The estimated cost of equity capital, or instead the return expected by stockholders, is one of the most debated issues in the Theory of Finance. Different theoretical accounts to gauge, due to the objectivist theory of the cost of capital, they found ample infinite in the fiscal literature, fueling the argument on the theoretical and empirical.

A decisive part to this consequence is due to Harry Markowitz ( 1952 ) , the male parent of Modern Portfolio Theory, which has provided a theoretical model for hazard analysis – public presentation. The writer, by contending the hazard antipathy by investors, he laid the basis for the designation of the two variables considered in investing determinations: the expected return and discrepancy, or standard divergence, of the portion.

Based on surveies of Markowitz, Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossin ( 1966 ) independently develop the Capital Asset Pricing Model, a theoretical account that predicts the expected return of the security, public presentation or market equilibrium, depending the investing hazard. In other words, the CAPM presuming a context of information efficiency, the absence of dealing costs, monoperiod skyline, homogeneousness of outlooks, the presence of riskless bonds – hazard free rate – etc. Indicates the tradeoff between hazard and return. In the theoretical account in inquiry become of import on three variables: the rate of return on authorities bonds, or riskless rate, the coefficient of systematic hazard, beta, and the expected premium for hazard.

Although some of the implicit in premises appear far from world, such as the ability to take and to impart without bound at the same hazard free rate, the absence of revenue enhancements, and others, the CAPM has been the past four decades the topic of lively argument in fiscal economic sciences. The first standards of the Capital Asset Pricing Model were made by Sharpe ( 1966 ) and Jensen ( 1967 ) on common financess with encouraging consequences. However, the thought of aˆ‹aˆ‹give and take a free loan bounds at the same hazard free rate appeared small relation to world, to get the better of this obstruction, and at the same time ease the empirical testing, Black ( 1972 ) studied a discrepancy of the theoretical account known as “ zero-beta theoretical account “ . This alteration includes the replacing of the riskless with another concern, rubric or portfolio uncorrelated with the market.

Black, Jensen and Scholes ( 1972 ) execute an empirical trial consequences demoing that while non to the full reflecting the outlooks of the authoritative version of the CAPM are in line with the zero-beta CAPM. Come to similar decisions Fama and MacBeth ( 1973 ) who consider the accomplishments, the most satisfactory and consistent with the zero-beta theoretical account. Over the old ages, the CAPM has been widely criticized the thought that the beta was non the lone factor that can explicate the returns of equities, has taken more and more organic structure. If the first grounds empirical, delivered via the market theoretical account, showed the additive relationship between hazard and return, subsequent trials revealed the inability of the beta to show that relationship. In this fits the Arbitrage Pricing Theory, developed by Ross ( 1976 ) and Roll ( 1977 ) , which shows that the factors involved in finding stock monetary values are legion. The APT, while non explicitly saying these factors, recognizes a cardinal function in some macroeconomic variables such as the oil monetary value, rising prices, involvement rates, GDP, etc.

The legion empirical anomalousnesss ensuing from the imperfect one-dimensionality of the relationship hazard – return, made them surmise the being of other factors likely to act upon more efficaciously on the returns of equities. Banz ( 1981 ) , for illustration, was the first to indicate out that the variable size is better able to construe the way of the CAPM theory, he notes the presence of a negative relationship between size and public presentation.

Fama and French ( 1992 ) show that the beta as an explanatory variable of the study hazard – return, do non to the full capture all the hazard factors.

The writers develop three-factor theoretical account, or three-factor theoretical account, through which show that the hazard premium depends on the factor market, as stated by the CAPM, that two other factors: the size of the company and the ratio of book value and market value. Harmonizing to the writers, the empirical grounds shows that the three-factor theoretical account is able to explicate the returns of equities. In Italy the CAPM is that the pricing theoretical accounts in general have found small application in the literature, likely due to the little size of the stock market.

The purpose of this work is to verify whether these two econometric theoretical accounts can besides happen verification of the Italian stock market. For this intent we investigate the cogency of the CAPM presuming a clip skyline of 20 old ages, 1985 – 2005, divided into five periods, utilizing 60 portions listed on the Milan Stock Exchange. Then we will detect the behaviour of the three-factor theoretical account on a shorter period. The purpose, finally, to look into the cogency of both theoretical accounts.

