The estimated cost of equity capital, or alternatively the return expected by shareholders, is one of the most debated issues in the Theory of Finance. Different models to estimate, due to the objectivist theory of the cost of capital, they found ample space in the financial literature, fueling the debate on the theoretical and empirical.
A decisive contribution to this effect is due to Harry Markowitz (1952), the father of Modern Portfolio Theory, which has provided a theoretical framework for risk analysis - performance. The author, by postulating the risk aversion by investors, he laid the groundwork for the identification of the two variables considered in investment decisions: the expected return and variance, or standard deviation, of the share.
Based on studies of Markowitz, Sharpe (1964), Lintner (1965) and Mossin (1966) independently develop the Capital Asset Pricing Model, a model that predicts the expected return of the security, performance or market equilibrium, depending the investment risk. In other words, the CAPM assuming a context of information efficiency, the absence of transaction costs, monoperiod horizon, homogeneity of expectations, the presence of risk-free bonds - risk free rate - etc. Indicates the trade-off between risk and return . In the model in question become important on three variables: the rate of return on government bonds, or risk-free rate, the coefficient of systematic risk, beta, and the expected premium for risk.
Although some of the underlying assumptions appear far from reality, such as the ability to take and to lend without limit at the same risk free rate, the absence of taxes, and others, the CAPM has been the past four decades the subject of lively debate in financial economics. The first criteria of the Capital Asset Pricing Model were made by Sharpe (1966) and Jensen (1967) on mutual funds with encouraging results. However, the idea of ​​give and take a free loan limits at the same risk free rate appeared little relation to reality, to overcome this obstacle, and simultaneously facilitate the empirical testing, Black (1972) studied a variant of the model known as "zero-beta model ". This change includes the replacement of the risk-free with another business, title or portfolio uncorrelated with the market.
Black, Jensen and Scholes (1972) perform an empirical test results showing that while not fully reflecting the expectations of the classic version of the CAPM are in line with the zero-beta CAPM. Come to similar conclusions Fama and MacBeth (1973) who consider the achievements, the most satisfactory and consistent with the zero-beta model. Over the years, the CAPM has been widely criticized the idea that the beta was not the only factor that can explain the returns of equities, has taken more and more body. If the first evidence empirical, delivered via the market model, showed the linear relationship between risk and return, subsequent tests revealed the inability of the beta to express that relationship. In this fits the Arbitrage Pricing Theory, developed by Ross (1976) and Roll (1977), which shows that the factors involved in determining stock prices are numerous. The APT, while not explicitly stating these factors, recognizes a key role in some macroeconomic variables such as the oil price, inflation, interest rates, GDP, etc.
The numerous empirical anomalies resulting from the imperfect linearity of the relationship risk - return, made them suspect the existence of other factors likely to influence more effectively on the returns of equities. Banz (1981), for example, was the first to point out that the variable size is better able to interpret the path of the CAPM theory, he notes the presence of a negative relationship between size and performance.
Fama and French (1992) show that the beta as an explanatory variable of the report risk - return, do not fully capture all the risk factors.
The authors develop three-factor model, or three-factor model, through which show that the risk 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. According to the authors, the empirical evidence shows that the three-factor model is able to explain the returns of equities. In Italy the CAPM is that the pricing models in general have found little application in the literature, probably due to the small size of the stock market.
The aim of this work is to verify whether these two econometric models can also find confirmation of the Italian stock market. For this purpose we investigate the validity of the CAPM assuming a time horizon of twenty years, 1985 - 2005, divided into five periods, using 60 shares listed on the Milan Stock Exchange. Then we will observe the behavior of the three-factor model on a shorter period. The aim, ultimately, to investigate the validity of both models.
2 The Italian Stock Exchange
In Italy, the financial market is based in Milan at Palazzo Mezzanotte, and is organized and operated by the Italian Stock Exchange. The origins date 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, later confirmed by the Commercial Code of 1882. Moreover, until 1977, the year of the establishment of narrow market, the Stock Exchange was the only regulated market exists in Italy.
