Testing the efficiency of markets : analyst recommendations as an investment tool in the United States

(1)

Faculty of Economics and Business

Bachelors’ Thesis

Testing the efficiency of markets: Analyst

recommendations as an investment tool

in the United States

By

Tugay Akbulut 10807349

Supervisor: MSc Pascal Golec

University of Amsterdam

(2)

2 Statement of Originality

This document is written by Student Tugay Akbulut who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

3

Abstract

The efficiency of markets is tested based on analyst recommendations on stocks for the period 1993-2017. Multiple strategies based on these recommendations are used. By buying the highest recommended stocks and selling the worst recommended stocks we find monthly abnormal returns of 0.011% for the period 1993-1999. Following the same strategy for the period 2000-2017, we find monthly abnormal returns of 0.017%. For both periods we use portfolios which are rebalanced every month. We show that these abnormal returns seem to persist over time. Comparing the periods 1993-1999 with 2011-2017 we show that markets became even more inefficient. We further note that the financial crisis of 2007-2008 did not impact the abnormal returns found by analysts. We conclude that markets do not incorporate all publicly available information in the stock prices. Information on analyst

(4)

4

1. Introduction

The efficient market hypothesis (EMH) is still a very important subject for scientific research. In 2013, Eugene Fama received the Nobel Prize in Economics for his contributions to the EMH. In the same year, however, Robert Shiller also received the Nobel Prize in Economics by challenging the EMH. This hypothesis indicates that in an efficient market stocks already reflect all available information (Malkiel & Fama, 1970). If movements of stock prices were predictable, this would be evidence against the efficiency of the stock market (Bodie, Kane & Marcus, 2014).

This paper uses the recommendations analysts give to stocks in the US to test the efficiency of markets. Analyst recommendations are publicly available information which can be used by any investor. We use recommendations of analysts in the largest brokerage houses and from local brokers. These analysts give stocks a rating between 1 and 5, where a rating of 1 means a strong buy, a 2 stands for a buy, 3 for a hold, 4 for a sell and a rating of 5 stands for a strong sell.

The main focus in this thesis is on the question if investors can earn abnormal returns when using analyst recommendations. Many papers at the end of the 20th century have shown that following analyst recommendations yield significant abnormal returns. This thesis compares the abnormal returns found in the years before 2000 with the abnormal returns after 2000. We test if following analyst recommendations with a monthly rebalancing of portfolios is still a viable strategy for investors.

Stocks are ranked in different portfolios based on the recommendations analysts give to these stocks. Eight portfolios are made with different strategies, which are explained in the

“Methodology and Data“ section. The highest rated stocks are compared to the worst rated stocks to see if there are any abnormal returns to be earned in the 21st century.

The efficiency of markets will be investigated by investing in these portfolios. Malkiel and Fama (1970) have shown that when markets are efficient, there should be no abnormal returns after adjusting for risk. However, Grossman and Stiglitz (1980) argued that markets are not fully efficient. This would mean that there would be some abnormal returns available to investors to profit from.

(6)

6 The next section will go through previous studies done on the efficiency of markets and we discuss the papers on investment strategies with analyst recommendations. Our methodology and regressions are explained in the third section. Further, here we explain our datasets and form our hypotheses. This section is followed by the results of our analysis. The discussion of these results will follow and that will lead to our conclusions.

2. Literature Review

This section discusses previous studies based on the efficiency of markets and on the usefulness of analyst recommendations when investing in stocks. Most results on the

efficiency of markets, which analyzed analyst recommendations, have different conclusions. Moreover, most papers in the years before 2000 conclude that there are significant abnormal returns to be made. We want to analyze this for the years after 2000 and see if there is any persistency in strategies based on analyst recommendations.

To be able to discuss and understand the theory behind using analyst recommendations as an investment tool, we first go through some papers about efficient markets. We then discuss papers based on strategies with analyst recommendations. For these papers not only the results are given, but the strategies used in the papers are stated too. After this sub-section we highlight tail events and we end this section with papers about the self-destruction of

strategies.

2.1 Efficiency of markets

Malkiel and Fama (1970) divide the efficiency of markets in three categories. First, Strong-Form tests look at whether stock prices reflect all information, including information of investors who have monopolistic access to this information. Second, Semi-Strong-Form tests are concerned with stock prices reflecting information that is publicly available to all

investors. Third, Weak-Form tests look at whether stock prices reflect historical price information. Malkiel and Fama (1970) have shown that there is strong evidence of Weak-Form and Semi-Strong-Weak-Form market efficiency.

However, Grossman and Stiglitz (1980) have shown that market efficiency is inconsistent when information is costly and argue against the findings of Malkiel and Fama (1970). They state that prices cannot reflect all available information. When markets always reflect all

(7)

7 available information, informed traders could not use their information to make a profit

(Grossman & Stiglitz, 1980). Traders will then stop paying for information, as it will not give any return. Analysts will then not be compensated for their efforts to find new information. This situation, however, cannot be an equilibrium as without any information in the market the competitive markets will break down (Grossman & Stiglitz, 1980).

2.2 Level and changes of analyst recommendations

Barber, Lehavy, McNichols & Trueman (2001) have shown that purchasing stocks with the best consensus recommendations and selling short the stocks with the worst consensus recommendations, together with daily portfolio rebalancing, yield an annual abnormal return of over four percent in the period 1985-1996. Rebalancing the portfolio less frequently will diminish these returns, but stays significant for the least favorable stocks (Barber et al., 2001). These results are found after controlling the returns for market risk and the three Fama-French Factors (Fama & French, 2003). These three factors are size, book-to-market and price

momentum effects.

Barber et al. (2001) state that their results are evidence that the EMH of Malkiel and Fama (1970) does not hold and that the market is Semi-Strong inefficient before accounting for transaction costs. After accounting for these costs, Barber et al. (2001) show that the abnormal returns found earlier are not significantly greater than zero.

Womack (1996) analyzed the pre-recommendation stock prices and their eventual values. He shows that the prices have a post-event drift. For buy recommendations this drift is +2.4% over the first month and for sell recommendations this drift is -9.1% over six months.

Moreover, Womack (1996) found significant initial prices changes. He finds that these prices are significantly influenced by changes in the recommendation rates given by analysts. He documented an average price increase of +3.0% for buy recommendations and a decline of -4.7% for sell recommendations for the three days centering around the recommendation change. The abnormal returns found by Womack (1996) are still significant after accounting for transaction costs. Womack (1996) concludes that analysts, therefore, are able to time the market and pick the right stocks.

Although the strategy of Barber et al. (2001) and Womack (1996) differ slightly, they both use analyst recommendations as their basis of investing. In contrast to the results found by Womack (1996), the results of Barber at al. (2001) indicate that abnormal returns disappeared

(8)

8 after accounting for transaction costs. This could be explained by the results of Malkiel

(2003), Shiller (2003) and Granger and Timmerman (2004). They have shown that strategies tend to self-destruct when these strategies are publicly known by investors. These papers and the self-destruction of strategies are further explained in sub-section 2.4.

