Speed of Adjustment and Infraday/Intraday Volatility in the Italian Stock and Futures Markets

doi:10.4236/me.2011.25082

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Modern Economy, 2011, 2, 735-742

doi:10.4236/me.2011.25082 Published Online November 2011 (http://www.SciRP.org/journal/me)

735

Speed of Adjustment and Infraday/Intraday Volatility in

the Italian Stock and Futures Markets

Pietro Gottardo

Dipartimento di Ricerche Aziendali, Facoltà di Economia, Pavia, Italy

E-mail: [email protected]

Received July 15, 201 1; revised August 19, 2011; accepted September 1, 201 1

Abstract

We estimate the speed of adjustment of prices to value changes in the Italian stock and futures markets using

variances in different return intervals. The paper presents evidence that an assumption of linearity for the

relationship volatility-time is untenable when intraday and infraday data are used jointly. Prices adjust to

new information within three days, but the process is complex with evidence of overshooting and divergent

movements in the smaller return intervals. Firms behave differently according to their inclusion or exclusion

from the MIB30 index. The speed of adjustment is strongly related to firm-specific characteristics and the

log of capitalization explains some of the cross-sectional variability in the adjustment coefficients for most of

the return intervals.

Keywords: Speed of Adjustment, Overshooting, Intraday returns, Stock Index Future

1. Introduction

The growing body of evidence on stock returns predict-

ability and overreaction challenges the traditional effi-

ciency view that stock prices reflect fully and quickly all

the relevant information. Event-based return predictabil-

ity, long term reversals and short term momentum, ex-

cessive stock prices volatility relative to fundamentals

are some of the findings of a large number of empirical

works in different areas, countries and time periods.

Daniel-Hirshleifer and Subrahmanyam [1] cite a large

sample of the relevant literature on these topics.

There is disagreement over the interpretation of this

evidence. The anomalies may be considered normal

chance deviations from the fundamental efficiency law

as suggested by Fama [2], but the regularity and dimen-

sion of these phenomena cast some doubt on the appro-

priateness of this hypothesis. An alternative explanation

is that many empirical regularities represent variations in

rational risk premia, even if this requires an asset pricing

model with extreme variability in marginal utility across

states and has other undesirable implications.

Daniel-Hirshleifer and Subrahmanyam [1] suggest a

psychological model based on imperfect rationality, in

particular they construct their model on two well-known

psychological biases: investor overconfidence about the

precision of his private information, and biased self-at-

tribution which causes individuals to strongly attribute

events that confirm the validity of their actions to high

ability and events that disconfirm the action to external

noise or sabotage.

Another stream of literature suggests instead a lagged

adjustment of security prices to new information. Patell-

Wolfson [3] and Hasbrouck-Ho [4] are just two exam-

ples of empirical studies showing that prices tak e time to

adjust to news. Patell-Wolfson [3] examine intraday

price changes associated with earnings announcements.

From a theoretical perspective the derivation of a partial

price adjustment model in security markets, showing that

this is the result of optimizing behavior by market mak-

ers is due to Garbade-Silber [5,6]. Goldman-Beja [7],

Amihud-Mendelson [8], and Damodaran [9] describe a

return process that can be applied to portfolios and ind ex

futures as well as single stocks which permits the deriva-

tion of a measure for the price adjustment coefficient.

The model derived in Amihud-Mendelson [8] and in

Damodaran [9] distinguishes between observed prices

and intrinsic value of a stock, measuring a finite speed of

adjustment of prices to value changes using the informa-

tion in various return intervals.