Legislative Decree No. 461/1996 provides for the initiation of the privatization of the Italian stock exchange, which led to the birth of the Italian Stock Exchange, which handles the stock exchange based in Milan. This facility became operational from January 2, 1998. Also under that decree, the Italian Stock Exchange merged in 1997 and also replaced all the smaller squares of exchange, which play a purely regional.
In 2007 the Italian Stock Exchange merged with the London Stock Exchange (London Stock Exchange). The stock exchange shall supervise the proper conduct of trading, defines the requirements and procedures for admission and stay on the market for issuing companies, defines the requirements and admission procedures for brokers, manages the information of listed companies. Italian Stock Exchange organizes and manages the Italian market by using a completely electronic trading system for the execution of trades in real time. It deals with the regulation and market management. The supervisory function is instead performed by Consob and Bank of Italy.
To complete the Italian stock exchange capitalization is 13th in the world. The trading of the shares belonging to the segments identified by the Italian Stock Exchange can be done with the intervention of specialists appointed by the issuer in the market to support the liquidity of shares listed. The law of concentration, which was introduced into Italian law 1 / 1991, requires that a regulated market intermediaries inoltrino to EU orders from Italian customers. Exemptions are provided for the exchange of large amount (called blocks) and for transactions where the broker will be able to get to their customers better terms than those on the trading book.
MiFID in November 2007 deleted from the law of concentration, allowing financial intermediaries such as banks and investment companies, to build its own exchange circuit of the licenses, said the multilateral trading system, or to operate as systematic internalisers offering directly trade execution services to its customers. The MiFID provides for detailed rules to protect transparency by establishing a set of consistent information to be disseminated before and after the trade from all trading venues (regulated markets, MTFs and systematic internalisers), and investors by requiring brokers compliance with the requirements of best execution.
The bargaining system run by the Italian Stock Exchange is divided into different markets:
• MTA (MTA) where the listed shares are traded on the stock market, the market is divided into three main classes and a residual on the basis of capitalization and liquidity of the securities
• Large-Cap (or Blue Chip) comprising the top 40 most capitalized companies with greater liquidity. Index of: FTSE MIB.
• Mid Cap includes the following 60 companies by market capitalization and liquidity. Index of: Italy FTSE Mid Cap
• Small Cap including other companies not part of the first business center, which exceed the criteria of liquidity. Index of: FTSE Small Cap Italy
• Micro-Cap includes other companies not part of previous groups, which do not meet the criteria for liquidity. Index of: Micro Cap FTSE Italy
• In addition there remain the following segments: STAR segment, which includes companies that meet certain criteria of transparency, governance and liquidity (with market capitalization between 40 million and 1000 million € €). Index of: FTSE Italy STAR.
• MTA International segment that houses the trading of equity securities of companies already listed on stock exchanges in the European Union.
• MIV (Electronic Market for Investment Vehicles), which replaced the MTF (Electronic Market Funds), is a regulated market dedicated to investment vehicles. The market consists of three segments depending on the type of securities that are traded: Closed-end funds, Investment Companies and Real Estate Investment Companies.
• MAC alternative capital market
• IDEM (Italian Derivatives Market) in this market, created in 1994, contracts are traded derivatives such as futures, options on securities and minifutures which fall in the S & P / MIB
• SEDEX where negotiations are covered warrants, leverage certificates, certificates of investment category
• MOT (Electronic Market for bonds and government securities) are traded in this market government bonds (BOT, BTP, CCT, CTZ), bonds of local authorities, non-convertible bonds and structured, euro-bonds, bonds foreign issuers and asset-backed securities. This market is divided into two segments:
DomesticMOT or where they are treated with liquid financial instruments clearing Italians.