Womack (1996) further states that immediate market reactions to changes in the recommendations are permanent and not mean-reverting. He states that analyst

recommendations are valuable information for investors and analysts have to be compensated for this. This results in direct evidence in favor of the results of Grossman and Stiglitz (1980) where informed traders have to be compensated for valuable information (Womack, 1996). In 2010, Barber, Lehavy and Trueman (2010) have shown that abnormal returns come both from the level of analyst recommendations as well as the change in these recommendations. This is exactly what Womack (1996) has shown too. Barber et al. (2010) show that when only taking into account recommendation levels, buying stocks with a buy or strong buy rating and shorting stocks with a sell or strong sell rating results in an average daily abnormal return of 3.5 basispoints. Making portfolios based on recommendation changes, buying stocks which received a double upgrade in their recommendation and selling stocks which received a double downgrade results in an average daily return of 3.8 basispoints.

Barber et al. (2010) conclude that analyst recommendations have predictive power and the results reflect the fact that analysts have the skill to choose the right stocks. This goes against the EMH.

Elton, Gruber & Grossman (1986) investigate the dataset of analyst recommendations and find that there are abnormal returns to be made when looking at the change in analyst recommendations. They found a two-month post-event drift (Elton et al., 1986). They show that instead of looking at the level of recommendation levels, using changes in

recommendation levels are giving a higher excess return (Elton et al., 1986). These results correspond to the results of Barber et al. (2010). They have shown that changes in analyst recommendations have investment value too.

Stickel (1995) states that analysts are able to pick the stocks which are under- or overvalued. He has shown that price changes based on the strength of a recommendation and on earnings forecast revisions are information effects that are permanent. Following the conclusions of Grossman and Stiglitz (1980), analysts should be compensated for this with abnormal returns. Furthermore, changes in recommendations that upgrade the rating two ranks have greater

(9)

9 price effects than changes in recommendations where the rating goes up by one rank and these differences are temporary (Stickel, 1995). Moreover, Stickel (1995) shows that analysts who have a better reputation can influence the stock prices more.

Jegadeesh, Kim, Krische & Lee (2004) have found that analysts’ recommendations only have value for stocks of firms which have favorable characteristics. These are, for instance, higher turnover, higher past growth and positive accounting accruals (Jegadeesh et al., 2004). Jegadeesh et al. (2004) show that for stocks of firms which do not have these favorable characteristics, higher recommendations result in worse returns.

Another point Jegadeesh et al. (2004) have shown is that recommendations and

recommendation levels themselves can be the reason for the price drift of stocks. This comes from the fact that stocks with a high buy rating receive more publicity. Jegadeesh et al. (2004) state that analysts do not bring new information about stocks to the market when the price drift comes from the recommendations itself. This is in line with the EMH of Malkiel and Fama (1970). However, the opposite result was found by Womack (1996) where he stated that analyst recommendations are valuable information for investors.

2.3 Tail events

In 2003, however, Barber, Lehavy, McNichols and Trueman (2003) have shown that stocks with the lowest analyst recommendations earned an annualized return of 13.44 percent. Stocks with the highest recommendations, however, underperformed the market by 7.06 percent (Barber et al., 2003). These returns are found over the years 2000 and 2001 and they are exactly the opposite as the results they have shown before for the years between 1985 and 1996 (Barber et al., 2001).

They found these results, because analysts kept recommending small-cap growth stocks during the years 2000 and 2001 when these stocks underperformed the market (Barber et al., 2003). Barber et al. (2003) state that one of the reasons for this result could be that analysts continued to recommend small-cap growth firms because of their greater investment banking business in the future. These findings put the usefulness of analyst recommendations at question.

(10)

10 2.4 Self-destruction of strategies

Malkiel (2003) argued that if there were any strategies in the stock market that would earn abnormal returns with information that is publicly available, these strategies would be arbitraged away and the strategies will self-destruct. Strategies based on publicly available information that earn abnormal returns will not persist for long (Malkiel, 2003). Shiller (2003) and Granger and Timmerman (2004) also found that abnormal returns tend to disappear with the passage of time and these returns would not persist in the market. Patterns in the market will not persist for long and will indeed self-destruct when followed by many investors (Granger & Timmerman, 2004).

Based on the conclusions of Malkiel (2003), Shiller (2003) and Granger and Timmerman (2004), the abnormal returns found by previous papers would not persist. Strategies that lead to abnormal returns should be arbitraged away as more investors get to know these strategies. However, Avramov, Cheng, & Hameed (2016) found that strategies based on momentum earn large profits in the most liquid markets and that, while people know about these strategies, it still persists in the market. This goes against the conclusions of Malkiel (2003), Shiller (2003) and Granger and Timmerman (2004).

The next section explains the methods used in this paper to test for the efficiency of the markets while taking into account analyst recommendations.

3. Methodology and Data

This thesis focuses on two periods and two sub-periods. The first period ranges from 1993 through 1999 and the second period ranges from 2000 through 2017. We also analyze the sub-period 2011-2017 and 2004-2009. These two main sub-periods are chosen, because many papers like Barber et al. (2001), Womack (1996) and Jegadeesh et al. (2004) found abnormal returns for datasets before the year 2000. Therefore, we are going to test this for the years after 2000 and compare the results. The data in 1993 starts from November due to the availability of this data.

The sub-period 2011-2017 is chosen to test the most recent data on analyst recommendations for abnormal returns. Further, the sub-period 2004-2009 is tested to see the effects of the

(11)

11 financial crisis on analyst recommendations. We capture three years before the crisis and three years after the start of the crisis in 2007 with this sub-period. We now start with formulating our hypotheses.

3.1 Hypotheses

With the rise of the computer and the technology we expect that it becomes easier to capture abnormal returns after 2000. Moreover, Langevoort (2009) states that the number of

institutional investors increased a lot in the United States. This would mean that abnormal returns would quickly disappear from the market as more institutions are active. Following the reasoning of Malkiel (2003), Shiller (2003) and Granger and Timmerman (2004), this suggests that abnormal returns would not persist in the market as more investors get to know about the available abnormal returns. This lead to the following hypotheses:

𝐻₀: 𝛼 = 0 𝐻1: 𝛼 ≠ 0

These hypotheses are tested over the two periods 1993-1999 and 2000-2017 and the sub-periods 2011-2017 and 2004-2009, while investing in different portfolios. To elaborate on the the sub-period 2004-2009, we expect that analysts are less aggressive with recommending stocks during the crisis and that this will lead to abnormal returns equal to zero.

The methods used to test these hypotheses are explained below. 3.2 Datasets and Portfolio construction

3.2.1 Consensus recommendations

The analyst recommendations used in this thesis are from the IBES database. The dataset used contains recommendations of more than 17,000 US firms and range from 1993 through 2017. The IBES database is made using data from the largest global brokerage houses and from regional and local brokers. The database includes recommendations of individual analysts per month for each firm in the US. A recommendation is a rating between 1 and 5. A rating of 1 stands for a strong buy recommendation, 2 stands for a buy, 3 for a hold, 4 for a sell and 5 for a strong sell. This is the most commonly used scale by analysts.

