THE RELATIONSHIP BETWEEN INFLATION AND STOCK RETURNS IN NETHERLANDS

(1)

Master Thesis

THE RELATIONSHIP BETWEEN INFLATION AND

STOCK RETURNS IN NETHERLANDS

Phan Trong Nghia

Thesis Supervisor: Dr. Laura Spierdijk

Faculty of Economics and Business

Master of Science in Econometrics, Operations Research

and Actuarial Studies

(2)

N. T. Phan, supervised by Laura Spierdijk Page 2

CONTENT

I. ABSTRACT

II. NONTECHNICAL INTRODUCTION AND NONTECHNICAL MOTIVATION

III. LITERATURE REVIEW

IV. DATA

V. MEAN VARIANCE FRAMEWORK FOR LONG-RUN HEDGE RATIO

VI. COINTEGRATION FRAMEWORK FOR LONG-RUN HEDGE RATIO

(3)

I. Abstract

(4)

II. NONTECHNICAL

INTRODUCTION

AND

NONTECHNICAL

MOTIVATION

In economics, inflation is defined as a rise in level of prices of goods and services over time. Inflation levels are measured by price indices and different kinds of price indices are used to measure changes in prices that affect different people. The most widely used index for which inflation rates reported in many countries is the Consumer Price Index (CPI), an index number measuring the average price of consumer goods and services purchased by households. Inflation is an important theoretical issue due to its effect on the returns to financial assets. The economy is strongly affected when inflation is high and volatile, as it leads to the mispricing of real and financial assets and creates extreme volatility in interest rates (the risk of investments is increased in case of mispricing so the interest rate is increased to compensate for that risk).

Nowadays people are more concerned about inflation which quietly reduces the value of their saving while no one is looking. Inflation can be particularly damaging for pensioner’s savings as with inflation running at 4.3% their savings are effectively halved in just 17 years. Among saving tools, pension plan has the longest term which may last longer than 30 years, depending on the age of the pensioner at the moment he joins the pension plan; therefore it is possible that pension benefits of an individual are built in vain due to the rapid growth of good prices. To protect theirs customers from inflation, pension-fund companies offer pension plans with inflation-linked annuity benefits for which the amount of the payments, which a pensioner received after retiring, is increased based on CPI. With inflation-linked annuity benefits, pensioners are 100% protected from inflation. In general, to maintain the solvency ability of pension funds, investment managers need to reserve for the liability in future by investing collected premiums (periodic payments paid by pensioners to be insured) in an inflation hedge. Inflation hedge can be defined in many different ways:

(5)

(2) A security is an inflation hedge if it offers “protection” again inflation, which in turn means the elimination or at least the reduction of the possibility that the real rate of return on the security will fall below some specified value such as zero (Cagan (1970));

(3) A security is an inflation hedge if and only if its real return is independent of the rate of inflation (Branch (1974)).

It should be pointed out that the three definitions of inflation hedge distinguished above are not mutually exclusive. It is quite possible for a security to qualify as a perfect inflation hedge in more than one sense, although the only security which could conform to all three definitions would be one with a completely riskless, non-negative real rate of return. In general, a good hedge has few key properties and the four most important criteria are:

− A hedge must hold its value during the inflation period.

− Another key criterion is marketability. This means that it must be easy for trade. Actually this is the essential property of any investment because a manager does not want to take into account the risk of insolvency when he is not able to sell the asset.

− The third key property is divisibility. This means that the asset is split into smaller parts without any loss of value. With this feature, a manager has a flexibility to switch a portion of his assets to another financial instrument which possibly provides a higher profit in a certain period.

− The final one is financing. An investor buys assets either with cash or credit (or mortgage). Cash-based hedges are good while the other is a bad choice. The reason is that assets bought on credit are prone to speculation and bubbles which can result in overvaluing hedges.

To find a good inflation hedge, a pension fund manager has to choose an investment which satisfies the above standards. In finance, the most common investment tools are real estate, gold and stocks. So the question is that which one is the best to be an inflation hedge?

(6)

premiums collected from pensioners so it can only purchase a real estate on credit. This violates the fourth criterion, the most vital pitfall to be a good hedge. Rising prices drive interest rate higher so mortgage rates may rise from 3%-4% to 12%-15% and the monthly payments could easily triple so the returns from real estate cannot cover its liability in future. This actually happened in US market during the 1970s and in the early 2000s. Moreover, it is easy to see that real estate also can not satisfy the other criteria: it takes a long time to sell or buy a real estate so it cannot meet the marketability criteria; the condition of divisibility is also violated because things such as houses are not divisible. In addition, there are many formal researches pointing out the less effectiveness in hedging inflation of real estate in comparison with common stocks: there is limited evidence to support the proposition that real estate provides a positive hedge against inflation or that it is a more effective hedge against inflation than common stocks for USA market in Hartzell (1987) and UK under the work of Limmack and Ward (1988); a recent study for the UK in Hoesli (1995)) has shown that real estate has poorer short-term hedging characteristics than shares but better characteristics than bonds; the study of Hamelink and Hoesli (1996) also provides evidence about the inflation hedging disability of Swiss real estate. Therefore, credited real estate is not only a poor hedge against inflation, but also a very risky one.

