An EMPIRICAL Evaluation of the Inter Temporal Camp - Stock Market in Spain

8/6/2019 An EMPIRICAL Evaluation of the Inter Temporal Camp - Stock Market in Spain

1/16

Joumai of Business Finance & Accounting, 16(5), Winter 1989, 0306-686X $2.50

AN EMPIRICAL EVALUATION OF THEINTERTEMPORAL CAPITAL ASSET PRICING

MODEL: THE STOCK MARKET IN SPAINGONZALO RUBIO*

INTRODUCTION

Previous empirical evidence on asset pricing seems to indicate that, in Spain,the traditional forms of the capital asset pricing model do not provide a

satisfactory description of security returns.' Unfortunately, European equitymarkets have experienced little or no empirical research on more complexmodels of asset pricing like the one suggested by Merton in his seminal work(1973).2

Accepting that unfavorable shifts in investment opportunities can be describedby future changes in interest rates, Merton argues that the equilibrium expectedreturn is explained not only by its beta coefficient but also by the ability ofthe asset to protect the investor against changes in the interest rates. Thishedging behavior becomes plausible by holding an additional asset or portfoliowhich is negatively correlated with the single state variable; i.e., the interest rate.

The Intertemporal Capital Asset Pricing Model (ICAPM) can be written as:

E{r,) = ^iM E{rM) + /3,H Eir^) (1)

where, (r,) is the expected return on asseti in excess of the risk free rate,E{r/^^) is the expected excess return on the true market portfolio, andE(rff)is the expected return on the hedging portfolio in excess of the riskless rate.It should be noted that the underlying theory refers to moments conditional

on available information at the beginning of the period over which instantaneousrates of return are measured.This paper presents an empirical test of (1) using recent developments on

multivariate fmancial econometrics. In particular, this work applies an extensionof the test statistic developed by G ibb on s, R oss and Shan ken (1986) which hasa tractable fmite sample distribution under the null hypothesis. On the otherhand, as recently pointed out by Shanken (1987b), multivariate statisticaltechniques that may be used to test unconditional asset pricing models may

'The author is from Universidad del Pai's Vasco and Instituto de Economia Publica, Spain. Thispaper was presented at the Fondements Theoriques de L'Economie des Marches Financiers,


2/16

730 RUBIO

be applicable in testing conditional pricing relations under changing conditionmeans and variances. It should be pointed out, however, that these testimplicitly impose constant (over time) betas and residual covariance matrix

This paper also reports empirical evidence on the ICAPM when thesassumptions are, somewhat, relaxed.It has carefully been discussed by Roll (1977) and Shanken (1987a), tha

both the true market portfolio and the hedging asset are conceptual constructionwhich are difficult to dup licate. T his implies tha t, in the context of the traditionaCAPM, there is an implicit joint hypothesis in the sense that the stock markeportfolio employed is a perfect instrument for the true value-weighted markeportfolio. In the ICA PM context, the notion ofa proxy is enlarged to incorporatea two-dimensional vector of variables which is assumed to account for all th

variation in the return of the fundamental economic aggregate; i.e., thmarginal utility of consumption.

This paper is organized as follows. In the next section recent developmenton multivariate fmancial econometrics are discussed. The description of thdata is presented in the third section,and the fourth section reports the em piricresults. Additional evidence regarding the validity of the ICAPM allowinconditional moments to vary with the levels of observable state variables iexamined in the fifth section, and the final section provides a summary of thresults.

MULTIVARIATE TEST OF MEAN-VARIANCE EFFICIENCY OF A PORTFOLIOOF k ASSETS

Multivariate analysis offers the advantage relative to other capital asset pricinmodel tests, of not requiring the exact form of the alternative pricinspecification.

It will be assumed throughout the next sections that the joint distributioof excess returns follows a stationary multivariate normal distribution over thperiod t = 1 , . . . T. We defme r, to be an A^-vector of excess returns at timeI, and r^i the excess return on a market portfolio index at timet. If we regresseach component of r, on r^ and a constant, we have the following multivariatemodel:

r, = a^ + ^^r^, + e, (2)

where E{ti) = 0, var(e,) = E, a^ is the A'^vector of a,>n's{i = 1, . . ., N), and/3^ is the N-vectOT of i3,vn's defined as cov(r,,r^)/var(r,n). e, is independent or^i, and E is an full A'^ XAf covariance matrix assumed to be positive definite


3/16

EMPIRICAL EVALUATION OF THE ICAPM 731

(r, ) = ^^, E(r,^,) (3)

which together with (2) implies that the null hypothesisfor mean-varianceefficiency is o! = 0.