## 2 The Italian Stock Exchange

In Italy, the fiscal market is based in Milan at Palazzo Mezzanotte, and is organized and operated by the Italian Stock Exchange. The beginnings day of the month back to 1808, when Eugene Beauharnais founded the Chamber of Commerce of Milan. “ The Commercial Code of 1865, said the public nature of the Italian Stock Exchange, set up at the Chambers of Commerce, subsequently confirmed by the Commercial Code of 1882. Furthermore, until 1977, the twelvemonth of the constitution of narrow market, the Stock Exchange was the merely regulated market exists in Italy.

Legislative Decree No. 461/1996 provides for the induction of the denationalization of the Italian stock exchange, which led to the birth of the Italian Stock Exchange, which handles the stock exchange based in Milan. This installation became operational from January 2, 1998. Besides under that edict, the Italian Stock Exchange merged in 1997 and besides replaced all the smaller squares of exchange, which play a strictly regional.

In 2007 the Italian Stock Exchange merged with the London Stock Exchange ( London Stock Exchange ) . The stock exchange shall oversee the proper behavior of trading, defines the demands and processs for admittance and remain on the market for publishing companies, defines the demands and admittance processs for agents, manages the information of listed companies. Italian Stock Exchange organizes and manages the Italian market by utilizing a wholly electronic trading system for the executing of trades in existent clip. It deals with the ordinance and market direction. The supervisory map is alternatively performed by Consob and Bank of Italy.

To finish the Italian stock exchange capitalisation is 13th in the universe. The trading of the portions belonging to the sections identified by the Italian Stock Exchange can be done with the intercession of specializers appointed by the issuer in the market to back up the liquidness of portions listed. The jurisprudence of concentration, which was introduced into Italian jurisprudence 1 / 1991, requires that a regulated market mediators inoltrino to EU orders from Italian clients. Exemptions are provided for the exchange of big sum ( called blocks ) and for minutess where the agent will be able to acquire to their clients better footings than those on the trading book.

MiFID in November 2007 deleted from the jurisprudence of concentration, leting fiscal mediators such as Bankss and investing companies, to construct its ain exchange circuit of the licences, said the many-sided trading system, or to run as systematic internalisers offering straight merchandise executing services to its clients. The MiFID provides for elaborate regulations to protect transparence by set uping a set of consistent information to be disseminated before and after the trade from all trading locales ( regulated markets, MTFs and systematic internalisers ) , and investors by necessitating agents conformity with the demands of best executing.

The bargaining system run by the Italian Stock Exchange is divided into different markets:

aˆ? MTA ( MTA ) where the listed portions are traded on the stock market, the market is divided into three chief categories and a residuary on the footing of capitalisation and liquidness of the securities

aˆ? Large-Cap ( or Blue Chip ) consisting the top 40 most capitalized companies with greater liquidness. Index of: FTSE MIB.

aˆ? Mid Cap includes the following 60 companies by market capitalisation and liquidness. Index of: Italy FTSE Mid Cap

aˆ? Small Cap including other companies non portion of the first concern centre, which exceed the standards of liquidness. Index of: FTSE Small Cap Italy

aˆ? Micro-Cap includes other companies non portion of old groups, which do non run into the standards for liquidness. Index of: Micro Cap FTSE Italy

aˆ? In add-on at that place remain the undermentioned sections: STAR section, which includes companies that meet certain standards of transparence, administration and liquidness ( with market capitalisation between 40 million and 1000 million a‚¬ a‚¬ ) . Index of: FTSE Italy STAR.

aˆ? MTA International section that houses the trading of equity securities of companies already listed on stock exchanges in the European Union.

aˆ? MIV ( Electronic Market for Investment Vehicles ) , which replaced the MTF ( Electronic Market Funds ) , is a regulated market dedicated to investing vehicles. The market consists of three sections depending on the type of securities that are traded: Closed-end financess, Investing Companies and Real Estate Investment Companies.

aˆ? MAC alternate capital market

aˆ? IDEM ( Italian Derivatives Market ) in this market, created in 1994, contracts are traded derived functions such as hereafters, options on securities and minifutures which fall in the S & A ; P / MIB

aˆ? SEDEX where dialogues are covered warrants, purchase certifications, certifications of investing class

aˆ? MOT ( Electronic Market for bonds and authorities securities ) are traded in this market authorities bonds ( BOT, BTP, CCT, CTZ ) , bonds of local governments, non-convertible bonds and structured, euro-bonds, bonds foreign issuers and asset-backed securities. This market is divided into two sections:

DomesticMOT or where they are treated with liquid fiscal instruments uncluttering Italians.