This thesis uses the consensus recommendations per month for each firm. The consensus recommendation is calculated as follows. The individual recommendations given by each analyst are summed up for each firm in every month. This number is then divided by the

(12)

12 number of analysts that have given a recommendation for that specific month. This gives the consensus recommendation:

𝐶𝑜𝑛𝑠𝑒𝑛𝑠𝑢𝑠 𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑎𝑡𝑖𝑜𝑛: 𝐴_𝑖𝑇 = 1

𝑛_𝑖𝑇∑ 𝐴𝑖𝑗𝑇

𝑛𝑖𝑇

𝑗=1

The database did include duplicates which were dropped from the dataset. After dropping these there were 397,690 observations of consensus recommendations left for the years 1993 through 1999 and 1,008,989 observations of these recommendations for the years 2000 through 2017. The mean consensus recommendation for the years 1993-1999 was 2.1115 and for the years 2000-2017 the mean was 2.2790.

Using the method of Barber et al. (2001), the firms are then divided into five portfolios based on their consensus recommendations. The first portfolio contains the best recommended stocks by the analysts. These stocks have a consensus recommendation between 1 ≤ AiT < 1.5;

for the second portfolio the stocks have a recommendation between 1.5 ≤ AiT < 2; the third

consists of stocks with 2 ≤ AiT < 2.5; for the fourth it is 2.5 ≤ AiT < 3 and for the final portfolio

the recommendation is between 3 ≤ AiT ≤ 5. These five portfolios are made for each month,

which means that for every month there is a rebalancing of portfolios. The portfolios are called P1, P2, P3, P4 and P5, respectively.

3.2.2 Monthly stock returns

The monthly stock returns are taken from the CRSP database. The CRSP database has

monthly data for each stock in the US. This thesis uses the monthly holding period returns for each stock. By using these holding period returns, the five portfolios made above can be evaluated. The monthly returns of the stocks per portfolio are calculated on an equally-weighted basis. This way the focus will not be only on the firms with a large market capitalization, but all firms in the US are taken into account equally.

3.2.3 Merging datasets

As we merged the IBES dataset with the CRSP dataset, we found that for some firms there were no recommendations given by analysts for some months. To be able to merge these two datasets we dropped the observations for the months where there were monthly return data available, but without a corresponding recommendation. We did the same for observations

(13)

13 where there were recommendations given, but without a corresponding monthly return. This left us with 279,600 observations for the period 1993-1999 and 569,009 observations for the period 2000-2017.

3.3 Strategies

Eight strategies will be tested for abnormal returns. The first strategy is going long in P1 and P2. The second strategy is going long in P1 and going short in P5. The third strategy is buying P1 and P2 and selling P5. The final five strategies are buying the individual portfolios

separately.

3.4 Portfolio evaluation and Regressions

The regressions used in this thesis are based on the methodology of Barber et al. (2001). First, we calculate the market-adjusted returns (Rp - Rm) for both periods to determine if the

portfolios outperformed the market during these periods. Rp is the return of portfolio p and Rm

is the average return on all NYSE, AMEX, and NASDAQ stocks taken from the CRSP database.

Second, following the methodology of Barber et al. (2001), multiple regressions are used to evaluate whether our different strategies have abnormal returns over the two periods. The regression model used is the Carhart four-factor model. This model consists of the two factors SMB and HML found by Fama and French (1993) and adds a third factor, MOM, found by Carhart (1997). The regression is given as follows:

(1) 𝑅_𝑝− 𝑅_𝑓= 𝛼_𝑝+ 𝛽_𝑝1(𝑅_𝑚− 𝑅_𝑓) + 𝛽_𝑝2(𝑆𝑀𝐵_𝑡) + 𝛽_𝑝3_{(𝐻𝑀𝐿}

𝑡) + 𝛽𝑝4(𝑀𝑂𝑀𝑡) + 𝜀𝑖

(14)

14 The variables used in our regression are as follows:

𝑅𝑝𝑡 = 𝑅_𝑓𝑡 = 𝛼𝑝 = 𝛽_𝑝 = 𝑅𝑚𝑡 = 𝜀𝑝𝑡 = 𝑆𝑀𝐵_𝑡 = 𝐻𝑀𝐿_𝑡 = 𝑀𝑂𝑀𝑡 =

The return of portfolio p in month t. The one-month Treasury bill rate.

The estimate of the abnormal return for portfolio p. The estimate of the market beta.

The average return on all NYSE, AMEX, and NASDAQ stocks. The error term of the regression.

The difference between the average return of small capitalization firms and large capitalization firms.

The difference between the average return of high book-to-market stocks and low book-to-market stocks.

The difference between the average return of stocks with good past 12-month performance and stocks with a bad past 12-12-month performance.

This regression gives us the estimates for the parameters: 𝛼𝑝, 𝛽𝑝1, 𝛽𝑝2, 𝛽𝑝3 and 𝛽𝑝4.

To elaborate on the use of the momentum factor in our regression besides the well known Fama and French (1993) factors SMB and HML has to do with our rebalancing period of one month. As we rebalance our portfolio every month, there could be some momentum in the stock prices in those months. To get more reliable abnormal returns from our regressions we control for this factor too.

3.5 Descriptive statistics

We now show some statistics of the five portfolios we have made. For each of these five ranked portfolios we state the number of observations, the average monthly returns and the standard deviation of these monthly returns. In the last row we give the total results for all portfolios together. These statistics are given in table 1 and table 2 below.

(15)

15

Table 1

Portfolio information for the period 1993-1999

This table consists of statistics of the five portfolios made based on consensus recommendations for the years 1993-1999. First, it reports the number of observations each portfolio has over this period. An observation is a consensus recommendation for any month given to a firm. For instance, the number of observations for portfolio 1 states that 45,167 monthly returns are included in this portfolio. This also means that 45,167 consensus recommendations are used for portfolio 1. Second, the table reports the average monthly returns per portfolio over this period. Finally, the standard deviation of these monthly returns is given in the final column. The final row calculates the statistics for all portfolios together.

Portfolio Number of observations Average monthly returns St. dev. average monthly returns 1 (best recommended) 45,167 0.0186 0.0569 2 59,654 0.0170 0.0539 3 92,342 0.0115 0.0456 4 41,048 0.0075 0.0442 5 (worst recommended) 41,389 0.0044 0.0455 Total 279,600 0.0125 0.0511 Table 2

Portfolio information for the period 2000-2017

This table consists of statistics of the five portfolios made based on consensus recommendations for the period 2000-2017. First, the number of observations for each portfolio is given. Second, the average monthly returns per portfolio in this period are given. Third, the standard deviation of these monthly returns is shown in the final column. The final row calculates the statistics for all portfolios together.

Portfolio Number of observations Average monthly returns St. dev. average monthly returns 1 (best recommended) 49,462 0.0158 0.0566 2 98,817 0.0135 0.0560 3 201,787 0.0104 0.0542 4 113,723 0.0071 0.0578 5 (worst recommended) 105,220 0.0055 0.0599 Total 569,009 0.0095 0.0568

It can be seen that there are more observations for the higher recommended portfolios in the period 1993-1999. However, in the period 2000-2017 the observations of the worst

(16)

16 recommended portfolios increased relative to the highest recommended portfolio. For the period 1993-1999, this suggests that analysts are more likely to give firms a higher recommendation. However, for the period after 2000 more recommendations were bad recommendations.