EuroMOT or where they are treated liquid financial instruments in foreign settlement systems
• Plus ETF by April 2, 2007 the Italian Stock Exchange has adopted a market dedicated to trading in financial instruments that replicate the performance of the market such as ETFs (exchange traded funds), ETC (Exchange Traded Commodities), structured ETFs.
3 Market Anomalies: Size effect and Value effect
Another of the objectives of this research is to verify that the considerations on the Italian market reached by Fama and French in their work on market anomalies. They have proposed an alternative model to the CAPM that solves one of the most enigmatic anomalies: the size effect and value effect. This anomaly is seen in the empirical evidence that long-term action of small-cap companies to make more of those large-cap and actions with high valuation ratios (such as dividend / price, earnings / price, book / price) obtain higher returns for companies with low ratios of assessment.
Basically, the small value stocks seem to make much more than large growth stocks, at least in the long run. The explanations given by financial economists are numerous and often too complex to examine them here, suffice it to say that these "effects" were often regarded as the market imperfections, since the yields of these actions were not "explained" using the famous model asset pricing called CAPM. While some researchers consider the inefficiencies of the market, others have interpreted as risk factors, attributable mainly to the so-called "distress risk": the selection of actions based on small-cap and the high evaluation reports would identify shares with low liquidity and / or companies with financial problems, that offer low returns just when the marginal utility of investors is high, ie during recessions. From these considerations were born, before the three-factor model of Fama and French, and then the four-factor model of Carhart.
The problem is that these models have no theory behind it, so these "anomalies" have been transformed into "risk factors" only ex-post, which may be considered questionable. All the more so as many studies seem to demonstrate the size effect and value effect depends on the time period in which they are analyzed, especially with respect to periods less than 80 years. Several researchers come to the conclusion that these anomalies are missing and perhaps had never existed, due solely to chance and calculation power of the computer for just such anomalies.
The fact remains that three-factor model with this anomaly disappears, and probably will happen in the Italian market.
4 The Capital Asset Pricing Model
The first studies on the risk-return trade-off date back to Harry Markowitz (1952) whose research is widely regarded as the "cornerstone" of Modern Portfolio Theory. The reasoning on which the analysis is based Markowitz is actually very simple. Investors as well as the desire to obtain high yields are by nature risk averse and therefore the attitude most logical and rational, that they take is to implement an effective policy of investment diversification to reduce risk. The rates of return for the license and the portfolio are given by:
where Pt-1 is the price paid to purchase the title at the beginning of the period, and Pt is the market value at the end of the period including the return generated by the title during the period, W0 is the aggregate purchase price at time t = 0 of titles in the portfolio, and W1 is the aggregate market value at time t = 1.
According to Markowitz, the investor Exchange, and then choose, each portfolio according to the rate of return associated with it, and randomly distributed, which in turn depends on expected value and standard deviation. Expected returns and standard deviations observed for each portfolio are the only two factors discriminating between current and deferred consumption.
The expected return of a portfolio is given by:
Where E (ri) measure the expected return on stock i and Wi the weight of I on the entire portfolio.
The assumptions in the Markowitz model are:
Monoperiodal horizon for all investors and only in respect of which maximize the expected utility of the performance of their portfolios;
rational actors and thus risk averse,
who select their portfolios based on the expected average return and variance hold.