(7)

investors could hedge them against inflation using gold. Due to its limited in hedge effectiveness, gold is not a perfect choice for inflation hedge by pension fund companies. The last option is stocks which are also the most common choice of investors. All the properties of a good inflation hedge are satisfied by stocks. Moreoever, the evidences of the hedge capacity of stocks are found in many other countries. Therefore, in comparison with real estate and gold, common stocks are prominent candidates for inflation hedge.

(8)

III. Literature review

In hope of giving a general view of a big picture about the studies on the relationship between inflation and stock, we will present the literature review in two separate parts: the results of previous analysis and technique basis reviews.

− Previous result review

There is a significant amount of empirical researches on the correlation between stocks and inflation. The theoretical basis for this strand of literature is the Fisher hypothesis which implies that there should be a one-to-one relation between expected nominal stock returns and expected inflation so that real stock returns are determined by real factors independently of the rate of inflation. A related implication is that assets which represent claim to real payments, such as common stocks, should offer a hedge against unexpected inflation, while assets which represent claim to nominal payment, such as bonds, should not expected to offer such a hedge possibilities. Due to this reason, most of pension fund companies choose to, in one hand, invest a part of their asset to bonds to generate fix and stable cashflows which can be used to maintain the solvency of their funds against the deaths of pensioners (death benefits) or other benefits such as health care, cash benefits (periodic payments for each 5 years or 10 years); while in the other hand, they invest the rest of the assets in common stocks as inflation protection.

However, many empirical studies observed a negative relation between inflation rate and stock returns which prove that stocks are a poor inflation hedge as they exhibit a significant negative correlation between inflation and real stock returns. This negative correlation is often termed the ‘stock return–inflation puzzle’ and found in a variety of countries: Bodie (1976) and Fama (1981) find this to be true in the US; Amihud (1996) with the study for Israel market; Gultekin (1983) and Kaul (1987) find it to be true in a variety of industrialized countries; the negative relationship between those two factors are also found in nine equity markets of the Asian countries by the work of Al-Khazali

(9)

unexpected inflation, stock returns still show a negative relation with both these two components.

To explain this phenomenon, many hypotheses are formulated and the fourth most well known ones are: Tax effective hypothesis of Feldstein and Summer (1979), Proxy hypothesis of Fama (1981), Money illusion hypothesis of Modigiani and Cohn (1982) and Wealth effects of Stulz (1986).

− Tax effective hypothesis:

Taxes in the United States are effectively a type of nominal contracts. Feldstein and

Summer (1979) shows that “with the existing tax laws, inflation substantially increases the effective tax rate on capital income in the nonfinancial corporate sector”. Before going further the above statement, we have to know these two points: (i) The depreciation tax shields which a company gets each year are fix amount so its

real value declines with inflation.

(ii) Taxes are charged on nominal income and on the nominal return on assets.

(10)

− Money illusion hypothesis:

This hypothesis was suggested as an explanation of the negative effect of unexpected inflation on stock prices. Modigliani and Cohn argue that in high inflation period, investors are misled in discounting real earning by using inappropriately high nominal discount rates. Unexpected inflation raises nominal interest rate and if investors use a higher rate to discount future earnings, ignoring the positive effect of inflation on nominal earnings, the result is an erroneous under-valuation of stocks. − Wealth effects

Unexpected inflation depreciates the real values of government liabilities held by the public, and also leads to an unexpected decrease in real after tax personal income because of the “creeping bracket” (in most countries, the marginal tax rate on income is positively related with the level of nominal income. As the latter increases with inflation, the real tax burden increases as the marginal tax rate applied to nominal income will rise) phenomenon. Investors, whose real wealth declines unexpectedly, rebalance their portfolios and reduce the real value of their equity investments.

− Proxy hypothesis:

In economics, unexpected inflation indicates an economics shock; therefore its effect on stock prices depends on its source. An aggregate demand shocks should create positive correlation between the resulting unexpected inflation and stock price, whereas aggregate supply shocks should create negative correlation. The latter type shock is implicit in Fama (1981) which argue that there is no causal relationship whatsoever between inflation rate and real equity returns; instead, based on the demand money theory that unexpected decline in real activity leads to an rise in inflation. Unexpected inflation is a proxy for real activity, and with the positive relation between stock prices and future growth rate of real activity, we observe a negative relationship between unexpected inflation and stock prices.

(11)

Fama (1981) using WWII US data and that performed by Kaul (1987) using post-WWII US, UK, German, and Canadian data both support the proxy hypothesis as a partial explanation of the relationship between inflation and real equity returns. In particular, they find that when the measures of future real output growth are added as explanatory variables in regressions of real equity returns on expected and unexpected inflation, the coefficient estimates on future real output growth are positive and significant while the coefficient estimates on expected and unexpected inflation are attenuated both in size and significance. However, the inflation variables, especially unexpected inflation, still retain some explanatory power which shows that the Fama hypothesis does not grasp the whole problem. The reason is that Fama assumes that movement in money supply is invariant with respect to real shocks while a complete model of the monetary sector should also take into account the response of the monetary authorities, i.e, the money supply process.