For the years 1993-1999, this observation is in line with the results of Womack (1996) and Barber et al. (2001). They state that analysts are reluctant to issue bad recommendations to larger firms. This is because a bad recommendation issued to these firms will cost money (Barber et al., 2001). These firms are candidates that will generate investment opportunities in the future and by issuing a bad recommendation brokerage houses might lose this client (Womack, 1996). This conclusion is in line with our findings for the years 1993-1999. For the years 2000-2017, however, relatively more bad recommendations are issued and this goes against the findings of Womack (1996) and Barber et al. (2001). This could be due to the increased transparency of information because of the rise in the technology used in computers at the start of the 21st_century.

Moreover, portfolio 1 gives the highest average monthly returns in both periods. This shows that the highest recommended stocks have the highest returns. The standard deviations of these returns are almost the same for all portfolios in both periods.

3.6 The effect of the financial crisis on analyst recommendations

To test whether the financial crisis of 2007-2008 influenced the recommendations given by analysts we look at three years before the crisis and the three years from 2007 onwards. This period thus covers the years from 2004 to 2009. For this sub-period we test for the abnormal returns found in two portfolios: the best recommended portfolio and the worst recommended portfolio.

We use the same regression as we explained in part 3.4, but now we include dummy variables. The regression becomes:

(2) 𝑅_𝑝− 𝑅_𝑓 = 𝛼_𝑝+ 𝐷_𝑐∗ 𝛽_𝑝0_{+ 𝛽}

𝑝1(𝑅𝑚− 𝑅𝑓) + 𝐷𝑐 ∗ 𝛽𝑝2(𝑅𝑚− 𝑅𝑓) + 𝛽𝑝3(𝑆𝑀𝐵𝑡) +

𝐷𝑐∗ 𝛽𝑝4(𝑆𝑀𝐵𝑡) + 𝛽𝑝5(𝐻𝑀𝐿𝑡) + 𝐷𝑐∗ 𝛽𝑝6(𝐻𝑀𝐿𝑡) + 𝛽𝑝7(𝑀𝑂𝑀𝑡) +

𝐷_𝑐∗ 𝛽_𝑝8_{(𝑀𝑂𝑀}

(17)

17

Dc is the dummy variable that is equal to one during the financial crisis and equal to zero

before the crisis. When this dummy variable is equal to one, we get the coefficients of our risk factors during the crisis. If these coefficients are significant, the crisis has a significant effect on our factors when comparing the years before and the years during the crisis.

The most important variable we are looking at is 𝛽𝑝0. This variable shows whether the

financial crisis has a significant effect on the abnormal returns we find.

3.7 Heteroskedasticity and autocorrelation

To get unbiased and efficient estimates in our regressions we need to check for

heteroskedasticity and autocorrelation in our results. All regressions made are tested for heteroskedasticity with the White test (White, 1980). This is a test that checks whether the variance of the error terms is correlated to the explanatory variables (Stock & Watson, 2015). The residuals are also tested on autocorrelation with the Breusch-Godfrey test (Breusch, 1978) (Godfrey, 1978). This test checks whether there is a relation in the residuals with residuals from the past (Stock & Watson, 2015). To solve these potential problems, we refer to the Appendix.

4. Results

In this section the results of the regressions of all portfolios made based on analyst

recommendations are given for the two periods and the two sub-periods. The portfolios we use are rebalanced every month. These results are already corrected for possible

autocorrelation and heteroskedasticity in the data. The results of the tests for these two issues are found in the Appendix. First, we show the results for the period 1993-1999 in table 3. In table 4 the results for the period 2000-2017 are given. Table 5 shows the results for the sub-period 2011-2017 and table 6 shows the results for the sub-sub-period 2004-2009. We end this section with the mean raw returns and the market-adjusted returns of the highest ranked to the lowest ranked portfolios in table 7 an 8.

(18)

18 4.1 The two main periods: 1993-1999 and 2000-2017

We start with showing our results of the two main periods we analyze. First, we show the regression results for the period 1993-1999 in table 3. Then we show the results for the period 2000-2017 in table 4.

Table 3 Regression results 1993-1999

This table shows the regression coefficients of the eight strategies used for the period 1993-1999. The first column contains the strategies. P stands for portfolio, where P1 is the portfolio with the best recommended stocks and P5 the portfolio with the worst recommended stocks. The second column gives the abnormal returns per strategy over this period. The third to sixth column show the coefficient estimates of the four factors in the Carhart four-factor model. The final column states the R2_{for each strategy. The t-values are given below the}

coefficient estimates. The standard errors are not given, as the standard error for the main coefficient we are analyzing (α) is too small. We see the t-value as a more informative statistic here. The t-values are calculated for the null hypothesis that the coefficient is equal to zero. (*) is for a significance level of 10%, (**) for a

significance level of 5% and (***) for a significance level of 1%. Number of observations: 74.

Portfolio strategy α Rm – Rf SMB HML MOM R2

P1 + P2 0.010*** (4.21) 2.181*** (34.92) 1.750*** (18.27) 0.005 (0.05) -0.226** (-2.19) 0.973 P1 – P5 0.005** (2.55) 0.243*** (4.65) 0.252*** (3.82) -0.093 (-0.95) 0.227*** (3.58) 0.572 (P1 + P2) – P5 0.011*** (3.88) 1.354*** (18.36) 0.998*** (10.71) -0.121 (-0.88) 0.080 (0.89) 0.910 P1 0.004*** (2.99) 1.069*** (26.08) 1.004*** (17.06) 0.033 (0.48) -0.080 (-1.32) 0.961 P2 0.002 (1.62) 1.109*** (41.78) 0.745*** (15.94) -0.033 (-0.53) -0.152*** (-3.00) 0.971 P3 -0.001 (-0.66) 0.987*** (27.15) 0.673*** (16.18) 0.179*** (3.67) -0.239*** (-4.92) 0.969 P4 -0.003* (-1.81) 0.940*** (26.06) 0.683*** (14.98) 0.289*** (4.28) -0.358*** (-8.18) 0.943 P5 -0.005* (-1.94) 0.824*** (13.27) 0.751*** (9.59) 0.121 (1.04) -0.312*** (-4.14) 0.842

From table 3 we can see that when going long in P1 and P2 together, we find a significant monthly abnormal return of 0.01%. Also, for the strategies going long in P1 and short in P5 we find monthly abnormal returns of 0.005%, which is again significant. The strategy of

(19)

19 taking a long position in P1 and P2, while shorting P5, gives the highest significant monthly abnormal returns of 0.011%. When looking at the individual portfolio strategies we see a clear pattern. The portfolio with the highest recommended stocks has the highest abnormal returns and the portfolio with the worst recommended stocks has the lowest (even negative) abnormal returns, both significant. The strategy of buying P2 or P3 does not yield any statistically significant abnormal returns. The values for R2 are high for all strategies, except for the strategy where we buy P1 and sell P5.