The limit of this theory is not to consider the existence of risk-free assets. James Tobin (1958) considered the possibility of investing in risk-free assets and borrow at the same rate. N denote the risk-free license, with the weight of Xn under the risk-free portfolio (and hence 1-n is the weight in the portfolio of risky assets), with the RF bond yield and risk-free return on risky assets Rr , The expected return of the portfolio is equal to:
To simplify the model is the strongest hypothesis postulated in addition to the above, namely:
d) no restrictions for investors to take or lend money to the risk free rate,
e) homogeneous expectations by investors on the expected values ​​of returns, the variances and covariances of bond yields and thus the same perception on the prospects of each title and, consequently, the entire portfolio, f) absence of taxes and imperfections markets. In the presence of risk-free activity, which can be purchased or
sold short, the frontier becomes linear. In connection with these additional assumptions, Sharpe (1963) elaborates the Single Index Model and Market Model, which expresses the linearity between risk and return. Sharpe had the brilliant idea to note that:
Is there a portfolio as the sum of all the portfolios of individuals,
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 risk-free rate of (R f) portfolio (M), on the efficient frontier, was obtained by the combination best combination of M and therefore in equilibrium all securities, or portfolios, they will end along the line R f - M called Capital Market Line
Ϭ
All portfolios which lie along the border feel increasingly are efficient and the point of absolute minimum variance (AMV) expressing the possible combinations of portfolios that minimize the overall variance. The limitation of the model is that it does not address the inefficient portfolios or individual securities. Considering all the securities, or portfolios, not falling on the efficient frontier should investigate what each activity is related to the other and, ultimately, the market portfolio. In other words, what is the risk contribution made ​​by an individual asset to the market portfolio? The answer to that question is provided by Sharpe (1964) through the Security Market Line, whose intercept is given by the risk free rate and angle expresses the risk-return trade off. The SML stems from the fact that terminated the benefits of diversification remains a part of the systematic risk of the portfolio, and that this percentage can be measured by the sensitivity of the individual security or portfolio to movements in the market portfolio.
The equation for the Security Market Line is:
Where rs is the price of reducing the risk of the securities and Cim is the covariance between the bond yield and the market. The value of r indicates that the expected return must be sacrificed for each unit of risk reduction, and the latter is measured by the covariance.
Because the market is a risk-free license, variance and standard deviation equal to zero, you can combine this title with any portfolio on the efficient frontier in order to hold a new portfolio risk-return characteristics that depend on the weights of individual activities portfolio. The investor will assess the likelihood of the generic title of the contribution offered by the latter to reduce overall portfolio risk. Hence the importance of quantifying the additional risk that the individual title added to the market portfolio. In other words, it is necessary to measure the reactivity of the title to changes in the market portfolio by the relationship between the title and the covariance of the market and the variance of the market, this report is the beta.
The beta of a portfolio equals the weighted average beta of individual stocks that make up the portfolio itself.
Based on these insights, SLM - Sharpe (1964), Lintner (1965) and Mossin (1965) - regardless, will establish the Capital Asset Pricing Model.
To formulate the model you add additional restrictions:
g) absence of transaction costs;
h) each investment and trading in the desired quantity without any limit, is angry that the investor can buy even a fraction of securities;
i) all market participants are price takers, meaning that none of them can individually affect the price of financial assets;
l) there are no restrictions on information, it is free and instantly available to all investors. In other words, the market is efficient in strong form and therefore prices
securities reflect all available information whether it be public or private nature.
The Capital Asset Pricing Model (CAPM) is a model that measures the expected return of individual securities, or return to market equilibrium, according to the risk of the investment, the investor, as Sharpe points out, is facing two prices: the price of time, or pure interest rate, and the price of risk that is the price of risk for each additional unit of expected return. The CAPM provides linearity between risk and return, in equilibrium, the expected return of each security is measured by the risk-free plus a premium for the additional risk in proportion to the marginal contribution that the title brings to the riskiness of the portfolio. In essence, the prize is a form of remuneration of not only the systematic risk and total risk.
3. The model of Fama and French: three-factor model
The model of Fama and French (1992), as mentioned above, on the recognition of non-perfect linearity between return and risk measured by beta and builds on the multifactorial. Inspired by the work of Basu (1977) and Banz (1981) the two scholars developed the three-factor model in which is important, in addition to the beta, the size of the company's size, the ratio of book value and market value, and risk premium as the difference between the yield on the market index and the yield on risk free.