EuroMOT or where they are treated liquid fiscal instruments in foreign colony systems

aˆ? Plus ETF by April 2, 2007 the Italian Stock Exchange has adopted a market dedicated to trading in fiscal instruments that replicate the public presentation of the market such as ETFs ( exchange traded financess ) , ETC ( Exchange Traded Commodities ) , structured ETFs.

## 3 Market Anomalies: Size consequence and Value consequence

Another of the aims of this research is to verify that the considerations on the Italian market reached by Fama and French in their work on market anomalousnesss. They have proposed an alternate theoretical account to the CAPM that solves one of the most puzzling anomalousnesss: the size consequence and value consequence. This anomalousness is seen in the empirical grounds that long-run action of small-cap companies to do more of those large-cap and actions with high rating ratios ( such as dividend / monetary value, net incomes / monetary value, book / monetary value ) obtain higher returns for companies with low ratios of appraisal.

Basically, the little value stocks seem to do much more than big growing stocks, at least in the long tally. The accounts given by fiscal economic experts are legion and frequently excessively complex to analyze them here, suffice it to state that these “ effects ” were frequently regarded as the market imperfectnesss, since the outputs of these actions were non “ explained ” utilizing the celebrated theoretical account plus pricing called CAPM. While some research workers consider the inefficiencies of the market, others have interpreted as hazard factors, attributable chiefly to the alleged “ hurt hazard ” : the choice of actions based on small-cap and the high rating studies would place portions with low liquidness and / or companies with fiscal jobs, that offer low returns merely when the fringy public-service corporation of investors is high, ie during recessions. From these considerations were born, before the three-factor theoretical account of Fama and French, and so the four-factor theoretical account of Carhart.

The job is that these theoretical accounts have no theory behind it, so these “ anomalousnesss ” have been transformed into “ hazard factors ” merely ex-post, which may be considered questionable. All the more so every bit many surveies seem to show the size consequence and value consequence depends on the clip period in which they are analyzed, particularly with regard to periods less than 80 old ages. Several research workers come to the decision that these anomalousnesss are losing and possibly had ne’er existed, due entirely to opportunity and computation power of the computing machine for merely such anomalousnesss.

The fact remains that three-factor theoretical account with this anomaly disappears, and likely will go on in the Italian market.

## 4 The Capital Asset Pricing Model

The first surveies on the risk-return tradeoff day of the month back to Harry Markowitz ( 1952 ) whose research is widely regarded as the “ basis ” of Modern Portfolio Theory. The logical thinking on which the analysis is based Markowitz is really really simple. Investors every bit good as the desire to obtain high outputs are by nature hazard averse and hence the attitude most logical and rational, that they take is to implement an effectual policy of investing variegation to cut down hazard. The rates of return for the licence and the portfolio are given by:

where Pt-1 is the monetary value paid to buy the rubric at the beginning of the period, and Pt is the market value at the terminal of the period including the return generated by the rubric during the period, W0 is the aggregative purchase monetary value at clip T = 0 of rubrics in the portfolio, and W1 is the aggregative market value at clip T = 1.

Harmonizing to Markowitz, the investor Exchange, and so take, each portfolio harmonizing to the rate of return associated with it, and indiscriminately distributed, which in bend depends on expected value and standard divergence. Expected returns and standard divergences observed for each portfolio are the lone two factors know aparting between current and deferred ingestion.

The expected return of a portfolio is given by:

Where E ( Rhode Island ) step the expected return on stock I and Wi the weight of I on the full portfolio.

The premises in the Markowitz theoretical account are:

Monoperiodal skyline for all investors and merely in regard of which maximise the expected public-service corporation of the public presentation of their portfolios ;

rational histrions and therefore hazard averse,

who select their portfolios based on the expected mean return and discrepancy clasp.

The bound of this theory is non to see the being of riskless assets. James Tobin ( 1958 ) considered the possibility of puting in riskless assets and borrow at the same rate. N denote the riskless licence, with the weight of Xn under the riskless portfolio ( and therefore 1-n is the weight in the portfolio of hazardous assets ) , with the RF bond output and riskless return on hazardous assets Rr, The expected return of the portfolio is equal to:

To simplify the theoretical account is the strongest hypothesis postulated in add-on to the above, viz. :

vitamin D ) no limitations for investors to take or impart money to the hazard free rate,

vitamin E ) homogenous outlooks by investors on the expected values aˆ‹aˆ‹of returns, the discrepancies and covariances of bond outputs and therefore the same perceptual experience on the chances of each rubric and, accordingly, the full portfolio, degree Fahrenheit ) absence of revenue enhancements and imperfectnesss markets. In the presence of riskless activity, which can be purchased or

sold short, the frontier becomes additive. In connexion with these extra premises, Sharpe ( 1963 ) elaborates the Single Index Model and Market Model, which expresses the one-dimensionality between hazard and return. Sharpe had the superb thought to observe that:

Is there a portfolio as the amount of all the portfolios of persons,

2 ) such as efficient portfolios imply that the market portfolio is efficient,

3 ) and that the tangent line to the “ Markowitz curve ” that combines the riskless rate of ( R degree Fahrenheit ) portfolio ( M ) , on the efficient frontier, was obtained by the combination best combination of M and hence in equilibrium all securities, or portfolios, they will stop along the line R f – Meter called Capital Market Line

I¬

All portfolios which lie along the boundary line feel progressively are efficient and the point of absolute minimal discrepancy ( AMV ) showing the possible combinations of portfolios that minimize the overall discrepancy. The restriction of the theoretical account is that it does non turn to the inefficient portfolios or single securities. Sing all the securities, or portfolios, non falling on the efficient frontier should look into what each activity is related to the other and, finally, the market portfolio. In other words, what is the hazard part made aˆ‹aˆ‹by an single plus to the market portfolio? The reply to that inquiry is provided by Sharpe ( 1964 ) through the Security Market Line, whose intercept is given by the hazard free rate and angle expresses the risk-return trade off. The SML stems from the fact that terminated the benefits of variegation remains a portion of the systematic hazard of the portfolio, and that this per centum can be measured by the sensitiveness of the single security or portfolio to motions in the market portfolio.

The equation for the Security Market Line is:

Where R is the monetary value of cut downing the hazard of the securities and Cim is the covariance between the bond output and the market. The value of R indicates that the expected return must be sacrificed for each unit of hazard decrease, and the latter is measured by the covariance.

Because the market is a riskless licence, discrepancy and standard divergence equal to zero, you can unite this rubric with any portfolio on the efficient frontier in order to keep a new portfolio risk-return features that depend on the weights of single activities portfolio. The investor will measure the likeliness of the generic rubric of the part offered by the latter to cut down overall portfolio hazard. Hence the importance of quantifying the extra hazard that the single rubric added to the market portfolio. In other words, it is necessary to mensurate the responsiveness of the rubric to alterations in the market portfolio by the relationship between the rubric and the covariance of the market and the discrepancy of the market, this study is the beta.

The beta of a portfolio equals the leaden mean beta of single stocks that make up the portfolio itself.

Based on these penetrations, SLM – Sharpe ( 1964 ) , Lintner ( 1965 ) and Mossin ( 1965 ) – regardless, will set up the Capital Asset Pricing Model.

To explicate the theoretical account you add extra limitations:

g ) absence of dealing costs ;

H ) each investing and trading in the coveted measure without any bound, is angry that the investor can purchase even a fraction of securities ;

I ) all market participants are monetary value takers, intending that none of them can separately impact the monetary value of fiscal assets ;

cubic decimeter ) there are no limitations on information, it is free and immediately available to all investors. In other words, the market is efficient in strong signifier and therefore monetary values

securities reflect all available information whether it be public or private nature.

The Capital Asset Pricing Model ( CAPM ) is a theoretical account that measures the expected return of single securities, or return to market equilibrium, harmonizing to the hazard of the investing, the investor, as Sharpe points out, is confronting two monetary values: the monetary value of clip, or pure involvement rate, and the monetary value of hazard that is the monetary value of hazard for each extra unit of expected return. The CAPM provides one-dimensionality between hazard and return, in equilibrium, the expected return of each security is measured by the riskless plus a premium for the extra hazard in proportion to the fringy part that the rubric brings to the peril of the portfolio. In kernel, the award is a signifier of wage of non merely the systematic hazard and entire hazard.

## 3. The theoretical account of Fama and Gallic: three-factor theoretical account

The theoretical account of Fama and French ( 1992 ) , as mentioned above, on the acknowledgment of non-perfect one-dimensionality between return and hazard measured by beta and physiques on the multifactorial. Inspired by the work of Basu ( 1977 ) and Banz ( 1981 ) the two bookmans developed the three-factor theoretical account in which is of import, in add-on to the beta, the size of the company ‘s size, the ratio of book value and market value, and hazard premium as the difference between the output on the market index and the output on hazard free.