Table 4: Regression results 2000-2017

Portfolio strategy α Rm – Rf SMB HML MOM R2

P1 + P2 0.016*** (6.83) 1.994*** (27.00) 1.278*** (9.96) 0.061 (0.63) -0.119 (-1.62) 0.926 P1 – P5 0.009*** (5.72) 0.147*** (2.93) -0.096 (-1.51) -0.352*** (-5.12) 0.282*** (5.03) 0.438 (P1 + P2) – P5 0.017*** (6.99) 1.181*** (16.64) 0.497*** (4.82) -0.286*** (-2.97) 0.238*** (4.31) 0.767 P1 0.009*** (6.10) 0.960*** (21.13) 0.685*** (9.04) -0.004 (-0.07) -0.075 (-1.54) 0.894 P2 0.005*** (5.60) 1.040*** (33.65) 0.590*** (10.81) 0.056 (1.33) -0.043* (-1.69) 0.934 P3 0.003*** (3.23) 0.976*** (28.70) 0.539*** (10.26) 0.193*** (4.12) -0.158*** (-3.99) 0.948 P4 0.000 (-0.45) 0.947*** (28.30) 0.595*** (11.11) 0.299*** (5.96) -0.293*** (-5.28) 0.946 P5 -0.002 (-0.90) 0.819*** (11.82) 0.778*** (7.75) 0.338*** (4.39) -0.358*** (-3.74) 0.885

(20)

20 For the period 2000-2017 we see a monthly abnormal return of 0.016% when going long in P1 and P2, which is statistically significant. Buying P1 and selling P5 gives us a monthly abnormal return of 0.009%, which again is significant. The highest abnormal returns per month are earned by going long in P1 and P2 and shorting P5. This results in a statistically significant monthly abnormal return of 0.017%. When looking at the individual portfolio strategies, we again see a consistent decline of abnormal returns when going from the highest recommended stocks to the lowest recommended stocks. Buying P1, P2 or P3 result in positive statistically significant abnormal returns of 0.009%, 0.005% and 0.003%,

respectively. For the strategies where we buy P4 or P5 we do not have significant abnormal returns. The R2 values are again high, except for the strategy where we go long in P1 and short in P5.

When comparing the two periods we see that for the first three strategies, which consists of multiple portfolios, the monthly abnormal returns are significant in both periods. For the periods 2000-2017, however, these abnormal returns are higher. When looking at the

individual portfolio strategies, we see that buying P1 in the period 1993-1999 earns monthly abnormal returns of 0.004%. In the period 2000-2017, however, following the same strategy we see monthly abnormal returns that are more than twice as high, 0.009%. These results are significant in both periods. Following the strategy P2 gives us monthly abnormal returns of 0.005% in the period 2000-2017, which is significant. However, following this strategy in the period 1993-1999 does not give any significant abnormal returns. For P3 we see statistically significant monthly abnormal returns for the period 2000-2017. For 1993-1999 these

abnormal returns are not significant. Comparing P4 and P5, we see significant negative abnormal returns in the period 1993-1999, while in the second period these returns are not significant.

Looking at the R2 of the two periods, we see that the R2 in the period 2000-2017 is lower for the first six strategies compared to the first period. Only for the strategies where we invest in P4 or in P5 results in a higher R2 for the period 2000-2017.

4.2 Results of the most recent years: 2011-2017

Now we test the period 2011-2017 to see the results for the most recent years. We used the same period length as we used for the years 1993-1999. The results are shown in table 5 below.

(21)

21

Portfolio strategy α Rm – Rf SMB HML MOM R2 P1 + P2 0.011*** (2.81) 1.975*** (15.33) 1.902*** (11.96) -0.501*** (-2.92) -0.179 (-1.41) 0.892 P1 – P5 0.009*** (3.49) 0.140 (4.65) 0.379*** (3.39) -0.525*** (-4.34) 0.168* (1.89) 0.401 (P1 + P2) – P5 0.013*** (3.30) 1.188*** (8.71) 1.289*** (7.67) -0.761*** (-4.19) 0.070 (0.53) 0.744 P1 0.007*** (2.92) 0.927*** (11.80) 0.992*** (10.23) -0.265** (-2.53) -0.081 (-1.05) 0.841 P2 0.004** (2.13) 1.048*** (17.47) 0.910*** (12.31) -0.236*** (-2.95) -0.098 (-1.66) 0.909 P3 -0.001 (-0.71) 0.966*** (24.44) 0.620*** (11.46) -0.009 (-0.14) -0.152*** (-5.51) 0.959 P4 -0.003*** (-3.01) 0.977*** (32.33) 0.515*** (13.80) 0.141*** (3.49) -0.163*** (-5.49) 0.968 P5 -0.003* (-1.78) 0.787*** (15.27) 0.614*** (9.65) 0.261*** (3.80) -0.249*** (-4.92) 0.905

The results we find are surprising. Five of the eight strategies we test show significant abnormal returns for a significance level of 1%. This is in contrast to the period 1993-1999 where three of the eight strategies show abnormal returns with a 1% significance level. Overall, the period 2011-2017 shows higher or equal abnormal returns for all strategies compared to the period 1993-1999.

(22)

22 We see that the strategy of buying P1 and P2, while selling P5 gives an abnormal return of 0.013% per month, which is statistically significant at the 1% significance level. Moreover, this strategy gives the highest abnormal returns compared to the other strategies, as was the case in the other periods too. The strategies based on the worst recommendations, P4 and P5, do show negative abnormal returns of -0.003% per month for both periods, statistically significant for the 1% significance level for P4 and for the 10% significance level for P5. When comparing the R2 for the periods 1993-1999 and 2011-2017, we see that for the first five strategies the R2 has dropped significantly. For the sixth strategy, buying P3, the R2 is roughly the same. However, for the last two strategies based on buying the worst

recommended portfolios the R2 actually increased. For the strategy of buying P4 we see an increase of 0.025 in the R2. For buying P5 we see an increase of 0.063.

4.3 Effect of the financial crisis on analyst recommendations

In this section we show the results of our second regression. We test for the significance of the effect of the financial crisis on the recommendations analysts give to stocks. Due to the number of coefficients we get from the regression with dummy variables we restate the regression we formed in section 3.6 here.

(2) 𝑅_𝑝− 𝑅_𝑓 = 𝛼_𝑝+ 𝐷_𝑐∗ 𝛽_𝑝0+ 𝛽_𝑝1(𝑅_𝑚− 𝑅_𝑓) + 𝐷_𝑐 ∗ 𝛽_𝑝2(𝑅_𝑚− 𝑅_𝑓) + 𝛽_𝑝3(𝑆𝑀𝐵_𝑡) + 𝐷_𝑐∗ 𝛽_𝑝4(𝑆𝑀𝐵_𝑡) + 𝛽_𝑝5_{(𝐻𝑀𝐿}

𝑡) + 𝐷𝑐∗ 𝛽𝑝6(𝐻𝑀𝐿𝑡) + 𝛽𝑝7(𝑀𝑂𝑀𝑡) +

𝐷_𝑐∗ 𝛽_𝑝8_{(𝑀𝑂𝑀}

𝑡) + 𝜀𝑖

The results of this regression are shown in table 6. To maintain the overview of all coefficients, we divide table 6 in two parts. The coefficients where we use a dummy are grouped together. Panel A contains the coefficients of the variables without a dummy and Panel B contains the coefficients of the variables with a dummy. It is important to note that both panels are part of the whole regression.