Although there may be an inverse relationship between size, measured by market value or market capitalization, and stock returns, this development is not accompanied
from the increase (or decrease) in beta. As a general rule, evidence of a larger company should be less risky and therefore less profitable. In contrast, the titles of the smaller companies should compute a greater risk and greater efficiency. This would lead investors to demand a higher premium to offset the additional risk. A similar argument is also valid for the ratio of book value and market value in light of the explanatory power. Specifically, a high ratio (lower Price / Book Value) stocks with distinctive low growth prospects and thus less risky securities that show a low value of the indicator in question (higher Price / Book Value) show good growth prospects and high activity
intangibles that reflect market value more than the book value (Damodaran, 2002). In fact, for both cases, size and book to market value, Fama and French (1993) found that the empirical evidence is quite different theoretical enunciation and that risk premiums do not depend solely and exclusively by the systematic risk, measured by beta, but instead show a greater sensitivity to the performance of the three factors considered together. Therefore infer that the expected premium for the risk can be expressed through the following relationship:
Where the coefficients bi, hi, and you are the slopes of the regression time-series, SMB and HML denote the size factor and the factor carrying amount / value of mercato.In particular, Small Minus Big is the difference between dividend yields more small and large ones and the difference between High Minus Low bond yields high BE / ME and those of securities with low BE / ME.
To test the validity of the model using a sample consisting of all the titles of the NYSE for the period 1963-1991, and aggregate them into 25 portfolios formed according to five levels of size and a similar BE / ME. Methodologically, to estimate parameters, follow the procedure suggested by BJS to test the CAPM. From this first survey found that the intercepts are almost always significantly different from zero and assume that the coefficients of determination values ​​well over 90%.
Also note that the beta is not directly linked to the returns of the portfolios, with reference to the size, Fama and French note that it increases the returns diminish. Taking as a reference instead of the ratio BE / ME also noted that an increase in the indicator implies higher returns but at the same time do not trigger an increase in risk. Fama and French (1995) argue that companies with low profits tend to have high BE / ME, with a positive coefficient for HML, and the most solid companies characterized by high earnings and low BE / ME compute a negative coefficient for HML. In essence, the two authors conclude arguing that markets are efficient, that most of the empirical anomalies can be explained by the three-factor model, and that the beta can not be considered the only variable able to fully capture the risk systematic
6. Metodology
The survey conducted on a sample here consists of a minimum of 47 titles, covering the years 1985-1990, to a maximum of 109 securities listed on the Italian stock market. The data for time series of adjusted prices and the series of the market, the overall BCI, adopted as a proxy of the market portfolio, were both acquired from the database of the Italian Stock Exchange. The bonds were identified based on a time horizon, full-blown, which would make the analysis reliable. Were excluded from the sample of the titles those companies who had a small series and have been examined, with some exceptions, only common shares.
Even with this limitation, however, considering the recent natural evolution of the Italian market, the sample was at the end of 2005 approximately 50% of the total capitalization of the stock. Have been used time series of prices of ordinary shares not only in the absence of ordinary data. However, for the same company have never given the time series of both their prices in order to avoid risks associated with multicollinearity.
The methodology followed in this work is suggested by Black, Jensen and Scholes (1972). This procedure was meant to test the reliability of both the market model that the CAPM. In the next chapters, I'll use the abbreviation "BJS" to refer about this work. The beginning is to test the CAPM apply initially to the classical equation of the market model yields a full,
at which time you are regressed monthly returns on monthly returns of the securities market index. Realizes, however, that in order to test the significance of 'using the t test is required and the interdependence of residues (E, E) = 0, which in our case can not be confirmed, they resort to the formation of portfolios in which the' interdependence of residues should be absorbed within the various clusters. In this way, some are built portfolios of stocks, sorted by risk, or in groups of beta, and then you calculate the monthly returns of portfolios that will be regressed on market index returns.