Cibbons, Ross and Shanken (1986) developa statistical procedure in orderto test the joint significance of the estimate values of a^ across all Af equations.It should be realized that (2) isa system that can be estimated using OLS foreach individual (i = 0, . . ., N) equation. The statistic suggested is given by:

d - [r/(i + el)] :. -' (4)

where, 6 = TJs^. is the time-series mean of r^, and ^ is the standarddeviation of the portfolio index excess return during the estimation period.

From multivariate statistics, [(7"-A'-l)/A'^(7"-2)]Q,has an exact small samplei^ distribution with deg reesof freedom TV and (T-N-i).^ On the other hand,the empirically implemented ICAPM canbe written as:

r, = &k + &k rkt + r) , (5)

where, 5^ is the TV-vector of 6,i's (z = 1, . . . ., A^), ^i, is th e A^ X 2 matrix offo's, r , = irmi,r/,,)', E{r],) = 0, var(77,) = V, and r^, is the excess return on thehypothetical hedging portfolio. Following the result discussed above,a necessarycondition for mean-variance efficiencyof the linear combination betweenr^ ,and r/,/ is dj^ = 0, for all t = 1 A.

To test the null hypothesis, the following statistic maybe used:

d* = Til + ri ft-' Ft)- ' 8l F - ' 6, (6)

where, 7 is a vector of sample means forr i, Cl is the sample covariance matrixfor r i, 'S t is a vector of the OLS estimates for 6^ based on th e N regressionequations in (5), and V is the unbiased covariance matrixof V.

It can be shown that [(T-N-k)/N{T-k-l)]Q* has an exact /^ distribution withTV and T-N-kdegress of freedom. Th e expression (6) will be used in the empirical

application.Alternatively, a cross-sectional test may be performed. Let us write the

ICAPM in the following way:

E = XT (7)

where X = {\,,:&^:&,), T = (70, 7i, 72)' and E = (r,). Note that from (5),we get an A^-vector of OLS estimators of/3 and /3/,; and therefore X = (iN'-^m '$/,) is actually used. Let 7be the time series mean of the excess return vectorr,. If we run a GLS cross-sectional regression of FonX, with covariance matrixV, we get:

^ F Xf (8)


4/16

732 RUBIO

It may be argued that the cross-sectional test allows a more explicit test oflinearity between risk and return than the time-series test. Unfortunately, asis well known, an exact small-sample test is not available given the estimationerror in the independent variables. In the context of the Capital Asset PricingModel (CAPM), Shanken (1985) proposes the following statistic to be usedin testing (7):

Q' = Te'V- e. (10)

It can be shown that the exact distribution of Q' is bounded above by the centralT' {N-3,T-2).' This means that when we accept the null hypothesis, we wouldactually have a small-sample result, assuming normality. The statistic reportedin the empirical application is approximately distributed as F{N-3,T-N + 2) and

is given by (l'[{T-N + 2)/{N-3){T-2)].

THE DATA

Data necessary to compute monthly returns for a period of eighteen years werecollected. The eighteen year period starts in January 1967, and ends inDecember 1984. This means that a total of 216 monthly returns are available.

Given that the Spanish Stock Exchange is a relatively thin equity market,monthly observations were preferred to observations over a shorter intervalof time. The use of daily or weekly returns would have reduced considerablythe number of securities in the sample. It should be taken into account thata small number of stocks account for an important percentage of the total tradingvolume, and that a substantial number do not trade regularly enough to providereliable daily or weekly returns. The final sample is composed of 160 stocks.^

During most of the period covered by this paper, there were three majorstock exchanges. Data on prices for shares trading on more than one stock

exchange were obtained from the exchange on which the share had the highesttrading volume.