(23)

23

Table 6 shows the regression coefficients of the two portfolios used for the period 2004-2009. We split these coefficient in two panels, A and B, to keep the overview of all 10 variables of the regression. The first column contains the strategies. P stands for portfolio, where P1 is the portfolio with the best recommended stocks and P5 the portfolio with the worst recommended stocks. The second column gives the abnormal returns per strategy over this period. The third to sixth column show the coefficient estimates of the four factors in the Carhart four-factor model. The final column states the R2_{for each strategy. The only difference in Panel A and Panel B is}

their independent variables. Panel A shows the independent variables without a dummy and Panel B shows the independent variables with a dummy. The t-values are given below the coefficient estimates. The standard errors are not given, as the standard error for the main coefficient we are analyzing (α) is too small. We see the t-value as a more informative statistic here. The t-values are calculated for the null hypothesis that the coefficient is equal to zero. (*) is for a significance level of 10%, (**) for a significance level of 5% and (***) for a significance level of 1%. Number of observations: 72.

Panel A Portfolio strategy α Rm – Rf SMB HML MOM P1 0.008*** (2.85) 0.972*** (5.99) 0.829*** (4.81) 0.193 (1.00) 0.069 (0.52) P5 -0.007*** (-3.31) 0.972*** (8.38) 0.557*** (4.52) 0.460*** (3.34) -0.128 (-1.34) Panel B Portfolio strategy α*D (Rm – Rf)*D SMB*D HML*D MOM*D R2 P1 -0.004 (-1.00) -0.014 (-0.08) -0.098 (-0.48) -0.511** (-2.46) -0.226 (-1.63) 0.945 P5 0.002 (0.79) -0.112 (-0.92) 0.028 (0.19) -0.020*** (-0.13) -0.220** (-2.22) 0.979

From table 8 we see that for the portfolio with the highest recommendations, P1, the effect of the financial crisis on abnormal returns is not significant at the 10% significance level. It has a t-value of -1.00 and the coefficient value is -0.004. The market factor, the small-minus-big factor and the momentum factor all show insignificant results as well. However, the high-minus-low factor does show a significant effect of the crisis with the coefficient being a negative value of -0.511% with a significance level of 5%.

In the period before the crisis, the portfolio P1 shows significant abnormal returns of 0.008% per month with a significance level of 1%.

(24)

24 For the portfolio with the worst recommendations, P5, we have similar results. The abnormal returns are not affected by the crisis. The value of 0.002 is not significant with a significance level of 10%. The factors HML and MOM are, however, significantly influenced by the financial crisis. Before the crisis we see significant negative abnormal returns of -0.007% with a significance level of 1%. Also, the market factor and the factors SMH and HML show significant values of 0.972, 0.557 and 0.460 before the crisis, respectively.

4.4 Raw returns and market-adjusted returns per portfolio

When looking from an investors point of view, we find it interesting to calculate the mean returns and the market-adjusted returns of our ranked portfolios based on recommendations over the periods 1993-1999, 2000-2017 and, for the most recent returns, 2011-2017. These are the monthly returns investors would get on average over the period. The results are given in table 7 and table 8.

Table 7: Mean raw returns

This table shows the mean monthly raw returns for the ranked portfolios. Portfolio 1 has the best

recommendations and portfolio 5 the worst recommendations. The returns are calculated for a rebalancing period of one month. Portfolio 1993-1999 2000-2017 2011-2017 1 (best recommended) 1.855% 1.580% 1.737% 2 1.701% 1.353% 1.593% 3 1.145% 1.039% 1.064% 4 0.748% 0.712% 0.909% 5 (worst recommended) 0.437% 0.547% 0.653%

(25)

25

Table 8: Mean market-adjusted returns

This table gives the mean market-adjusted returns earned per ranked portfolio. These returns are calculated as the mean raw returns from table 7 minus the value-weighted return on all NYSE/AMEX/NASDAQ stocks.

Portfolio 1993-1999 2000-2017 2011-2017 1 (best recommended) 0.111% 1.016% 0.479% 2 0.042% 0.789% 0.335% 3 -0.598% 0.475% -0.195% 4 -0.996% 0.147% -0.350% 5 (worst recommended) -1.306% -0.018% -0.606%

From the results in table 7 and table 8 we can see that the mean market-adjusted returns over the period 2000-2017 are significantly higher than the mean market-adjusted returns over 1993-1999. We see mean market-adjusted returns of 1.016% in the period 2000-2017for the best recommended portfolio, while for the period 1993-1999 the mean market-adjusted return is only 0.111%. For the worst recommended portfolio we see mean market-adjusted returns of -0.018% in the period 2000-2017, while for the period 1993-1999 this return was -1.306%. Moreover, when comparing the market-adjusted returns over the periods 1993-1999 and 2011-2017, we see that these returns are higher in the period 2011-2017 for every single portfolio.

5. Discussion

In this section we discuss the results we find compared to the results of previous research. We first go through the abnormal returns we find and compare these to the results of Barber et al. (2001). Then we discuss the publicity of stocks and their price drifts. We then look at the persistence of the abnormal returns and the financial crisis of 2007-2008. This is then

followed by the EMH and the Carhart four-factor model we used for our analysis. In the sub-section that follows we discuss the transaction costs that arise with monthly rebalancing and we end this section by discussing the market-adjusted returns.

(26)

26 5.1 Abnormal returns on most recommended stocks

The results we find are quite interesting. As Barber et al. (2001) have shown, purchasing stocks with the best recommendations and selling the stocks with the worst recommendations does give us statistically significant abnormal returns. They have also mentioned that

rebalancing less frequently compared to daily rebalancing would diminish these returns and would only stay significant for the least favorable stocks (Barber et al., 2001). When

rebalancing monthly, we find that the abnormal returns are indeed small. However, not only the least favorable stocks show statistically significant abnormal returns. The most

recommended stocks show abnormal returns which are significant as well. Moreover, the strategies of buying the portfolios with the best recommended stocks (P1+P2), buying the best recommended portfolio and selling the worst recommended portfolio (P1-P5) and buying the two best recommended portfolios while selling the worst recommended portfolio ((P1+P2)-P5) show abnormal returns which are significant. So, looking at the period after the years Barber et al. (2001) analyzed, we find not only statistically significant abnormal returns for the least favorable stocks when rebalancing monthly, but we see significant abnormal returns for the most recommended stocks too. This shows that abnormal returns for the highest rated stocks became significant after 1993. This might be due to the development of the technology and computers at the end of the 20th century. Analysts have more options to find abnormal returns. This development might be the reason why analysts were better in picking the right stocks and finding abnormal returns.