Unlike the work of BJS, in this work has not been possible to construct 10 portfolios and then if they are formed that contain 7 a significant number of titles. Despite this, only since 1989 have portfolios containing a number of securities large enough that they can benefit from diversification.
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 year are estimated beta for a five-year period does not overlaps with the year in which the portfolios are formed. The monthly returns of portfolio p (where p = 1,2, ... 7) were calculated as the average monthly returns of these securities in that portfolio size based on the beta, the previous five years, of similar order.
For each year, therefore, the portfolio returns were calculated using the following formula:
where j,t represent the number of securities in the portfolio eg the monthly each year. Following this procedure results in a series of 336 monthly returns for each portfolio.
Then we regress the monthly returns of the portfolios on the market index to estimate the beta of the portfolios and assess the statistical significance of
Alfa.
This procedure was initially performed on the entire period (1985-2005) with results in line with the findings from BJS. Specifically, except for the negative alpha of the sixth book, which was not statistically different from zero, three of the four alpha positive and statistically different from zero occur for less risky portfolios (p = 1, 2, 3). Consistent with findings from BJS, the long-term securities of companies less risky compute higher returns than predicted by the classical version of the CAPM. In contrast, the stocks included in portfolios riskier record yields lower than the estimate of the model.
The same procedure was repeated on the five subperiods.
Table1: Beta estimation for subperiod
time\ portfolios
1
2
3
4
5
6
7
Beta
85 - 90
0,7145
0,6435
0,9032
1,0622
0,9354
0,9986
1,0365
91 - 95
0,4523
0,7183
1,0003
0,9831
1,1332
0,9424
1,2783
96 - 00
0, 5074
0,6259
0,9145
0,8441
0,8672
0,8557
1,5964
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 not stationary during the five subperiods. The statistically different from zero are found for three sub-portfolio in the second and one for the respective sub-portfolios 1, 4 and 5, all other cases the hypothesis of nullity of the intercept of the CAPM is confirmed. In the work of BJS beta followed a negative trend for risky portfolios, and readings are positive and statistically significant in the case of portfolios less risky assumption that, with some exceptions, is also confirmed in this analysis. The R2 results goes from a 0,5321 in the portfolio 1 to a 0,7944 in the portfolio 7. In the middle, the results follow the pattern: from the lowest level (1) to the highest (7)
6.1. The results of the cross-section analysis
To better examine the results and check the linearity of the equation of the CAPM is used to test cross-sectional through which you can investigate the linearity of the predicted risk-return relationship. In addition to the formula to yield full, you can use the equation to yield in excess of:
Where Rpt is the return of the i-th title of period t, Rmt is the return on the market index over the same period and FRG is the efficiency of risk-free rate at time t. always
To check the validity of previous results (and consistent) making a second regression between the average returns of portfolios Rj = 1 / N Σ RJT (where T j are the portfolios and the months of the time) and estimated by βj the previous regression, obtaining the following equation:
whole period
Subperiod
1/85- 12/05
85 - 90
91 - 95
96 - 00
01 - 05
Ï’0
0,016043*
0,02215
-0,00005
0,031
0,000312
Rf
0,000245
0,000356
0,00094
0,00311
0,00264
Ï’1
0,000031
-0,00002
0,00073
0,0079
0,009452
Rm
0,001136
0,001976
0,00009
0,02806
0,000023
MRP = Rm - Rf
0,001698
0,01028
-0,009232
0,00243
-0,00452
t (Ï’o)
3,5782
1,874
-0,4301
2,4512
0,00256
t (Ï’1)
0,1922
-0,00375
0,5867
0,56341
1,15131
R2
0,00469
0, 000003
0,00358
0,0092
0,32675
Both the table is easy to see from the graphs that for the entire period and for the first sub-intercept is statistically different from zero. The equality between the market rate of return estimated and observed is never statistically significant, and also for the entire period, the line is almost flat
Cross - section graph analysis of 85 - 05
Cross - section graph analysis of 85 - 90
In the first and second subperid ​​assume even negative value, and at other times the slope as well as positive although not statistically significant, show insignificant R2. These results are quite bizarre and merit further analysis, especially given the relationship Beta / R2, but the first symptom that the CAPM model does not follow too well the Italian market.