The returns on all securities in the sample were used to compute an estimateof the monthly return on the market portfolio. A value-weighted market indexwas calculated, where the weights are the market values of each security atthe end of the preceding year.

On the other hand, given that Spain did not have short-term governmentsecurities during most of the period covered by this research, the riskless ratewas based on lending rates offered by financial institutions. Although these

rates were not insured, the assumption seems to be a reasonable approximation.Treasury Bills sold by auction and priced at a discount were traded for the


5/16


control over the timing of the issues and the level ofits interest rates. Moreover,the conditions which the issues had to meet in order to qualify; i.e., to be eligiblefor investment by the savings banks, were perfectly defined. This implies serious

difficulties for non-qualified bonds, since individual investment in fixed incomesecurities represented a very small amount. At the same time, the secondarymarket for governme nt securities reached a very low percentage out of the totalvalue of the market. Due to the extreme regulations imposed by the authorities,this low trading volume refiected the freezing of most outstanding public debtin the portfolios of financial institutions. For these reasons, market data forlong/medium term government securities were collected only from January 1979to December 1984.

On the other hand, the return on gold was based on the London Stock

Exchan ge Gold Index which is reported in dollars per oun ce. T here is no goldtrading on the Madrid Stock Exchange. However, an index in pesetas per gramcomputed from the London Gold Index is available. Data cover the periodbetween January, 1967, and December, 1984. Both indexes will be used inthe empirical application.

It should be taken into account tha t such a hedging asset would have negativecorrelation with interest rates and absence of correlation with the market return.

Finally, and given the methodology proposed, an inversion of the fullNxNcovariance matrix is required. At the same time,A^ must always be less thanT. Therefore, some aggregation of data is needed. Gibbons, Ross and Shanken(1986) point out that, for a given set of A'^assets, the multivariate test describedin the previous section is invariant to how grouping is performed. In fact, itwould be plausible to constructA? portfolios with very little dispersion in betaswith no impact on the power of the test statistic. In the present case, for eachyear, the number of securities with complete data was observed. These securitieswere ranked according to their market value at the end of the preceding year.This ranking was maintained throughout the year, and ten equally weightedportfolios with approximately the same number of securities were obtained.Hence, A' is equal to 10, where portfolio one contains the smallest firms andportfolio ten the largest.

EMPIRICAL RESULTS

Before testing the ICAPM, it was decided to provide some additional empiricalevidence on the traditional form of the asset pricing model. The efficiency of

the value-weighted market portfolio index was tested using the exactF testproposed by Gibbons, Ross and Shanken (1986). Rubio (1988) already pointed


6/16


7/16


Ta b l e 1

Efficiency Tes t o f the V alue -W eigh ted Por t fo l io Inde x Us in g Mo nth ly D ata

Regressions based on 10 market-value sorted portfolios:

where, r,, is the excess return on portfolio ; andr^ i is the excess return on thevalue-weighted market portfolio index.

Null hypothesis: ,, = 0, V, = 1, . . ., 10

F = J^{T-N-iyNiT-2)] a where a ^ [77(1 + Ol)] K ^ - ' S,and e^ = r^/s^.

Sub-periods 1967-72 1973-78 1979-84 1967-84

F(10,61) 1.569 2.509 2.909(/(-value) (0.138) (0.013) (0.005)

F(10,205) _ _ _ 2.885(/)-value) (0.002)

Table 2

Correlation Coefficients among Government Bond Index, Cold, MarketPortfolio Index and Riskless Rate (1967-1984)

CorrelationCoefficients

MarketReturnRiskless

RateGold(dollars)Gold(pesetas)Gvt.BondIndex

MarketReturn

1

RisklessRate

0.181

1

Gold(dollars)

- 0 . 0 11

0.100

1

Gold(pesetas)

- 0 . 0 2 1

0.169

0.929

1

Gvt. BondIndex*

- 0 . 0 2 2

0.082

- 0 . 1 3 6

- 0 . 1 7 6

1

* Series available for the period 197984 only.

asset is assumed to be the government bond index. The/7-value equals 0.024.This is somewhat higher than the /(-value under gold returns. It is also


8/16

736 RUBIO

Table 3

Exact F Tests of the Intertemporal Capital Asset Pricing Model UsingMonthly Data

Regressions based on 10 market-value sorted portfolios:

'./ = h + fiim {''ml) + 0ih {''hi) + Vii

where, r,, is the excess return on portfolioi, r^^ is the excess return on the value-weighted market portfolio index andr/,i is the return on the hedging portfolio in

excess of the riskless rate.