5.2 Publicity of stocks and their price drift

It seems that abnormal returns started to appear in the market after Barber et al. (2001) did their analysis. An important event in the period we tested is the dot-com bubble. As Jegadeesh et al. (2004) have shown, recommendations themselves can be the reason for price drifts of stocks and consequently for abnormal returns. During this period, stocks received more publicity which drove their prices up. This might be the reason for the statistically significant results we find. Indeed, the differences in our results with the results of Barber et al. (2001) are for the best recommended stocks, which received the most publicity.

Another reason for the fact that we see abnormal returns in the market is based on the conclusions of Womack (1996). He stated that prices are significantly influenced by

(27)

27 for buy recommendations and -9.1% over six months for sell recommendations after the recommendation is made (Womack, 1996). As our rebalancing period is one month, we are able to capture these drifts. For instance, the price drift of 2.4% per month for buy

recommendations would be captured in the time we rebalance again. This might explain why we find abnormal returns our analysis.

5.3 Persistence of abnormal returns and the financial crisis in 2007-2008

For the period 2000-2017 we see that abnormal returns did persist after they were found in the period 1993-1999. This goes against the results of Malkiel (2003), Shiller (2003) and Granger and Timmerman (2004), which state that strategies that show abnormal returns will self-destruct after these strategies get publicly known. As stated above, analysts might be able to pick the right stocks due to the development of the technology used. With this in mind, the abnormal returns can persist over time. The development of the technology would mean that analysts can quickly find new stocks and abnormal returns in the market and adjust their recommendations accordingly.

In the period 2011-2017, we see that the abnormal returns are even more significant compared to the period 1993-1999. This might be due to the financial crisis of 2007-2008, because the crisis exacerbates the mispricing by analysts. Analysts might be more careful and less aggressive with their recommendations. They are more likely to give a recommendation that might quickly become a bad recommendation during a crisis, because of the large swings in the economy. To avoid wrong recommendations, analysts would give a more conservative recommendation to stocks. This relationship between the crisis and the mispricing by analysts, however, contradicts with our results. Our results show that the financial crisis had no significant impact on the abnormal returns analysts found in the market. This could be due to the continuous development of the stock-picking abilities of analysts.

5.4 The EMH and the Carhart four-factor model

Almost all the results we find show significant abnormal returns over the period 1993-2017. This suggests that the EMH (Malkiel & Fama, 1970) does not hold perfectly and that analyst recommendations are indeed valuable information. As Grossman and Stiglitz (1980) have shown, analysts do need to be compensated for their work by earning abnormal returns. This

(28)

28 paper is in line with the conclusion of Grossman and Stiglitz (1980) as abnormal returns are found over the period 1993-2017 using analyst recommendations.

Also, the R2 is lower for most of the strategies used in the period 2011-2017 compared to the period 1993-1999. This is especially true for the strategies that include high recommended stocks. This suggests that in the current state of the financial markets more risk factors are needed to adjust returns for risk and that the Carhart four-factor model (Carhart, 1997) is not as reliable as it was before the year 2000.

5.5 Transaction costs

Until now we did not go over the transaction costs that would arise with a monthly

rebalancing strategy. Although we find significant abnormal results with our strategies, the results themselves are economically small. Keim and Madhavan (1998) researched the costs that would arise with equity trading and they conclude that an accurate prediction of

transaction costs requires detailed data on the stocks and brokers that are used. To get an idea of the costs of our research we look at the results of Barber et al. (2001). They looked at the turnover ratio per portfolio per period to be able to make conclusions about the transaction costs.

As our abnormal returns are economically small, it is possible that the transaction costs are bigger than the returns we find. This is in line with the results Barber et al. (2001) have shown during their research period. However, our results do show that abnormal returns are available in the market and with institutional investing these transaction costs can be minimized

significantly due to the economies of scale. We further note that despite these transaction costs, the market does show an inefficiency when using analyst recommendations due to our significant abnormal returns. For the remainder of this paper we use the returns we found without accounting for transaction costs. In our conclusion we add some points to this subject.

5.6 Market-adjusted returns

Looking at the mean market-adjusted returns we see the same results as with the abnormal returns. We noted that for the period 2000-2017 the abnormal returns are higher than for the period 1993-1999. The mean market-adjusted returns are indeed significantly higher for the period 2000-2017 than for the period 1993-1999. Moreover, we stated that the period

(29)

2011-29 2017 shows higher or equal abnormal returns for all strategies compared to the period 1993-1999. The mean market-adjusted returns are higher for the period 2011-2017 compared to the period 1993-1999 for every single portfolio. This could again be due to the development of the technology used by analysts in the 21st century. With better technology, analysts might be able to choose the right stocks and act more quickly to change their recommendations.

6. Conclusion

When markets are efficient, all available information should be incorporated in the stock price (Malkiel & Fama, 1970). This paper analyzed the efficiency of markets by using analyst recommendations as an investment tool. For the period 1993-1999, we find that investing based on analyst recommendations, while rebalancing the portfolios every month, can yield statistically significant abnormal returns. Buying the two best recommended portfolios yield a monthly abnormal return of 0.01%. Also, buying the two best recommended portfolios and shorting the worst recommended portfolio yield monthly abnormal returns of 0.011%. This suggests that markets are not fully efficient and does not incorporate all publicly available information.

For the period 2000-2017 we again find abnormal returns. Buying the two best recommended stock portfolios yield a monthly abnormal return of 0.016%, while buying the best

recommended stocks together with selling the worst recommended stocks yield a monthly abnormal return of 0.017%. When focusing on the sub-period 2011-2017 to get the results for the most recent years, we find abnormal returns of 0.013% for buying the best and selling the worst recommended stocks.

What is still surprising is that although these strategies are publicly known, they still earn abnormal returns which persist over time. Moreover, the market-adjusted returns in the period 2011-2017 are higher for every portfolio we test compared to the period 1993-1999. Reasons could be the development of the stock-picking abilities of analysts or the development of the technology analysts are using to find abnormal returns in the market.

We also see that the financial crisis of 2007-2008 did not impact the abnormal returns found by the analysts significantly. We can conclude that during this recent crisis, a strategy based on analyst recommendations would have earned abnormal returns.

(30)

30 Although our results are significant, there are some limitations to our research. One of these limitations is that we did not account for any accurate transaction costs that occurs with a monthly rebalancing strategy. These abnormal returns might not persist for investors when investing by themselves, due to these transaction costs. Future research could go into this area by analyzing these costs using methods mentioned by Keim and Madhavan (1998). It might further be interesting to analyze these periods with a daily rebalancing strategy to see if abnormal returns are still available with such short term holding periods. Moreover, it would be interesting to see if abnormal returns also persist during crises other than the financial crisis in 2007-2008. Finally, as we mentioned above in the section before, more risk factors might be used in the regressions due to the fall of the R2 when comparing the period 2011-2017 to the period 1993-1999. This might result in more explanatory power in the tests. We can conclude that investors can earn abnormal returns when using analyst

recommendations and that this also persist over multiple periods. Not all publicly available information is incorporated in the stock price and thus markets are not fully efficient. This adds value to the already puzzling research area on the efficiency of markets.

