy of capital account liberalization. So, the volatility that was
there will remain even after and during the process of liberalization. So, the role of
government just becomes to pursue the capital account liberalization as decided and not
to surprise the agents. That is, not to deviate too much from the ‘tax’ path.
Excessive erratic fluctuation in price of stock is not a very good sign as far as the
domestic economy is concerned, as it introduces price risk and exposes the stock market
to the speculators. With a fully convertible capital account with the scope of free inflow
and outflow of global speculative funds may create the scope for capital flow reversal
leaving the domestic economy in deep trouble. Hence, the government has a role to
reduce the volatility of stock market. The objective of the policy should be to keep the
price of the stock as close as possible to its true value. Transparency regarding business
data and policy data is the prerequisite in this direction so that, the possibility of over
expectation of asset prices becomes the least. Government should ensure that the business
sector regularly publish data about their ongoing projects and the government should
come clear about their short and long run policy and the let the people have the
- 10 -
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
opportunity to acquire the required information before taking their decision. Secondly,
the government should frame its policies to encourage the development of the risk
minimizing financial instruments. That will directly and favorably attack the π
component in equation 9. Mature and advance financial structure is the precondition for
successful capital account liberalization. Some authors including Krugman (2000) and
Stiglitz (2002) have argued that the financial markets of the emerging markets are poorly
developed and thus they do not function properly like that of advanced countries. So
before phasing out regulations on capital flow it requires to improve the financial
structure by introducing necessary financial instruments. And while introducing the
strategy, the government must be transparent and as well as be firm on the execution of
the policy, so that no confusion arises among the agents.
IV. Concluding Remarks:
Liberalization of capital account has become the imperative of time. It cannot be
avoided. However, the policy makers of the emerging countries are very skeptical as far
as financial globalization is concerned. There are reasons to be so as it may instigate
financial crisis, which may bring about a sudden reversal of capital, leaving the country
in grave financial crisis. Instances of such financial crisis are not at all rare. The major
concern of these policy makers is that liberalization might inject additional volatility in
the financial system of the country. Here, in light of rational expectation hypothesis we
see that if information regarding the pace of liberalization is known to all the agents it
cannot inject any additional volatility. Hence, the process of liberalization cannot be
blamed for the erratic fluctuation and the resulting economic crisis. In fact, there are
systemic or institutional errors in the underdeveloped financial structure of the emerging
market economies, which should be corrected before phasing out restrictions on the flow
of overseas capital.
___________________________________
- 11 -
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Appendix: I
The (expected) rate of return of a unit of stock, purchased at the beginning of period t at
price Pt and sold at the beginning of period t+1 at price Pt+1 has two components: (1) the
net (net of ‘tax’) dividend earned and (2) the (expected) capital gain. This implies,
r
Pt 1  Pt (d t   t )

Pt
Pt
(A.1)
 1 
Pt 1  (d t   t )
or, Pt  
1  r 
Here, the expected rate of return, r is assumed to remain constant overtime. Even if we
introduce fluctuating expected rate of return the main proposition of the model will
remain unaltered. So, to avoid unnecessary computational complications r is supposed to
be fixed here.
In presence of the possibility of arbitrage, r must be identical with the sum of risk free
 1 
interest and risk premium. Setting R  
and introducing the expectation operator
1  r 
we have Pt  R[ E t Pt 1  (d t   t )] , which is equation (1).
Appendix: II
Substituting the values of dt, and τt from equation 1, 2 and 3 in equation 4 we have:
Pt  R[ Et Pt 1  a(1   ) t  u t   t 0  et2 ]
(A.2)
Pushing one period forward
Pt 1  R[ Et 1 Pt  2  a(1   ) t 1  u t 1   t 1 0  et21 ]
Taking expectation conditional on information at time t in both the sides of the equation
Et Pt 1  R[ Et Pt  2  a(1   ) t 1  Et u t 1   t 1 0 ]
(A.3)
 Et {Et 1 Pt  2 }  Et Pt  2 , which is due to law of iterative expectation. And as it is assumed
earlier that E (et2 )  0 .
Substituting A.3 in A.2 we have
- 12 -
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Pt  R 2 Et Pt  2  Ra (1   ){1  R(1   )}  R t 0 (1  R )  R{RE t u t 1  u t }
Extending in this way by repeated substitution,
Pt  Lim R i Et Pt 1i  Ra (1   )[1  R(1   )  {R(1   )}2 .......]
i 

 R t 0 [1  ( R )  ( R ) 2  .......]  R  R i Et u t i
(A.4)
i 0
Equation 2 implies u t 1  u t  et11
Now taking expectation conditional on information at time t
Et u t 1  u t ; By repeated substitution we have Et u t i   t u t . Substituting the value of
Et ut i for each i=0, 1, 2, 3……….in A.4 we find equation 5.
Appendix: III
If Pt  Pt *  Bt then Et Pt 1  Et Pt *1  Et Bt 1 ;
Replacing Pt and Et Pt 1 in equation 4 we have:
Pt*  Bt  R[ Et Pt*1  Et Bt 1  (d t   t )]
Hence, Bt  R[ Et Bt 1 ]
(A.5)
A.5 leads to equation 7
___________________
- 13 -
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
Note
1. Blanchard Oliver Jean and Stanley Fischer (1989), “Multiple Equilibria, Bubbles,
and Stability” chapter 5 Pp 213-274 Lectures on Macroeconomics. Prentice Hall of
India Pvt. Ltd. ---has showed a technique to solve the expectetional difference
equation. We have followed that methodology.
References
1. Bacchetta Philippe and Eric van Wincoop (1998); “Capital Flows to Emerging
Markets: Liberalization, Overshooting and Volatility” NBER Working Paper No.
6530, April 1998
2. Edwards Sebastian, Javier Gomez Biscarri and Fernando Perez de Gracia (2003),
“Stock Market Cycles, Financial Liberalization and Volatility” NBER working
Paper Working Paper 9817, July, 2003
3. Erturk Korkut A. (2005); “Economic Volatility and Capital Account
Liberalization in Emerging Countries”; International Institute of Applied
Economics; Vol. 19 No. 4; October.
4. Henry, P.B (1997a), “Stock Market Liberalization, Economic Reform, and
Emerging Market equity Price”,mimeo, September.
5. Henry, P.B. (1997b) “Do Stock Market Liberalizations Cause Investment
Booms?”, mimeo, November.
6. Jayasuriya, Shamila (2005) “Stock market liberalization and volatility in the
presence of favorable market characteristics and institutions”; Emerging Markets
Review Volume 6, Issue 2, June 2005, Pages 170-191.
7. Krugman, P., 2000. The Return of Depression Economics. Norton, New York.
8. LeRoy, Stephen, and Richard Porter. (1981). “The Present-Value Relation: Tests
based on Implied Variance Bounds,” Econometrica 49(May), pp. 555-574.
9. Shiller, Robert. (1981). “Do Stock Prices Move Too Much to be Justified by
Subsequent Changes in Dividends?” American Economic Review 71(June), pp.
421-436.
10. Stiglitz, J., 2002. Globalization and its Discontents. Norton, New York.
- 14 -
Financial Globalization and Stock Price Volatility: A Rational Expectation Model
11. West, Kenneth. (1987). “A Specification Test for Speculative Bubbles,” The
Quarterly Journal of Economics 102(August), pp. 553-80.
12. West, Kenneth. (1988). “Dividend Innovations and Stock Price Volatility,”
Econometrica 56(January), pp. 37-61.
______________________________
- 15 -