Null hypothesis: 1, = 0, V, = 1, . . . 10

F = l{T-N-k)/N(T-k-l)] d', where Q* = T{\ + r ' fl-' r^ )- ' 1^ F " ' 6^and k = 2.

Sub-periods 1967-72 1973-78 1979-84 1967-84

Gold Pesetas

F( 10,60)(/)-value)F(10,204)(/)-value)

Gold DollarsF(10,60)(/)-value)F( 10,204)(/i-value)

Government Bond/="(10,60)(/)-value)

1.525(0.153)

1.493(0.165)

Index''N.A.

2.495(0.014)

2.485(0.015)

N .A .

0.003(0.003)

3.113(0.003)

2.279(0.024)

2.825(0.003)

3.053(0.001)

N .A .

^ Series available for the period 197984 only.

in the riskless rate. In the present case, given the positive correlation betweethe interest rate and the government bond index (or gold), a negative|3^ wouldimply a good degree of protection of the security. W hen the governm ent bonindex was used as a prox y, the ave rage /3^ across the ten portfolios w a0.471. On the contrary, when gold was imposed, the average/3^ was 0.036.This again seems to imply that the government bond index is playing a closerole than gold in behaving as a hedging asset.

Empirical results from cross-sectional tests are reported in Table 4. Linearit

for both gold in pesetas and the government bond index is rejected. Amen tioned earlier, the reported /?-values are just app roxim ation s to the tru


9/16

EMPIRICAL EVALUATION OF THE ICAPM

Table 4

737

Approximate F Tests of the Intertemporal Capital Asset Pricing ModelUsing Monthly Data

Cross-sectional regressions based on 10 market-value sorted portfolios.

Null hypothesis; E = XT, where X = (1;^; &: (3/,), T = (70, 7 b 7 2) ' ^"dE = E{ri). ri is the N-vectov of excess return.

F = Q_' (T-N_+2.)/{N-3){T-2), where Q' = Te' K"' eand e = T X T.

Period

Gold PesetasF(7,208)(/7-value)

1967-84

4.101(0.0003)

Period

Government BondF(7,64)(/(-value)

1979-84''

Index3.425

(0.004)

7-0(std. error)7 l(std.error)7 2(std.error)

- 0 . 0 0 6 0 1(0.00758)0.00997

(0.00825)0.01100

(0.02104)

7-0(std. error)7 l(std. error)7 2(std. error)

- 0 . 0 0 9 0 0(0.00777)0.01393

(0.01015)-0 .01110*

(0.00415)

' Series available for the period 197984 only.* Means that the estimated coefficient is more than two standard deviations from

and 1984, 71 equals 1.39 percent with a ^value of1.372. On the other hand,72 is negative and statistically different from zero. This might be interpretedin the sense that the greater the protection a risky asset provides against changesin the state variable, the lower the return the investor is expected to earn. Itmay therefore be concluded that the empirically implemented ICAPM has notsignificantly improved the performance of the CAPM in explaining riskyreturns. Unfortunately, the failure of the model might be due to the practicalimpossibility of finding an adequate hedging asset. More research in thisdirection is largely justified."'

As Shanken (1987b) points out, m ultivariatei tests implicitly impose constan t(over time) betas and residual covariance matrix. Moreover, the disturbanceterm is assumed to be normally distributed and serially indep end ent. Th e first

problem may be partially solved by assuming that betas depend linearly onthe state variable and on a dummy variable which equals one in January andth i


10/16

738 RUBIO

Ta b l e 5

Exac t F Te s ts o f the In te r tem po ra l Cap i ta l Asse t Pr ic ing Mo del U s ingM o n t h l y D a t a

Regressions based on 10 market-value sorted portfolios with betas depending onstate variables:

Ul = îk + îm (rml) + ^,7, i'-hl) + Vii

where each of the beta s, /3,^ and/3,7,, is assumed to be linear in the riskless rate anda dum m y va riable, Ja n , w hich equals one in Ja nu ar y and zero otherwise, r,, is thexcesss return on portfolio i, r^, is the excess return on the value-weighted marketportfolio index and r/;, is the return on the hedging portfolio in excess of the riskless rat

Nu ll hypo thesis: l.t = 0, V,- = 1, . . . 10F = [{T-N-k)IN{Tk-\)] Q*, where (2* = T{\ + ^ Cl'^ 7,,)-^ Sj, f^' 6ând A: = 6.