Appendix

Heteroskedasticity

When the variance of the error term (𝜀_𝑖) of our regressions, conditional on the independent variables, is not constant, we have heteroskedasticity in our data (Stock & Watson, 2015). This will result in unreliable, inefficient estimates of the coefficients. To test for

heteroskedasticity, we use the White test (White, 1980). The test statistic for the White test is 𝑛𝑅2_~𝜒2_{, where n stands for the sample size and R}2_{for the coefficient of determination,}

which are taken from the new regression explained below.

This test takes the residuals from our initial regression and regresses the square of these residuals against the independent variables, the square of the independent variables and the cross-products of our initial regression (White, 1980). The error terms in our original regression are heteroskedastic if the estimates of the new coefficients are significantly

(31)

31 different from zero and the R2 is high (White, 1980). This R2 is used in the test statistic of the White test.

If the dataset contains heteroskedasticity, we need to use a robust regression to overcome this problem (Stock & Watson, 2015). The results of the White test are given in table I, II, III and IV below.

Autocorrelation

Autocorrelation of the residuals in our data leads to inefficient and thus inaccurate coefficient estimates (Stock & Watson, 2015). To test whether the residuals of our initial regressions are correlated with residuals from the past we use the Breusch-Godfrey test (Breusch, 1978) (Godfrey, 1978).

The residuals we find from our initial regressions are regressed on all our initial explanatory variables and on lagged residuals. We then determine if these lagged residuals have a

significant impact and thus check if these residuals are significantly correlated with each other (Stock & Watson, 2015). How many lagged residuals we need to use is determined by a rule of thumb stated by Schwert (1989). This rule of thumb is the following equation: 𝑘_𝑚𝑎𝑥 = [12 ∗ ( 𝑡

100) 0.25

], where t stands for the number of observations. The following distribution can be used as an asymptotic approximation for the test statistic: 𝑛𝑅2~𝜒2, where n is the number of observations and R2_{the coefficient of determination.}

As seen from the results below, we have one regression where we observe both significance in heteroskedasticity and autocorrelation in our error terms. To solve this dual problem, we can use the Newey-West variance estimator. The results are given in table I, II, III and IV below.

(32)

32 Table I: White test and Breusch-Godfrey test: Period: 1993-1999

In the table we provide the p-values of the White test and Breusch-Godfrey test for the period 1993-1999. (*) stands for significance with a significance level of 5%.

Portfolio strategy White test for Heteroskedasticity

Breusch-Godfrey test for Autocorrelation P1 + P2 0.002* 0.358 P1 – P5 0.306 0.153 (P1 + P2) – P5 0.200 0.513 P1 0.046* 0.237 P2 0.003* 0.503 P3 0.000* 0.524 P4 0.739 0.671 P5 0.312 0.270

Table II: White test and Breusch-Godfrey test: Period: 2000-2017

Breusch-Godfrey test for Autocorrelation P1 + P2 0.000* 0.301 P1 – P5 0.000* 0.609 (P1 + P2) – P5 0.001* 0.314 P1 0.000* 0.278 P2 0.000* 0.530 P3 0.000* 0.466 P4 0.000* 0.999 P5 0.000* 0.014*

(33)

33 Table III: White test and Breusch-Godfrey test: Period: 2011-2017

Breusch-Godfrey test for Autocorrelation P1 + P2 0.341 0.423 P1 – P5 0.316 0.450 (P1 + P2) – P5 0.413 0.520 P1 0.364 0.518 P2 0.405 0.727 P3 0.035* 0.128 P4 0.300 0.297 P5 0.136 0.182

Table IV: White test and Breusch-Godfrey test: Period: 2004-2009

Breusch-Godfrey test for Autocorrelation

P1 0.194 0.325

(34)

34

References

Avramov, D., Cheng, S., & Hameed, A. (2016). Time-Varying Liquidity and Momentum Profits.Journal of Financial and Quantitative Analysis, 51(6), 1897-1923.

Barber, B., Lehavy, R., McNichols, M., & Trueman, B. (2001). Can Investors Profit from the Prophets? Security Analyst Recommendations and Stock Returns. Journal of Finance,

56(2), 531-563.

Barber, B., Lehavy, R., McNichols, M., & Trueman, B. (2003). Reassessing the Returns to Analysts' Stock Recommendations. Financial Analysts Journal, 59(2), 88-96.

Barber, B., Lehavy, R., & Trueman, B. (2010). Ratings Changes, Ratings Levels, and the Predictive Value of Analysts’ Recommendations. Financial Management, 39(2), 533-553.

Bodie, Z., Kane, A. & Marcus, A.J. (2014). Investments: Global Edition

Breusch, T. (1978). Testing for Autocorrelation in Dynamic Linear Models. Australian

Economic Papers, 17(31), 334-355.

Carhart, M. (1997). On Persistence in Mutual Fund Performance. Journal of Finance, 52(1), 57-82.

Elton, E., Gruber, M., & Grossman, S. (1986). Discrete Expectational Data and Portfolio Performance. Journal of Finance, 41(3), 699-713.

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.

Grossman, S., & Stiglitz, Joseph E. (1980). On the impossibility of informationally efficient markets. The American Economic Review, 70(3), 393-408.

(35)

35 Godfrey, L. (1978). Testing against general autoregressive and moving average error models

when the regressors include lagged dependent variables. Econometrica, 46(6), 1293-1301.

Jegadeesh, N., Kim, J., Krische, S., & Lee, C. (2004). Analyzing the Analysts: When Do Recommendations Add Value? Journal of Finance, 59(3), 1083-1124.

Keim, Donald B., & Madhavan, Ananth. (1998). The cost of institutional equity trades. Financial Analysts Journal, 54(4), 50-69.

Langevoort, D. (2009). The SEC, Retail Investors, and the Institutionalization of the Securities Markets. Virginia Law Review, 95(4), 1025-1083.

Malkiel, B., & Fama, E. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance, 25(2), 383-417.

Malkiel, B. (2003). The Efficient Market Hypothesis and Its Critics. Journal of Economic

Perspectives, 17(1), 59-82.

Shiller, R. (2003). From Efficient Markets Theory to Behavioral Finance. Journal of

Economic Perspectives, 17(1), 83-104.

Stickel, S. (1995). The Anatomy of the Performance of Buy and Sell Recommendations.

Financial Analysts Journal, 51(5), 25-39.

Stock, J.H., & Watson, M.W. (2015). Introduction to Econometrics: Global Edition

Timmermann, & Granger. (2004). Efficient market hypothesis and forecasting. International

Journal of Forecasting, 20(1), 15-27.

White, H. (1980). "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity". Econometrica, 48 (4): 817–838.

Womack, K. (1996). Do Brokerage Analysts' Recommendations Have Investment Value?

Testing the efficiency of markets : analyst recommendations as an investment tool in the United States

Faculty of Economics and Business

Bachelors’ Thesis