Although there may be an reverse relationship between size, measured by market value or market capitalisation, and stock returns, this development is non accompanied

from the addition ( or lessening ) in beta. As a general regulation, grounds of a larger company should be less hazardous and hence less profitable. In contrast, the rubrics of the smaller companies should calculate a greater hazard and greater efficiency. This would take investors to demand a higher premium to countervail the extra hazard. A similar statement is besides valid for the ratio of book value and market value in visible radiation of the explanatory power. Specifically, a high ratio ( lower Price / Book Value ) stocks with typical low growing chances and therefore less hazardous securities that show a low value of the index in inquiry ( higher Price / Book Value ) show good growing chances and high activity

intangibles that reflect market value more than the book value ( Damodaran, 2002 ) . In fact, for both instances, size and book to market value, Fama and French ( 1993 ) found that the empirical grounds is rather different theoretical diction and that hazard premiums do non depend entirely and entirely by the systematic hazard, measured by beta, but alternatively demo a greater sensitiveness to the public presentation of the three factors considered together. Therefore infer that the expected premium for the hazard can be expressed through the undermentioned relationship:

Where the coefficients Bi, hello, and you are the inclines of the arrested development time-series, SMB and HML denote the size factor and the factor transporting sum / value of mercato.In peculiar, Small Minus Big is the difference between dividend outputs more little and big 1s and the difference between High Minus Low bond outputs high BE / ME and those of securities with low BE / ME.

To prove the cogency of the theoretical account utilizing a sample consisting of all the rubrics of the NYSE for the period 1963-1991, and aggregate them into 25 portfolios formed harmonizing to five degrees of size and a similar BE / ME. Methodologically, to gauge parametric quantities, follow the process suggested by BJS to prove the CAPM. From this first study found that the intercepts are about ever significantly different from zero and presume that the coefficients of finding values aˆ‹aˆ‹well over 90 % .

Besides note that the beta is non straight linked to the returns of the portfolios, with mention to the size, Fama and Gallic note that it increases the returns diminish. Taking as a mention alternatively of the ratio BE / ME besides noted that an addition in the index implies higher returns but at the same clip make non trip an addition in hazard. Fama and French ( 1995 ) argue that companies with low net incomes tend to hold high BE / ME, with a positive coefficient for HML, and the most solid companies characterized by high net incomes and low BE / ME compute a negative coefficient for HML. In kernel, the two writers conclude reasoning that markets are efficient, that most of the empirical anomalousnesss can be explained by the three-factor theoretical account, and that the beta can non be considered the lone variable able to to the full capture the hazard systematic

## 6. Metodology

The study conducted on a sample here consists of a lower limit of 47 rubrics, covering the old ages 1985-1990, to a upper limit of 109 securities listed on the Italian stock market. The information for clip series of adjusted monetary values and the series of the market, the overall BCI, adopted as a placeholder of the market portfolio, were both acquired from the database of the Italian Stock Exchange. The bonds were identified based on a clip skyline, matured, which would do the analysis dependable. Were excluded from the sample of the rubrics those companies who had a little series and have been examined, with some exclusions, merely common portions.

Even with this restriction, nevertheless, sing the recent natural development of the Italian market, the sample was at the terminal of 2005 about 50 % of the entire capitalisation of the stock. Have been used clip series of monetary values of ordinary portions non merely in the absence of ordinary informations. However, for the same company have ne’er given the clip series of both their monetary values in order to avoid hazards associated with multicollinearity.

The methodological analysis followed in this work is suggested by Black, Jensen and Scholes ( 1972 ) . This process was meant to prove the dependability of both the market theoretical account that the CAPM. In the following chapters, I ‘ll utilize the abbreviation “ BJS ” to mention about this work. The beginning is to prove the CAPM use ab initio to the classical equation of the market theoretical account yields a full,

at which clip you are regressed monthly returns on monthly returns of the securities market index. Realizes, nevertheless, that in order to prove the significance of ‘using the t trial is required and the mutuality of residues ( E, E ) = 0, which in our instance can non be confirmed, they resort to the formation of portfolios in which the ‘ mutuality of residues should be absorbed within the assorted bunchs. In this manner, some are built portfolios of stocks, sorted by hazard, or in groups of beta, and so you calculate the monthly returns of portfolios that will be regressed on market index returns.

Unlike the work of BJS, in this work has non been possible to build 10 portfolios and so if they are formed that contain 7 a important figure of rubrics. Despite this, merely since 1989 have portfolios incorporating a figure of securities big plenty that they can profit from variegation.