The screening among all these models is just an em-

pirical matter, only the real behavior of prices in security

markets can shed some light on the subject. In what fol-

lows we use Damodaran adjustment model in the correct

P. GOTTARDO

736

form derived by Brisley-Theobald [10], with a signifi-

cant difference in h is assumption with resp ect to the rela-

tionship between time and v olatility, to analyze the price

adjustment in the Italian futures and stock markets. The

primary contribution of this paper is a refinement of the

model in Damodaran [9] to account for the estimation of

adjustment coefficients using together intraday and in-

fradaily data and its application to a new data-set to dis-

entangle the relative merits of the above models. We

calculate returns and variances over non-overlapping

periods and estimate the price adjustment coefficients at

intraday intervals of five, fifteen, thirty, sixty minutes,

two, four, and eight hours and at infraday frequencies

from one to ten days. The relationship between time and

volatility is a key empirical problem, usually solved as-

suming the linearity of this relationship. Using on ly daily

returns a linear approximation could be reasonable but

not with the inclusion of in traday returns. As we show in

section 3 the inclusion of both infraday and intraday

measurement intervals has a severe impact on the linear-

ity of the relationship, so that the usual assumption is

untenable using datasets and models that take into ac-

count jointly information on the volatility within a trad-

ing day (intraday intervals) and across trading days (in-

fraday interv als). Section 2 presents the price adjustment

model used. We analyze in section 3 the return behavior

of the Italian stock index and stock index futures together

with a selection of single stocks. The choice is useful to

screen possible differential adjustment processes for the

index, futures and the single securities as half of this

sample is given by stocks not included in the index over

which the futures contract is designed. Section 4 con-

cludes with a discussion of our results and some policy

implications about the efficiency and liquidity improve-

ment of the assets negotiated in these markets.

2. Price-Adjustment Model

The price adjustment model of Amihud and Mendelson

[8] distinguishes between the intrinsic value of a stock,

futures or portfolio, Vt, and the observed price, Pt.

A generalization of their interpretation of this model

allows for market-related, specific information and noise

to be reflected in the return process, resulting in an im-

perfect (partial or lagged) price adjustments to value

changes, but also for overshooting phenomena (a more-

than-perfect adjustment) or divergence from value. The

basic model is

,,1,,1 ,

it itit itit

PgVP u





 



(1)

where g represents the speed of price adjustment: g = 1

implies a full and almost immediate (as the one period

lag can be small as you like) adjustment of prices to

every change in value, g > 1 represents a tendency for

the asset to overreact to news affecting its value, whereas

0 < g < 1 includes all cases of partial and lagged adjust-

ment. Last but not least for importance is the case when

g < 0 that implies price divergence from the intrinsic

value.

The possibilities of overreaction or divergence from

value have been totally neglected in the theoretical de-

velopments of this model by Amihud-Mendelson [8] and

Damodaran [9] but given the results in DeBondt-Thaler

[11] and the implications of behavioral or psychological

models for the price generation process we believe that a

careful investigation is called for. The noise term, ui,t in

Equation (1) is determined by information and markets

structure related factors such as liquidity trading, noise,

bid-ask spread. It is assumed to be a sequence of i.i.d.

random variables with zero mean and finite variance, σ2i

and independent across stocks.

To derive a measure of g, Damodaran [9] uses the

variances in different return intervals that can be written



,,,

Var 22

ijt

ij ij

Rjv







(2)

where Var(Ri,jt) is the variance for the observed returns

assuming j as measurement interval, while gj is the ad-

justment coefficient measured for the same j-interval

returns, and v2 is the variance of the intrinsic value proc-

ess.

A restrictive by-product of the original assumptions of

this model is that v2 is linear in j, as {Vt} is an i.i.d. ran-

dom variable and the intrinsic variance and noise proc-

esses are assumed to be independent. This assumption is

apparently innocuous given that a linear relationship

between volatility and calendar time is almost standard

in many areas of research in finance. Unfortunately even

with daily data it is a well known and established result

that a linear relation between volatility and time is at best

a first approximation as weekends and other non-work-

ing holidays have a less than proportional effect on stock

volatility. The problem is of great concern here because

our intention is to measure the price adjustment coeffi-

cients using together intraday and infradaily data, see for

instance Amihud-Mendelson [12], Amihud-Mendelson

and Murgia [13], and Gottardo [14]. To the degree that

this hypothesis is violated, the model estimates of gj will

be grossly flawed. We suggest to replace Equation (2)

with the following more general formulation:



,,,

Var()

ijt

ij ij

Rfjv







(2’)

analyzing three different forms for the relationship be-

P. GOTTARDO

737

tween intrinsic volatility and return measurement inter-val:

() 1 and 1 for 1 1 for

empirical average relation between t ime and volatility

jjk

fj jdj kdjldlj k









 







The first one is the usual assumption of linearity in

variance while the second form give us some freedom

particularly u seful if we choose the poin t of discontinu ity

l of this relationship to represent the passage from intra-

day to infraday return intervals.

With the third formulation we relay on the data to de-

termine without theoretical constraints what is the em-

pirical law characterizing the volatility evolution through

measurement intervals.

We can now use a sequence of n observed unit-inter-

val returns to estimate the variances for different return

intervals (j = 1, 2,…, k) and assume that this sequence is

of sufficient length to allow gk = 1. Given Equation (2’)

we can then derive the price adjustment coefficients gj if

we impose some structure for the noise and intrinsic

variance components.

The assumption in Damodaran [9] was that the two

components could be written as functions of the covari-

ance and variance in k-interval returns. But this is just a

matter of convenience, the model offers no theoretical

support for this choice. We retain only partially this hy-

pothesis assuming the intrinsic variance to be function of

the k-interval variance while the noise component de-

pends from all the auto-covariances in the infraday return

intervals. The reason is that while the choice of the k-

interval variance is innocuous and easily in terchangeable

given a clear association between volatility and time, this

is untrue for the covariances that change in a manner

unpredictable through time with large swings even from

positive to negative values and vice-versa. Using the

average auto-covariance over all infraday intervals we

minimize the effect on the results obtaining more stable

gj’s estimates. Writing the noise and intrinsic variance

components as



2,,1

Cov ,

iijtijt

ljkRR





 (3)





2Var() 2Cov,

ikti jti jt

RRR





,1

(4)

On the base of Equation (2’) we can calculate for each in-

terval j, the difference between the variance in j-interval

returns and the equivalent variance in k-interval returns.

Substituting for v2 and σ2 and solving through for gj, we get

Equation (5).

In theory (5) could be used to estimate the speed of

adjustment for return intervals until j = k – 1, with only

the information available in the time series of unit-in-

terval returns data. In practice given that unit-interval

returns of intraday frequency do not contain information

with respect to the overnight returns we need an addi-

tional data source that could be represented by the daily

stock returns.

3. Estimation and Results

3.1. Data Sample and Methodological Choices

To estimate the speed of price adjustment, we use 5 min-

utes as unit-interval from July 4, 1995 to May 30, 1997.

The sample includes the index of the 30 most important

Italian stocks (MIB30), the futures contract on this index

(FIB30), all the firms included in the MIB30 (for the

whole sample period or partially) as well as the biggest

firms not included in this index. The final sample is

composed of 58 stocks listed on the Italian Stock Ex-

change.

The primary reason for the sample size and the crite-

rion for inclusion was the availability of data combined

with enough liquidity for each stock. We use all returns

from opening to close (10 a.m. to 17 p.m. for the stock

market and 9.30 a.m. 17.30 p.m. for the futures market)

and the daily returns to estimate for each stock, the index

and the futures, the variances with return frequencies

ranging from five minutes to ten days.

We calculate returns and variances over non-overlap-

ping periods and estimate the price adjustment coeffi-

cients at intervals of five, fifteen, thirty, sixty minutes,

two, four, and eight hours and at daily frequencies from

one to ten days. The first empirical problem to solve is

related to the relationship between time and volatility.

Using only daily returns a linear approximation could be

reasonable but not with the inclusion of intraday returns.