In recent empirical evidences, econometricians found that the negative between inflation and stock is just a short-term phenomenon. In previous studies, the long run relationship between dependent and independent variables was eliminated because the differences of inflation and stock series were used instead of the levels of those series because they were preferred than the levels due to their stationary property. The studies in recent years turn their attention to the long run relation of those factors because even though in short run inflation and stocks can perform in opposite directions but in long run inflation and stocks may can have a positive relation due to the a cointegration relationship. The works of Anari and Kolari (2001), Luintel and Paudyal (2006), Ely and Robinson (1997) provide evidences for the capacity of stocks in maintaining their value relative to the movement of good prices in long term relationship by applying cointegration approach of

Engle and Granger (1987). As a result of their work, cointegration has emerged as important method used for analyzing stocks and good prices.

− Technical basis review

(12)

technical basis (Please refer Appendix A for a summary table of both result review and technique review)

− Bodie (1976)

Bodie uses CPI series to measure the index of purchasing value and the NYSE (New York Security Exchange) index is used to measure the return from stocks. The sample runs from 1953 to 1972 including annual, quarterly and monthly observations. To measure the correlation of inflation and stock returns, he uses the mean variance frame work. As this method is presented in the chapter V of this thesis so at this time we don’t discuss in detail about this method.

− Amihud (1996)

The study period is January 1986-October 1991. The data consists of 1404 daily return series on stock and bonds that include seventy monthly announcements of the CPI.

t

RS : The daily return on the value weighted index of all stocks traded on the TASE, excluding bank stocks, and

t

RB : The daily return on the index of government bonds whose principal and coupons are fully linked to CPI (the bonds are longer term). In Israel, the CPI-linked government bonds, with both principal and coupons fully adjusted to the CPI, provide a direct market-based measure of unexpected inflation which is unavailable in the United States

The effect of unexpected inflation on stock returns is tested by model

0 1 1 2 2 3 4 1 5 2 6 t t t t t t t t

RS

RB

DRBANN

β

ε

− − − −

=

+

(13)

negative and significant for the entire period which mean unexpected inflation has a negative effect on stock prices.

− Gultekin (1983)

Data used in this paper are collected from International Financial Statistics and Capital International Perspective. The sample runs from 01/1947 to 12/1979 with the monthly inflation rates for individual countries as the percent changes in CPI and stock returns including 60% of the market value of all shares traded in the most active stock exchange in each country (totally 26 countries). Besides, 90-day Treasury Bill is used to stand for the short term interest rate.

In order to investigate the relation between nominal stock returns and inflation, the three different estimates of the expected inflation rate are used in the regression model:

1

(

|

)

t t _t t

R

=

α

+

β

E

π φ

₋

+

ε

where

R

_t is the nominal return on common stocks, π_t is the inflation rate and

φ

_t is the information set that investors use in forming their expectations

First, he uses the contemporaneous inflation rates as proxies for expected inflation.

t

R

=

α

+

βπ

+

ε

where

R

_t is the nominal return on common stocks,

π

_t is the inflation rate and

φ

_t is the information set that investors use in forming their expectations.

Secondly, he decomposes inflation into expected and unexpected components by ARIMA models. Inflation forecasts from ARIMA model are used as estimates of expected inflation, and the estimated residuals are used as the unexpected part of inflation in the below regression model:

1

(

)

2

( )

t t t _t t

R

=

α

+

β

E

π

+

β π

_



−

E

π



_

+

ε

Finally, short-term interest rates are used as predictors of inflation. The expected and unexpected inflations are estimated from the equation:

1

t

I

_t t

(14)

Then the regression of stock returns on expected and unexpected inflation is made in a similar way to the second method.

− Anari and Kolari (2001)

They use monthly data series for six national stock prices indexes: S&P500 (US), TSE300 Composite (Canada), FTSE100 (UK), SBF250(France), DAX(Germany), and Nikkei (Japan). The CPIs of those six countries are used to present good prices. The sample runs from January 1953 to December 1998. All variables are transformed into natural logarithms. The method they use to assess the correlation between inflation and stock are cointegration framework in which Johansen’s Trace test is used to verify the cointegration relationship of the two factor and a vector autoregressive (VAR) model is apply. As this method is used in Chapter VI of this thesis, we will not explain it in details at this moment.

− Luintel and Paudyal (2006)

(15)

− Ely and Robinson (1997)

Their analysis begins with an examination of the time-series properties of stock prices and goods prices for 16 industrialized countries. Three measures of goods prices are examined: a consumer price index, a producer price index, and the gross domestic product (GDP) deflator index. The data is quarterly and expressed in logs, and for most of the countries analyzed, the time period runs from 1957:1 through 1992:3. Again in this paper the cointegration framework is applied.

According to the data and methods used in the above studies, we can see that the most common serie used to present inflation is CPI and the main stock index of each country provides the information to calculate the stock return. Normally, all the series are transformed to logarithm form. The current trend of using cointegration frame work to analyse the relationship between inflation and common stocks is revealed in the technique review. Therefore, we apply the cointegration framework to test with the Netherlands data. To demonstrate the importance of cointegration in the relationship between inflation and stocks, we make a comparison between the hedge ratio of the mean-variance frame work of Scholman and Schweitzer(2000) (which does not take in to account the cointegration between these two factors) and that of cointegration frame work.