Cross - section graph analysis of 91 -95
Cross - section graph analysis of 96 - 00
Cross - section graph analysis 01 - 05
The highest value of the coefficient of determination is recorded in the first (25.78%) and fifth subunit (21.61%). E 'in that it could not exclude the proper functioning of the linear model considered in the report.
Even with more robust statistically, a similar situation is also reflected in the work of BJS although the number of securities that form the 10 portfolios is much wider (from 582 in 1931 to 1094 in 1965). In particular, in their fourth subperiod the beta is negative. The estimated market rate of return is lower, and statistically significant compared to that observed during the whole period. In this work, the risk premium the market is good for the entire period and for other 2 subunits, in contrast, is negative for two subperiods including one in which the model expresses a certain linearity that not exclude the proper application. Thus, this model is not necessarily wrong, as applied to the Italian market, but at least inaccurate and require further analysis.
6.2. The results obtained by the three-factor model
The sample used to test the Fama-French model is the same as described above with the exception that the time horizon is reduced to fifteen years (1990-2005) because of the unavailability of financial information of the company prior the period under review. Each year the securities were classified according to their market value to form four groups discriminated against in relation to size from each group were obtained four portfolios based on the ratio BE / ME for a total of sixteen portfolios. In June of each year, coinciding with the availability of accounting data for each of the sixteen portfolios we calculated the average monthly yield as the average yield of securities belonging to the portfolio for the next twelve months starting from July of t to June of
t +1. Calculated the returns of the portfolios for the entire range investigated (fifteen years), we regressed the returns of each portfolio compared to the market resulting in the post-ranking beta.
For the variable size, as mentioned, reference 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 estimate the risk premium of the market was finally used the monthly return of the three-month Treasury bills as the risk free rate. The portfolios are formed according to an ascending order of magnitude of the two variables. The study of Fama and French (1992), used 25 portfolios in this work, so I decided to construct 10 portfolios to address the lack of data makes it more reliable analysis.
Table 3: yields and risk premiums monthly portfolios of the three - factor model (1990 - 2005)
As shown in the table, increasing the size of the portfolio returns diminish, and this does not reject the hypothesis of an inverse relationship between returns and size. The risk premium assumes decreasing values ​​depending on the size portfolios and for the last two readings are negative.
From the results obtained, it is easy to see how the beta showing all statistically significant and almost half of the intercepts (7 out of 16) are statistically different from
zero at a confidence level of 5%.
The coefficients of determination values ​​assume little relevance to the portfolios with lower market values, while they are higher for portfolios with high market values. However, something very unusual is the fact that the portfolios of larger profiles are characterized by riskier, and conversely, the smaller companies seem to qualify for the lowest risk. The coefficient of the size factor is almost always statistically significant, it would seem then assume a proper role in the extent to which it adds or subtracts to the performance of portfolio excess returns.
Intercepts but two were never significantly different from zero and the beta, all
statistically significant, does not decrease as the size, but rather increase, and do not seem to follow particular trends with increasing book-to-market value. The value of the coefficient are almost always statistically significant, decrease as the size, in some cases is negative. On the contrary, did not suggest definite relationship between the coefficient and the ratio BE / ME. Only the second and third book takes on a nearly linear trend. The parameter μ, then representing the coefficient of HML variable, taking values ​​mostly significant for portfolios characterized by higher values ​​of BE / ME.
7. Conclusions
The Capital Asset Pricing Model and the three-factor model were investigated in this work. The results suggest, however, some caution in drawing conclusions, and for the limited number of securities considered to be the time horizon over which it was possible to investigate the extent of which is lower than that of other studies.