The plot in the Figure 1 below shows the average

stock volatility for the intraday return intervals. As can

be seen a linear relationship is acceptable as a first ap-

proximation only for the intervals between two and eight











,,,1

,,,,

2Var() Cov,()

Var()( )Var()2Cov,

ijtijtijt

ijtiktijtijt

RfjRR fj

RfjRkRR k











 1

(5)

P. GOTTARDO

738

hours, the inclusion of smaller or greater measurement

intervals (as the daily interval with its overnight effect)

has a severe impact on the linearity of the relationship.

Three other figures not included here but available

upon request show the empirical relation that exists be-

tween volatility and measurement interval for the futures,

the stock index and the single stocks. In this last case the

average empirical law as been estimated using the ob-

served variances for each stock in every return interval.

The conclusion is that a linear relationship does a good

job for return intervals ranging from one to nine days and

perhaps in some intraday range for the futures and the

stock index but overall it is a poor approximation of the

true relation that seems to exist between time and volatil-

ity. This result is particularly true looking at single

stocks.

3.2. Adjustment Coefficients Estimates

To measure the impact of this methodological choice

on the adjustment coefficients we present three series of

results using: a) a linear relation between intrinsic vari-

ance and time; b) a linear relation but with a flat step

going from the eight-hours to one-day return intervals; c)

the empirical relationships. The cross-sectional average

of the adjustment coefficients for all stocks in our sample,

as well as the coefficients for the index and index futures

are reported in Table 1.

From the results we can draw some interesting obser-

vations. First, there seems that the form of the relation

ship time-volatility has a strong effect on the estimates,

even if as could be expected the differences between the

three sets of results decay exponentially and are almost

zero after the eight hours interval. Second, the adjust-

ment coefficients estimated for the index and the futures

contract suggest strong overshooting effects over the

smaller measurement intervals that only after three days

(four days for the index) of continuous trading are reab-

sorbed. This finding is consistent with herding behavior

and psychological overshooting models. Third, the aver-

age cross-sectional coefficients for the 58 stocks displays

even more interesting properties, as they suggest diver-

Figure 1. Average volatility for 58 securities in the intra-

day return intervals. Period 1995:7-1997:5.

Table 1. Speed of price adjustment: 1995/7 to 1997/5. Cross sectional averages, index and index futures coefficients for seven-

teen return intervals ranging from five minutes to ten days.