Sub-periodsGold Pesetas

/="(10,56)(p-value)f(10,200)(/)-value)

Government BondF(10,56){p-vaXxie)

1967-72

1.084(0.390)

Index"N.A.

1973-78

2.284(0.025)

N .A .

1979-84

2.958(0.005)

2.092(0.040)

1967-84

2.756(0.003)

N .A .

Series available for the period 197984 only.

where, Rf stands for the rate of return of the riskless asset.

To con sider the mo nth of Ja nu ar y as an add itional state variable does noimply the necessity of incorporating a nev^f hedging asset. On the other hanthis is clearly justified given that the nature of the price formation in Januarseems to be different from the rest of the year." January, is not only thmonth in which investors have been rewarded for accepting risk, but it is alsthe month in which small firms clearly outperformed the rest of the marke

The empirical procedure is similar to the one employed in getting the resulof Table 3. However, k in this case equals six. The results are provided byTable 5. As in Table 4, gold in pesetas and the government bond index ar

assumed to be the hedging assets. The overall p-value for gold is similar the one obtained earlier. However, the performance has slightly improved i


11/16


non-constant betas are allowed, the empirically implemented ICAPM offersa more adequate description of security returns than the traditional CAPM,at least when the government bond index is employed as the hedging asset.

TESTING ASSET PRICING MODELS WITH CHANGING CONDITIONALMOMENTS

This section replicates, with Spanish data, Shanken's (1987b) asymptoticmethodology to investigate the empirically implemented ICAPM in the presenceof conditional residual heteroskedasticity.

In this case, it will be allowed the intercepts, 6,/., as well as the stock market

and bond market betas to change linearly with the level of interest rates andwith monthly seasonality. Hence, the intercept may be written as:

5,t = a,o + an Rf + a,-2 J a n (12)

and a regression with nine independent variables will be performed. Underthe null hypothesis that 6,^ = 0 for all assets, the coefficients a,o, a,i and a,2must also be zero for every portfolio.

On the one side, the presence of residual heteroskedasticity does not permitto implement the exacti tests used in the previous section. On the other hand,

to allow the intercept to vary with the level of the state variable might provideadditional evidence on the reasons behind the strong rejection of the model.Heteroskedasticity-consistent standard errors are obtained using White's (1980)consistent covariance matrix estimator. This estimator has the advantage ofnot relying on a specific model of the structure of the heteroskedasticity. Itshould be pointed out that, in some cases, the standard errors were much largerthan the OLS errors.

Table 6 contains the statistical significance of the three components of theintercept, stock market betas and government bond betas for each size portfolio.The mciximum, in absolute value, ^-statistic presented in Table 6 allows, asShanken (1987b) points out, a test of the joint hypothesis that all coefficientson a given explanatory variable are zero. The reported /;-values are an upperbound on the probability of obtaining a maximum ^-statistic as large as thatobserved.''^

As expected, the con stant co mp onent of stock market betas is highly jointlysignificant. At the same time, it is not possible to reject the hypothesis thatstock betas are indepe nden t ofa Ja nu ar y seasonal, although they tend to vary

with the level of the riskless rate. O n the oth er ha nd , the constant com ponen tof government bond betas is not statistically different from zero. They are,h i d d fth l l f th i k f d h i id


12/16

740 R U B I O

3

2Q

o

-oo

bDC

'G

O H

H _Q .KJ

O

o

cocI)

TJC

O

oj rt

o . i :

li-ra

Tl 3t Jg XI

u ra

c0

s>

EE3

g

E -3 5

U -i^

T!CraXV

TJc

" "

o

t. .

oD.

uura

TJEU

.cbp

B:i)

_3"ra>

x :

coc3u

euuOJ

x:

6

1oQ .boC

'bbTJ

OJJ :

OJ

x ;*^cS

TJOJc3t

XOJ

-ac

TJCo

X I

cV

rnm

OJ>

ELaOJ

boc_o

OJ

*

CO1O l

c ri" ^

e

v

u

Tlu

o

4J

..c

1 :1 2o u a.ex _^ E

^ 8- w IJ

g to i-i

3 J! "=

S S guXOJQJ

*- '

foo

0a .

g:^

"DCrt

CQ.

o o o o o o o o o o

C ^ C V C - J O O

I ! I IE ^ O O O O cr) O

OI

' O C O O '

, .., o I I I

o .I I

o oI I

. I CO O

I i I I I I t I t I

I I I

I I I I I I I I I


13/16


is jointly significant. This is particularly relevant for the three smallest portfolios.The estimated coefficient of the smallest firms equals 2.64 percent per month,whilst the coefficient for the largest firms is negative 0.84 percent per month.Of co urse, this justifies the use ofa January seasonal as the state variable, andit is also consistent with the previous empirical evidence reported by Rubio(1987). Moreover, there exists significant evidence of an interest rate componentin the intercepts.'^

Final ly, Tab le 7 presents evidence of cond i t ional dis tu rban ceheteroskedasticity. Again, the residual variance for each portfolio from theprevious ten time series regressions is assumed to be linear in the riskless rateand a dumm y v ariable, Ja n , which equals one in Ja nu ary and zero otherwise.

Table 7

Residual variance for each portfolio is assumed to be linear in the risklessrate and a dum m y v ariable, Ja n , which equals one in Ja nu ar y and zerootherwise. Regressions of the squared residuals from Table 5 on aconstant, the riskless rate and Jan. Heteroskedasticity-consistent standarderrors are in parentheses. The long term government bond index usedas the hedging portfolio, 197984.

Fortfoiio i

M V 1

M V 2

M V 3

M V 4

M V 5

M V 6

M V 7

M V 8

M V 9

MV 10

Constant

0.00164(0.00112)0.00071

(0.00105)0.00116

(0.00104)0.00040

(0.00109)0.00040(0.00079)

-0 .00062(0.00063)

-0 .00041(0.00051)

-0 .00012(0.00050)

- 0 . 0 0 0 0 8(0.00025)

-0 .00234*(0.00083)

Estimated Coefficient

Rf0.16020

(0.15253)0.25442

(0.18588)0.12264

(0.17780)0.31752

(0.19477)0.16495(0.14589)0 .29921 '

(0.13379)0.31311*

(0.10204)0.17358*

(0.07900)0.12008*

(0.04847)0.55045*

(0.16155)

Jan

0.00025(0.00156)

-0 .00154*(0.00061)

-0 .00027(0.00063)

- 0 . 0 0 11 6

(0.00086)-0 .00041(0.00058)

- 0 . 0 0 1 0 5(0.00054)

-0 .00030(0.00075)0.00135

(0.00131)-0 .00052*

(0.00021)0.00245

(0.00198)


14/16

742 RUBIO

The interest rate component of residual variance is statistically joisignificant. It is interesting to note that this component is individually significant for the five largest portfolios,'* and that the estimated coeffiis positive for every portfolio. T he re is no evidence of a Ja nuar y seasonresidual variance.

CONCLUSIONS

Given the past empirical evidence on the traditional forms of asset pricthis work reports exact multivariate tests on Merton's (1973) ICAPM uSpanish data. The model is strongly rejected assuming either gold orgovernment bond index as hedging assets. The performance of the mod

slightly improved w hen non-con stant stock m arket betas and gov ernm ent betas are allowed. On the other hand, using an asymptotic methodoproposed by Shanken (1987b), the IGAPM, in the presence of conditiresidual heteroskedasticity, is strongly rejected particularly during the mof Ja nu ar y when the so called 'Ja nu ary effect' is observed. Stock mark et bvary with the level of the interest rate, and government bond betas are foto shift du rin g Ja n ua ry . Residua l variance also chang e with the level ointerest rate. Of course, it is not clear that the value-weighted stock maindex and the government bond index or, alternatively, the gold index, capadequately the variability ofthe fundamental aggregate; i.e., the marginal uof consumption. Finally, it seems clear that the Spanish capital market issufficiently rich, so that the choice ofthe relevant state variable or the hedassets might not reasonably correspond to theoretical constructs.