Regarding the verification of the CAPM following the methodology proposed by BJS, the results appear quite encouraging in terms of risk-return relationship. Cross-sectional analysis did not suggest a strong relationship between beta and returns of the portfolios and the values ​​recorded by the coefficient of determination show a relationship
very weak for all periods. The market risk premium assumed in some cases negative interception, except in two cases, it is never significantly different from zero. It 'should however be noted that the value of the coefficient of determination of the fifth subunit (21.61%) findings, despite the lack of significance of the parameters, not to exclude the proper functioning of the linear model considered in the report. Although statistically more robust results with similar situations are also found in the work of BJS although the number of securities that form the 10 portfolios is much wider (from 582 in 1931 a1094 in 1965). In particular, in their fourth subperiod the beta is negative. The estimated market rate of return is lower, and statistically significant, than those observed during the whole period.
Apparently the most interesting results were obtained by applying the three-factor model. In this case the variable size accompanied the beta seems to have more explanatory power. The beta, all statistically significant, not decrease as the size, but rather increase, and do not seem to follow particular trends with increasing book-to-market value. The values ​​of coefficient "lambda" are almost always statistically significant, decrease with increasing size, indicating a higher risk premium for riskier securities as predicted by CAPM. In such circumstances, including the portfolio returns, with some exceptions, fall, and this does not reject the hypothesis of a relationship between returns and size. As for the relationship between earnings and BE / ME there are no linear trends as in the work of Fama and French (1992).
This work also confirms the tendency of beta to grow with increasing size as measured by market capitalization, it also confirms the importance of the size factor in explaining bond yields. The achievements of the three-factor model, therefore, seem to confirm the existence of additional factors that can explain the returns. And this is not the only work that expresses concerns about the empirical validity of CAPM, the results produced by the international literature are quite obvious in spite of numerous efforts by supporters to defend the model.
Even in Italy the results are not unique in emphasizing clearly different positions: some works confirm the validity of Capital Asset Pricing Model. On the other hand a theoretical framework so weakened by strong empirical evidence that they have no theoretical support, and no specific position in the paradigm of risk - return, causing skepticism. This evidence, however, if further confirmed causing serious damage to the CAPM, since the criterion for estimating the cost of equity capital most common in all countries of the world (Graham and Harvey, 2001).
Proponents of the CAPM are defended by attributing the cause of non-linearity of the model several factors, including statistical sampling errors, selection bias, the patterns of data mining, the irrationality of the markets, the latter situation that is increasingly finding space in the scientific community (Kahneman and Tversky, 1974, Shiller, 2000). The idea of ​​data mining is actually rather taken into account by Black (1993) which proposes the analysis conducted by BJS for the same period is similar but not identical. Extending the analysis to 1991, he is weaker than the values ​​obtained during the period 1931-1965, stocks with a record low beta securities with higher yields high beta. He believes, however, that the frequency with which the low-beta securities "do better" of the riskiest securities is the same, considering, therefore, untimely "death" of the CAPM. through regression analysis, is the indicator of risk to which the majority relies on financial analysts' Italian (AIAF, 2001).
Do not forget that the model is widely adopted not only for the risk-return analysis of stocks, which provide a contribution of exceptional importance in understanding the logic of the pricing of risky assets, on the contrary,
suitable for many applications in the field of financial analysis. Just think of the increasingly widespread use of methods based on discounted cash flow analysis for the evaluation of investment projects both public and private, with equal frequency, however, the same method is used in the evaluation of the economic capital of the company. In each case, the discount rate used to discount cash flows, which is unlevered levered, is calculated according to the cost of equity capital.
Ultimately, therefore, the results presented in this study are preliminary and suggest further study, which will be more robust confirm or deny the thoughts contained herein.
Sources
H. Markowitz, "Portfolio Selection", in Journal of Finance, Vol. VII, n.1, March 1952, pp. 77- 91.