(16)

IV. Data

The data of the series used in this thesis is downloaded from DataStream and the sample runs from January 1970 to March 2008, with 423 monthly observations. Monthly data is used to provide more observations. All variables are transformed into natural logarithms. To measure inflation, we use the CPI index to present for good prices and the AMI index (Amsterdam Midkap Index) to stand for stock prices. For stock price, we have two indicators for Netherlands stocks: AMI and AEX (Amsterdam Exchange Index). However, we will omit one of those two series, depending on their stationarity property which is explained in detail in the later part of this section. In time series analysis, it is important to have stationarity of the series to make sure that their statistical properties do not depend on time. In general, stock prices and good prices are found to be integrated at first order I(1), which means that they are non-stationary but their first differences are stationary. To make it in accordance with the previous studies, we want to verify the stationary property of the data.

To test for stationarity of the series, we first have a look at figures of log levels and differences of the series to have a visual evidence about I(1) property of the series (Please refer the figure 1, 2, 3 in the Appendix B for details). All figures show a non-stationary trend of the series at the levels but stationary at the first differences. In addition to the visual test, we also make a statistical test for the stationary of data. The most popular method used for this kind of test is the augmented Dickey-Fuller (ADF) test; however, because of the importance of stationary, we use a stronger test: the modified Dickey-Fuller t-test (MDF) proposed by Elliott, Rothenberg, and Stock (1996). This test is similar to (ADF). This test has significantly greater power than ADF as the time series is transformed via a generalized least squared (GLS) regression before performing the test.

(17)

(18)

V. Mean variance framework for long run hedge ratio

As mentioned in the literature review, there is a new trend in studying the relation between in inflation and stock as many researchers pay their attention to cointegration method to reveal the long run relationship. To make a comparison between the traditional method and the cointegration method which is presented in the next section, we follow the work of previous studies to analyze Netherlands data and calculate the long term hedge ratio when the cointegration relationship is ignored.

Firstly, a simple regression is made to give an initial view about this relationship. All the previous studies used to work with inflation rate and inflation returns which are the differences of inflation and stock series because they were integrated at the first order.

Granger and Newbold (1974) pointed out that using the levels of non stationary series could result in a spurious regression with these problems:

- The hypothesis of H0:

α

=

0

is too often rejected - Surprisingly high R2 value.

- DW statistics takes small values (indicating positive autocorrelation) (To have a detailed explanation please refer to Phillips (1986)) We have the regression result as:

0.0073 -1.48.

t t t

RS

=

PR

+

µ

(1) (0.643)

(19)

run. Investors whose real wealth is diminished by high inflation can expect that this effect to be compounded by a lower than average return on the stock market.

Now we decompose inflation into unexpected and expected inflation components to have a deeper view about the relationship. According to Schotman and Schweitzer (2000), inflation is assumed to be generated by the AR(1) process:

1

(

)

1

t t t

PR

₊

=

µ α

+

PR

−

µ

+

η

₊ (2) In the regression (2), we have that current inflation depends on the long run inflation

µ

, the deviation of inflation in the previous period from the long run value and the independent shocks

η

_t₊₁with variance

σ

_η2. We have the expected inflation equal to the fitted values of the regression. The independent shock

η

_t₊₁ is used to present the unexpected inflation component.

The estimated value of the parameters in (2):

_.0028

µ

=

Std. Err 0.0003

_0.38

α

=

Std. Err 0.0427 And the standard error of

η

_t₊₁ is equal to

σ

ηt+₁

=

0.004

The value of

α

=

0.38

1

satisfies the strong stationary property of the inflation rate found in the data analysis. Having the unexpected and expected components of inflation, we make a regression of stock returns on expected and unexpected inflation:

1

E[PR

1

]

1 1

t t t t

RS

₊

= +

c

β

₊

+

φη

₊

+

ε

₊ (3) and estimated parameters are:

_-3.91

(20)

_-0.27

φ

=

. Std. Err 0.697

0.01 c

=

.

The specific risk term

ε

_t₊₁ with standard error

σ

ε

=

0.058

.

The result of (3) shows that stock returns have a strong negative relation with expected inflation. This relation was also found in the work of Fama (1981) when he estimated with US data and this coincidence gives a strong support for the accuracy of our study. However, the equation (3) only provides a short run relation between stock returns and inflation in each month. To find a long term relation, Schotman and Schweitzer (2000) proposes a simple mean-variance framework to evaluate hedge tools. In finance, the selection of portfolios based on the means and variances of their returns: an investor chooses a portfolio which has high mean return with its variance is as low as possible and this condition, called mean-variance criterion, is the basis of mean-mean-variance framework.