Interval stocks mib30 fib30 stocks mib30 fib30 stocks mib30 fib30

5’ –9.9376 25.4676 15.525 –8.0501 15.2178 8.8659 –4.2434 18.9577 12.3483

15’ –3.6171 9.6901 6.0333 –2.8442 5.6918 3.436 –1.7994 7.374 4.8174

30’ –1.6365 5.3059 3.612 –1.2941 3.1873 2.0716 –1.016 3.9234 2.8557

1 hour –0.4495 3.3333 2.4242 –0.3915 1.9947 1.4041 –0.3672 2.4766 1.8909

2 hours 0.386 2.3333 1.854 0.1917 1.3926 1.0894 0.2101 1.7395 1.4186

4 hours 0.8697 1.8284 1.5957 0.5344 1.09 0.9559 0.6078 1.365 1.1912

8 hours 1.1559 1.589 1.4927 0.7374 0.9596 0.9144 0.8459 1.1673 1.0843

1 day 0.8537 0.9623 0.9413 0.8537 0.9623 0.9413 0.8732 1.1662 1.0791

2 days 0.9572 0.9135 0.8824 0.9572 0.9135 0.8824 0.9644 1.072 1.0382

3 days 0.9999 0.9192 0.8936 0.9999 0.9192 0.8936 0.9862 1.0403 1.0218

4 days 0.9817 0.9253 0.9096 0.9817 0.9253 0.9096 0.9956 1.0257 1.0137

5 days 0.9942 0.8835 0.906 0.9942 0.8835 0.906 0.9953 1.0203 1.0097

6 days 1.0377 0.8613 0.8312 1.0377 0.8613 0.8312 1.0182 1.0158 1.0091

7 days 1.0357 0.8662 0.8456 1.0357 0.8662 0.8456 1.0188 1.0114 1.0064

8 days 1.0211 0.9059 0.8885 1.0211 0.9059 0.8885 1.0139 1.0066 1.0038

9 days 1.0465 0.9514 0.9519 1.0465 0.9514 0.9519 1.0003 1.0029 1.0015

10 days 1 1 1 1 1 1 1 1 1

P. GOTTARDO 739

gent movements from value within 60 minutes docu-

mented by negative values for the price adjustment coef-

ficients. For intervals of more than one hour there is a

lagged process of incorporation of the new information

in the stock prices and the average coefficient is positive,

going from 0.210 in the 60 minutes interval to 0.986 for

the three-day returns. Last, in all cases the adjustment of

security prices is almost completed between three and

five days of trading, this is true for the index and the fu-

tures but also for every single stock.

The results in Table 1 are consistent with a market

that adjusts slowly to new information, in agreement

with the findings in Damodaran [9], Patell-Wolfson [3],

and Hasbrouck-Lo [4] even if the adjustment process is

not “linear”, as it may result in very short term over-

shooting and divergence from equilibrium. Very short

here refers to periods on the order of five minutes to few

hours of trading. What about individual firms? Given

that the speed of adjustment is a function of market-wide

and firm-specific information, we should find significant

differences among stocks related for instance to the in-

clusion of a stock in the index, as it is likely that the fu-

tures trading has significant feedback effects on the stock

market, cfr. Tang [15] and Tang-Lui [16]. Size can also

be important, but as the single stocks are included in the

MIB30 on the base of size and trading the effect of this

variable could be intermingled with the previous one. A

similar conclusion is possible for other measures of the

quality and amount of information as volume of trading

or other liquidity proxies. A graphic analysis non in-

cluded here shows the dispersion across securities and

through return intervals for the estimated adjustment

coefficients. We see a rapid incorporation of new infor-

mation in prices for all stocks but it is noteworthy that

the variability in the speed of adjustment is higher as the

measurement interval is lessened. But a careful analysis

of the results shows that there are significant regularities

in the coefficients. Average adjustment coefficients for

firms classified as included for the entire sample period,

never included or partially included in the index of the

30 most important Italian stocks (MIB30) show that the

inclusion in the index seems to be a relevant factor in-

fluencing the measured adjustment coefficients. The

MIB30 stocks display the strongest movements away

from value up to intervals of two hours, while the ad-

justment of the no-index stocks is almost zero in the five

minutes interval but after that converges quickly to one.

For the stocks included in the index the price adjustment

is only 21 percent after four hours, and reaches the 80

percent only after one day of trading. This finding may

seem a bit surprising but we should remember two facts.

The first one, is that the higher liquidity induced also by

the trading in the futures contract increases the volatility

in the underlying stocks. The gain in efficiency related to

the creation of a futures contract has to be paid in some

way. A complete psychological model of price formation

should account for trial and error in the trading process

and learning as prices incorporate new information to

reach their underlying value. This is likely to be reflected

primarily in the prices of the most liquid stocks where is

concentrated the activity of traders and analysts. Second,

the nontrading has subtle effects on the way single stock

prices adjust to value. The trading in the biggest stocks is

really continuous while it is a step process for the other

stocks for well known reasons re lated to liquidity, cost of

trading, interest of institutional and other traders as well

as analysts following. The smaller stocks and, in general,

the stocks not included in an index underlying a futures

contract are then likely to be “followers”, i.e. stocks that

incorporate new information after the fact. This does not

necessarily imply that their price has a slower speed of

adjustment with respect to the big stocks, paradoxically

the high transaction costs (bid-ask spread and price im-

pact of trading) and a low liquidity may result in a

speedy adjustment process. What we mean is that the

cost of errors is too high in a small stock transaction and

(unless we are talking about a piece of firm-specific in-

formation), this induces the traders to concentrate their

activity on the stock index futures or in the liquid under-

lying stocks. In these two market segments the costs are

low, the liquidity is high and there is plenty of room for

learning and reverse a trade in case of errors (overshoot-

ing or misinterpretation of a piece of information). This

could explain why the firms not included in the MIB30

seem to adjust more quickly in the intraday intervals and

why the big stocks display some evidence of movements

away from equilibrium for intervals up to two hours.