Our seven portfolios were sorted by increasing value given by the lowest beta ( portfolio 1 ) to highest ( portfolio 7 ) . Similarly, as suggested by BJS each twelvemonth are estimated beta for a five-year period does non overlaps with the twelvemonth in which the portfolios are formed. The monthly returns of portfolio P ( where P = 1,2, … 7 ) were calculated as the mean monthly returns of these securities in that portfolio size based on the beta, the old five old ages, of similar order.

For each twelvemonth, hence, the portfolio returns were calculated utilizing the undermentioned expression:

where J, t represent the figure of securities in the portfolio eg the monthly each twelvemonth. Following this process consequences in a series of 336 monthly returns for each portfolio.

Then we regress the monthly returns of the portfolios on the market index to gauge the beta of the portfolios and measure the statistical significance of

Alfa.

This process was ab initio performed on the full period ( 1985-2005 ) with consequences in line with the findings from BJS. Specifically, except for the negative alpha of the 6th book, which was non statistically different from nothing, three of the four alpha positive and statistically different from zero occur for less hazardous portfolios ( p = 1, 2, 3 ) . Consistent with findings from BJS, the long-run securities of companies less hazardous compute higher returns than predicted by the classical version of the CAPM. In contrast, the stocks included in portfolios riskier record outputs lower than the estimation of the theoretical account.

The same process was repeated on the five subperiods.

Table1: Beta appraisal for subperiod

## A

time portfolios

1

2

3

4

5

6

7

BetaA

85 – 90

0,7145

0,6435

0,9032

1,0622

0,9354

0,9986

1,0365

## A

91 – 95

0,4523

0,7183

1,0003

0,9831

1,1332

0,9424

1,2783

## A

96 – 00

0, 5074

0,6259

0,9145

0,8441

0,8672

0,8557

1,5964

## A

01 – 05

0,4241

0,7693

0,8325

0,9042

0,9246

1,0134

1,4232

Looking at Table 1 reveals that the betas are non stationary during the five subperiods. The statistically different from nothing are found for three sub-portfolio in the 2nd and one for the several sub-portfolios 1, 4 and 5, all other instances the hypothesis of nothingness of the intercept of the CAPM is confirmed. In the work of BJS beta followed a negative tendency for hazardous portfolios, and readings are positive and statistically important in the instance of portfolios less hazardous premise that, with some exclusions, is besides confirmed in this analysis. The R2 consequences goes from a 0,5321 in the portfolio 1 to a 0,7944 in the portfolio 7. In the center, the consequences follow the form: from the lowest degree ( 1 ) to the highest ( 7 )

## 6.1. The consequences of the cross-section analysis

To better analyze the consequences and look into the one-dimensionality of the equation of the CAPM is used to prove cross-sectional through which you can look into the one-dimensionality of the predicted risk-return relationship. In add-on to the expression to give full, you can utilize the equation to give in surplus of:

Where Rpt is the return of the i-th rubric of period T, Rmt is the return on the market index over the same period and FRG is the efficiency of riskless rate at clip t. ever

To look into the cogency of old consequences ( and consistent ) doing a 2nd arrested development between the mean returns of portfolios Rj = 1 / N I? RJT ( where T J are the portfolios and the months of the clip ) and estimated by I?j the old arrested development, obtaining the undermentioned equation:

## A

whole period

A Subperiod

## A

## A

## A

## A

1/85- 12/05

85 – 90

91 – 95

96 – 00

01 – 05

I’0

0,016043*

0,02215

-0,00005

0,031

0,000312

Releasing factor

0,000245

0,000356

0,00094

0,00311

0,00264

I’1

0,000031

-0,00002

0,00073

0,0079

0,009452

Rm

0,001136

0,001976

0,00009

0,02806

0,000023

MRP = Rm – Releasing factor

0,001698

0,01028

-0,009232

0,00243

-0,00452

T ( I’o )

3,5782

1,874

-0,4301

2,4512

0,00256

T ( I’1 )

0,1922

-0,00375

0,5867

0,56341

1,15131

R2

0,00469

0, 000003

0,00358

0,0092

0,32675

Both the tabular array is easy to see from the graphs that for the full period and for the first sub-intercept is statistically different from nothing. The equality between the market rate of return estimated and observed is ne’er statistically important, and besides for the full period, the line is about level

Cross – subdivision graph analysis of 85 – 05

Cross – subdivision graph analysis of 85 – 90

In the first and 2nd subperid aˆ‹aˆ‹assume even negative value, and at other times the incline every bit good as positive although non statistically important, show undistinguished R2. These consequences are quite eccentric and deserve farther analysis, particularly given the relationship Beta / R2, but the first symptom that the CAPM theoretical account does non follow excessively good the Italian market.