Considering a portfolio which is invested into stocks at a fraction of

w

and the rest is invested into risk free discount bond of maturity

k

. The maturity

k

is equal to the horizon of investments. An investor will try to maximize the mean variance criterion:

( )

var[

]

max

[

]

2

k k t k w t t k

r

E r

γ

+ +

−

(4) where ( ) ( ) ( ) ( ) ( ) ,

(

)

(1

)(

)

k k k k k t k t k t k f t t k

r

₊

=

w RS

₊

−

PR

₊

+

−

w RS

−

PR

₊

is the cumulative real return on the portfolio from time t to time t+k,

RS

_{t k}( )₊k is the cumulative stock return,

PR

_{t k}( )₊k is the cumulative inflation,

RS

( )_{f t}k_, the nominal risk free cumulative return on a discount bond with maturity

k

, and

γ

the risk tolerance parameter. The value of

w

is calculated to have a maximum return of portfolio after adjusted for its variance.

(21)

N. T. Phan, supervised by Laura Spierdijk Page 21 ( ) ( ) _{( )} _{( )} , ( ) ( ) ( )

[

]

cov[

,

]

var[

]

var[

]

k k k k t k f t k t k t k k k t k t k

E RS

RS

PR

w

RS

γ

₊ ₊ ₊ + +

−

=

+

(5)

The first term is the demand for stock as a result of the equity premium. The second term is the hedging demand for stock depending on the covariance with inflation. The hedging demand, denoted

∆

( )k , is also the minimum variance hedge ratio (MVHR) proposed by

Johnson (1960) when he applied modern portfolio theory to the hedging problem. It was the first time that definitions of risk and return in terms of mean and variance of return were employed to this problem. It should be mentioned that the minimum variance hedge is proved to be the coefficient of the regression of hedged instrument on futures price.

With k =1, we have: 2 (1) 2 2 2

cov[

,

]

var[

]

t t t

RS PR

RS

η η ε

φσ

φ σ

σ

∆

=

+

(6) For a given k, we have

2 1 2 ( ) 2 2 2 2 1 2

(

)

(

2 )

k k k k k

k

η η ε

φ ψ

φ

β

ψ β σ

φ

ψ φβ ψ β σ

σ

+

∆

=

+

(7) With 1

1 (

)

1

k k

k

α

ψ

α

−

=

−

2 2 2 2 2

1

1 (

2 )

(1

)

1

k k k

k

α

ψ

α

−

=

−

The optimal hedge ratio is calculated at different horizon of k which is suitable to different terms of investments. As mentioned in the beginning of the thesis, the investment term of a pension fund is very long so we are interested in the convergence of the hedge ratio.

(22)

N. T. Phan, supervised by Laura Spierdijk Page 22 2 ( ) 2 2 2 2

((1

)

lim

(1

)

((1

)

k k η ε η

α φ αβ σ

α σ

α φ αβ σ

→∞

−

+

∆

=

−

+

−

+

(8) We apply the estimated values which are calculated from the equation (1) and (2) above to have the estimated value of the long-run hedge ratio. The result for the hedge ratio under mean variance frame work is -0.02. It means that in long run, the value of cov[RS_{t k}( )₊∞ ,PR_{t k}( )₊∞ ] is negative or stock returns and inflation move in opposite direction so the increase in stock returns cannot cover for the increase of inflation. This can lead to the conclusion that stocks are poor hedges for inflation. Actually, this is not unpredictable as it coincides to the result of previous studies which does not take into account the cointegration.

In an effort to explain for this result, we figure out that the persistence of inflation rate is an important factor which impacts on the result because according to calculation of Schotman

and Schweitzer (2000) for all over 16 countries, they point out that if the inflation persistence

α is less than 0.7, stocks become poor hedges despite the value of parameterβ. Here in data analysis of the previous chapter, we have that the inflation series is quite strong stationary so the negative, therefore this is the reason that hedge ratio in long run under that calculation of mean variance frame is become negative. Moreover, stationary is one of important properties of the difference series which is the reason why previous study choose to use it instead of use the levels of inflation and stock index. We can think that using the differences of inflation and stock prices are not a good choice to evaluate the long run relation of those factors. In addition, the extreme small magnitude of the negative hedge ratio of mean variance framework does not give a strong support for the negative relationship between stock and inflation in long run.

(23)

(24)

VI. Cointegration frame work for long run hedge ratio

As explained in the previous section, the reason that the differences of stock prices and inflation are widely used in the previous studies is that they are stationary while the levels of those series are not stationary. However, a disadvantage of differenced series is that any long term trend in the data is removed. To reserves the long term relationship of series, the information based on the raw prices, rate or yield data has to be taken full advantage and for that reason, cointegration method is built. Since the seminal work of Engle and Granger

(1987), cointegration has become the relevant tool of time-series econometrics. Cointegration has emerged as a powerful technique for investigating common trends in multivariate time-series, and provides a sound methodology for modeling both long-run and short-run dynamics in a system.

(25)

variance is preferred than the Johansen criterion of maximum stationarity; thirdly, there is often a natural choice of dependent variable in the cointegrating regressions (for example, in equity index arbitrage).

Before applying the first step of the method, the data must satisfy the conditions that all series are I(1) and that a cointegrating vector exists between the series. The first condition is already tested in section IV. With the second condition, it is necessary to explain it in a slightly technical way: two integrated series are considered 'cointegrated' if there is a linear combination of these series, called the 'cointegrating vector' and denoted z, that is stationary. In mathematical terms, x and y are cointegrated if x, y ~ I(1) and there exist

α

such that

z

= −

x

α

y

~I(0). We verify the second condition by using the cointegration test of Johansen(1991). The result of this test showed in Table 3 (presented in the Appendix B) is explained as: the test rejects max rank at level 0 but cannot reject at level 1 which gives evidences of the existence of one cointegration vector. When only two integrated series are considered for cointegration, there can be at most one cointegrating vector, because if there were two cointegrating vectors the original series would have to be stationary.