3.3. Results on Speed of Adjustment and Firm

Characteristics

The results thus far are consistent with individual stocks

adjusting to market-wide and firm-specific news on the

base of characteristics as liquidity, size, inclusion in the

index underlying a futures, trading intensity and volume

of trading. To substantiate this hypothesis we present in

Table 2 the parameter estimates from regressions relat-

ing price adjustment coefficients and firm-specific fac-

tors. The proxy for size is represented from the log of

capitalization at the end of our sample period, the vol-

ume of trading is simply the average value of transac-

tions in every five-minutes interval for each single stock.

We measure the intensity in the trading process as the

percent of five-minutes intervals with a recorded transac-

tion in that stock. A dummy (D30) captures the effect of

inclusion in the MIB30, while another dummy, BIG6,

P. GOTTARDO

740

Table 2. Price adjustment coe ffic ients and individual stocks characteristics. (a) Results for the relationship between 5-minute s

adjustment coefficients and firm specific factors such as the log of capitalization, trading intensity (% of unit-intervals with a

recorded transaction), volume of trading (average value of transactions in a unit-interval) and inclusion in the MIB30. T-stats

are in parenthesis; (b) Results for the relationship between the individual stocks speed of adjustment and firm size measured

as the log of capitalization in mid 1997 in every return interval from 5 minutes to 9 days.

(a)

Model Intercept Size Trading intensity Volume of trading D30 BIG6 Adj. R2

1 35.33** (3.08) –4.81** (–3.49) 0.16

2 3.69 (0.91) –14.63* (–2.16) 0.06

3 –2.70 (–1.34) –0. 15 ( –1. 44) 0.02

4 34.86* (2.41) –4.74* (–2.50) –0.24 (–0.05) 0.15

5 40.81** (2.85) –5.91** (–2.69) 6.55 (0.65) 0.15

6 56.16** (3.80) –7.53** (–4.08) 14.79* ( 2.14) 0.21

(b)

Return interval Intercept Size Adj. R2

5’ 35.33** (3.08) –4.813** (–3.49) 0.16

15’ 19.82** (3.27) –2.630** (–3.60) 0.17

30’ 14.90** (3.34) –1.936** (–3.60) 0.17

1 hour 10.70** (3.45) –1.346** (–3.60) 0.17

2 hours 7.07** (3.69) –0.834** (–3.62) 0.17

4 hours 4.25** (4.24) –0.443** (–3.67) 0.18

8 hours 2.57** (5.46) –0.210** (–3.70) 0.18

1 day 1.84** (4.78) –0.118* (–2.54) 0.09

2 days 1.28** (8.08) –0.039* (–2.03) 0.05

3 days 1.07** (8.87) –0.010 (–0.71) 0

4 days 0.97** (8.98) 0.003 (0.21) 0

5 days 0.89** (10.14) 0.013 (1.22) 0.01

6 days 0.78** (7.30) 0.029* (2.24) 0.07

7 days 0.73** (7.42) 0.035** (2.96) 0.12

8 days 0.78** (7.66) 0.028* (2.26) 0.07

9 days 0.83** (6.66) 0.021 (1.43) 0.02

Superscripts **, *, and represent significance at the 1%, 5% and 10 % level.

singles out the six biggest Italian stocks (Generali, Fiat,

Telecom, Eni, Tim, Stet).