Cross – subdivision graph analysis of 91 -95

Cross – subdivision graph analysis of 96 – 00

Cross – subdivision graph analysis 01 – 05

The highest value of the coefficient of finding is recorded in the first ( 25.78 % ) and 5th fractional monetary unit ( 21.61 % ) . E ‘in that it could non except the proper operation of the additive theoretical account considered in the study.

Even with more robust statistically, a similar state of affairs is besides reflected in the work of BJS although the figure of securities that form the 10 portfolios is much wider ( from 582 in 1931 to 1094 in 1965 ) . In peculiar, in their 4th subperiod the beta is negative. The estimated market rate of return is lower, and statistically important compared to that observed during the whole period. In this work, the hazard premium the market is good for the full period and for other 2 fractional monetary units, in contrast, is negative for two subperiods including one in which the theoretical account expresses a certain one-dimensionality that non except the proper application. Therefore, this theoretical account is non needfully incorrect, as applied to the Italian market, but at least inaccurate and necessitate farther analysis.

## 6.2. The consequences obtained by the three-factor theoretical account

The sample used to prove the Fama-French theoretical account is the same as described above with the exclusion that the clip skyline is reduced to fifteen old ages ( 1990-2005 ) because of the inaccessibility of fiscal information of the company prior the period under reappraisal. Each twelvemonth the securities were classified harmonizing to their market value to organize four groups discriminated against in relation to size from each group were obtained four portfolios based on the ratio BE / ME for a sum of 16 portfolios. In June of each twelvemonth, co-occuring with the handiness of accounting informations for each of the 16 portfolios we calculated the mean monthly output as the mean output of securities belonging to the portfolio for the following 12 months get downing from July of T to June of

T +1. Calculated the returns of the portfolios for the full scope investigated ( 15 old ages ) , we regressed the returns of each portfolio compared to the market ensuing in the post-ranking beta.

For the variable size, as mentioned, mention is made to the market value of the securities, while the variable Book Equity / Market Equity has been considered the relationship between value book equity and market value of the company. To gauge the hazard premium of the market was eventually used the monthly return of the three-month Treasury measures as the hazard free rate. The portfolios are formed harmonizing to an go uping order of magnitude of the two variables. The survey of Fama and French ( 1992 ) , used 25 portfolios in this work, so I decided to build 10 portfolios to turn to the deficiency of informations makes it more dependable analysis.

Table 3: outputs and hazard premiums monthly portfolios of the three – factor theoretical account ( 1990 – 2005 )

As shown in the tabular array, increasing the size of the portfolio returns diminish, and this does non reject the hypothesis of an opposite relationship between returns and size. The hazard premium assumes diminishing values aˆ‹aˆ‹depending on the size portfolios and for the last two readings are negative.

From the consequences obtained, it is easy to see how the beta demoing all statistically important and about half of the intercepts ( 7 out of 16 ) are statistically different from

nothing at a assurance degree of 5 % .

The coefficients of finding values aˆ‹aˆ‹assume small relevancy to the portfolios with lower market values, while they are higher for portfolios with high market values. However, something really unusual is the fact that the portfolios of larger profiles are characterized by riskier, and conversely, the smaller companies seem to measure up for the lowest hazard. The coefficient of the size factor is about ever statistically important, it would look so presume a proper function in the extent to which it adds or subtracts to the public presentation of portfolio extra returns.

Intercepts but two were ne’er significantly different from nothing and the beta, all

statistically important, does non diminish as the size, but instead addition, and do non look to follow peculiar tendencies with increasing book-to-market value. The value of the coefficient are about ever statistically important, lessening as the size, in some instances is negative. On the contrary, did non propose definite relationship between the coefficient and the ratio BE / ME. Merely the 2nd and 3rd book takes on a about additive tendency. The parametric quantity I? , so stand foring the coefficient of HML variable, taking values aˆ‹aˆ‹mostly important for portfolios characterized by higher values aˆ‹aˆ‹of BE / ME.

## 7. Decisions

The Capital Asset Pricing Model and the three-factor theoretical account were investigated in this work. The consequences suggest, nevertheless, some cautiousness in pulling decisions, and for the limited figure of securities considered to be the clip skyline over which it was possible to look into the extent of which is lower than that of other surveies.