After verifying the existence of cointegration, we can begin the first step of the Engle-Granger-Yoo method by estimating the long-run parameters in the static model of stock returns and inflation:

3.752

2.002

t t t

S

= −

+

P

+

ε

(9) (0.081)

(26)

In stage two, we use the residual

ε

t from (9), as the deviation from long-run equilibrium in

period t-1, to estimate the ECM model, which is argued to have this form:

₁ 1 1 p p t t S Si t i Sj t j s St i j

S

α

β

S

₋

β

P

₋

θ ε

−

u

= =

∆

=

+

∑

∆

+

∑

∆

+

(10) The ECM model shows how the change of

S

_tresponds to stochastic shock

u

_Stand the deviation of the previous period from long run equilibrium (

ε

t−1

=

S

_t₋₁

−

2.002 P

_t₋₁

+

3.752

). Therefore, the coefficient

θ

_s can be interpreted as the speed of adjustment parameter. The larger value of

θ

_s, the greater the respond of

S

_tto the previous period’s deviation from long-run equilibrium. If

θ

_s and all the coefficients

( )

Sj

j

β

are equal to zero, it shows

∆

S

_t is not affected by

P

_t. In other words, if the Granger causality for cointegrated variables exists, the speed of adjustment coefficient is different from zero.

To estimate equation (10), we first use Akaike's information criterion (AIC) to choose the lag length for

∆

S

_tand

∆

P

_t. The length of lags suitable with the model is m=n=13. After omitting insignificant variables, we have the final model for regression (10):

∆

S

_t

=

0.007 1.52

−

∆

P

_t₋₁

−

1.87 ∆

P

_t₋₂

−

2.70 ∆

P

_t₋₅

+

1.76 ∆

P

_t₋₆

(0.737) (0.811) (0.770) (0.809)

+

2.77 ∆

P

_t₋₉

+

0.14 ∆

S

_t₋₁

+

0.13 ∆

S

_t₋₁₀

−

0.011 ε

t

+

u

_St (11)

(0.755) (0.047) (0.048) (0.006)

(27)

The residuals

u

tare used in the third-stage regression:

u

t

=

δ θ

[

−

P

_t₋₁

]

+

v

_t (12) The estimated value

δ

of regression (12) then used to correct first stage estimate (together

with its standard deviation, which provides the correct standard deviation for the long run elasticity of inflation in regression (9)).

From (12), we have

δ

=0.105 (with its standard error is 0.93) and the corrected long run elasticity of inflation is

δ

+

2.002 =

2.107

. This result is also found to be similar to the study of Hein and Mercer(1999) which report Fisher coefficient that are significantly greater than 1, ranging from 1.26 to 2.19.

Knowing the long run relationship between stock and inflation from the equation (9), we can calculate the long run hedge ratio. According to Abdulnasser and Eduardo (2006), the optimal hedge ratio may be defined as the quantities of the hedged instrument and the hedging instrument that ensures the total value of the hedged portfolio does no change. This can be more formally expressed as follows:

h SI HI

V

Q

SI

Q

HI

∆

=

∆

−

∆

(13) Where

h

V is the value of the hedged portfolio SI

Q is quantity of hedged instrument HI

Q is quantity of hedging instrument

SI is price of hedged instrument

HI is price of hedging instrument If

∆

V

_h

=

0

then HI SI

Q

SI

h

Q

HI

∆

=

∆

, where

h

is the hedge ratio.

(28)

*

t t t

SI

= +

a

h HI

+

e

(14) Replacing SI and HI by inflation and stock price, we have the optimal hedge ratio estimated from an ordinary least squares (OLS). It is worth to mention that in case of two series, it does not matter which of series is taken as the dependent variable in the expression of long term relationship under cointegration frame work. But when there are more than two series, the regression may suffer from bias and it should be absolutely clear which series is to be used as the dependent variable in the regression. This is one of the disadvantages of Engle-Granger-Yoo method. Besides we also want to take a note that conventional OLS approach provides a constant hedge ratio while GARCH model (generalized autoregressive conditional heteroscedasticity) provides a time-varying hedge ratio. However, the study of

Lien(2002) shows that OLS hedge ratio provides a smaller hedged portfolio variance than the GARCH hedge ratio. This result is tested with ten pairs of hedged and hedging series covering currency futures, commodity futures and stock index futures. So we believe that using OLS estimate can give a good estimate for the hedge ratio in long run between stock prices and inflation.

From the equation (9) we have the long run hedge ratio as:

(29)

Robustness Checking

The data used in this study runs for 30 years with monthly observations. However, it seems relatively short for such a long term research in pension. To make sure that the result from our study can provide a robust over long run, we will check it with bootstrap technique. To maintain the relationship between inflation and common stocks, we have to generate bootstrap samples which consist of values of stock and inflation in each observation. As there is no study about the join distribution of stock and inflation, we decide to use non-parametric block bootstrap for testing.