NOTES

1 See Rubio (1988).2 The Spanish capital market is in clear need of empirical research. Unlike the US market w

there has been an extraordinary amount of empirical research on the price formation of finaassets, the Spanish market has experienced little empirical research of this type. This pprovides further evidence regarding the return generating process in Spain. In this senscomplements Alonso, Rubio and Tusell (1987) and Rubio (1988). Moreover, the applicabof modern financial theory has received practically no attention in thin equity markets, wtrading volume and market capitalization are relatively small.

3 What Gibbons, Ross and Shanken (1986) actually show is that the statistic has a nonce/^distribution. Their result gives the conditional distribution ofthe statistic under the hypothesis; i.e., the noncentrality parameter equals zero, as well as the alternative hypothi.e., the noncentrality parameter different from zero.

4 See Shanken (1985).5 In 1984, the market capitalization ofthe Madrid Stock Exchange reached $21,392 millThis represented 0.56 percent out ofthe total world capitalization. The market capitaliza


15/16


the Sharpe-L inter equ ilibrium model and the joint hypothesis that the Spanish value-weightedstock index explains more than 25 percent of the variability of the true market portfolio canbe rejected from 1963 to 1982.

7 Unfortunately, in Spain, consumption data are not available frequently enough to test the

Consumption Capital Assets Pricing Model (CCAPM).8 Similar results were found w hen the cross-sectional GLS regression was run between 1979 and1984.

9 Note, however, that if rejection ofthe null hypothesis occurs, the usual interpretation ofthet-statistic is inappropriate.

10 It was suggested by J . Ur rutia of the Instituto de Eco nom ia Pubiica that real estate andconstruction firm s should be a reasonable proxy for the hedging asset. A lthough, these comp anieshad a low negative correlation with the riskless rate, the correlation with the market returnwas highly positive.

11 See Rubio (1988).12 The reported p-value equals the number of parameters in the joint test (10 portfolios) times

the usual two-sided p-value. See Shanken (1987b) for details.13 Similar results are obtained when gold in pesetas is used as the hedging asset.14 W hen gold in pesetas was used, nine out ofth e ten portfolios presented evidence that the residual

variance varied with the level of the interest rate.

REFERENCES

Alonso, A., G. Rubio and F. Tusell (1987), 'Asset Pricing and Risk Aversion in the Spanish StockM a r k e t ' , Southern European Economics Discussion Series( S E E D S ) , N o . 53 ( 1 9 8 7 ) .

Gibbons, M., S. Ross and J. Shanken (1986), 'A Test of the Efficiency of a Given Portfolio',Research Pape r 853 (Stanford U niveristy, 1986).

Merton, R. (1973), 'An Intertemporal Capital Asset Pricing Model',Econometrica 41 (1973),pp. 8 6 9 - 8 8 7 .

Roll, R. (197 7), A Cri tique of the Asset Pricing The ory 's Test s; Part I: On Past and PotentialTestability of the Theory',Journat of Financiai Economics 4 (1977), pp. 129176.

Rubio, G. (1988), 'Further International Evidence on Asset Pricing: The Case ofthe SpanishCapital Market', Joumai of Banking an d Finance, 12 (1988), pp. 221242.

Shanken, J. (1985), 'Multivariate Tests ofthe Zero-BetaCAPM' Joumai of Financial Economics 14(1985), pp. 327-348.

(1987a), 'Multivariate Proxies and Asset Pricing Relations: Living with the Roll Critique',Journal of Financial Econom ics 18 (1987) , pp . 91 110 .

. (1987b), 'T he Intertem poral C apital Asset Pricing Mo del: An Em pirical Investigation',Mimeo (University of Rochester, 1987).White, H. (1980), 'A Heteroskedasticity-Consistent Govariance Matrix Estimator and a Direct

Test for Heteroskedasticity', Econometrica 48 (1980), pp. 817-838.


16/16

Documents

An EMPIRICAL Evaluation of the Inter Temporal Camp - Stock Market in Spain