Table 2(a) shows the results with the five-minutes

adjustment coefficients as dependent variable. The vol-

ume of trading per se seems unrelated to the speed of

adjustment in the unit-interval, while the effect of the

variable measuring trading intensity becomes not sig-

nificant when we add size to the regression. This is

probably due to the positive correlation existing between

size and this variable. Size is always significant and its

beta is negative so that an increase in size is associated

with a reduction in the adjustment coefficient. In terms

of unit-interval gi’s this implies more cases of over-

shooting between small stocks and an increase in the

frequency of divergent movements as size grows.

The dummy for inclusion in the MIB30 is not signifi-

cant when we control for size but the dummy for the six

most important stocks retains its significance and this has

the effect of reversing the impact of size on the adjust-

ment coefficient for high levels of capitalization.

Table 2(b) presents the regression results for the rela-

tionship between speed of adjustment and stock size in

each return interval. The results in Table 2(b) confirm

that firm size is strongly related to the measured speed of

adjustment.

The relationship between adjustment coefficients and

the log of capitalization is consistently negative for

measurement intervals ranging from five minutes to three

days and statistically significant but for the last interval.

The direction of this relationship is reversed for return

intervals of four days or more, but in this case size is

significant only for the intervals from six to eight days.

The results presented in Table 2 are based on the ad-

justment coefficients estimated using the empirical rela-

tionship between time and volatility but qualitatively the

results are the same even if we use the other two forms

P. GOTTARDO 741

of the relationship.

Overall our results support the proposition that stock

prices adjust slowly to new information but in a different

manner for small and big firms and this is reflected in a

highly significant relation between adjustment coeffi-

cients and stock size. The inclusion in the MIB30 index

does not seem to be a relevant factor but this is the result

of two facts. First, only the biggest stocks are included in

the index, adding size as explanatory variable is likely to

dim any effect related to a dummy controlling for the

participation in the index. Second, among the big firms

the trading is highly concentrated in few stocks and is

not by chance that in Table 2(a) a dummy like BIG6 is

significant even when the MIB30 dummy is added to

model 6 (not shown). These six stocks are the core of

every portfolio whose aim is to replicate the index and

are necessary to implement any strategy requiring trading

in the futures and the unde rl ying m a rk et .

4. Conclusions

The degree of efficiency in the stock and futures markets

can be measured by the speed with which prices adjust to

incorporate new information. This process may be slow

with prices that take time to reflect value changes or very

speedy. It is also possible that in very short intervals or

in the long period prices display patterns that lead away

from equilibrium (at least temporarily) or give rise to

under and ov erreaction phenomen a.

This paper adapts the model developed in Amihud-

Mendelson [8] and Damodaran [9] to consider jointly

intraday and infraday data. The speed of adjustment is

estimated as function of the variances in different return

intervals from five minutes to ten days, as well as the

covariances in the infraday intervals. The approach is

then applied to the Italian index (MIB30) and index fu-

tures (FIB30), and to a sample of the most important

stocks listed in this market.

We show that the assumptions about the form of the

relationship between return volatility and time are critical

for the measured adjustment coefficients, the hypothesis

of linearity cannot be accepted using jointly intraday and

infraday returns as the resulting estimates are grossly

inflated for the smaller measurement intervals. We find

evidence that prices adjust slowly to new information,

three to five days of trading are necessary to complete

the adjustment and this is true for the index futures but

also on average for each individual stock. We also find

evidence that there is no simple intraday adjustment

process, the futures seems to overreact for small return

intervals, while on average the individual stocks diverge

from value for intervals up to two hours and then show a

pattern of lagged adjustment.

There are peculiar regularities in the price adjustment

of single stocks and the firms included in the index un-

derlying the futures behave differently from the others.

The analysis of the relationship between adjustment co-

efficients and firm characteristics confirms that size is

strongly related to the measured speed of adjustment for

most of the measurement intervals

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