There are 10000 bootstrap samples generated to provide prudent result. With each sample, we regress inflation series on stock series and the estimated coefficient or long run hedge ratio is collected. We have the histogram of the bootstrap estimated hedge ratio:

(30)

present the joint distribution of stock and inflation. Due to the limitation of a master thesis, we will leave this issue for a further research.

Further discussion with the result

When taking cointegration relationship into account, we have that the hedge ratio under the cointegration framework is higher than that of mean variance framework. This result happens to be identical to a result of Lien (2004) which under a certain condition ignoring cointegration relationship can result in a smaller hedge ratio and the condition is:

(

S _P _S

)

0 k

=

θ θ

−

h

θ

<

(16) Where

θ

_S is from equation (10),

θ

_P and

h

are derived from the equations below:

₁ 1 1 p p t t S Si t i Sj t j P Pt i j

P

α

β

S

₋

β

P

₋

θ ε

−

u

= =

∆ =

+

∑

∆

+

∑

∆

+

(17)

₁ 1 1 m n t t i t i j t j t t i j

S

α

β

S

₋

β

P

₋

θε

−

h P

u

= =

∆

=

+

∑

∆

+

∑

∆

+

+ ∆ +

(18) In an effort to verify the condition with Netherlands data we have the estimated value of

θ

_P,

h

and

k

:

_P

_0.0064

θ

=

,

_0.0002

h

= −

5

(

)

7.10

0

S P S

k

θ θ

h

θ

−

=

−

= −

<

(31)

(32)

VII. Conclusions

(33)

References

Abdulnasser Hatemi-J and Eduardo Roca (2006). “Calculating the optimal hedge ratio: constant, time varying and the Kalman Filter approach “.Applied Economics Letters, Volume 13, Issue 5, pages 293 – 299.

Al-Khazali, O. (2004). "The generalized Fisher hypothesis in the Asian markets". Journal of

Economic Studies, Volume 31, pp.144-57.

Amihud, Y. Feb. (1996). “Unexpected inflation and stock returns revisited—evidence from Israel”. Journal of Money, Credit, and Banking 28(1): 22–33.

Anari, A. and Kolari, J. (2001). “Stock prices and inflation”. Journal of Financial Research, pages 587–602.

Bodie, Z. May (1976). “Common stocks as a hedge against inflation”. Journal of Finance 31(2): 459–470.

B. Branch, "Common Stock Performance and Inflation: An International Comparison," Journal

Business, 1974, 47, 48-52.

P. Cagan, "Common Stock Values and Inflation-The Historical Record of Many Countries,"

National Bureau Report Supplement, New York, 1974.

Capital Risk Management (2004). “Inflation Hedge or Fool’s Gold?”.

Chua, J. and Woodward, R.S.(1981). “Gold as an inflation hedge: A comparative study of six major industrial countries”. Journal of Business Finance and Accounting: 191-197.

Elliott, G.; Rothenberg, T.J. and Stock, J.H. (1996), “Efficient Tests for an Autoregressive Unit Root”, Econometrica 64, 813–836.

Ely, David P. and Kenneth J. Robinson (1997). “Are Stocks a Hedge Against Inflation? International Evidence Using a Long-run Approach”. Journal of International Money and

(34)

Engle, R. F. and S. Yoo (1991). “Cointegrated economic time series: an overview with new results”. Chapter 12 in Engle and Granger (eds.), Long run economic relationships - Readings in

Cointegration. Oxford University Press.

Engle, R. F. and C. W. J. Granger (1987). “Cointegration and error correction: representation, estimation and testing”. Econometrica, 55,251-76.

Fama, E.Sept. (1981). “Stock returns, real activity, inflation, and money”. American Economic

Review 71(4): 545–565.

Feldstein, M. Dec. (1980). “Inflation and the stock market”. American Economic Review 70(5):839–847.

Feldstein, Martin and Lawrence Summer. (1979). “Inflation and the taxation of Capital Income in the corporation Sector”. National Tax Journal 32, 445-70.

Foort Hamelink, and Martin Hoesli (1996).” Swiss real estate as a hedge against inflation: New evidence using hedonic and autoregressive models”. Journal of Property Finance, Vol 7, 1,33-49.

Granger, C. W. J. and Newbold, P. (1974). "Spurious regressions in econometrics". Journal of

Econometrics 2: 111–120

Gultekin, N. B. Mar. (1983). “Stock market returns and inflation: evidence from other countries”. Journal of Finance 38(1): 49–65.

Hartzell, D., Hekman, J., Miles, M. (1987), "Real estate returns and inflation", AREUEA Journal, Vol. 15 pp.617-37.

Hein, S. E. and J. M. Mercer (1999). “Comovements of stock prices and consumer good prices”. Working paper presented at the 1999 Southern Finance Association conference.

(35)

Jaffe, J. and Mandelker, G. (1976). “The Fisher effect for risky assets: An empirical investigation”. Journal of Finance 31, 447-58.

Johansen, S (1991). “Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models”. Econometrica 59, 1551-80.