Sing the confirmation of the CAPM following the methodological analysis proposed by BJS, the consequences appear rather encouraging in footings of risk-return relationship. Cross-sectional analysis did non propose a strong relationship between beta and returns of the portfolios and the values aˆ‹aˆ‹recorded by the coefficient of finding show a relationship

really weak for all periods. The market hazard premium assumed in some instances negative interception, except in two instances, it is ne’er significantly different from nothing. It ‘should nevertheless be noted that the value of the coefficient of finding of the 5th fractional monetary unit ( 21.61 % ) findings, despite the deficiency of significance of the parametric quantities, non to except the proper operation of the additive theoretical account considered in the study. Although statistically more robust consequences with similar state of affairss are besides found in the work of BJS although the figure of securities that form the 10 portfolios is much wider ( from 582 in 1931 a1094 in 1965 ) . In peculiar, in their 4th subperiod the beta is negative. The estimated market rate of return is lower, and statistically important, than those observed during the whole period.

Apparently the most interesting consequences were obtained by using the three-factor theoretical account. In this instance the variable size accompanied the beta seems to hold more explanatory power. The beta, all statistically important, non diminish as the size, but instead addition, and do non look to follow peculiar tendencies with increasing book-to-market value. The values aˆ‹aˆ‹of coefficient “ lambda ” are about ever statistically important, lessening with increasing size, bespeaking a higher hazard premium for riskier securities as predicted by CAPM. In such fortunes, including the portfolio returns, with some exclusions, autumn, and this does non reject the hypothesis of a relationship between returns and size. As for the relationship between net incomes and BE / ME there are no additive tendencies as in the work of Fama and French ( 1992 ) .

This work besides confirms the inclination of beta to turn with increasing size as measured by market capitalisation, it besides confirms the importance of the size factor in explicating bond outputs. The accomplishments of the three-factor theoretical account, hence, seem to corroborate the being of extra factors that can explicate the returns. And this is non the lone work that expresses concerns about the empirical cogency of CAPM, the consequences produced by the international literature are rather obvious in malice of legion attempts by protagonists to support the theoretical account.

Even in Italy the consequences are non alone in stressing clearly different places: some plants confirm the cogency of Capital Asset Pricing Model. On the other manus a theoretical model so weakened by strong empirical grounds that they have no theoretical support, and no specific place in the paradigm of hazard – return, doing incredulity. This grounds, nevertheless, if farther confirmed doing serious harm to the CAPM, since the standard for gauging the cost of equity capital most common in all states of the universe ( Graham and Harvey, 2001 ) .

Advocates of the CAPM are defended by imputing the cause of non-linearity of the exemplary several factors, including statistical sampling mistakes, choice prejudice, the forms of informations excavation, the unreason of the markets, the latter state of affairs that is progressively finding infinite in the scientific community ( Kahneman and Tversky, 1974, Shiller, 2000 ) . The thought of aˆ‹aˆ‹data excavation is really instead taken into history by Black ( 1993 ) which proposes the analysis conducted by BJS for the same period is similar but non indistinguishable. Widening the analysis to 1991, he is weaker than the values aˆ‹aˆ‹obtained during the period 1931-1965, stocks with a record low beta securities with higher outputs high beta. He believes, nevertheless, that the frequence with which the low-beta securities “ do better ” of the riskiest securities is the same, sing, hence, prematurely “ decease ” of the CAPM. through arrested development analysis, is the index of hazard to which the bulk relies on fiscal analysts ‘ Italian ( AIAF, 2001 ) .

Do non bury that the theoretical account is widely adopted non merely for the risk-return analysis of stocks, which provide a part of exceeding importance in understanding the logic of the pricing of hazardous assets, on the reverse,

suited for many applications in the field of fiscal analysis. Just think of the progressively widespread usage of methods based on discounted hard currency flow analysis for the rating of investing undertakings both public and private, with equal frequence, nevertheless, the same method is used in the rating of the economic capital of the company. In each instance, the price reduction rate used to dismiss hard currency flows, which is unlevered levered, is calculated harmonizing to the cost of equity capital.

Ultimately, hence, the consequences presented in this survey are preliminary and suggest farther survey, which will be more robust confirm or deny the ideas contained herein.

## Beginnings

H. Markowitz, “ Portfolio Selection ” , in Journal of Finance, Vol. VII, n.1, March 1952, pp. 77- 91.