Johansen, S and Juselius, K (1990). “The Full Information Maximum Likelihood Procedure of Inference on Cointegration with Applications to the Demand for Money.”. Oxford Bulletin of

Economics and Statistics 52, 169-210.

Johnson. L. (1960). “The theory of speculation in commodity futures”. Review of Economic

Studies, 27, pp. 139-51.

Kaul, G. June (1987). “Stock returns and inflation”. Journal of Financial Economics 18(2): 253– 276.

Lien, D. (2004). “Cointegration and the optimal hedge ratio: The general case”. Quarterly

Review of Economics and Financial 44, pp 654-658.

Lien, D.; Tse, Y.K. and Tsui, A.K.C. (2002). “Evaluating the Hedging Performance of the Constant-Correlation GARCH Model”. Applied Financial Economics, 12, 791-798.

Limmack, R.J., Ward, C.W.R. (1988), "Property returns and inflation", Land Development

Studies, Vol. 5 pp.47-55.

Luintel, K. B. and Paudyal, K. (2001). “Stock Returns and Inflation: Some New Evidence”.

Economics and Finance Working papers, Brunel University, 01-08.

Luintel, K. B. and Paudyal, K. (2006). “Are Common stocks hedge against inflation?”. The

Journal of Financial Research, Volume 29, Number 1: 1-19.

Modigliani, F., and Cohn, R. A. 1982. “Inflation, rational valuation and the market”. In

Saving,Investment, and Capital Markets in an Inflationary Economy (M. Sarnat, and G. P. Szego, eds.).Cambridge, MA: Ballinger, pp. 121–166.

(36)

Phillips, P.C.B. (1986). “Understanding spurious regressions in econometrics”. Journal of

Econometrics 33, 311-340.

Rapach, D. E. (2002) “The long-run relationship between inflation and real stock prices,” Journal of Macroeconomics 24, 331-51.

Schotman, P.C. and Schweitzerb, M. (2000). “Horizon sensitivity of the inflation hedge of stocks”. Journal of Empirical Finance Volume 7 (3-4), 301-315.

(37)

io n sh ip b et w ee n in flat io n a n d s to ck r et u rn s i n N et h er lan d s . P h an , s u p er v is ed b y L au ra Sp ie rd ijk P ag e 37

ix

A

: S

u

m

ar

y

on

p

re

vi

ou

s

re

su

lt

a

n

d

t

ec

h

n

iq

u

e

re

vi

ew

Data Sample period Inflation

representer

Common stocks

Bodie (1976) US 1953-1972 CPI NYSE index Monthly, Quarterly, Yearly Mean-variance frame work

Fama (1981) US 1954-1976 CPI NYSE index Monthly, Quarterly, Yearly The demand money theory:

unexpected inflation is a proxy for real activity.

Amihud (1996) Israel 1986-1991 CPI-linked

government bonds

weighted index of all stocks traded on the TASE excluding bank stocks

Daily Regression stock return on lag of itself, current and lags of CPI-linked government bond, and DCPI (the difference of CPI). The coefficient of DCPI represents the relation between inflation and stocks

Gultekin (1983) 26 Industrial

countries

1947-1979 CPI _{60% of the market}

value of all shares traded in the most active stock exchange in each country

Monthly Regression stock returns on expected and unexpected inflation. Inflation is decomposed in turn under ARIMA model and short term interest rate

Anari and Kolari (2001)

US, Canada, UK, France, Gemany, Japan

1953-1998 CPI _{S&P500, TSE300,}

FTSE100, SBF250, DAX, Nikkei.

Monthly Cointegartion frame work

Luintel and Paudyal (2006) UK 1955-1998 RPI (Retail Price Index) FTA

(FT All Share Index)

Monthly Cointegartion frame work

Ely and Robinson (1997)

16 industrialized countries1957-1992 CPI,PPI, GDP Main stock index in each country

Quarterly Cointegartion frame work

Positive Conclusion on the relationship between inflation and common

Paper Market research Data frequency Research method

Negative ( common stocks is not

(38)

Appendix B

Figure 1: The monthly (Log) levels of CPI and AMI

(39)

Figure 3: The monthly (log) stock returns - AEX.

(40)

Table 1: MDF Test for (log) levels of CPI, AMI, AEX series.

Test Statistics value

[Lags] CPI AMI AEX

5% Critical Value 11 -0.96 -1.54 -1.94 -2.85 10 -0.80 -1.53 -1.69 -2.85 9 -0.71 -1.34 -1.78 -2.85 8 -0.86 -1.24 -1.66 -2.86 7 -0.84 -1.30 -1.54 -2.86 6 -0.71 -1.26 -1.61 -2.87 5 -0.10 -1.26 -1.61 -2.87 4 0.27 -1.25 -1.56 -2.87 3 0.64 -1.33 -1.65 -2.88 2 0.25 -1.26 -1.64 -2.88 1 0.08 -1.27 -1.60 -2.88

Table 2: MDF Test for the first difference of (log) CPI, AMI, AEX series.

Test Statistics value

[Lags] CPI AMI AEX

(41)

Table 3: The result of Johansen test for number of cointegrating vector between inflation and stock prices

Max. rank Trace statistics 5% critical value

0 17.6729 15.41